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Investigations on Microwave Mode Transducers for Remote Sensing Antennas

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Thesis for Award of the Degree of
D octor Of P hilosophy
In
Microwave and Antenna Engineering
$ -
S t i' 2308
Title
Investigations on M icrow ave M ode Transducers f o r R em ote
Sensing A ntennas
By
VIJAYKUMAR SINGH
Scientist/ Engineer
Antenna Systems Area
Space Applications Center (SAC), ISRO
Ahmedabad-380 015, India
Under the Supervision of
Dr. S. B. SHARMA
Deputy Director
Antenna Systems Area
Space Applications Center (SAC), ISRO
Ahmedabad-380 015, India
September 2008
(REG. N o .: 4843, January 22, 2002, Gujarat University)
ProQuest Number: 3736468
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A Thesis Submitted
To
Gujarat University
For Award of the Degree of
D o c t o r O f P h il o s o p h y
In
Microwave and Antenna Engineering
Title
Investigations on Microwave Mode Transducers for Remote
Sensing Antennas
By
VIJA Y KUMAR SINGH
Scientist/ Engineer
Antenna Systems Area
Space Applications Center (SAC), ISRO
Ahmedabad-380 015, India
Under the Supervision of
Dr. S. B. SHARMA
Deputy Director
Antenna Systems Area
Space Applications Center (SAC), ISRO
Ahmedabad-380 015, India
September 2008
(REG. N o .: 4843, January 22, 2002, Gujarat University)
STRUCTURE O F T H E THESIS
Declaration by th e Author
1
C ertificate by The Supervisor
II
Acknowledgement
III
Bio-data of th e Author
IV
Summary
VI
Scientific Progress from th e Thesis Work
VII
Contents
VIII
List of Tables
XI
List of Figures
XII
Details of th e Thesis Work
1-153
Hard Copy of International Publications
iDeclaration
I hereby declare that the thesis entitled “Investigations on Microwave Mode
Transducers for Remote Sensing Antennas” is a genuine record of research
work carried out by me and no part of this thesis has been submitted by anybody to
any University or Institution for the award of any degree or diploma.
*
\
(Vijay Kumar Singh)
Space Applications Centre
Ahmedabad
September, 2008
CERTIFICATE
This is to certify that the thesis entitled “Investigations on Microwave Mode
Transducers fo r Remote Sensing Antennas” is a bona-fide record of research
work done by Shri Vijay Kumar Singh, Registration No. 4843, dated 22nd January
2002, in fulfillment of requirement for the degree of “Doctor of Philosophy” (in
Engineering) submitted to the Gujarat University, Ahmedabad.
I certify that this work has not been submitted by anyone for any other degree or
diploma to any other University/Institution.
(Dr. S. B. Sharma)
Space Applications Centre
Ahmedabad
September, 2008
Ph. D. Supervisor
II
ZkfznowCedgement
The author expresses his deep gratitude and indebtedness to Dr. S. B Sharma, Outstanding
Scientist and Deputy Director, Antenna Systems Area, Space Applications Center, Ahmedabad
fo r his constant encouragement and able guidance throughout the period o f this work It is only
due to his keen interest, valuable suggestions, comments and motivation, the author could
complete this work.
I am highly indebted to Dr. S. B. Chakrabarty, Head, Microwave Sensors Antenna Division,
Antenna Systems Area, Space Applications Center (SAC) fo r his continuing interaction, excellent
comments and suggestions during the course o f this research work and during the writing o f the
thesis. He has helped much more than a co-guide.
My sincere thanks are due to the former directors, SAC, Dr. K. N. Shankara, Dr. A. K S.
Gopalan and the present Director Dr. R. R. Navalgund fo r permitting me to work fo r my Ph. D.
thesis and extending support in terms o f excellent facilities and infrastructure o f the center.
Special thanks are due to Sanjeev Kulshrestha, Ranajit Dey, Anil Solanki, B. K. Pandey, lla
Agnihotri, Devendra Sharma, Gaurav Upadhyay, C. Sri Harsha, Mohit Khanna, A. K. Pandey,
Shobha Ben and all other colleagues and seniors at MSAD/ASA, SAC, Ahmedabad and Prof.
Dhaval Pujara o f Nirma University, Ahmedabad fo r providing necessary technical support
during the course o f work
Thanks are due to V. F. Pariyal, Samir Sakhre and N. H. Kinariwala fo r providing support for
mechanical drawing generation and hardware development. Special thanks are due to R. K.
Malaviya, R. M. Makwana, K. P Bhalsod, K. P. Raja, V. R. Seth and H. S. Solanki o f AMD/ASA,
SAC, fo r providing necessary supportfo r measurement. I thank Y. H Trivedi, A.C. Mathur, SAC,
Ahmedabad and D Sam Dayala Dev, IISU, Trivandrom fo r providing necessary support in
mechanical design and integration. My sincere thanks to Rajeev Jyoti, Head SCAD, K K. Sood,
M.B. Mahajan and Dr B. S. Munjal o f SAC fo r their valuable inputs and fo r boosting my
enthusiasm fo r the work
Last but not the least, I am personally indebted to my teachers, my grand father, my parents, my
brothers- Ambika and Santosh, sisters-Sangeeta and Reeta, wife Pratima, daughter Shubham,
son Utkarsh and all other near and dear fo r all kinds o f support which gave me enough strength
to complete this challenging assignment. Their remains the pleasant task o f acknowledging
indebtedness to all those who have directly or indirectly rendered th i' 1 ' 1 g this work
Vijay &umar Singh
Space Applications Centre
Indian Space Research Organization
September, 2008
in
(Bio-data oftde fMutdor
VIJAY KUMAR SINGH was bom on August 21, 1967 in Bahraich District of Uttar Pradesh, 1
India He received B. Tech, in Electronics and Communication Engineering from J. K.
Institute of Applied Physics and Technology, Allahabad University in 1990 and M. Tech, in
Electronics Engineering (Microwave) from Institute o f Technology, B.H.U., Varanasi in
1992. Since, 1993, he has been with the Antenna Systems Group, Antenna Systems Area,
Space Applications Centre, Indian Space Research Organization (ISRO), Ahmedabad.
Working as project manager for Radar Imaging Satellite (RISAT) as well as Oceansat-II
missions, currently he is involved in the design and development o f space-bome active phased
array antenna and pencil beam scanning scatterometer antenna, respectively. His area of
interest is multi-mode couplers, microwave mode transducers, wideband multi-frequency
feeds, millimeter wave antennas, beam waveguide systems, reflectors and dual-polarized
microstrip SAR antennas for satellite remote sensing applications. He has nearly 27
international as well as national publications related to the design o f microwave antennas for
space-bome remote sensing applications.
List o f Publications and Patents
(a) Publications
[1]
S. B Sharma, V. K. Singh, Ranajit Dey, S. B. Chakrabarty, “Analysis of post discontinuity in
an oversized circular waveguide,” IEEE Trans. Microwave Theory Tech, submitted fo r
publication.
[2]
S. B. Sharma, V. K. Singh, Ranajit Dey, S. B. Chakrabarty, “Analysis o f coaxial probe
as discontinuity in circular waveguide,” submitted for publication.
[3]
S. B. Sharma, V. K. Singh, S B Chakrabarty, “Multi-frequency waveguide orthomode
transducer,” IEEE Trans. Microwave Theory Tech, vol. MTT-53, no. 8, pp. 2604-2609, Aug.
2005.
[4]
S. B. Sharma, V. K. Singh, “Parabolic dish antenna with offset elliptical multi-mode feeds for
space-bome remote sensing application,” Microwave Opt Technol. Lett., vol. 39, no. 2, pp.
138-141, Oct. 2003.
[5]
S.B. Sharma, V. K. Singh, “Multifrequency corrugated feed with groove discontinuity at
input,” Electron. Lett., vol. 37, no. 18, pp. 1121-1122, Aug. 2001.
IV
[6]
S. B. Sharma, V. K. Singh, ” Design of common aperture hybrid mode corrugated horn for
multifrequency scanning microwave radiometer,” IETE Technical Review, vol 16, no.l, Jan.Feb. 1999, pp. 47-52.
[7]
V. K. Singh, S.B. Chakrabarty, Anil Solanki, R. Dey, Ila Agnihotri, S. B. Sharma, “Mode
Transducers for Ku-band dual-channel microwave rotary joint,” in Int. Conf Microwaves,
Antenna Propagation and Remote Sensing, ICRS, Jodhpur, India, Feb. 2008.
[8]
V. K. Singh, S. B. Chakrabarty, S. B. Sharma, and Arun Kumar, “Evaluation of common
phase center of multi-frequency feed for radiometric applications,” in Int. Conf. Antenna
Technologies (ICAT), Space Applications Center (ISRO), Ahmedabad, India, pp. 279-283,
Feb. 2005.
[9]
V. K. Singh, R. M. Makwana, R. K. Malaviya, P. D. Ramavat, S. B. Sharma, “Model
analysis of cascaded circular waveguide sections of 8-port ortho-mode transducer for multi­
frequency operation of horns”, in National Symp. Advances in Microwaves and Light
waves, Mar. 25-28,2000. pp.153-156.
[10]
V. K. Singh, R. M. Makwana, R. K. Malaviya, K. P. Bhalsod, S. B. Sharma, “ High gain
elliptical coaxial feed”, in National Symp. Advances in Microwaves and Lightwaves, Mar.
25-28,2000. pp. 95-98.
[11]
S.B. Chakrabarty, V. K. Singh, S. Kulshrestha, G. Upadhyay, and S. B. Sharma, “TMoi mode
transducer using circular and rectangular waveguides, ” in Int. Conf Microwaves, Antenna
Propagation and remote sensing, ICRS, Jodhpur, India, Feb. 2008.
[12]
V. K. Singh and S. B. Sharma, “Sudur samvedanopyogi antenna kaa aadhar
stumbh:Vidyut chumbkiya vidhayen (electromagnetic modes),” in Takneeki Hindi
Seminar, Space Applications Centre, Ahmedabad, India, Jan. 2003.
[13]
V. K. Singh and S. B. Sharma, “Sudoor samvedan upyogi aadhunik sukshmtarang
antenna neetbhar,” in Hindi Conference, Space Applications Center, Ahmedabad,
India, Mar. 2002.
[14]
S. B. Sharma, S. B. Chakrabarty, and V. K. Singh, “Moment method analysis o f a slot
coupled circular waveguide orthomode transducer,” Microwave Opt. Technol. L e tt,
vol. 34, no. 4, pp. 285-289, Aug. 2002.
(b) Patents
[15]
“A waveguide transducer assembly for efficient excitation of circular waveguides”,
International Patent application No. 198098, Granted on January 30,2006.
[16]
“Dual Channel Rotary Joint for Space Borne Scanning Antenna,” Application No.
PCT/1N2008/000161, filed on March 28,2008.
[17]
“Multimode prime focal feeds for highly efficient elliptical beams for microwave
sensors,” Application no. PCT/IN2008/000224, filed on March 28,2008.
[ 18]
“A waveguide rotary j oint,” Application Ref.: MVG/RV, filed on June 19,2001.
V
SUMMARY
The investigation and realization o f novel types o f microwave mode transducers have been
presented in this thesis. Circular waveguide discontinuities which occur in a multi-frequency
mode transducer have been modeled and analyzed. A common ortho-mode transducer
operating at widely separated frequency bands has been conceptualized, designed and
developed. The design is based on modal analysis approach to give optimum performance o f
return loss, mode purity, inter-port isolation and insertion loss at all the frequency bands.
Dominant mode purity o f circular waveguide is obtained in the outermost section o f OMT at
each frequency band which ensures desired radiation patterns o f a corrugated horn antenna
fe d by the OMT Power has been estimated in the higher-order modes and the
electromagnetic modeling o f the rectangular to circular waveguide transitions has been done
to arrive at the optimum design o f OMT. This concept has been utilized also to develop a
mode transducer operating at three widely separated frequency bands centered at frequencies
higher than the center frequencies o f the four frequency OMT. The simulated and measured
results o f the mode transducers are presented.
Hybrid mode transducers in the form o f corrugated horns have been designed and developed
yielding optimum radiation performance at all the frequency bands. The design has been done
using the technique o f harmonic operation o f corrugation depth to operate at all the four
frequency bands. The horn geometry is optimized to get proper power ratio in the various
modes at the horn aperture in order to yield symmetric fa r field co-polar patterns and low
level o f cross-polar radiations at all the frequency bands. The horn has been tested with the
developed 8-port OMT. The measured performance o f OMT and horn are in close agreement
with the simulated results. A multi-mode corrugated horn has also been developed at three
widely separated frequency bands to be fe d by a common three frequency mode transducer.
Multi-mode transducers in the form o f elliptical and circular multi-mode feeds have been
designed and developed at Ku-band yielding sector shape primary radiation patterns in order
to achieve high gain beams o f the reflector antenna. Measured and simulated performance o f
multi-mode feeds are presented
New type o f mode transducers supporting circularly symmetric TEoi and TMoi modes o f a
circular waveguide have been designed to develop a compact dual-channel rotary joint at Kuband using modal analysis approach. The simulated and measured results o f the rotary joints
are presented fo r return loss, insertion loss, isolation between channels, mode coupling
behavior, variation o f return loss and insertion loss with 360 degree rotation.
VI
Scientific Progress from the Thesis Work
•
Electromagnetic modeling and analysis o f radial post and coaxial probe
discontinuities in an over-sized circular waveguide have been done using
Method o f Moments technique. These problems have been attempted first
time by the author to study the behavior o f higher-order modes excited due to
discontinuities in multi-frequency mode transducer.
•
A new type o f Ortho-mode Transducer (OMT) capable o f operating at four
widely separated frequency bands have been designed, developed and
reported for the first time by the author. A patent is granted on the waveguide
transducer assembly of the OMT.
•
A hybrid mode transducer in the form o f corrugated hom designed and
developed by the author, works at widely separated frequency bands covering
nearly two octave bandwidth. Earlier works on corrugated hom using simple
corrugations report a maximum bandwidth o f 1.6 (maximum to minimum).
•
A new multimode transducer in the form o f elliptical multimode feeds have
been designed, developed and reported by the author to generate sector
shape radiation patterns for achieving high gain beams o f reflector antenna. A
patent has been filed for design.
•
Circularly symmetric dual mode transducers in the form o f compact dual
channel rotary joint at Ku-band are designed and developed using new
excitation mechanism for TM01 mode in the presence o f TE01 mode in a very
%
compact configuration. A patent has also been tiled for design.
VII
CONTENTS
Titles
1
2
Page No.
Introduction
1-9
1.1
8
Organization of Thesis
Electromagnetic Analysis of Discontinuities in Circular Waveguide Mode
Transducers
10-40
2.1
Coupling Mechanism and Discontinuities in a Multi-frequency Mode
Transducer
10
2.2
Asymmetric Discontinuities in Circular Waveguide
12
2.2.1
Post Discontinuity in Circular Waveguide
12
2.2.1.1
Formulation and Analysis of Post Discontinuity
13
2.2.1.2
Results and Discussions for Post Discontinuity
17
2.2.2
Coaxial Probe discontinuity in Circular Waveguide
2.2.2.1
Formulation and Analysis of Coaxial Probe Discontinuity
2 2 .2.2 Results and Discussion for Coaxial Probe Discontinuity
3
4
21
22
28
2.3
Symmetric Discontinuities in Circular Waveguide
31
2.4
Mode Transducers to Excite Circularly Symmetric Modes
36
2.5
Conclusion
39
Multi-frequency Ortho-mode Transducer
41-63
3.1
Design and Analysis
41
3.1.1
Modal Analysis of Waveguide Sections Cascaded with Step
Junctions
42
3.1.2
Waveguide Sections Cascaded with Tapered Sections
44
3.1.3
Effects of Co-axial Probes
46
3.1.4
Design of Multi-frequency Ortho-mode Transducer
49
3.1.5
Measured and Simulated Results o f 8-Port Ortho-mode Transducer
53
3.2
Mode Transducer at Three Frequency Bands
57
3.3
Conclusion
63
Multi-frequency Hybrid Mode Transducer
64-85
4.1
Feed for Four Frequency Bands
65
4.1.1
65
Design and Analysis
VIII
4.1.2
Measured and Simulated Results
68
4.1.3
Horn Radiation Patterns with Pure TEn Mode Excitation
69
4.1.4
Horn Radiation Patterns with multi-Frequency OMT
73
Feed for Three Frequency Bands
78
4.2.1
Design Approach
78
4.2.2
Design and Simulation
78
4.2.3
Measured Radiation Performance o f Horn
82
4.2
4.3
5
86-108
5.1
Elliptical Multi-mode Transducer Feeds for Scatterometer Antenna
86
5.1.1
Design and Simulation
87
5.1.2
Simulated and Measured Results
93
5.3
5.4
Circular Multimode Transducer Feed for Reflector Antenna of Altimeter
97
5.2.1
Simulation and Design
97
5.2.2
Simulated and Measured Results
’
98
Circular Multimode Transducer Feed (Dual-ring) for Reflector Antenna o f
Altimeter
5.3.1 Design and Simulation
102
5.3.2
104
Simulated and Measured Results
Conclusion
102
108
Mode Transducers for Circularly Symmetric Modes
109-130
6.1
Excitation of TMoi Mode in the Circular Waveguide
109
6.2
Excitation o f TEoi Mode in the Circular Waveguide
116
6.3
Excitation of TMoi and TEoi Modes in a Common Circular Waveguide to
Realize a Dual-channel Rotary Joint
Compact Design of Dual-channel Rotary Joint
118
122
6.4.1
Simulated Results of Compact Dual-channel Rotary Joint
123
6.4.2
Simulated Performance with 360 Degree Rotation
125
6.4.3
Measured Results of Compact Dual-channel Rotary Joint
127
6.4
6.5
7
85
Multi-mode Transducers for Radiation Pattern Control
5.2
6
Conclusion
Conclusion
130
Summary Conclusion and Future Scope
IX
131-135
7.1
Summary and Conclusion
131
7.2
Future Scope o f the Work
134
References
136-142
Appendix A
143-153
A. 1
Coaxial Probe Coupling in Circular Waveguide with Perfect Short
143
A.2
Coaxial Probe Coupling in Circular Waveguide with Tapered Short
145
A.3
General Expression of Dyadic Green’s Function
A.4
Expression for Components o f Green’s Function
A.5
Mode Matching Technique for Step Junction Discontinuity in
Circular Waveguide
X
147
148
149
LIST OF TABLES
Table No.
page jy0i
2.1
Electrical parameters of hom
35
2.2
Modal amplitudes in the oversized circular waveguide excited with slot coupled
rectangular waveguides
The design dimensions of the waveguide sections at different frequencies
38
45
The power (dB) in dominant and higher-order modes in section-Dj for tapered
junction
47
3.4
The power (dB) in the dominant and higher-order modes in section-DT in the
presence of mode transducers
Modes at the aperture of the cascadedmode transducer at 36.5 GHz
51
59
4.1
Modes at the aperture o f hom with TEn mode transition at its input at 6.6 GHz
69
4.2
Modes at the aperture o f hom with TEi i mode transition at its input at 21 GHz
70
4.3
Simulated and measured illumination taper in dB o f the hom
70
4.4
4.5
Measured and simulated cross-polar radiation performance with pure TEn mode
excitation.
Modes at the aperture of mode transducer in the presence o f groove at 36.5 GHz
71
80
4.6
Modes at the aperture o f the hom in the presence of groove at 36.5 GHz
80
4.7
Modes at the aperture o f the hom without groove at 36.5 GHz
80
4.8
Modes at the aperture o f the hom with groove at 18.7 GHz
80
4.9
Modes at the aperture of the hom with groove at 23.8 GHz
81
5.1
Modal amplitude and phase at aperture to realize shaped radiation patterns
89
5.2
Amplitudes and phases o f TEin and TMin modes at the aperture of the elliptical
multi-mode feed
Measured parameters of secondary radiation pattern for vertical polarization
91
95
3.1
3.2
3.3
5.3
5.4
5.5
5.6
5.7
Amplitudes and phases o f TEin and TMin modes at the aperture o f the single ring
coaxial multi-mode feed
Measured parameters of secondary radiation pattern for Altimeter antenna for single
ring feed
Amplitudes and phases o f TEin and TMin modes at the aperture of the two ring
co-axial multi-mode feed
Measured parameters of secondary radiation pattern for Altimeter antenna with 2ringfeed
XI
98
99
103
106
LIST OF FIGURES
Fig. No.
Page No.
2.1
The schematic of a multi-frequency mode transducer
11
2.2
Circular waveguide loaded with a post discontinuity
13
2.3
Return loss performance for a post discontinuity in a circular waveguide
18
2.4
Return loss performance for different sizes o f the waveguide with post discontinuity
2.5
Forward power for a post discontinuity in a circular waveguide
19
2.6
Modal power in TMoi mode for post discontinuity
19
2.7
Modal power in TE21 mode for post discontinuity
19
2.8
Modal power in TE31 mode for post discontinuity
20
2.9
Scattering performance o f post of height 11mm over wider frequency range
20
2.10
Hardware of circular waveguide with post discontinuity
20
2.11
Simulated and measured values o f return loss for post height o f 11mm
21
2.12
Circular waveguide loaded with coaxial probe discontinuity
22
2.13
Return Loss o f probe loaded circular waveguide
29
2.14
Forward power in the dominant TEi 1 mode for probe discontinuity
29
2.15
Power in TM 01 mode for probe discontinuity
29
2.16
Power in TE21 mode for probe discontinuity
30
2.17
Power coupling to the coaxial line
30
2.18
Hardware o f circular waveguide section with coaxial line fed probe discontinuity
30
2.19
Scattering performance o f probe o f height 11mm over wider frequency range
31
2.20
Step junction between two smooth-walled waveguides o f different radii
32
2.21
2.24
Smooth wall conical waveguide approximated by incremental step junctions to apply
mode matching using cylindrical modes
32
Circular waveguide to conical waveguide mode transducer (a) conical horn,
(b) a corrugation represented as a pair o f step junctions at z = 0
33
The modal amplitudes for flare angles (a) 5 degree (b) 10 degree (c) 45 degree and
(d) 90 degree
34
Return loss of the corrugated hom
35
2.25
Scheme o f TM 01 mode excitation in circular waveguide
36
2.26
Slot coupling of an oversized circular waveguide to propagate TE 01 mode
37
2.22
2.23
xn
18
2.27
3.1
Scheme o f TEoi mode excitation in circular waveguide using four slots located at
circumference
Multi-frequency waveguide sections joined with step junctions
39
43
3.2
Circular waveguide sections A,, Bt, Ct and Dt cascaded with tapered sections
44
3.3
Waveguide sections excited with coaxial probe at different frequencies
47
3.4
3.9
(a) Schematic of OMT at single frequency band, (b) Schematic of a common 8-port
OMT at four frequency bands.
Radiation patterns at 18 GHz for a horn fed with the OMT o f optimized step
transformers and reduced depth probes at 6.6 and 10.65 GHz.
Return loss for 6.6 GHz circular to rectangular waveguide mode transducer for both
the orthogonal ports
Return loss for 10.65 GHz circular to rectangular waveguide mode transducer for
both the orthogonal ports
Measured isolation of 10.65 GHz signal with 6.6 GHz coaxial probe
port with parallel polarization
Measured return loss and isolation for 18 GHz OMT
3.10
Measured isolation o f 18 GHz signal with 6.6 GHz and 10.65 GHz ports
55
3.11
Measured return loss and isolation for21GHzOM T
56
3.12
3.13
Measured isolation o f 21 GHz signal with other lower frequency ports for parallel
polarization
Photograph of 8-port common OMT at 6.6,10.65,18 and 21 GHz
56
57
3.14
Different configuration to combine waveguide sections at 3 frequencies
59
3.15
Simulated and measured return loss at 18.7 GHz
60
3.16
Simulated and measured return loss at 23.8 GHz
60
3.17
Simulated and measured return loss at 36.5 GHz
61
3.18
61
3.20
Measured and simulated isolation performance of 36.5 GHz signal with 18,7 and
23.8 GHz ports
Measured and simulated isolation performance of 23.8 GHz signal with 18.7 GHz
port
Tri-frequency mode transducer at 18.7,23.8 and 36.5 GHz
4.1
Geometry of a corrugated horn
66
4.2
4.3
Corrugation surface reactance, (a) a = 17.5 mm, b = 32.7 mm (b) a = 43.6 mm,
b = 55.6 mm
The photograph o f the developed four frequency corrugated horn
67
71
4.4
The measured and simulated radiation performance o f the horns excited with pure
3.5
3.6
3.7
3.8
3.19
XIII
49
52
53
54
54
55
62
62
4.5
4.6
TEn mode transitions at (a) 6.6 GHz, (b) 10.65 GHz, (c) 18 GHz and (d) 21 GHz
72
The measured co-polar and cross-polar radiation patterns o f the horn fed with an 8port OMT for one polarization (v-port)
73
The measured eo-polar and cross-polar radiation patterns o f the horn fed with an
8-port OMT for orthogonal polarization (h-port)
4.7
The photograph o f the developed 8-port OMT integrated with four-frequency
corrugated horn
4.8
75
Measured and computed secondary radiation performance at (a) 6.6 GHz, (b) 10.65
GHz, (c) 18 GHz and (d) 21 GHz
4.9
74
77
Schematic o f the multi-frequency corrugated feed with a groove discontinuity. The
horn is fed with the multi-frequency mode transducer
81
4.10
Measured and predicted far-field radiation patterns with groove at 18.7 GHz
82
4.11
Measured and predicted far-field radiation patterns with groove at 23.8 GHz
83
4.12
(a)The measured radiation patterns with and without groove at 36.5 GHz(E-plane)
83
4.12
(b )The measured radiation patterns with and without groove at 36.5 GHz(H-plane
84
4.13
The photograph o f the tri-frequency horn
84
5.1
The synthesized shaped radiation pattern (a) all modes in same phase, (b) TE21 mode
with 45 degree phase and rest o f the modes in same phase
90
5.2
The schematic o f the optimized elliptical feed
91
5.3
Developed elliptical multi-mode feeds
92
5.4
Schematic diagram o f the antenna with reflector, feeds, inner-outer beams and
scanning axis
5.5
93
Measured and simulated (HFSS) E and H-plane primary radiation patterns o f the
elliptical feed for vertical polarization
94
5.6
Secondary radiation patterns when elliptical feed at the focus
95
5.7
Secondary radiation patterns o f displaced elliptical feed in the focal plane
96
5.8
Reflector antenna with two displaced elliptical feeds
96
5.9
The schematic o f the optimized multimode circular feed
97
5.10
Measured and simulated (on HFSS and CHAMP) E and H-plane primary radiation
patterns o f the single ring coaxial multi-mode feed
100
5.11
Secondary radiation patterns with single ring feed at focus
100
5.12
Single ring coaxial multi-mode feed
101
5.13
The photograph o f the lab model o f the reflector antenna integrated with
the single ring coaxial feed
5.14
101
The schematic o f the optimized multimode circular feed(dual-ring)
xrv
103
5.15
The measured and computed primary radiation patterns
104
5.16
(a) The computed primary radiation patterns at different frequencies in E-plane
104
5.16
(b) The computed primary radiation patterns at different frequencies in H-plane
105
5.17
5.18
The comparison of measured and predicted secondary patterns o f the reflector with
two ring multimode feed
Two ring coaxial multi-mode feed
107
107
5.19
Flight model elliptical feeds
108
5.19
Parabolic reflector with elliptical feeds
108
6.1
(a) Field configuration o f TMoi mode in circular waveguide, (b) Scheme of TMoi
mode excitation in circular waveguide using axial probe from the end of the
waveguide
Schematic of TMoi mode transducer
110
112
6.2
6.3
The simulated modal amplitudes for different modes in the circular waveguide for
TMoi mode excitation
112
6.4
113
6.5
Single channel rotary joint with doorknob transition for TMoi mode excitation in the
circular waveguide
Simulated insertion loss of the single-channel rotary joint with rotation
113
6.6
Simulated return loss of the single-channel rotary joint with rotation
114
6.7
Measured return loss of the single-channel rotary joint with rotation
114
6.8
Measured insertion loss o f the single-channel rotary j oint with rotation
115
6.9
Rectangular to circular waveguide transition for exciting TMoi mode in circular
waveguide
115
6.10
6.11
6.12
6.13
6.14
6.15
6.16
6.17
(a) Field configuration of TEoi mode in circular waveguide,
(b) Scheme of TEoi mode excitation in circular waveguide using four slots
TEoi mode excitation in the circular waveguide using (a) 4-way power divider
(b) ring waveguide surrounding circular waveguide
The photograph of the dual channel rotary joint
(a) Measured return loss at the input port o f channel-1 ( TMoi channel),
(b) Measured insertion loss of channel-1 (TMoi channel)
(a) Measured return loss at the output port of channel-2 (TEoi channel)
(b) Measured insertion loss of channel-2 (TEoi channel
Measured isolation between channel-1 and channel-2
Solid model o f the compact dual channel rotary joint with TMoi and TEoi mode
excitation in the circular waveguide
(a) Modal amplitudes of fundamental and higher order modes for the optimized
XV
116
117
119
120
121
121
122
6.19
mode transducer for channel-1 (TMoichannel), (b) Modal amplitudes of
fundamental and higher order modes for the optimized mode transducer for channel-2
(TEoichannel)
(a) The simulated return loss, insertion loss and isolation between two channels of
dual channel rotary joint, (b) The orientation of rotary joint ports
The return loss performance of TM0i channel in the absence of TE0i channel
124
125
6.20
The return loss performance of TEoi channel in the absence of TMoi channel
125
6.21
Simulated performance with rotation in presence of both channels simultaneously,
(a) Insertion loss for TMoi channel,(b) insertion loss for TEoi channel, (c) Return loss
for TMoi channel, (d) Return loss for TEoi channel, (e) Isolation between TMoi and
TEoi channels
Measured performance o f the compact dual channel rotary joint (a) Return loss at the
input port of channel-1 (TMoi channel), (b)Measured insertion loss o f channel-1
(TMoi channel)
Measured performance o f the compact dual channel rotary joint (a) Return loss at the
input port of channel-2 (TEoi channel), (b)Measured insertion loss of channel-2
(TEoi channel
6.18
6.22
6.23
6.24
123
126
128
6.25
Measured isolation between channel-1 and channel-2 for the compact dual-channel
rotary joint
The photograph of the compact dual channel rotary joint
129
129
6.26
The photograph of the compact dual channel rotary joint (flight model)
130
XVI
Chapter 1
Introduction
The antennas o f microwave sensors for remote sensing applications [l]-[3] demand multifrequency, multi-polarization and multi-channel operation with stringent specifications on
electrical parameters such as beam shape, gain, cross-polarization, side lobe level, return
loss, insertion loss and scanning capability. All these features are generally met using
antenna and feed systems which employ special type of mode transducers. The mode
transducers transform a certain mode of one waveguide to a different mode or modes of the
other waveguide and thus become a very important component of the antenna and feed
system. The design and realization o f these mode transducers is very challenging in terms
of achieving mode purity o f the desired modes for a particular application.
In view of the wide spectrum applications of mode transducers in various microwave and
antenna systems, the investigations on mode transducers have attracted the attention of
researchers for a long time [4]-[l 1] and various designs of mode transducers have been
reported by these researchers. Broadband coaxial line to circular waveguide mode
transducers are illustrated in [4] and [7]. These are single mode and single frequency band
transducers. Ortho-mode transducers (OMT) are described in [4], [7], [10], where the
orthogonal polarizations are fed into or coupled out of the circular waveguide. The effect of
putting short septum or pins in circular waveguide OMT is described in [7],
A. M. Boifot, et al. [12], [13] and J. Uher et al. [14] have presented various broadband
ortho-mode transducers. They have classified OMTs with waveguide to waveguide
transitions in three main groups. The classification is based on symmetrical properties of
the device.
Class-I represents simplest OMT where main arm is used for one mode and
side arm for the other mode. In Class-II OMTs, side arm is split in to two symmetrical parts
to achieve a broadband and good isolation behavior. In Class-Ill OMTs, both the main and
side arms are split in to two symmetrical parts. Therefore, unwanted symmetrical higher-
1
order modes are cancelled in both arms resulting into broadband behavior o f the device.
The hardware and test results are described for such broadband OMTs at single frequency
band in [12].
Waveguide orthomode transducers based on turnstile junction are presented in [15], [16],
[17]. Meyer and Goldenberg [15] have discussed several applications o f turnstile junctions
including OMT. The ortho-mode transducer presented in [16] consists o f a circular
waveguide with input port and rectangular waveguides with output ports. This device meets
return loss, isolation and insertion loss performance at K-band (18-26 GHz). The turnstile
junction based OMT presented in [17] has a circular waveguide input and two WR10
rectangular waveguide outputs to separate the two input polarizations. This OMT offered
good isolation, return loss and insertion loss performance over 75-110 GHz band. These
broad band OMTs are limited to single frequency band operation.
Robertson [18] has reported new applications o f the wide-band fin-line couplers, where it is
possible to separate two waves perpendicularly polarized to each other for single frequency
mode. S. J. Skinner and G. L. James [19] have also reported an OMT based on finline
technique and quadridged waveguide geometry to feed a wide band corrugated horn in the
range 2.4:1.
In [20], Ludivicio et al. have described a hybrid computer-aided-design technique for the
efficient and stable analysis of compact OMT’s. The electromagnetic simulators are used
for the efficient computer-aided optimization of the OMT and a procedure for the
dynamical optimization is introduced and established by designing several OMT’s
operating separately at L, S, and Ku frequency bands.
Sharma et al. [21], [22] carried out a method of moment analysis of a class o f mode
transducer consisting of T-junction of slot coupled circular to rectangular waveguides. The
extension of this work by incorporating another orthogonal rectangular waveguide port to
form a waveguide ortho-mode transducer has been presented in [23],
2
The previously mentioned literature elaborates on the design of single frequency OMTs
including the bandwidth enhancement techniques. The design details o f OMTs for more
than two frequency bands for dual-polarization operation are not reported in the literature.
Since, the multi-frequency OMTs and feeds covering more than two bands o f frequencies
are widely used in antennas for radiometers and satellite communication payloads, it is
worthwhile to carry out a systematic investigation to design and develop multi-frequency
OMTs and feed horns.
The prime objective in the design o f a multi-frequency OMT is to achieve frequency
isolation, polarization isolation and purity of dominant mode at the output of OMT at each
frequency band. Multi-frequency OMTs can be realized by cascading circular waveguide
sections and probe coupling mechanisms at individual frequency bands. As a result of
cascading, discontinuities in the form o f multiple probes or posts and waveguide junctions,
excite undesired higher-order modes and deteriorate the performance o f the multi­
frequency OMT. These discontinuities needs to be modeled in order to analyze higherorder mode scattering properties which is prerequisite to the design and realization of
multi-frequency OMTs. The power coupling probes act like post discontinuity in
waveguide. The analysis of post loaded rectangular waveguides has been reported in [24],
[25] but the available literature on the analysis o f post discontinuity in circular waveguides
is very much limited. The paper [26] presents simulated and experimental results for the
reactance o f the post discontinuity in circular waveguide. In [27], a pair o f metallic post
discontinuities in a TEn mode circular waveguide has been analyzed using multi-strip
current representation and the data on the equivalent susceptance is presented. The
literature [26], [27] presents the analysis of post discontinuity in circular waveguide which
supports only the dominant "TEn mode and it does not provide any information about the
scattering parameters of the higher-order modes supported by the post loaded circular
waveguide. The problem o f determining the input impedance o f a co-axial line fed probe in
a waveguide has been addressed by many authors for rectangular as well as circular
waveguide [28]-[32]. But, taking coaxial probe as a discontinuity in an oversized circular
waveguide supporting higher-order modes, has not been attempted earlier. The magnetic
current source in the coaxial region and the electric current source on the probe have to be
considered to analyze a probe discontinuity. The general expressions o f dyadic Green’s
3
function for electric and magnetic type current sources for circular and coaxial waveguides
are presented in [33]. Using these expressions the formulations may be developed to
analyze the coupling and higher-order mode characteristics o f a probe discontinuity at
higher frequencies.
The multi-frequency OMTs are used to excite a common aperture feed horn capable o f
operating at multi-frequency bands. Corrugated horns which are based on corrugated
waveguides should be preferred as feed elements due to their wide bandwidth operation.
The corrugations o f the horn are used to convert the incident dominant mode o f a circular
waveguide into the hybrid-modes (a combination o f TEin and TMin modes) o f the
corrugated waveguide. Thus, this class of feeds also form special types o f mode
transducers. The design details o f such hybrid mode transducers in the form o f corrugated
horns are not available in the literature for multi-frequency operation. The conventional
corrugated horns [34]-[51] can operate only for the bandwidth ratio of 1.6:1. The
bandwidth can be enhanced to ratio of 2:1 by using ring-loading [45], [46]. Homs with
dual-depth corrugations are described in [47]-[50] to cover two widely separated frequency
bands. But even dual-band horns can not be used for satisfactory performance if the two
bands are separated by more than 1.5:1 frequency ratio. In order to meet the requirement of
common aperture radiometer antenna, the feed system has to be designed for a maximum to
minimum frequency ratio of the order of 3.2:1 or more for a radiometer which uses
common aperture antenna covering C, X, Ku and Ka bands with dual-linear polarization
operation. Since the design details of such wideband corrugated horns are not available, it is
of paramount importance to carry out research for the design and development of multi­
frequency horns for dual-polarization operation. The radiation properties o f the horns can
be found out by exciting them with multi-frequency OMTs.
The multi-mode feeds are also a type of mode transducer [9]-[l 1] in which the single
dominant mode at the feed input gets transformed to multiple modes [52]-[54] having
different field configurations [55], [56] at the feed aperture. The combination o f various
modes at the feed aperture may be utilized to get shaped far-field radiation patterns. The
feeds having broad [57] or sector shape [58] primary patterns can provide uniform
illumination o f a reflector antenna and accordingly enhance the overall gain of the antenna.
4
The pencil beam scanning scaterrometer antenna [3] requires two angularly spaced beams
having high gain, low side lobe level and low cross polarization. The angularly spaced
beams can be achieved with two laterally displaced feeds in the reflector focal plane. But,
the lateral displacement o f feeds in the focal plane results into rising o f the side lobe level
and the reduction in the overall gain of antenna due to scan loss. These problems can be
avoided by designing elliptical feeds yielding sector shape radiation patterns with larger
amplitude taper in the plane o f the feed displacement. The design details of elliptical multimode transducer feeds yielding sector-shape radiation patterns are not available in the
existing literature to the best of author’s knowledge. Though, the feeds having elliptical
aperture are reported in [59], [60] but these feeds do not yield shaped radiation patterns.
Sector shape patterns can be achieved with circular aperture multimode feeds where power
is distributed in TEin and TMin modes at the aperture in such a way that resultant far-field
patterns becomes sector shape.
In [61], the methodology to achieve sector shape pattern from circular coaxial aperture has
been discussed but the design details in terms of the distribution of amplitude and phase of
various modes is not given. The required number of modes, their amplitude and phase
distribution to achieve sector shape patterns can be found out from the radiation pattern
synthesis techniques described in [62], [63]. Coaxial multi-ring feeds [61] are lower in size
and weight than the dual hybrid mode corrugated feeds [64]-[66] for providing sector shape
pattern. Therefore, coaxial feeds have been presently preferred as feeds for scatterometer
antenna. These feeds can also be used for achieving high gain of the reflector antenna for
altimeter sensor. In order to realize asymmetric sector shape patterns of the feeds for
scatterometer antenna, the concept of circular coaxial rings presented in [61] has been
extended presently to elliptical "feeds having elliptical rings. These new elliptical multimode feeds which can be utilized as compact feed for efficient reflector antenna, call for a
detailed investigation unveiling the characteristics of individual TEin and TMi„ modes and
the combination of all these modes in proper amplitude and phase to optimize the radiation
pattern of the feeds.
The scan mechanism of the pencil beam scanning scatterometer antenna requires special
type of mode transducers to realize dual-channel rotary joints at Ku-band in order to
5
achieve uninterruptible transmission o f power from the fixed source to the rotating antenna.
These mode transducers are generally based on the excitation of circularly symmetric
modes in waveguides. These modes have symmetric field configuration about the axis of
rotation. TMon and TEon modes in circular waveguide have no circumferential variation o f
fields in the cross section of the circular waveguide. Because o f the circular symmetric
nature of TMo„ and TE0n modes, the mode transducers supporting these modes form a very
important class of microwave component applicable to waveguide rotary joint, tracking
feeds and low attenuation transport o f guided waves at millimeter wave frequency. These
modes in circular waveguides are higher-order modes and since the dominant mode in
circular waveguide is asymmetric circumferentially, the excitation of circular symmetric
modes with mode purity poses a very challenging task.
The circularly symmetric mode transducers for rotary joints have been described in [67][74], Basic design concepts o f single channel rotary joints or motional joints are described
in [67]. The authors in [68] have reported the excitation o f TMoi and TEqi modes for dual­
channel waveguide rotary joint. As described in [68], TMoi mode is excited in the circular
waveguide from a rectangular waveguide through central probes and TEoi mode is excited
in circular waveguide using slots at the periphery o f the circular waveguide. However, the
authors in [68] did not present any details of design other than the conceptual layout o f the
device. Tomiyasu [69] built an annular rotating joint which permits multiple stacking to
provide a number of channels with the help o f directional couplers and E-plane joints. A
high-power rotary waveguide joint is described by Smith and Mongold [70], where 1: 16
waveguide power divider is used to generate TEoi mode in the circular waveguide. A
multi-channel waveguide rotary joint is described by Boronski [71], where the joint consist
o f essentially o f three E-Plane waveguide rings o f equal diameter, mounted coaxially with
the narrow walls in contact, the middle ring being cut along its electrically neutral axis to
allow rotation. A dual-channel rotary joint for high average power operation is described by
O. M. Woodward [72] where, a new type of dual-channel rotary joint combining the TMoi
mode and the circularly polarized TEn modes in circular waveguide has been developed for
an X-band antenna employed in a satellite communication link. In [72], low loss and a
decoupling of 35-40 dB was achieved between two channels. In [73], full wave analysis of
non contacting rotary joint choke section is presented. In the work of [73] different types of
6
possible waveguide inodes suitable for rotary joints are described with expression for
internal surface currents for different modes. In [74], single channel rotary joints are
described in which ridged waveguide sections have been used for phase adjustment.
In view of this type of mode transducer which yields circular symmetric modes, it is of
importance to carry out systematic investigation to excite TMoi mode in the presence of
TEoi mode utilizing a compact configuration. Simultaneous excitation of these modes in a
circular waveguide has to be investigated. Generally, rectangular waveguides are used as
transmission lines. Therefore, suitable transitions have to be designed to convert
rectangular waveguide’s TEi0 mode to circular waveguide’s axis symmetric TM0i and TE0i
modes. Using these transitions compact dual-channel rotary joints have to be developed
offering minimum insertion loss, high isolation between channels and invariance of the
electrical parameters with 360 degree rotation.
Based on the literature survey, it is o f relevance to carry out rigorous investigations on
•
Discontinuities in overmoded and oversized circular waveguides for multi­
frequency operation.
•
Multi-frequency (four frequencies) mode transducer (MT) using circular waveguide
as primary waveguide and rectangular waveguide as the secondary waveguide.
•
Multi-frequency (four frequencies) hybrid mode transducer in the form of a
common aperture corrugated hom.
•
Multi-mode transducers in the form o f elliptical and circular multimode feeds
yielding sector shape patterns to enhance the over all efficiency of the reflector
antenna
•
Waveguide mode transducers to excite circularly symmetric modes in circular
waveguide.
7
1.1 Organization of Thesis
The thesis has been organized in seven chapters.
C hapter 1 describes the relevance o f the present investigations, literature survey, outline o f
investigations and finally the organization of the thesis.
Chapter 2 presents electromagnetic modeling and analysis of discontinuities in oversized
circular waveguides. Circular waveguides having asymmetrical discontinuities such as
radial post and coaxial probe have been analyzed using moment method based
formulations. Scattering parameters for dominant and higher-order modes have been
computed. Symmetrical waveguide discontinuities have also been analyzed using mode
matching technique for step junction. Using this technique a waveguide geometry having
tapered section between two cylindrical wayeguides and a conical horn geometry have been
analyzed. Higher-order mode coupling is studied as a function o f flare angle o f the tapered
waveguide section. The mechanism of excitation o f circularly symmetric modes in circular
waveguide and associated problems are also discussed.
C hapter 3 presents the design and development of a four-frequency probe coupled
common orthomode transducer (OMT) at 6.6, 10.65, 18 and 21 GHz using circular
waveguide as primary waveguide and rectangular waveguide as the secondary, waveguide.
Modal analysis based design technique is used to minimize the inter-port coupling and to
maximize the power in the dominant mode in the outermost section o f the OMT. The
simulated and measured performance o f the developed 8-port orthomode transducer (OMT)
are presented The complexities and problems faced at higher frequencies in the presence of
lower frequency mode transducers with coaxial probe coupling mechanism are discussed.
The design o f a tri-frequency mode transducer at 18.7, 23.8 and 36.5 GHz has also been
presented in die same chapter.
C hapter 4 presents the design and development o f a common aperture multi-frequency
hybrid-mode transducer in the form o f a corrugated hom. The simulated and measured
performance o f the composite hom and OMT are presented at all the four frequency bands.
8
The design, simulation and measured results of a new multi-mode tri-frequency horn are
also presented.
Chapter 5 presents mode transducers which couple multiple TEin and TMjn modes with
proper amplitude and phase to control the radiation pattern from the aperture o f the multimode feed. Using this concept, the design and development of new elliptical multi-mode
feeds for scatterometer and multi-mode circular feeds for altimeter antenna are presented
for space-borne remote sensing applications. The feeds have been designed to yield sector
shape patterns through coupling of power into higher order modes of elliptical and circular
wave guides to enhance the over all efficiency o f the reflector antenna. The measured and
simulated results for primary and secondary performance are presented for reflector
antenna using these types o f mode coupler feeds.
Chapter 6 describes the excitation of circular symmetric TMoi and TEoi modes in circular
waveguide. This chapter presents the design, modal analysis, simulation and measured
performance o f different types of waveguide mode transducers which are used to develop
the dual-channel waveguide rotary joints. Different configurations o f mode transducers are
investigated to excite circular waveguide TMoi and TEoi modes for the realization of dualchannel rotary joints. The simulated and measured results o f a compact dual-channel rotary
joint for the scan mechanism of a pencil beam scanning scatterometer antenna are presented
for return loss, isolation and insertion loss and their variation with 360° rotation.
Chapter 7 contains summary, conclusion and future scope.
9
Chapter 2
Electromagnetic Analysis of Discontinuities in Circular
Waveguide Mode Transducers
Discontinuities in waveguides act as mode transducers which excite higher-order modes in
oversized waveguides. The content of these higher-order modes have to be minimized or
maximized depending on the application sought for. In this chapter, circular waveguides
having asymmetrical discontinuities such as radial post and coaxial-line fed probes have
been analyzed in the context o f multi-frequency ortho-mode transducers (OMT) using
moment method based formulation. Scattering parameters for dominant and higher-order
modes have been computed as function of geometrical parameters of the discontinuities.
Symmetrical waveguide discontinuities have also been analyzed using mode matching
technique for step junction. Using this technique a waveguide geometry having tapered
section between two cylindrical waveguides and a conical horn geometry have been
analyzed. Higher-order mode coupling is studied as a function o f flare angle o f the tapered
waveguide section. The mechanism o f excitation o f circularly symmetric modes and
associated problems is also discussed for microwave rotary joints. The validity o f the
results is checked through comparison of the data computed using commercially available
electromagnetic tools such as TICRA’s CHAMP/FEED for symmetric discontinuities and
Ansoft HFSS for asymmetric discontinuities. The experimental and computed data on
return loss for post and probe discontinuity problems are also presented.
2.1 Coupling Mechanism and Discontinuities in a Multi-frequency Mode
Transducer
A common mode transducer operating over multiple frequency bands is generally preferred
as compared to separate mode transducers for each frequency band. These multi-frequency
mode transducers can be realized with cascaded circular waveguides having co-axial line
fed probes as coupling element as shown in Figure 2.1.
10
Co-axial line fed probes are used to couple power in the dominant mode of the circular
waveguide at individual frequency bands. In the Figure 2.1, straight waveguide sections at
each frequency band are terminated at their inputs with tapered sections to allow
propagation o f signal at all the frequency bands o f the multi-frequency mode transducer.
The junction between straight and flared waveguide sections act as symmetrical
discontinuity exciting undesired higher-order modes along with the fundamental mode. If
orthogonal polarizations are required, polarization matched probes have to be used to
couple power at different frequency bands. In such cases, the probe in the lower frequency
section acts as asymmetrical discontinuity which not only reflects and couples the next
incident higher frequency signal but also excites higher-order modes at higher frequencies.
The higher-order modes at higher frequency can affect the performance of a horn which is
fed with multi-frequency mode transducers. It is of importance to carry out electromagnetic
modeling and analysis o f symmetrical and asymmetrical waveguide discontinuities to
investigate the behavior o f fundamental and higher-order waveguide modes as function of
physical parameters o f the discontinuities. The problems which should be investigated for
the device shown in Figure 2.1 are coaxial to circular waveguide junction, scattering from
probe or post discontinuities and the discontinuities in the form of step and tapered
junctions in circular waveguides.
11
2.2 Asymmetric Discontinuities in Circular Waveguide
In a probe excited circular waveguide, the impedance matching is achieved at a particular
depth (resonant condition) of the probe as reported in [28]. While, the probe excited
circular waveguide reported in [28] is perfectly shorted (see Appendix A.1) at its input end,
the input ends o f the probe excited sections in a multi-frequency mode transducer (Figure
2.1) are terminated with cut off tapers offering a tapered or virtual short. The probe excited
circular waveguides having tapered short at its input has not been investigated earlier. An
approach o f achieving impedance matching in probe coupled circular waveguide having a
tapered short at input is described in Appendix A.2 along with the perfect short case for the
sake of completeness. To match the impedance offered to the probe in a circular waveguide
to that of the coaxial line, the computed probe depth from the expressions in [28] comes
nearly quarter of free space wavelength. This depth of probe acts like a metallic post
discontinuity and generates a number of higher-order modes in the circular waveguide at
various frequency bands. Since, the waveguide junction at lower frequency band is
oversized at higher frequency bands, this will support some of the higher-order modes
generated at the post or probe discontinuity. These propagating higher-order modes have
special radiation characteristics which influence the overall radiation pattern of the feeds
excited by the multi-frequency mode transducer. Asymmetric post discontinuities are also
used in a variety of microwave filters and tri-mode matched hom feeds [75], [76], [77]. The
analysis of a post or probe discontinuity in an oversized circular waveguide which supports
higher-order modes has not been reported earlier to the best of author’s knowledge. Thus, it
is worthwhile to investigate the scattering characteristics o f a post or probe loaded circular
waveguide to get an insight about the behavior of higher-order modes which in turn provide
more insight into the design of multi-frequency mode transducers presented in Chapter 3.
2.2.1 Post Discontinuity in Circular Waveguide
In this section, the formulation and analysis of scattering characteristics of a radial post
discontinuity in an oversized circular waveguide is presented, using Galerkin’s Method of
Moments (MoM) considering the entire domain basis functions. Dyadic Green’s function
for the radial current has been derived using the approach as given in [28]. The moment
12
method formulation has been employed by approximating the induced current on the post
as a line current and also taking the testing point on the surface of the post as a line. Return
loss characteristics and the power coupled to higher-order modes have been found out for
various heights o f the post. The data on the scattering parameters computed by the present
method have been compared with HFSS to justify the validity o f the present analysis.
Experimental data on return loss of the dominant TEn mode have been compared with the
data computed by the present method. Close agreement has been observed between the
experimental and computed data o f the return loss.
2.2.1.1 Formulation and Analysis of Post Discontinuity
The geometry to be analyzed is shown in Figure 2.2. It consists of a circular waveguide
with a radial post discontinuity. The incident TEn mode polarized in the direction of the
post induces electric current on the post. The induced current on the post generates infinite
modes in TE (transverse electric) and TM (transverse magnetic) configurations in both the
directions. Depending on the size o f the waveguide some modes will be propagating while
the other modes will be evanescent.
Poi
lucid
mod<
Post discontinuity
Figure 2.2 Circular waveguide loaded with a post discontinuity.
13
The tangential components o f total electric field E* at the post surface should be zero. This
is the boundary condition to be satisfied on the surface o f the metallic post. With this
boundary condition, the electric field integral equation can be written as,
E mc + E S = E ‘ = 0
=> E mc = - E s
(2.6)
where, Es represents scattered field from the post and is given by,
E{p,(j>,z) =
■J (p )d fi
(2.7)
where, Gpf)(p,$,z,p,<ji,£) is the dyadic Green’s function which has been derived using the
approach given in [28]. In [28], the Green’s function is derived with one end o f the
waveguide shorted and the other end terminated at a perfectly matched load. But in the
present case the Green’s function is derived considering both ends o f the waveguide
terminated with matched loads. Considering all the TEmn and TMmn modes o f circular
waveguide, the radial component o f electric type Green’s function ( Gpp,) for z > z can be
written as [28].
( A # ,z , p ' , = — — X X
Bp
*
+
CO
Cmn(p,<j>\z') cm(m<f>)Jm(r'mnP) e
72—1
CO
22=1
cmn(p
cos(nuf>) JL {Jm(ymnP)) e aw,Z - , z > z
(2.8)
dp
m-0 b
where, J m(y mnp ) and J m(YnmP) are the Bessel functions o f order m.
For z < z , the'expression for radial component o f electric type Green’s may be obtained
by changing the sign o f argument o f the exponential terms in Equation (2.8).
Using the method described in [28], cmn( p ,$ ',z') and c mn( p ->(j)\z') have been derived
as,
=
)) cos(m0‘)e~v '
(2.9)
Jm(rm„p) cos(m0') e1
(2.10)
----------------------------- - L ( J m{ymP
4
4 ,0 ® '.* '.* ') = ^
2
Urn mn* mn mn do
m
mG>mj'lPmnP
From equations (2.8)-(2.10), the expression for the required Green’s function can be written
as,
14
m
Gp p ,(p ,^ z,p \< t,',z ')= YlBL Y Z
2
01=1 «=!
T J m (y 'm n P
cos(mf)cos(m<f>') 0*™^ + J ^ 2 ^ 2 ] ----- —
1(08 '»=0 »=i 2^-0rafflm„yra„
dp
{J,n(VmnP))e
) J m ( Y mnP )
8
'2‘1IE0mO:>mn7mna mnPP
“ ”"Z C O S (w ^)C O S (m ^')
5/?
z >z
;
(2. 11)
m
™
^ m=4»=4
cos(mfi)co$(md>) + —
- ^—
1 Y2 T
0 /V»C* w
01=0 n = l
J m ifm n P ) 6
A f t S ^ C Q ^ Y mn(Xmnp p
“ i - . . . . - e - - ''
■
E ^ E 0 m(OmnYmn
A ( / . 0 - _ p ') )
®P
JL (Jm{ymnp ) ) e am"z co$(m<j>)cos(m<l>) ;
z< z
(2.12)
dp
y mn, a mnaxe the cutoff wave numbers and phase constants respectively for TEnm modes and
represented by,
y
/
x
,
= mn
mn
y 2
f mn
a
=
/ y ^ 4 - Jr^
u , m n ^ n’
amn= j0mn= 4 r'L -k 1
rn=l,2,3 ... andn= 1,2, 3....
t
where, x mn is the n* root of j m(x) =0. Similarly ym„,OCm„ are the cutoff wave numbers and
phase constants respectively for TMmn modes and represented by,
rL = cc2mn+ k2
a mn = jpm„ = J r L ~
i m=0,l,2,3,....... andn= l,2,3,....
where, xmn is then* root o f Jm(x)= 0 .
The unknown surface current J (p ) of equation (2.7) on the post can be expressed in terms
of basis functions as,
J( p ) = Y pU
(2.13)
p)
P-l
where fp(p) is entire domain basis function given by,
fp
sin( p k ( p - a + h))
sin(kh)
(2.14)
\ p ~ 1, 2...N
15
Taking the inner product o f the equation (2.6) with testing function f q (same as the basis
function-Galerkin’s technique)
< f q, E s> = < f q, - E mc>
(2.15)
where, f , = M q U . p - ° + K »
9
sin(kh)
;q = l , 2 , ..... N
\ E J q{p)dp = - \ E mcf qi p ) d p
(2.16)
Using equations (2.7), (2.13) and (2.15) w e get,
J
s-K
J M dP
p p p=l
p
(2.17)
Y j2p \\ fP(p )Gpp.(p,<!>,Z,P,4',z')fq(p)dpdp
p=1
pp
(2.18)
- ~ \ E mcfq{P)dp
p
The equation (2.18) can be expressed in matrix form as,
[zli]=[v]
(2.19)
where the elements o f the matrix [Z] and matrix [V] are,
(2.20)
ZPt = f | fP(P )G ( A <<>, p',ft,z')fq(p)dpdp
PP
Vg = ~
where, E
(2.21)
me f q ( P ) d p
1
=pd\ (xn ) V^ [ ( ^ 'n )
cos(#)
1P) e
JPnZ
and
xn = 1.841.
1)
The integration limits for both p and p' are from (a-h) to (a). Matrix P] contains
unknown coefficients o f the current distribution on the post. Solution o f matrix equation
(2.19) w ill give the unknown coefficients (Ip) and putting these values o f coefficients in
equation (2.13), the current J(p') on the post surface can be computed. Once the current is
known, the scattered field corresponding to different modes and the other electrical
parameters o f interest can be found out.
16
2.2.1.2 Results and Discussions for Post Discontinuity
Using the formulation as discussed in Section 2.2.1.1, a MATLAB based computer
program has been developed. The scattering parameters have been computed for a circular
waveguide o f diameter 32.54 mm with a circular cylindrical post of diameter 1.6 mm.
Sixteen point Gaussian integration has been used to solve the integral expressions given in
equations (2.20) and (2.21). Sixteen TE and TM modes have been taken into consideration
to ensure converged solution. Return loss for the incident TEn mode in the circular
waveguide is shown in Figure 2.3. The return loss has been plotted for different heights of
the post. As shown in these plots, the return loss becomes poor when the post height is
increased. At 10 GHz, it becomes -16 dB for a post height o f 11 mm as compared to -54 dB
when there is no post (i.e., post height 0.0 mm). Ripple like behavior has been noticed in
the return loss plot over the 7 to 14 GHz frequency band. The plot has dips at 9 GHz 12.4
GHz indicating improved return loss performance. These dips occur independent o f the
height of the post for a fixed size of waveguide. As shown in Figure 2.4, the dips show
frequency sensitivity when the size of the waveguide is changed. For larger size waveguide,
the response and dips move towards lower frequency and for lower waveguide size they
move towards higher frequencies. The frequencies where dips occur can be selected as
higher frequency bands for a multi-frequency mode transducer so that they are least
affected due to the presence of post at lower frequency. The power carried forward in the
dominant TEn mode is shown in Figure 2.5. This plot also shows that maximum power is
confined in the dominant TEn mode where dips occur in the return loss plot. Above 7 GHz,
the waveguide becomes oversized and supports higher-order modes. The power coupled to
higher-order TMmn and TBnm modes have been computed and it has been found that the
power couples significantly to higher-order asymmetric TMoi, TE21, TE31 modes and it
shows negligible coupling in the TMin and TEi„ modes. The power coupled to TM 01 mode
for different heights is shown in Figure 2.6. The power in TE21 and TE31 modes is shown in
Figures 2.7 and 2.8 respectively. Scattering performance o f the post over wide frequency
(6-21 GHz) range for post height o f 11mm is shown in Figure 2.9. The results for higher
order modes show that a particular higher-order mode gets coupled only at a frequency
where the waveguide size becomes above cut off for that mode. The power in higher-order
modes increases with post height. As shown in Figures 2.3-2.8, the results computed from
the present method are in close agreement with HFSS results. In order to verify the
simulated results, the appropriate hardware has been developed in which two rectangular-
17
to-circular waveguide transitions are placed back to back with a radial post in the circular
waveguide section as shown in Figure 2.10. Using a PNA series network analyzer (E 8363
B), the measurements were carried out for the post height o f 11 mm in the frequency range
of 7-9 GHz and the results are plotted in Figure 2.11. As shown in Figure 2.11, the
measured and the simulated results are in close agreement. Slight deviation above 8.4 GHz
may be attributed due to the fact that WR-137 works up to 8.2 GHz, while the measured
values are presented up to 9 GHz. The rippled behavior of the measured return loss plot for
post discontinuity is due to the reflections in the realized rectangular to circular waveguide
transitions. In the absence of the post, the measured return loss o f the transitions (put backto-back) alone is o f the order o f 21 dB having ripples o f ± 3.0 dB as shown in Figure 2.11.
Post Height 11 mm (Present Method)
x x x Post Height 11mm (HFSS)
------- Post Height 7mm (Present Method)
Post Height 5mm (Present Method)
a- *
■ r - f - v Post Height 3mm (Present Method)
h—i— h
Post Height 3mm (HFSS)
m
"O
J aTlYlTlTlTlTffffi'
-50
_ 0 Q Ti. .I i IM~<fr
7
Gt -fiL-
1nrflsJA teB,ftJL
10
8
11
12
13
14
Figure 2.3 Return loss performance for a post discontinuity in a circular waveguide.
Figure 2.4 Return loss performance for different sizes of the waveguide with post
discontinuity.
18
Figure 2.5 Forward power for a post discontinuity in a circular waveguide.
Forward Power in TMG1 mode (dB)
20
10
-
v v
v
Post Height 11 mm (Present Method
-------- Post Height 11 mm (HFSS)
b-
b
-a Post Height 7mm (Present Method)
- - -
-10
-
7
Post Height 5mm (Present Method)
x-m-k Post Height 3mm (Present Method)
8
9
10
11
Frequency (GHz)
12
13
14
Figure 2.6 Modal power in TM01 mode for post discontinuity.
P ost Height 11 mm (Present Method)
P ost Height 7 mm (Present Method)
Pcwer in TE21 mode (dB)
10
P o st Height 5mm (P resent M ethod)
0
P ost Height 3 mm (P resent Method)
P ost .Height 11 mm (HFSS)
-10
-20
-30
-4019
10
11
12
Frequency (GHz)
13
Figure 2.7 Modal power in TE21 mode for post discontinuity.
19
14
o
i
cn
i
o
cn
■
—*
N)
i
o
oi
i
ro
Power in TE31 mode (dB)
------- Post height 11 mm (Present Method)
— — Post height 7mm (Present Method)
o o o Post height 5mm (Present Method)
a - a - a Post height 3mm (Present Method)
x x x Post height 11mm (HFSS)
-30 J ___ I___ I___ I___ I___ |___ |___ I___ I___ I___ I___ I___ I___ I___ I___ I___ I___ I___ I___ l___ I___ I___ I___ I___ I___ I___ I___ I___ L
14.0C
12.50
12.75
13.00
13.25
13.50
13.75
Frequency (GHz)
Figure 2.8 Modal power in TE3 1 mode for post discontinuity.
R e tu r n lo s s f o r in c id e n t T E 1 1 m o d e
-----------F o r w a r d p o w e r in T E 1 1 m o d e
-9
F o r w a r d p o w e r in T M 0 1 m o d e
v
F o r w a r d p o w e r in T E 2 1 m o d e
o o - o
F o r w a r d p o w e r in T M 1 1 m o d e
o -
v
*
-*- + -»• F o r w a r d ”p o w e r in T E 3 1 " m o d e "
CD
TD
8
9
10
11
12 13 14 15 16
Frequency (GHz)
17
18
19 20
21
Figure 2.9 Scattering performance of post of height 11mm over wider
frequency range.
Figure 2.10 Hardware of circular waveguide with post discontinuity.
20
30 c-
P o s t H e ig h t 1 1 m m ( P r e s e n t M e t h o d )
x
x
x P o s t H e ig h t 1 1 m m ( H F S S )
---------- P o s t H e ig h t 11 m m ( M e a s u r e d )
' W ith o u t P o s t (M e a s u r e d )
co
■a
w
Figure 2.11 Simulated and measured values of return loss for post height o f 11 mm.
2.2.2 Coaxial Probe Discontinuity in Circular Waveguide
The analysis presented in Section 2.2.1 describes electromagnetic scattering by a post.
However, in multi-frequency OMT, the coaxial probe also acts like an asymmetric
discontinuity at lower frequency and has to be analyzed considering die magnetic current in
the coaxial aperture region and the current induced on the probe. Using these current
sources, electric and magnetic field integral equations have to be formulated applying
proper boundary conditions on the surface o f the probe and over the coaxial aperture
respectively. In addition, expressions for electric and magnetic type dyadic Green’s
functions have to be found out for both the electric and magnetic current sources at the
locations of probe and the coaxial aperture. The probe at lower frequency will not only
reflect and couple the incident signal but also excite higher-order modes at higher
frequencies.
In this section, the formulation and analysis for a probe discontinuity in a circular
waveguide is presented, where two separate equations have been formed by applying
boundary conditions on the probe surface and on the surface of the coaxial aperture. In
order to formulate the expressions for the scattered field, dyadic Green’s functions have
been derived by considering two different current sources. The integral equations are
21
solved using method o f moments technique. Computed data on return loss and power
coupling in the dominant and higher-order modes from the present method have been
compared with the data computed using Ansoft HFSS. Measured data on return loss is also
given.
2.2.2.1 Formulation and Analysis of Coaxial Probe Discontinuity
The geometry o f a circular waveguide loaded with a coaxial probe is shown in Figure 2.12,
where TEn mode has been assumed to be incident at Port-1. The incident TEn mode has
the electric field orientation in the direction o f the probe. The incident mode induces
electric current on the probe and magnetic current over the coaxial aperture. Depending on
the size o f the waveguide, these current sources may couple power in the different modes
corresponding to the incident mode.
Port-2
Figure 2.12 Circular waveguide loaded with coaxial probe discontinuity.
Let E™']^, H™"cw be the incident electric and magnetic fields corresponding to the
dominant TEn mode in the circular waveguide. Let the scattered electric and magnetic
fields in the circular waveguide due to electric current source J ( R ') on the probe are
F / C(p , H~s Cw
due to magnetic current source M(R') over the coaxial aperture
22
are e “cw , H XCW . Let the scattered electric and magnetic fields in the coaxial waveguide
due to magnetic current source over the coaxial aperture are ¥ f CXiV , JTxcxsr .The
cylindrical co-ordinate systems are represented as r,(j),z and rx,<f>x, z x for circular and
coaxial waveguides, respectively as shown in Figure 2.12.
In general, the electric field due to an electric current source J(R') [33] is given as,
E(R) = j(<>Mo JJ[ G el(R,R')■J{R')dV'
(2.22)
The electric field due to a magnetic current source
m (r ')
is given as,
1 (1 )= - j | [v x G 2(R, ]? ')]• M(R')dS'
(2.23)
where, magnetic current M(R') is related to aperture field E(R') as M ( R ’) ~ - n x E ( R ’)
and Gel (R, R') is an electric dyadic Green’s function of first type and We2(R,R') is electric
dyadic Green’s function o f second type.
The magnetic field due to the electric current source J (i?') is given as,
H ( R ) = J J J r |v
X
Wtl ( R , F ')J J { R ' ) d V ’
(2.24)
Vxfcl=Im2
where, Gm2(R,R’) is magnetic dyadic Green’s function o f second type.
The magnetic field due to a magnetic current source M(R') is given as,
( 2 -2 5 )
H( R) = -ja>s0 g W e2(R, R') M(R')dS'
V xG e2=Gml
where, Gml(R,R') is magnetic dyadic Green’s function o f first type.
The general expressions for Ge],Ge2 and Gml ,Gm2 for cylindrical and coaxial waveguide are
given in [33] and also described in Appendix A.3 for the sake o f completeness. From these
expressions the required components of the Green’s functions have been derived for the
present coaxial probe problem and are presented in Appendix A.4.
On the probe surface, the boundary condition is applied on the tangential component of the
total electric field. Assuming probe to be a perfect conductor, the tangential component (in
23
the radial direction) of the total electric field E ‘ at the probe surface should be zero. This
boundary condition is expressed as,
J7 J
& S .C W
. p M
+ ^S ,C W
, p 72? 11
+ & mc.CW
E 1= 0
(2.26)
Over the coaxial aperture, the boundary condition is applied on the azimuthal component of
the total magnetic field. The azimuthal component of the total magnetic field should be
continuous across the coaxial aperture. This boundary condition is expressed as,
, TT U
Tt J
11 S,CW
, t t TEM
+ n S,CW + n mc
_
IT M
~ n s,C X W
\L .H )
The unknown surface current on the probe can be expressed in terms o f basis functions as
1V
J(r) = ^ I pf p(r); where,
f p \ r ) is entire domain basis function.
(2.28)
p =i
Taking entire domain basis functions to expand the unknown surface current (assumed as
line current at the axis of the of the thin cylindrical probe) as,
sm(pk(r-a + h))
sin(&&)
(2.29)
;p = 1, 2...N
A TEM mode distribution has been assumed for the coaxial aperture field (or magnetic
current).
The expressions for field components are derived as,
K cw = \\G rr{r,r')Jr{r')dr'
(230)
Hlcw= - H J
z smtx+H'cos<t>x
= “ l p 2r(r,r')J(r')sm^xdr' + JjG ^(r,r')/(/)cos^r'
(2.31)
K c w = “ \ p r^ r,r')E „ cos(f>xrxdrxd<j)x + \\G n (r,r')Erx sin f a j b M x
(232)
K c m = ^ ( r , r ’)E„rxd r M
(233)
H ‘s,Cw = fjG *(r,r')En s\n<j>xrxdrxd<t>x - ffG ^{r,r')E„ cos<f>xrxdrxcl<j>x
(234)
+
'■')£„ *m+xrxdrxd ix - JjG # ( r ,r ') £ „ cos <f>xrxdrxd^x
= — { j-C T E ^ o s P ^
pakcp
a
(2.35)
24
^ o - f l T s m ^ + fl^ c o s^
= -}jG^(r,r')J(r,)sin # > '+ |jG#(r,r')/(r')cos#>'
(2.36)
/ i f = CTEil— AVi Wi) c o sf e(-'Al'ttn') + ArVjCxQcos^ •e("7A‘rtan^
ja>M
(2.37)
H™=CTEn -A.
(DfJ,
(2.38)
g (~ J 0 n r t m $)
where, x^ = 1.841
cm n‘
* (* !?-1)
•AW,)
By taking inner product of the equation (2.26) with the testing functions, which are same as
basis functions, the equation (2.26) can written as,
( / „ , * / . or
) + { f g, E ” c w ) = - { f t >E%]ln, )
(239)
Similarly, equation (2.27) can written as
(l,H J
Sjar ) + ( l ,H “CW) + ( l , H Z U) = ( l ,Hlcxw )
(2-40)
where,
< f , K c w >= f jG U r S ) ( jtlpf P)f,(r')dr'<lr
p=l
1V
= X V Zn
^=i
(2.41)
where,
( i- W d r
=
< fq>Es,cw > = - \ \ G rt(r,r')E„ co s </>'Jt (r)r,drW ,dr
..
(2.42)
+ J j G > , r ' ) £ „ sin & f,(r)r;dr;dfcdr
In the coaxial waveguide
25
< fq >Es,cw >= -
\ \ G rt
(r,r')E0 cos </>'Jq(r)dr'xd<j>'xdr + JJg „ (r,r')E0 sin $ J q{r)drxd<j>'xdr
(2.43)
<
fq > Es,cw > = E 0 • Zf2
(2.44)
(r, r ') cos (t>'xf q (r)drxd f xdr + JjG re ( r ,r ') sin ^ / ?( r ) ^ ^ « i r
where, Zf2 = <
>= - f J G*-(r>r') ( £ l pf p{r'))sm<f>xdr'rxdrxd<j>x
p=i
+ \\%
r ')(X Ipfp ('•')) cos <t>xdr'rxdrxd<t>x
(2.45)
p -i
> = U p 'Z 2\
z n = - \p z r M fp ( r r) ^ A 'r d r ^ + \ p &(r, E ) / ^ cosf>xdr'r drdj>
(2.46)
< l,F " cr >= J|Gzz(r,r')£ra s\rx$xr’xdr’xd$xrdr d<j)
~ J j ^ ( r , r ') £ ra cos(t>'xr'xdr'xd<f>'xrxdrxd<j>x + JjG ^ r,? -')^ sm</>'xrxdrxd0'xrxdrxd</>x
-
(2.47)
cos$xr'xdr’xd$xrxdrxd$x
<l’Hfcw >= JJGZ3G ,r')E0 sinfixdr’xd(f>'xrxdrxd(f>x
~ \ \ Gzt(r>r')E0cos(j)xdr'xd^'xrxdrxd$x + \\G ^(r,r')E 0smfixdr'xd</>'xrxdrxd<f>x
(2.48)
- \ \ G^(r,r')E 0 cos<j>’xdr'xd<l>'xrxdrxd<f>x
The azimuth component of magnetic filed in coaxial region is given as,
<h Hf c x w >= 2 * 2£ 0(r2 - r 1)(r22 - r 12) / Z o
(2.49)
<l>Hs.cir > - < ^ Hs,cm >= llGn (r ’r')E0sm<j>'xdr'xd<t>'xrdr d(j>
~ \ p z t G’r')E0cos fixdr'xd<Exrxdrxd(f>x + jp ^ (r,r ')E 0sm</>’xdrxd<f}’xrxdrxd<l>x
~ \\G4, f r’r')Eocos<
j>
'xdr'xdfixrxdrxd<j>x
- r*) I ZB
(2.50)
26
^ 1’ * * s tCW >
< - 1’ ** S.CXW ~
> ~ & 0 ■Z 22
z 22 = f j < 7
-
(r>r') sia ^ dr'M'xrxdrxd^)x
JJG* (r’r')cosfcdrW ,rxdrxd4x + JJ ^ (r, r') sin f xd r ^ r xdrxd^x
g
(2.51)
- JjG« (r-r')cos<P'AWxrxdrxd<}>x - 2 * 2(r2- r l)(r* -r? )IZ B
In the above expressions, the expressions for G rr,G n , G r<>,G zr,G^r ,G a> G2fS, G ^ , G ^ have
been derived from the general expressions o f dyadic Green’s functions Wel,Ge2 and Gml
, Gn2. These
derived expressions are presented in Appendix A.4.
For the incident terms of the matrix
V\ =<fq>Eav
> “
(2.52)
\ \ E ™cwf<l(.r)dr
E™ = — ^ —CTEn c o s j J ^ p ) •e(- j A M
p a k cf i
V2 = < l , H ‘cw
a
(2.53)
>= l l H ^ . l r ’d r 'd fir d r d fi
V2 = < l,H ™ >=
- JjAr;M
M .sin <t>xr'dr'd<f>'rdrd<j)
(2.54)
. 1. cos <j)xr'dr'd<t>'rdrd<f>
+
Thus equation (2.39) and (2.40) can be written in the matrix form as,
'
(2.55)
------- 1
Z 22
7
1
Z 21
Z 12
1_____
Z 11
Equation (2.55) contains unknown coefficients (Ip) of the current distribution on the probe
and the unknown peak field ( E 0) over the coaxial aperture. The solution o f matrix equation
(2.55) will give these unknown coefficients and using these coefficients, the current
distribution on the probe, the scattered fields corresponding to different modes, power
coupled to the coaxial line and the other electrical parameters o f interest can be found out.
27
2.22.2 Results and Discussion for Coaxial Probe Discontinuity
Using the formulation presented in the previous section, a MATLAB based computer
program has been developed. The scattering parameters have been computed for a circular
waveguide (diameter 32.54 mm) having a co-axial line fed probe of diameter 1.6 mm. The
diameter of the inner and outer conductors of the coaxial line were taken as 1.6 mm and 6.5
mm, respectively. Return loss for the incident TEn mode in the circular waveguide mid die
power coupled to higher order modes and to the coaxial line port have been computed and
compared with the data from HFSS. The return loss has been computed for the different
depths of the probe. The computed data for return loss is shown in Figure 2.13. Improved
return loss (-10 dB) has been observed at lower frequency for probe in comparison to the
return loss (-3.6dB) for post (see Figure 2.9) o f similar height (11 mm). This may be due to
the fact that probe couples part (-3.8 dB) o f the incident signal into the coaxial line unlike
that o f post. Return loss also varies, with prob,e depth (or height) in circular waveguide. For
example at 7 GHz, it becomes -10 dB for a probe height o f 11 mm as compared to -50 dB
when there is no probe (probe height 0 mm). The forward power carried by the dominant
TEn mode is shown in Figure 2.14. It is observed that the power coupling to the dominant
TEn mode is increased when probe height is reduced. The probe also acts as asymmetrical
discontinuity in circular waveguide exciting higher-order TM qi, TE21, TE31 modes above 7
GHz. The Figure 2.15 shows the power coupled into higher order TM 01 mode. The power
coupled into higher order TE21 mode is shown in Figure 2.16. The power in higher order
modes increases with probe height. The part o f the incident power gets coupled to the
coaxial probe which is shown in Figure 2.17. The hardware shown in Figure 2.10 has also
been used to verify the probe analysis results. In this hardware ( Figure 2.18 ), a coaxial line
fed probe of height
11
mm was used in place o f the post in a circular waveguide section.
Measured return loss and forward power for the incident TEn mode in the circular
waveguide are shown in Figures 2.13 and 2.14 respectively. The power coupled to the
coaxial port with respect to incident TEn mode in the circular waveguide is shown in
Figure 2.17. Scattering performance o f probe o f height 11 mm over wider frequency range
for few higher order modes is shown in Figure 2.19. The results computed from the present
method are in close agreement with the data computed from HFSS and measurements. In
the absence of the probe, the measured return loss o f the transitions (put back-to-back)
itself is o f the order o f 21 dB having ripples o f ± 3.0 dB up to 9 GHz. This causes ripples in
the measured return loss plot for the probe discontinuity as shown in Figure 2.13.
28
30
Height
Height
Height
Height
Height
Height
20
10
o
V
o
S11 (dB)
o
11mm (Present Method)
11 mm (HFSS)
7mm (Present Method)
3 mm (Present Method)
3 mm (HFSS)
0 mm (Present Method)
o
o
"T
70
75
80
85
90
95
100
Frequency (GHz)
— —— Probe Height 11mm (Present M ethod)
p - v - v Probe Height 7 mm (Present Method)
o - o - o Probe Height 3 mm (Present Method)
Probe Height 11 mm (Measured)
^
i
o i o o i o o i o c n o
— — — Probe Height 11mm (HFSS)
No
W
lO
M
o
^
S21 (dB)
IO
Figure 2.13 Return Loss o f probe loaded circular waveguide.
80
85
90
100
Frequency (GHz)
Figure 2.14 Forward power in the dominant TEi i mode for probe discontinuity.
Frequency (GHz)
Figure 2.15 Power in TM qi m ode for probe discontinuity.
29
20
• • • TE21-Post height 1 1 mm (HFSS)
--------TE21-Post height 7 mm (Present Method)
-------- TE21-Post height 3 mm (Present Method)
--------TE21-Post height 11 mm (Present Method;
10
o
-1 0
00
"O
-2 0
-30
-40
-50
9.00
9.25
9.50
9.75
10.00
F requency (GHz)
Figure 2.16 Power in TE21 mode for probe discontinuity.
D
O
0 ( Mt
-
P ro b e H eight 11m m (H FS S )
P ro b e H eight 7 m m (H FS S )
P ro b e H eight 3 m m (P re s e n t M eth o d )
O
P ro b e H eight 7 m m (P re s e n t M eth o d )
P ro b e H eight 11 m m (P re s e n t M eth o d )
r
O
O
O
J (
O
O
S31 (dB)
O
P ro b e H eight 11 m m (M e a s u re d )
O
O
I
f
)
c
(
7.0
7.5
8.0
8.5
9.0
9.5
10.0
Frequency (GHz)
Figure 2.17 Power coupling to the coaxial line.
Figure 2.18 Hardware of circular waveguide section with co-axial line
fed probe discontinuity.
30
20
---------- T M 0 1 M o d e ( H F S S )
10
o
o
o T M 0 1 (P r e s e n t m e th o d )
---------- T E 2 1 M o d e ( H F S S )
0
w v
v T E 2 1 ( P r e s e n t m e th o d )
---------- T E 1 1 M o d e r e tu r n lo s s ( H F S S )
-10
CD
X3
-20
-30
r:
■/
f
J
y
-40
-50
\ ... 1..
I 11 I I I
8
9
10
I 11 I I 11 I I I I iulII I lllmi 11 I H I I I I ■>.!
11 12 13 14 15
Frequency (GHz)
16
17
18
19
20
Figure 2.19 Scattering performance o f probe o f height 11mm over wider frequency range.
The computed results for probe discontinuity show that the probe deteriorates the return
loss performance, couples the part o f incident signal and excites higher-order modes at
higher frequencies. This study gives a good insight about the nature o f coupling and the
higher-order modes excited due to the co-axial probe discontinuity. This analysis may be
very useful in the design of multi-frequency ortho-mode transducers, where the probe at
lower frequency ports acts as asymmetrical discontinuity, thereby affecting the
performance o f higher frequencies.
2.3 Symmetric Discontinuities in Circular Waveguide
The symmetric waveguide discontinuities in waveguides also act as mode transducers and
generate another type o f higher-order modes as compared to asymmetric discontinuities. In
the multi-frequency mode transducer (Figure 2.1), two consecutive cylindrical waveguide
sections are joined with tapered waveguide sections. The tapered section between two
smooth wall cylindrical waveguides acts as a symmetrical discontinuity and it may excite
higher-order modes. The discontinuities formed with tapered sections can be analyzed in
terms of step junctions. A step discontinuity is created at the junction between two uniform
waveguides which are o f different cross-sections. The step junction discontinuity as shown
in Figure 2.20 acts as a mode transducer [10], [11], which excites number o f higher order
modes depending on the size of the output waveguide with respect to the input waveguide.
As described in [35], [42] smooth wall conical horns, corrugated horns and any specific
waveguide geometry can always be represented as a series o f step junctions. Therefore, if a
31
single step junction can be modeled and analyzed properly, other mode transducers
represented as series of step junctions can also be modeled and analyzed by cascading
scattering matrices of the individual step junctions [42].
Region 1
T E ([
M m odes
Incident mode
2=0
Figure 2.20 Step junction between two smooth-walled waveguides o f different radii.
Modal field matching is a very powerful technique to analyze step junctions. Although, this
technique for step junctions in circular waveguide has been presented in detail in [35], [42],
it is described briefly in Appendix A.5 for the sake of convenience. A tapered waveguide
junction between two waveguides can be analyzed using this technique after representing
the tapered waveguide section as series of step junctions as shown in Figure 2.21. The
scattering matrix of the individual step junctions can be cascaded to obtain overall
scattering matrix of the tapered geometry.
Conical section
replaced with
sjggj unctions
Figure 2.21 Smooth wall conical waveguide approximated by incremental step junctions to
apply mode matching using cylindrical modes.
32
The waveguide geometries such as smooth wall conical horn or corrugated hom can also be
represented in the form of cascaded step junction discontinuities. A schematic o f a circular
to conical waveguide mode transducer in the form of a corrugated hom is shown in Figure
2.22(a). Each corrugation can be represented in the form of a pair o f step junctions as
shown in Figure 2.22(b), whose scattering matrix can be computed using expression for
mode matching technique. The complete hom can be analyzed after computing scattering
matrix for each pair of step junction along the hom and subsequently scattering matrices for
all the junctions can be cascaded to obtain an overall scattering matrix o f the hom.
Figure 2.22 Circular waveguide to conical waveguide mode transducer (a) conical
hom. (b) a corrugation represented as a pair of step junctions at z = 0.
Using the formulations [35], [42] for mode matching technique as described in Appendix
A.5, a computer program was developed using MATLAB. Using this program, the
geometry o f Figure 2.21 has been analyzed to deduce higher order modes. A unit amplitude
TE h wave is assumed to be incident at the plane o f discontinuity (z = 0) as shown in Figure
2.20. At the discontinuity higher-order modes are generated part o f which is reflected back
and part transmitted. Figure 2.23 shows the computed modal amplitudes for 2ai = 11 mm
and 2a2 = 32.54 mm over the frequency range from 16 GHz to 30 GHz for flare angles 5,
10, 45, and 90 degrees for the tapered section. This figure shows that the maximum
power is confined to the dominant TEn mode when flare angle is less than 10 degrees.
Power coupling from incident TEn mode to higher order modes increases with flare angle
and reaches to maximum when flare angle is 90 degrees. At flare angle o f 90 degrees, the
geometry of Figure 2.21 changes into the geometry of Figure 2.20, i.e., it becomes a step
junction. The power coupling to higher-order modes changes with frequency for fixed flare
33
angle. These observations will be very useful while designing a multi-frequency mode
transducer where purity in the dominant TEn is required. Also this analysis will be useful
for designing a multi-mode coupler hom, where higher order modes will be needed for
achieving shaped radiation patterns.
<w
08
02
_ —
.xv— G-------
—------- O - --------4j>.»
g .—
GOt
TE11 mode
-0 4
©■©•© TM11 mode
Flare angle = 5 DEG
9
9
Lt-l-i-i i-i I t m
16
17
18
I t i l l ! h i i Ll i i i l i i i i l i m l i i i i l i n t i t m l n i i l i m i n
19
20
21
22
23
24
25
26
27
28
29
TE12mode
TM12mode
Return loss
-10
30
ni,li,iuiA,u.>lm tii.i,aixn.*i.u.uiu.iiiin,i Lu.t Luu.lt.uil u.ixLtu
16
F re q u e n c y (G H z )
BBB
Flare angle » 1 0 DEG
CO
-0 8
TE11 mode
<0
G O E3 TE12 mode
▼
Return lose
-0 6
—-
O O Q TMUmode
^
-0 2
CM
M o d a l A m p litu d e
04
9 9
M o d a l A m p litu d e
0&i-
17
18
19
20
21
22
23
24
25
26
27
28
29
30
F r e q u e n c y (G H z )
(b)
18
19
20
21
22
23
24
25
26
27
28
29
4k
0
b£
0
Q
0
tO
6
4>>
0
17
-10
30
16
F re q u e n c y (G H z )
TE11 mode
G - e - 0 T M 11 m ode
Q-BEI TE12 mode
TM12 mode
O
6
6
18
1---1---— -
TE13mode
CD
M o d a l A m p litu d e
M o d a l A m p litu d e
(a)
Return loss
17
in u la .
18 19 20
liiiiiliiiiln
jj n
21
22
23
24
25
26
27
28
29
30
F re q u e n c y (G H z )
(c)
(d)
Figure 2.23 The modal amplitudes for flare angles, (a) 5 degree, (b) 10 degree, (c) 45 degree,
(d) 90 degree.
A horn geometry (Figure 2.22) having 10 corrugations with input diameter (D,) o f 45.7
mm and output diameter (D0) o f 59 mm (semi flare angle 15 degrees) has also been
analyzed using the developed code based on mode matching technique. The pitch (p) of
corrugations is 2.5 mm and width (w) is 2 mm. The depth of corrugations are optimized to
achieve performance from 6 GHz to 12 GHz. The optimized depth of the corrugation at the
input (1st corrugation) of the hom is 14.2 mm and at the out put (10th corrugation) is 12.6
mm. The depth of all other corrugations are in between the depths o f these two
34
corrugations. The return loss plotted m Figure 2.24 shows a very close agreement between
the results computed from the developed code and the results from TICRA’s
CHAMP/FEED code. The computed modal amplitudes at the aperture o f the hom are found
within close agreement (±0.03) with the results computed from CHAMP/FEED which is a
commercial tool based on mode matching to analyze circular waveguide geometries. The
far-field radiation patterns have been computed from these modal amplitudes using far-field
expressions given in [63]. The electrical parameters computed for the hom are presented in
O
Return loss (dB)
Table 2.1.
—
C H A M P Package
o - e •© D e v e l o p e d c o d e
-60
-70
_j __ i__ i__ l
6
1
1
1__ i
7
I___i__ i__ '
8
^
1
' __ i__ i__ i__ 1__i— i . .
11
9
10
Frequency (GHz)
12
Figure 2.24 Return loss o f the corrugated hom.
Table 2.1 Electrical parameters of hom.
TMn
Cross
Beam
Beam
amplitude amplitude loss
Pol.
width
width
(dB)
(dB)
(dB)
(dB)
Frequency
TEn
(GHz)
Return
7
0.95
0.31
-25.3
-25.4
46.0
48.6
8
0.94
0.38
-31.5
-30.0
40.7
41.8
9
0.92
0.36
-32.0
-31.0
36.8
37.5
10
0.96
0.22
-38.0
-25.0
30.0
34.0
11
0.97
0.18
-43.5
-23.0
26.0
30.0
The analysis for circular waveguide geometries shows that the power from the incident
TEn mode at a junction gets coupled to the higher order TEi„ and TMin modes, which have
azimuthal dependence of unity. These modes can be exploited to yield shaped symmetric
radiation characteristics with low cross-polarization in feed horns.
35
2.4 Mode Transducers to Excite Circularly Symmetric Modes
Mode transducers based on circularly symmetric modes are very useful for realizing
microwave rotary joints which are used to deliver uniform transmission o f power with
rotation. Two such modes in circular waveguide are TMoi and TEoi modes. In the sequence
o f modes in a circular waveguide TEu is the first mode followed by TMoi, TE21, TMn,
TE01, TE31 modes and all the other higher order modes. TMn and TE01 are degenerate
modes having same cut off wavelengths. If any particular mode is excited in a waveguide,
the other lower order modes get automatically supported. Therefore, the excitation
mechanism of a particular mode should be evolved in such a way that all the lower order
modes are suppressed or rejected. It would be easier to excite a mode which has less
number o f lower order modes. Therefore, TMoi mode, which has only one lower order TEu
mode can be excited easily. TMoi mode can be excited in a circular wave guide using a
circular coaxial waveguide fed probe mechanism as shown in Figure 2.25. If the TMoi in
circular waveguide is to be excited from a rectangular waveguide, a transition from
rectangular to coaxial waveguide can be used as shown in the Figure 2.25. The diameter of
the circular waveguide should be preferably between the cut off diameter of this mode and
the cut off diameter o f the next higher order mode which is the TE21 mode. Although, TEu
mode is the lower order fundamental mode, it is unlikely to be excited with such excitation
mechanism and pure TMoi mode can be obtained.
Coaxial
Waveguide (them mode)
Rectangular
Waveguide
(TE10 Mode)
yS
Metallic post
forming a loo]
in rectangular
wave guide
Figure 2.25
Scheme o f TMoi mode excitation in circular waveguide using axial probe.
36
A geometry o f Figure 2.25 was simulated at 13.4 GHz, using a WR-75 rectangular
waveguide (1 9 mm X 9.5 m m ), a circular waveguide of diameter 31.5 mm and a coaxial
waveguide of outer conductor diameter 4 mm and inner conductor diameter 1.3 mm. The
diameter of the probe in circular waveguide was also taken as 1.3 mm. At 13.4 GHz, this
waveguide size was oversized and supported the dominant TEn mode and the higher-order
TMoi mode and TEoi modes. It was found from the simulated results that maximum power
gets coupled into TMoi mode ( >-0.1 ) and the power in the other lower and higher order
modes was very low (< -70 dB) for 250 MHz bandwidth. The next higher order circularly
symmetrical mode in circular waveguide is the TEoi mode. It would be difficult to control
the purity of this mode since it has four lower order modes which are TEn, TMoi, TE21,
TMn respectively. Apart from this, the next higher order TE31 mode will also get supported
if the waveguide diameter is selected sufficiently above the cut off diameter o f the desired
TEoi mode. The excitation mechanism should be such that the maximum power is coupled
to TEoi mode only and all the other non desired modes get cancelled or suppressed. TEoi
mode can be excited in a circular waveguide using slot coupling. Since, the waveguide size
to support TE0i mode will automatically support lower order modes, a single slot may not
give pure TEoi mode. Single slot coupling may result into sufficient power coupling in the
non desired lower or higher order modes. In order to verify this and to know the power
coupling characteristics of undesired modes, an oversized circular waveguide supporting
TEoi mode was simulated using HFSS at 13.4 GHz. The circular waveguide was excited
from rectangular waveguides using longitudinal slots on the periphery o f the circular
waveguide as shown in Figure 2.26. The diameter (31.5 mm) of the circular waveguide was
taken 15 % above the cut off diameter for TEoi mode. The length and width of slots were
11.5 mm and 2 mm respectively. WR-75 rectangular waveguide (19 mm X 9.5 mm) was
used. The computed cut off diameter for TEoi mode comes 27.3 mm at 13.4 GHz.
Figure 2.26 Slot coupling of an oversized circular waveguide to propagate TEoi mode.
37
The simulation was carried out to compute the modal power in various modes in the
circular waveguide for single slot, two opposite slots and four equally spaced slots,
respectively. The rectangular waveguides outputs were combined using 2-way and 4-way
waveguide power combiners for the cases o f coupling with two and four slots. The
simulated results for single slot coupling show that the power couples significantly in TEn,
TE2i, TE31 modes along with desired TE01 as shown in Table 2.2. Results for coupling with
two slots show that the power couples in only TE21 and TE31 modes and other modes are
cancelled. For the case o f coupling using four slots (having uniform amplitude and phase)
the power is coupled only in the required circularly symmetric TE01 and all the other modes
were rejected as shown in Table 2.2.
Table 2.2 Modal amplitudes in the oversized circular waveguide excited with
slot coupled rectangular waveguides.
Mode
Mode
Number Name
1
TEn
Modal amplitudes in Modal amplitudes in Modal amplitudes in
circular waveguide
circular waveguide
circular waveguide
(Single slot)
(Two slots)
(Four slots)
-13.34*
-63.10
-61.06
2
TM01
-62.02
-81.20
-79.31
3
t e 21
-6.22*
-2.57*
-49.27
4
TE01
-8.84*
-3.72*
-0.12*
5
TMn
-47.96
-73.90
-72.04
6
TE31
-2.632*
-54.80
-51.98
7
Return
loss
-14.76
-16.70
-20.0
* modes in which significant coupling takes place
It is clear from the simulated results that it would be appropriate to use four slots [68]
instead o f just one, on the periphery o f the circular waveguide for pure excitation o f TE01
mode. Such excitation mechanism (using four slots ) is shown in Figure 2.27. All the four
slots should be excited with equal amplitude and phase to get maximum power coupling in
the desired TE01 mode and negligible power in the non desired modes.
38
2
Figure 2.27 Scheme ofTEoi mode excitation in circular waveguide using
four slots located at circumference.
The design o f single rotary joints would be easier due to the requirement o f only one
circularly symmetric mode in a circular waveguide. But, the design of dual channel rotary
joints would be much more complex due to the requirement of simultaneous excitation of
two circularly symmetric modes in a circular waveguide. These modes should be excited in
such a way that there is high isolation or minimum cross-talk between channels. In view of
this, the details o f various excitation mechanisms of mode transducers have been
investigated in Chapter 6 in order to achieve the purity of circularly symmetric modes and
to realize microwave rotary joints.
2.5 Conclusion
In this chapter various types of discontinuities occurring in multi-frequency mode
transducers and mode couplers have been analyzed. Asymmetrical discontinuities such as
radial post and coaxial probe discontinuities in circular waveguide have been analyzed for
higher-order modes using method of moments technique. Symmetrical step junction
discontinuities have also been analyzed using mode matching technique. The characteristics
of fundamental and higher-order waveguide modes as function of physical parameters of
the discontinuities have been studied in circular waveguides which become overmoded or
oversized at higher frequencies. It was found from these studies that step junction, post [78]
and probe [97] discontinuities in circular waveguides have profound effect on return loss
and power coupling to dominant and higher-order modes. Subsequent chapters deal with
the design and development of circular waveguide based mode transducers having multiple
39
discontinuities. The analysis of discontinuities presented in this chapter will help in the
design and realization o f mode transducers in terms o f controlling non-desired modes
which depend on the size and nature o f waveguide discontinuities. For example, in the
design of multi-frequency mode transducers presented in Chapter 3, the angle o f tapered
section between waveguides and the probe heights can be selected based on the
observations in this chapter so as to confine the power in the dominant TEn mode at the
output of the mode transducer at higher frequencies where waveguide becomes overmoded.
The analysis results o f step junction in this chapter can help in the design of multi-mode
transducers (Chapter 5) such as multimode feeds for controlling power in higher-order
modes as function o f parameters like taper angle and step size so that shaped and
symmetric radiation patterns are achieved. Simulation o f an end wall probe excited circular
waveguide (Figure 2.25) showed that the pure circularly symmetric TMoi mode can be
achieved. The simulation o f a slot-coupled oversized circular waveguide shows that the
power coupling in the lower-order modes can be avoided and maximum power can be
coupled to the desired circularly symmetric higher-order TEoi mode by using a coupling
mechanism with four slots (Figures 2.26 and 2.27)
waveguide.
40
on the periphery o f the circular
Chapter 3
Multi-frequency Ortho-mode Transducer
The analysis in Chapter 2 shows that the higher-order modes get coupled in an oversized
circular waveguide having a discontinuity. This chapter deals with multiple discontinuities
in the form o f circular waveguide junctions having coaxial probes for coupling at different
frequency bands. The design, modal analysis and measured results of a new type of ortho­
mode transducer are presented. In this device, cascaded circular waveguides excited by
rectangular waveguides through co-axial line fed probes are used. Mechanisms of
cascading o f waveguides, excitation o f cascaded circular waveguides and transitions have
been investigated in order to achieve the intended performance at widely separated
frequency bands. A four frequency Orthomode Transducer (OMT) at 6.6,10.65,18 and 21
GHz has been designed and developed. This concept has been utilized also to develop a
three frequency mode transducer at 18.7, 23.8 and 36.5 GHz. The simulated results are
compared with measured results. These transducers may find wide applications in the feed
systems for reflector type of antenna for scanning microwave radiometer sensors.
3.1 Design and Analysis
The design complexity o f mode transducers working at multiple frequency bands increases
due to the presence o f multiple discontinuities (symmetrical and asymmetrical) in the path
of propagating signals at different frequency bands. A suitable method to design such
transducers would be to cascade the mode transducers at individual frequency bands such
that the cross-sectional dimensions at higher frequency bands are at cutoff for the lower
frequency bands (see Figure 2.1). But, the waveguide sections at lower frequency bands
(supporting only the dominant mode) become over-sized at higher frequencies and support
higher-order modes, which are excited because o f structural discontinuities. If orthogonal
polarizations are required at individual frequency band, then polarization matched power
sensing mechanisms have to be used in the cascaded sections. In this case, the higher
frequency dominant mode signal gets coupled to the lower frequency power sensing ports
41
thereby increasing the insertion loss of the device. In the mode transducers investigated in
this chapter, the higher-order modes are generated because o f (i) transition in the form of
step or tapered discontinuity between two waveguides of different cross-sections and (ii)
probe which senses power at lower frequency band acts as a radial discontinuity and
coupler for higher frequency signal. Since, the design goal is to ensure dominant mode
purity at each frequency band, the higher-order modes have to be suppressed and all the
frequency ports have to be decoupled. The dominant mode purity at each frequency band of
OMT will ensure the desired radiation patterns of a corrugated hom antenna Hence, it is
worthwhile to estimate the modal amplitude of different higher-order modes generated
because o f the discontinuities.
Finite element method (FEM) based Ansoft’s HFSS
software has been used for modeling, analysis, design-optimization and estimation of
amplitudes of different higher-order modes. In the OMT design, the frequencies considered
are 6.6 GHz, 10.65 GHz, 18 GHz and 21 GHz, which correspond to frequencies of a
radiometer. The design steps for the development of four-frequency ortho-mode transducer
are explained in the following sections.
3.1.1 Modal Analysis of Waveguide Sections Cascaded with Step
Junctions
It is simple to join primary waveguides (main arms) o f OMTs at individual frequency bands
using step junctions between waveguides as shown in Figure 3.1. But this geometry should
be analyzed in terms of higher-order modes. Figure 3.1 shows four straight circular
waveguide sections As, Bs, Cs and Ds joined together to form stepped waveguide
transitions. When pure TEn mode is incident in section-As, Bs, Cs, Ds corresponding to 21,
18, 10.65 and 6.6 GHz respectively, it is of interest to evaluate the modal power in the
output waveguide section-Ds which is oversized for 21,18 and 10.65 GHz and supports the
higher-order modes generated due to step junctions between waveguide pairs As, Bs and Bs,
Cs and Cs, Ds The analysis presented in Section 2.3 for single step junction showed that
sufficient power couples in the higher-order modes (see Figure 2.23), if the output
waveguide section is over-sized. Here, simulation has been done for four cascaded step
junctions (see Figure 3.1) to find out the modal power of the desired dominant mode (TEn
mode) and the undesired higher-order modes in the output waveguide section Ds.
42
Incident
TEn mode
at input
Modes at
output
As
Bs
Cs
Figure 3.1 Multi-frequency waveguide sections joined with step junctions.
For the 3-D model o f the step junctions used in HFSS, the diameters o f sections As, Bs, Cs
and Ds are chosen as 9.4, 11,19 and 32.54 mm for the propagation of dominant TEn mode
at 21, 18,10.65 and 6 .6 GHz respectively. The lengths of the individual sections have been
selected as 34, 53, 54 and 78 mm respectively. The higher-order propagating modes
supported at the waveguide section-Ds that feeds a corrugated horn are TMoi, TE21, TE01,
TM n, TE31, TM21, TE41, TE 12, TM02, TM 31 at 18 GHz. Along with these modes, additional
propagating higher-order modes at 21 GHz are TE 51, TE22, TE02, TM 12. At 10.65 GHz,
TM 01 and TE 21 are the higher-order propagating modes in section-Ds.
From the modal analysis results it is found that the dominant mode purity is not achievable
in the section Ds (Figure 3.1) and almost half o f the power gets coupled to higher-order
modes (TMn and TE12) at 18 and 21 GHz. Additionally, step discontinuity also causes
reflection of the input power. The modal amplitudes (in dB) of different modes at the
output of
6 .6
GHz section for the geometry o f Figure 3.1, have been computed at all the
four frequency bands. It is found that for the incident TEn mode in the section-Ds and Cs at
6 .6
and 10.65 GHz respectively, there is no power coupling in the higher-order modes but
there is a reflection of 3.6% power at 10.65 GHz in the waveguide section-Cs. At 18 GHz,
for the incident TEn mode in the section-Bs> 11,4% power is coupled to TE12 mode,
33.04% power is coupled to TMn mode, power in the desired TEn mode is only 53.19% in
section-Ds and 10.48 % power is reflected in section-Bs. Similar behavior was observed at
21 GHz. These results show that the step discontinuity in cascaded circular waveguides
couples power mainly in the higher-order TEin (n>l)and TMi„ (n>l) modes at
10,
18 and
21 GHz. Thus, the modal analysis shows that waveguide sections cascaded with the step
junctions not only couple sufficient power in the higher-order modes at higher frequencies,
but they also reflect the incident power since they act as sharp discontinuity. Sharp
43
discontinuities should be changed into gradual tapers in order to minimize losses due to
reflection and higher-order mode coupling.
A common aperture conical corrugated horn (with 15° flare angle, 40 mm length and 16
number of corrugations) when excited with pure TEn mode at its input, offered optimum
performance at all the four frequency bands. With pure TEn mode excitation, the horn
resulted into cross-polar radiation level better than 27 dB at 18 and 21 GHz. Similar,
performance was observed at 10.65 and 6.6 GHz. But, if this horn is excited by the mode
transducer o f Figure 3.1, the computed radiation patterns become asymmetric in the
azimuth planes and cross-polar radiation level also deteriorates to -13.5 dB at 18 and 21
GHz as compared to -27 dB with pure TEn mode excitation. This was due to higher-order
mode coupling at these frequencies. The analysis presented in Section 2.3 for symmetrical
discontinuity in the form o f waveguide sections joined with tapered section showed that
maximum power couples in the dominant TEn mode, if the taper angle is less than 10
degrees (see Figure 2.23). Therefore, in order to minimize reflected power and the power
coupled to higher-order modes at higher frequencies, the step junctions have to be replaced
by gradual tapered junctions. The next section deals with design and modal analysis of
different waveguide sections joined by tapered sections.
3.1.2 Waveguide Sections Cascaded with Tapered Sections
Figure 3.2 shows four circular waveguide sections At, Bt, Ct and Dt joined together by a
tapered section between two successive waveguide sections. The dimensions of the straight
waveguide sections are same as mentioned in previous section for Figure 3.1.
Modes at
output
Figure 3.2 Circular waveguide sections At, Bt, Q and Dt cascaded with tapered sections.
44
The taper angle and length of the tapered sections between waveguide sections At,
Bt(9i,Ai), Bt, Ct(02,A2) and Bt, Ct (83^ 3) have to be optimized in order to minimize the
power in the higher-order modes and maximize the power in the desired dominant TEn
mode. Taking some initial taper angle and length of the tapered section between two
successive waveguide sections, a 3-D model of the structure (Figure 3.2) was modeled
using Ansoft HFSS. The taper angles and taper lengths were optimized to minimize power
in higher-order modes in the section Dt. The optimum flare angles for the geometry (Figure
3.2) have been found to be between 3 to 6 degrees to confine power in TEn mode. The
optimized design dimensions o f the waveguide sections at different frequencies are
presented in Table 3.1.
Table 3.1
The design dimensions o f the waveguide sections at different frequencies.
Frequency
(GHz)
Wavelength
(mm)
Cut off Diameter for TEn
mode in CWG*
(mm)
6.60
10.65
18.00
45.45
28.17
16.67
14.29
26.64
16.51
9.77
8.37
21.00
Selected
Diameter
o f CWG
(mm)
32.54
19.00
Flare Angles o f the
Tapered Section
(Degree)
5.68
4.97
11.00
2.86
9.40
90.0 (perfect short)
* CWG stands for circular waveguide
The modal power was computed at 21 GHz at the output waveguide section (Dt) having the
largest cross-sectional dimension considering a unity power incident at the input waveguide
sections at each frequency. It is found that for optimum flare angles, the power coupling in
higher-order modes is negligible and 99 % (0.044 dB) power is confined in the desired TEn
mode in the waveguide section Dt The power in the dominant TEn mode at 18 GHz is of
the same order and it is better at 10.65 and 6.6 GHz for the optimized transition. The
reflected power is less than 0.7 % (-21.6 dB) at all the frequencies. This configuration
(Figure 3.2) avoids the power conversion into higher-order modes due to discontinuity
between two circular waveguides (i.e., for symmetrical discontinuity) and its also does not
deteriorate the return loss in the axial direction. Therefore, this configuration (Figure 3.2)
with tapered section can be used for the design o f cascaded orthomode transducers at four
frequency bands,
45
The radiation patterns of the corrugated horn (described in Section 3.1.1) excited with the
mode transducer geometry o f Figure 3.2 was computed at 18 GHz and 21 GHz. The
computed radiation patterns showed symmetrical patterns and cross polar radiation better
than -27 dB, cross-polar level and pattern symmetry at 6.6 and 10.65 GHz were same as
that of the horn excited with pure TEn mode. Thus, the desired radiation performance of a
corrugated horn can be achieved at each frequency band, if the horn is fed by waveguide
sections joined with tapered sections ensuring TEj i mode purity.
3.1.3 Effects of Co-axial Probes
For exciting TEn mode in the circular waveguide sections, coaxial probes have been used.
Since, a common aperture OMT is to be used for all the frequency bands to excite the horn
antenna, the waveguide sections for individual frequency bands cannot be short terminated
for maximum power coupling. As shown in Figures 3.3, the waveguide section for 6.6 GHz
frequency band is terminated by waveguide section (Ct) at 10.65 GHz through a tapered
transition which is at cut-off for 6.6 GHz. Similarly, 18 GHz section (Bt) is at cut-off for
10.65 GHz and 21 GHz section (At) is at cut-off for 18 GHz. In this configuration, the
location o f the probe from the cut-off region which is in the form o f tapered transition can
be optimized for a particular depth of the probe for maximum power coupling to the
primary circular waveguide.
Presently three probes are taken in waveguides at 6.6, 0.65 and 18 GHz for higher-order
mode analysis at 21 GHz. The probe depths and locations for coupling maximum power in
the circular waveguide have been computed using the expressions given in [28] and
described in Appendix A.1 and A.2. The earlier works have been done on the mutual
impedance between probes in a circular waveguide [79], [80] supporting only the dominant
mode. The higher-mode analysis treating multiple probes as discontinuity in cascaded
circular waveguides has not been investigated earlier. Presently, modal analysis using
Ansoft HFSS is carried out at 21 GHz in the presence o f coaxial probes in 6.6,10.65 and 18
GHz waveguide sections to compute power coupled to the higher-order modes in the output
section Dt, for the geometry of Figure 3.3. As analyzed in Chapter 2, probe or post
discontinuities couple power in the higher-order TEon, TMon, ( n> l) and TEni, TMni (n>l)
modes.
46
Coaxial-line fed
Figure 3.3 Waveguide sections excited with coaxial probe at different frequencies.
The results of higher-order mode analysis for multiple probe discontinuities (Figure 3.3) is
shown in Table 3.2 for all the frequencies. Power coupled to successive lower frequency
probes is also given in the Table 3.2.
Table 3.2
The power (dB) in dominant and higher-order modes in
section-Dj for tapered junction.
Input signal
Frequency
(GHz)
Higher-order
modes
TE„
Mode
21.0
18.0
-9.56
-8.55
-6.09
-4.37
-22.0
10.65
6.6
-12.35
<*40
-1.36
-0.002
<-99
<-99
21 GHz
port
18 GHz
port
10.65 GHz
port
6.6 GHz
port
-2.83
-15.6
-4.12
-25.9
-18.2
<-99
<-99
-7.29
<-99
It was found that for the incident TEn mode in the waveguide section (At) at 21 GHz,
11.07% power gets coupled to higher-order modes, 52.17% power (i.e., -2.S3 dB) couples
to IB GHz coaxial probe, 2.69% couples to 10.65 GHz coaxial probe, 0.26% couples to the
6.6 GHz coaxial probe, 6.67% power is reflected by probes and the power in the required
TEn mode is only 24.59% (i.e., -6.09 dB). The modal analysis was also carried out at 18
GHz in the presence of coaxial probes in 6.6 and 10.65 GHz waveguide sections.
It was found that for the incident TEn mode in the waveguide section (Bt) at 18 GHz, 14
% power couples to the higher-order modes, 38.73% couples to 10.65 GHz coaxial probe,
1.53% couples to the 6.6 GHz coaxial probe, 9.53% power is reflected by probes and the
47
power in the required TEn mode is only 36.56%. Thus, at higher frequencies the power is
couples to higher-order modes and also to the lower frequency ports, which effectively
reduces the power in the desired TEn mode.
At 10.65 GHz, for TEn mode incident in the section (Q), 5.82% gets coupled to TMoi
mode, 18.66% gets coupled to 6.6 GHz probe, 2% gets reflected from the probe at 6.6 GHz
and 73.2 % remains in the required TEn mode. Thus, this modal analysis, shows that at
higher frequency bands, the power incident from the dominant mode waveguide section,
not only couples to the higher-order modes but also couples to lower frequency ports.
Far field radiation pattern o f the corrugated horn excited with the geometry shown in Figure
3.3 was computed at 18 GHz in the presence of coaxial probes at 6.6 and 10.65 GHz and at
21 GHz in the presence of coaxial probes at 6.6,10.65 and 18 GHz. It is found that the
presence o f probes in the lower frequency sections degrades the pattern symmetry and
increases cross-polar radiation at higher frequency bands. The cross-polar performance at
18 and 21 GHz deteriorates to around -11 dB as compared to -27 dB for the configuration
of Figure 3.2, where no probes are considered at lower frequency bands.
The analysis results for post and probe discontinuities presented in Sections 2.2.1 and 2.2.2
showed that the power coupling to higher-order modes reduces if the depth o f the probe (or
post) is reduced. It has also been found through simulation and through antenna pattern
measurement that the cross-polar performance at 18 and 21 GHz improves if the depth of
the probe at 6.6 GHz and 10.65 GHz is reduced from its optimum value for maximum
power .coupling. Radiation pattern performance improves further if the higher frequency
and lower frequency ports o f same polarization are decoupled. But, with the reduction o f
the depth o f the probes, the impedance matching deteriorates at 6.6 GHz and 10.65 GHz
ports, though there is an improvement of cross-polar performance at 18 and 21 GHz. Thus,
the design challenge for this type o f multi-frequency mode transducer is to ensure mode
purity in the output section (Dt) at all the frequency bands and at the same time to achieve
/
optimum power coupling, impedance matching and port to port isolation. The overall
design of the multi-frequency OMT is presented in the next section.
48
/ 3o$ »L
3.1.4 Design of Multi-frequency Ortho-mode Transducer
The present design of the mode transducer is based on coupling from primary cascaded
circular waveguide sections to output rectangular waveguides WR-137 for 6.6 GHz, WR75 for 10.65 GHz and WR-42 for 18 and 21 GHz. The schematic of the ortho-mode
transducer (a circular to rectangular waveguide end-launcher) at single frequency band at
6.6 GHz is shown in Figure 3.4(a). The ortho-mode transducers at separate frequency bands
are cascaded to realize a common 8-port device (Figure 3.4 (b)) operating at all the 4frequency bands.
Port -1
10.65 GHz
6.6 GHz
Figure 3.4 (b) Schematic of a common 8-port OMT at four frequency bands.
The orthogonal ports at the same frequency band have been separated by an axial distance
of X.g/2 and the angular spacing of 90° to achieve the desired isolation between the two
49
ports. As described in the previous section, the reduction o f the depth o f the probes in the
lower frequency waveguide sections from their resonant depths (quarter wavelength)
improves the cross-polar performance at higher frequency bands due to reduced power in
the higher-order modes.
For example, in the 6.6 GHz orthomode transducer section, 11.6 mm depth o f the coaxial
probe which is o f the order o f a quarter wavelength gives good return loss matching but
this depth couples sufficient power in the higher order modes at 18 and 21 GHz. The
analysis results presented in Sections 2.2.1 and 2.2.2 for post and coaxial probe
discontinuities in circular waveguide showed that power coupled to non-desired higherorder modes decreases with the reduction in the depth o f the post or the coaxial probe.
Therefore, depths of the probes have been reduced in the lower frequency sections in order
to minimize higher order modes excited at higher frequencies.
The depth o f probes in the 6.6 and 10.65 GHz section was reduced by more than 40 percent
from full depth (quarter wavelength). The probe depths were reduced from resonant depths
o f 11.6 mm to 7.5 mm in 6.6 GHz section, from 7 mm to 4.2 mm in the 10.65 GHz section
and from 3.6 mm to 2.5 mm in the 18 GHz section. But the reduction in probe depth
reduced the real part and increased the reactive part of the impedance seen by the probe in
the circular waveguide. This change in impedance deteriorated the return loss of the signal
which was coupled to the circular waveguide from a frill-depth probe. For example, the
simulated return loss with reduced depth probe was only -4.5 dB as compared to frill depth
probe where it was better than -17 dB at 6.6 GHz. Although, the method o f matching of
coaxial line to rectangular waveguide is described in [81], there are no details available in
the existing literature on the methodology to achieve matching from circular to rectangular
waveguide for multi-frequency operation. In the present design, to improve the return loss,
the real part of the impedance seen by the coaxial probe of reduced depth has been matched
to a rectangular ridged-waveguide by varying the ridge height and width. The ridged
waveguide was further transformed to a rectangular waveguide using stepped ridge
waveguide transformer. The heights of different ridge steps are optimized to get optimum
matching. Ridged waveguides have been treated in [82]-[84], The expressions derived by
Wolfgang et al. [84] are used to compute cut off wavelength, guide wavelength,
50
characteristic impedance and design dimensions o f the ridged waveguide step transformer
in the present design of mode transducer. To make a compact design, the characteristic
impedance of the ridged waveguide step transformers has been chosen to follow cosine
profile as described in [85]. The reactance due to reduced depth probe was cancelled by
using a stub pin in the coaxial section shorting the inner and outer conductor of the coaxial
section (like a single stub) as shown in the Figure 3.4(a). The shorting pins at 18 and 21
GHz were not required in the coaxial sections of the mode transducer. The location of the
steps of the ridges in the rectangular waveguide with respect to the coaxial section have
been found to affect inter-port isolation significantly. For example, a displacement of 0.25
mm of the step from its optimum position of 0.5 mm from the onset o f the coaxial section,
reduced the isolation of 18 GHz signal with 6.6 GHz port from -41 dB to -10.8 dB. Step
locations were optimized for best isolation between lower and higher frequencies.
Modal power distribution and coupling of power to other ports have been computed in the
presence o f optimized mode transducers consisting of optimized step transformers and
lower depth probes giving best return loss at 6.6 and 10.65 GHz. The simulated results for
the optimized mode transducers are presented in the Table 3.3, which shows that the
maximum power is confined in the dominant TEn mode at all the frequencies. The return
loss at 18 and 21 GHz with optimized mode transducers also improved to the order of -15
dB as compared to -10 dB for the case of full depth coaxial probes present at lower
frequencies. The return loss at 6.6 and 10.65 GHz was optimized for better than -17 dB.
Improved values of port-to-port isolation and reduced values of coupling to higher-order
modes have been achieved as shown in Table 3.3.
Table 3.3 The power (dB) in the dominant and higher-order modes in section-DT
in the presence of mode transducers.
Input
signal
Frequency
(GHz)
Higher-order
modes
TE„
Mode
21 GHz
port
18 GHz
port
10.65 GHz
port
6.6 GHz
port
(dB)
(dB)
(dB)
(dB)
(dB)
(dB)
21
18
10.65
6.6
-13.03
-13.01
-26.38
-36.0
-1.55
-0.441
-0.068
-0.005
-7.0
-21.7
<-99
<-99
-22.0
-18.0
-27.5
-41.0
-19.1
51
<-99
<-99
<-99
With the optimized mode transducer of reduced depth probe at 6.6 GHz, the predicted
mode purity in the TEn mode at 10.65 GHz is o f the order o f 98.45% and only 0.23 %
couples to TMoi mode and 1.23% couples to 6.6 GHz port for same polarization. As there
is no port in front o f 6.6 GHz port, all power is confined in TEn mode at 6.6 GHz.
Modal power distribution and coupling of power to lower frequency ports at 18 GHz have
been computed in the presence o f mode transducers consisting of optimized step
transformers and lower depth probes giving best return loss at 6.6 and 10.65 GHz. The
power in the dominant mode at 18 GHz for the optimized mode transducers at 6.6 and
10.65 GHz with reduced depth probes was 90.34% and the total power in the higher order
modes was o f the order of 5%. In the presence o f optimized mode transducers with reduced
depth probes at 6.6 and 10.65 GHz, the coupling of 18 GHz signal to 10.65 GHz port was
reduced to 1.79% from that of 38.73%, reflected power reduced to 2.9% from that o f 9.53%
which was with the full-depth coaxial probes (see Table 3.2). Thus, simultaneous objectives
of maximizing dominant mode power at 18 GHz, its isolation with lower frequency ports
and return loss matching at 6.6, 10.65 GHz frequencies with reduced depth probes were
achieved.
Figure 3.5 Radiation patterns at 18 GHz for a horn fed with the OMT o f optimized step
transformers and reduced depth probes at 6.6 and 10.65 GHz.
Patterns at 18 GHz o f corrugated horn ( mentioned in section 3.1.1) with simple coaxial
probes o f reduced heights 7.5 and 4,2 mm in the optimized mode transducer at 6.6 GHz
and 10.65 GHz respectively have been plotted. At 18 GHz, the simulated radiation patterns
52
o f a hom fed by the OMT o f optimized step transformers and reduced depth probes are
given in Figure 3.5. Simulated results show 9 dB better cross-polar radiation (-20 dB)
performance o f the hom fed with the OMT o f reduced depth probes than the cross-polar
radiation (-lld B ) achieved with full depth probes in the lower frequency sections. This
improvement is due to the higher isolation with lower frequency ports and less coupling to
higher order modes. The predicted mode purity in the dominant TEn mode at 21 GHz is o f
the order o f 70 % with optimum isolation achieved with lower frequency ports. The power
in the higher-modes at 21 GHz resulted into asymmetry in the predicted co-polar patterns
and the cross polar radiation level was o f the order o f -18 dB in the presence o f all the
lower frequency ports. To keep the coaxial probe in the center o f coaxial line and to
maintain its orthogonality with respect to other port, a dielectric bead was used at the base
o f the coaxial probe in the 6.6 GHz coaxial section.
3.1.5 Measured and Simulated Results of 8-Port Orthomode Transducer
The simulated and measured return loss for 6.6 GHz frequency and isolation between
orthogonal ports is presented in Figure 3.6. The measured isolation between orthogonal
ports at 6,6 GHz is better than -36 dB at the specified bandwidth o f 250 MHz. In Figure
3.6, Sii and S22 represent the scattering parameters for return loss at port-1 and port-2 (see
Figure 3.4(a)) and S 12 represents the scattering parameter for isolation between ports 1 and
2. Port! and port 2 are the orthogonal rectangular waveguide ports o f OMT (see Figure
3.4(a).
Figure 3.6 Return loss for 6.6 GHz circular to rectangular waveguide mode transducer
for both the orthogonal ports.
53
At 10.65 GHz, -15 dB return loss bandwidth o f 300 MHz is achieved by using circular to
ridged rectangular waveguide mode transducer. Slightly shifted return performance towards
higher frequency was achieved at this frequency as shown in Figure 3.7. Measured
decoupling of -18 dB as shown in Figure 3.8 was achieved for 10.65 GHz signal with 6.6
GHz coaxial probe. An isolation o f better than -2 9 dB was achieved between orthogonal
ports over the band.
F re q u e n c y (G H z )
Return loss for 10.65 GHz circular to rectangular waveguide mode transducer
for both the orthogonal ports.
Is o l a t i o n ( d B )
Figure 3.7
F re q u e n c y (G H z )
Figure 3.8
Measured isolation o f 10.65 GHz signal with 6.6 GHz coaxial probe
port with parallel polarization.
54
The measured results for 18 GHz OMT are shown in Figure 3.9. The Figure 3.9 presents
return loss at the orthogonal ports of the mode transducer at 18 GHz. When the probe
depth at 18 GHz is 2.5 mm, -15 dB return loss bandwidth obtained is 300 MHz. The
measured isolation between orthogonal ports at 18 GHz is o f the order o f -25 dB over the
band. The measured isolation of 18 GHz signal is better than -30 dB and -20 dB with 6.6
GHz and 10.65 GHz ports respectively for same polarization as shown in Figure 3.10.
Figure 3.9 Measured return loss and isolation for 18 GHz OMT.
v-
o
o
CO
O
iO
O
Isolation(dB)
CM
o
O
op
-7 0
-8 0
1 7.6
177
178
179
180
181
182
183
184
1 8 .5
186
Freq uen cy(G H z)
Figure 3.10 Measured isolation of 18 GHz signal with 6.6 GHz and 10.65 GHz ports.
55
At 21 GHz, with the probe depth o f 3.1 mm, -15 dB return loss bandwidth o f 360 MHz
was obtained as shown in Figure 3.11. The measured isolation between orthogonal ports is
of the order o f -25 dB over the band. As shown in Figure 3.12, the isolation of 21 GHz
signal with 6.6 and 10.65 GHz was better than -20 dB over the band. The measured
isolation of 21 GHz signal with 18 GHz port was only -7 to -10 dB over the band, which
could not be improved due to the comparable size of OMT at 21 GHz to that o f 18 GHz.
The poor isolation adds to increased insertion loss at 21 GHz. The measured insertion loss
of the OMT is 0.5,0.7,1.1 and 1.6 dB at 6.6,10.65,18 and 21 GHz, respectively.
F r e q u e n c y (G H z )
Figure 3.11 Measured return loss and isolation for 21 GHz OMT.
0
-10
Is o la tio n (d B )
-20
-30
-40
r
-50
-60
*
* v#
\
21 GHz and 18 GHz(H-ports)
^
21 GHz and 10 63 GHz(H-ports)
1
21 GHz and 6 6 GHz(H-ports)
21 GHz and 18 GHz(V-ports)
-70
21 GHz and 10 65 GHz(V-ports)
_21 GHz and 6 6 GHz(V-ports)
-80
204
..1 . 1..t - i ...i..1..i ..i...i..i ..I..i ..i i
205
206
207
20.8
20.9
l , i i. ,i,i. L i .,i..i ..i..I..i..i..i..i..t ..i..i..i..i.
21 0
21 1
212
213
214
F re q u e n c y (G H z )
Figure 3.12 Measured isolation of 21 GHz signal with other lower frequency
ports for parallel polarization.
56
The photograph of the developed 8-port OMT [86] for which the simulated and measured
results were presented in Figures 3.6-3.12, is shown in Figure 3.13.
21 GHz OMT Ports
18 GHz OMT Ports
10.65 GHz OMT Ports
6.6 GHz OMT Ports
Figure 3.13 Photograph of 8-port common OMT at 6.6, 10.65, 18 and 21 GHz .
3.2 Mode Transducer at Three Frequency Bands
Altimeter needs a nadir looking radiometer operating at 18.7 ± 0.2 GHz, 23.8 ± 0.3 GHz
and 36.5 ± 0.5 GHz frequencies for atmospheric correction. The system requirement is of
single linear polarization at these three frequency bands. Since, the effect of discontinuities
as described in previous sections of this chapter is envisaged to be more stringent at the
highest frequency of 36.5 GHz, it is worthwhile to investigate the modal behavior at the
highest frequency in the presence of lower frequency ports and to arrive at an optimum
design which yields optimum performance at all the frequency bands. Following the
concept and design methodology developed for four frequency OMT (Section 3.1), the
development of tri-frequency mode transducer has been carried out. The simulation and
measured results are presented.
57
Three cases have been studied for three frequency common mode transducer and are
discussed in order.
Case 1:
The configuration for case-1 is shown in Figure 3.14(a). The performance is
simulated at 36.5 GHz in the presence of mode transducers at 23.8 GHz and 18.7 GHz.
Here, all ports at 18.7, 23.7 and 36.5 GHz are aligned i.e., polarization matched. In this
case, the return loss at 36.5 GHz, is -15.14 dB. The signal at 36.5 GHz is isolated from the
23.8 GHz port by -17.61 dB and from by 18.7 GHz port by -21.46 dB. From the data
presented in Table 3.4, it is clear that more power couples in the higher-order modes at the
aperture at 36.5 GHz.
Case 2: The configuration for case-2 is shown in Figure 3.14 (b). The performance is
simulated at 36.5 GHz in the presence of mode transducers at 23.8 GHz and 18.7 GHz.
Here, ports at 18.7, 23.7 are aligned and orthogonal to 36.5 GHz. In this case return loss at
36.5 GHz is -11.04 dB. The signal at 36.5 GHz is isolated from the 23.8 GHz port by 70.98 dB and from 18.7 GHz port by -58.85 dB. The Table 3.4, shows that more power
couples in the higher-order modes at the aperture at 36.5 GHz.
Case 3: The configuration is shown in Figure 3.14 (c). The performance is simulated at
36.5 GHz in the presence of mode transducer at 23.8 GHz and 18.7 GHz. Here, ports at
36.5, 23.7 are aligned and orthogonal to 18.7 GHz as shown in Figure 3.14 (c). In this case
return loss at 36.5 GHz is -14.29 dB. The signal at 36.5 GHz is isolated from the 23.8 GHz
port by -18.45 dB and from 18.7 GHz port by -38.65 dB. The Table 3.4, shows that
maximum power (-1.15 dB) couples in the dominant TEn mode and minimum power
couples in the higher order modes at the aperture at 36.5 GHz in the presence of all the
ports. This configuration gives the optimum performance at all the frequencies, therefore,
this can be considered as final design configuration. This configuration has been designed,
developed and measured for electrical performance. The modal analysis results for this
configuration show that the return loss at 23.8 GHz is -17.49 and the isolation o f 23.8 GHz
signal with 18.7 GHz is -58.61 dB. Maximum power couples in the TEn mode which is of
the order of -0.095 dB and minimum power is in the higher-order mode. This configuration
58
gives maximum power in the desired TEn mode at 18.7 GHz and negligible power in the
higher-order modes which are not supported in the outermost section.
Simulated and
measured performance of the cascaded mode transducer (Figure 3.14 (c)) operating at all
the three frequency bands are given in the next section.
Figure 3.14 Different configuration to combine waveguide sections at 3 frequencies.
Table 3.4 Modes at the aperture of the cascaded mode transducer at 36.5 GHz.
Mode names
Modal Amplitude
(dB)for Fig.3.14 a
Modal Amplitude
(dB)for Fig.3.14 b
Modal Amplitude
(dB) for Fig.3.14 c
TE„
-1.37
TMo,
-8.82
t e 21
-11.04
TEoi
-48.21
TM U
-55.46
-1.36
-50.41
-7.33
-38.10
-52.99
-1.15
-23.33
-7.74
-37.60
-48.11
The measured and simulated performance of the combined three frequency mode
transducer (Figure 3.14 (c)), which gave optimum performance in terms of return loss,
isolation and higher-order mode coupling have been found out. The results are compared
with the performance at individual mode transducers. Figures 3.15, 3.16 and 3.17, show the
return loss performance at 18.7, 23.8 and 36.5 GHz. The performance at 23.8 GHz
frequency band is slightly affected due to the presence of 18.7 GHz port in front of 23.8
59
GHz port as compared to the performance o f individual mode transducer at 23.8 GHz. The
performance at 36.5 GHz is more affected by the presence of two lower frequency ports at
18.7 GHz and 23.8 GHz in front of the 36.5 GHz port. Measured isolation of 36.5 GHz
signal with 23.8 GHz port is of the order o f 20 dB over 80 percent o f the desired frequency
band and the isolation with 18.7 GHz port is of the order o f -25 dB as shown in Figure
3.18. The measured isolation o f 23.8 GHz signal with 18.7 GHz port is o f the order o f -50
R e tu rn Lo ss(d B )
dB as shown in Figure 3.19.
ot
W w
o oi o
M
i
i
i
— .... Simulated ( with 18 7 and 36 6 GHz ports)
cn
Simulated (without 18 7 and 36.5 GHz ports)
O)
i
i
Return Loss(dB)
Figure 3.15 Simulated and measured return loss at 18.7 GHz.
------- Measured (without 18 7 and 36 5 GHz ports)
T
o
1.....1.....| .....I..... I,, I ,
Figure 3.16 Simulated and measured return loss at 23.8 GHz.
60
K
O
CO
o>
CO
CM
00
fs>
J L . J __ 1__ i__ i__ f___I__ I__ I__ I__ I__ L
CO
CM
CO
00
CM
No
*■
a
t
• • • Measured (with 18 7 and 36 5 GHz ports)
0
-5
Return Loss(dB)
-10
-15
-20
-25
-30 f
Simulated (without 18 7 and 23 8 GHz ports)
-35 r
- —
Measured (without 18 7 and 23 8 GHz ports)
-40 L
—
Measured (with 18.7 and 23 8 GHz ports)
m -m- m
Simulated (with 18 7 and 23 8 GHz ports)
-45
-50 ~i l i t. I
36 0 36 1
i i i I i
36 2
36 3
36 4
36 5
36 6
36 7
..I„i ,i..i i, l , i„i„i..t
36 8
36 9
37 0
lsolation(dB)
Figure 3.17 Simulated and measured return loss at 36.5 GHz.
Figure 3.18
Measured and simulated isolation performance o f 36.5 GHz
signal with 18.7 and 23.8 GHz ports.
61
o
o
N)
o
W
o
^
o
CJi
o
O)
o
N
o
Isolation(dB)
V
\l
*
------- Simulated
-80
Measured
-90
-100
23.5
23.6
23.7
23.8
23.9
24.0
24.1
Frpni ipnrWf^H7\
Figure 3.19
Measured and simulated isolation performance of 23.8 GHz signal
with 18.7 GHz port.
36.5 GHz mode
transducer
23.8 GHz mode
transducer
18.7 GHz mode
transducer,
Figure 3.20 Tri-frequency mode transducer at 18.7, 23.8 and 36.5 GHz.
The photograph of the tri-frequency mode transducer is shown in Figure 3.20.
62
3.3 Conclusion
A novel design of four frequency band OMT to feed a common corrugated horn has been
presented. In the multi-frequency environment, the methods o f controlling power in the
higher-order modes and improving isolation o f higher frequencies with lower frequency
ports are described. Modal analysis has been performed to estimate the effects of
symmetrical step, taper and asymmetrical probe discontinuities in the main waveguide
particularly at higher frequencies [86], [87]. An optimum configuration o f multi-frequency
OMT yielding desired isolation o f orthogonal ports, isolation o f higher frequencies with
lower frequency ports o f same polarization and maximum power in the dominant TEn
mode has been obtained [86]. As it was not possible to fabricate the OMT device using a
single piece, it was fabricated in a number of pieces and assembled to make the 8-port
device. The slight deviation o f the measured data from simulated data may be attributed to
fabrication tolerances and minor assembly and alignment errors. The modal analysis based
design approach presented in this paper may be applied to the design o f multi-frequency
ortho-mode transducers at other frequency bands. The multi-frequency design concept has
been successfully utilized to develop a mode transducer at 18.7,23.8 and 36.5 GHz.
In order to find out the radiation characteristics o f the multi-frequency mode transducers, it
became imperative to realize composite feeds operating at widely separated frequency
bands. These feeds are discussed in Chapter 4.
63
Chapter 4
Multi-frequency Hybrid Mode Transducer
This chapter presents composite feed systems having common aperture horn as radiating
element and multi-frequency mode transducer as exciting element The mode transducers
presented in Chapter 3 were analyzed in terms of power coupling in dominant and higherorder modes and it was observed that some amount o f power was coupled to higher-order
modes at higher frequencies at the output section o f the mode transducer. The extent up to
which it can degrade the radiation performance o f a common aperture horn as compared to
pure mode excitation, can be judged by exciting the horn with the multi-frequency mode
transducer and consequently testing it for radiation characteristics. In order to find out the
radiation characteristics, it became necessary to design and develop common aperture
corrugated horns operating at frequency bands as that o f the mode transducers presented in
Chapter 3. Corrugated horns are also a type o f mode transducer converting dominant TEn
mode of a smooth wall circular waveguide into the hybrid-modes (a combination o f TEin
and TMin modes) o f a corrugated circular waveguide. These horns offer wide band
performance in terms of beam symmetry and low cross-polar radiation. The hom should be
fed at its input with a pure TEn mode for successful operation. Any contamination in its
content due to presence of higher-order modes at input will result into the degradation of its
radiation performance.
This chapter presents the design and development o f multi-frequency mode transducers to
convert circular waveguide TEn mode into hybrid-mode. A composite feed system having
corrugated hom as radiating element and the multi-frequency mode transducers as exciting
element has been designed at 6.6, 10.65, 18 and 21 GHz, The measured performance of the
corrugated hom excited with pure TEn mode as well as excited with multi-frequency mode
transducers discussed in Chapter 3 are presented for comparison. A composite feed system
at 18.7, 23, and 36.5 GHz has also been designed and developed along with the measured
results of the hom excited with three frequency mode transducer presented in the previous
chapter
64
4.1 Feed for Four Frequency Bands
The design o f a horn operating at frequency bands covering approximately two octave
bandwidth is a major challenge. By using ring loading of corrugations, a maximum
bandwidth ratio of 2 : 1 can be achieved. The harmonic operation of corrugation remains
only a hope to realize the horn for frequency bands covering two octave bandwidth. The
operating higher frequency bands should be multiple of lower frequency bands in order to
apply harmonic operation. Although in the present work, the higher frequencies are not the
exact multiples of lower frequencies, the concept o f harmonic operation of corrugation has
still been applied in an optimum manner.
4.1.1 Design and Analysis
Corrugated horns provide improved radiation characteristics over larger bandwidth than
smooth wall waveguides. The factors considered in the design o f a corrugated hom include
the number of slots required, slot width to pitch ratio, the depth o f the input slot, the
variation in slot depth, the size o f the input waveguide and the size o f the radiating aperture.
The characteristic o f the hom-aperture field is determined by the number o f corrugations
per wavelength and the admittance seen from the entrance o f the corrugation slot. The
improvement o f the aperture field is achieved over the frequency range in which the slot
admittance is between large capacitive reactance and small inductive reactance which
results into minimum surface current. The hom has been designed at 6.6 ± 0.125 GHz,
10.65 + 0.15 GHz, 18.0 ± 0.2 GHz and 21 ± 0.2 GHz. The number o f corrugations per
wavelength have been taken as 5-6 corrugations at highest frequency i.e., 21 GHz. Even 5-6
corrugations result into very fine corrugations having pitch equal to 2.5 mm and the width
of the teeth equal to 0.5 mm to get an anisotropic surface. In order to improve the
performance o f the hom at all frequency bands, the corrugation’s depth and pitch have been
optimized based on frequency harmonic concept and varying depth of corrugations. The
design is optimized to achieve cross-polarization level better than 27 dB over the frequency
65
band from 5.7 GHz to 10.8 GHz and better than 30 dB over the frequency band from 5.9 to
7.2 GHz.
Since, the performance at corrugation depth of X/4 and 3774 are similar because of
harmonic periodicity, the satisfactory performance of the hom over the band 5.9 to 7.2 GHz
will repeat over the frequency band 17.7 to 21.6 GHz. The reactance of the corrugation as
seen from entrance should reflect the harmonic operation of corrugation. The reactance can
be computed for a particular geometry of slot to see this behavior.
The basic geometry of a cylindrical corrugated horn is shown in Figure 4.1, where ‘a’ is the
waveguide radius (i.e., inner corrugation radius) and ‘b’ is the waveguide radius including
the depth of corrugation ( i.e., outer corrugation radius).
Figure 4.1 Geometry of a corrugated hom.
The expression for the corrugation slot surface reactance [42], [45] is given as,
x
5 J \ (ka)Y\ (kb) ~ Yi (ka)J i (kb)
J ](ka)Yl (kb) - Tj (ka)Jl (kb)
6 = ratio of slot width to pitch
k = free space wave number
a = inner corrugations radius
b = outer corrugations radius
66
Using Equation (4.1), the slot reactance has been computed for two different values of
corrugation depth and the waveguide radius. The reactance as function of frequency is
shown in Figure 4.2. The computed data on slot reactance as a function o f frequency shows
that the slot can provide capacitive reactance in widely separated frequency bands which are
related harmonically. This property of corrugations is utilized to design the horn so that 6.6
GHz and 10.65 GHz frequency bands are covered in the fundamental frequency band and
the 18 and 21 GHz frequency bands are covered in the first harmonic bands. It is shown in
the Figure 4.2 (a)-(b), that a corrugation geometry can provide capacitive reactance in the
continuous band from 6.6 GHz to 10.65 GHz as well as in the harmonic band ranging from
18 GHz to 21 GHz.
cn
o
oi
o
Surface Reactance
o
15
-15
-20
8 10 12 14 16 18 20 22 24 26 28 30 32 3
Frequency (GHz)
Frequency (GHz)
(b)
(a)
Figure 4.2
Corrugation surface reactance, (a) a=17.5 mm, b=32,7 mm.
(b) a=43.6 mm, b=55.6 mm.
The depth of corrugations to meet hybrid mode condition in corrugated horns have been
computed from the expression given in [36] as:
i
d\ = — exp
f 11
(4.2)
\2.5ka j
where, a is the radius o f corrugated waveguide and k is free space propagation constant
The depths o f all the corrugations o f the horn are optimized to get large capacitive reactance
over both bands, which is responsible for low cross-polarization and pattern symmetry of
67
the hom. The depth of corrugations were varied from the throat to the horn aperture to
achieve best input match and good pattern symmetry.
Optimum results at all the four frequency bands was obtained when the depth of the first
corrugation (at input o f hom) was half wavelength (0,5 X) at 9.85 GHz corresponding to k
a = 3.6 and the depth of the last corrugation (at the hom aperture) was quarter wavelength
(0.25 A) at 7.3 GHz
corresponding to
k a = 8.4 respectively. For the smooth wall
waveguide at the input o f the hom, k a = 3.16 was taken at the center frequency o f the
fundamental frequency band (6.6 to 10.65 GHz). In order to achieve the required radiation
pattern amplitude taper, the hom aperture size and semi flare angle was selected as 220 mm
and 15°, respectively. The hom semi angle (flare angle) of 15° was achieved in two steps of
\
6° and 9° in the throat region to avoid power splitting into non desired modes which are
responsible for the deterioration o f cross-polar radiation performance at higher frequencies.
It has been found from simulated results that a cross polarisation level better than 25.0 dB is
obtained at 18 GHz (third harmonic of 6 GHz) and at 21 GHz (third harmonic of 7 GHz).
4.1.2 Measured and Simulated Results
The corrugated hom has been modeled on a mode matching technique based software
package-CHAMP/FEED to yield optimum amplitude tapers at all the frequency bands. The
basic concepts of mode matching technique can be understood from the analysis and
formulation given in [35], [42] and also described in Appendix A.5 for a corrugated
cylindrical waveguide mode converter. Iterations have been performed on TICRA’s
CHAMP/FEED software to optimize the co-polar and cross-polar radiation performance of
the hom. The return loss, gain, front to back ratio, modal amplitudes and phases o f different
modes have been found through simulation for optimum electrical performance of the hom.
The radiation patterns of the hom excited with pure TEn mode at its input as well as
excited with multi-frequency OMT presented in Chapter 3 are given in the next section.
68
4.1.3 Horn Radiation Patterns with Pure TEMMode Excitation
The simulated results show that the number o f propagating TEjn and TMin modes at horn
aperture are 5, 8, 14 and 29 at 6.6,10.65,18 and 21 GHz, respectively. The return loss of
17.57, 29.43, 24.64, 34.92 dB; Gain o f 21.15, 23.41, 24.74, 24.93 dBi; front-to-baek ratio
o f 57.94, 57.48,49.73,47.23 dB have been achieved in simulation at 6.6,10.65,18 and 21
GHz, respectively. The modal amplitude and phase at the aperture o f the optimized horn
which gave the desired far field radiation patterns o f the horn for pure TEn mode excitation
at the input of horn are shown in Tables 4.1 and 4.2 at 6.6 and 21 GHz, respectively. The
horn has been excited through circular waveguide transitions at each frequency band
offering pure TEn mode. This means that the excitation mechanisms o f frequency bands
other than the simulated (or measured) frequency band are removed from the transition in
order to avoid higher-order mode generation due to discontinuity.
Table 4.1 Modes at the aperture of hom with TEi i mode transition at its input
at 6.6 GHz.
Mode no.
TMj n
TEin
n
Amplitude
Phase(degree)
Amplitude
Phase(degree)
1
0.794119
-69.368
0.485899
128.585
2
0.268582
-8.297
0.173665
-140.147
3
0.081995
96.006
0.050804
-4.862
4
0.034798
-123.598
0.018508
152.083
69
Table 4.2
Modes at the aperture of horn with TEi i mode transition
at its input at 21 GHz.
Mode no.
TMi a
TEin
n
Amplitude
Phase(degree)
Amplitude
Phase(degree)
1
0.254966
45.400
0.200668
-105.341
2
0.252458
72.734
0.170559
-44.875
3
0.257735
121.579
0.215579
-23.859
4
0.329899
-165.993
0.323599
12.536
5
0.347312
-82.650
0.309651
81.904
6
0.269169
12.646
0.220347
-179.098
7
0.174955
123.913
0.175122
-63.098
8
0.109618
-110.854
0.141216
48.240
9
0.067754
22.960
0.099841
157.840
The horn and transitions were fabricated and radiation performance was measured with
transitions at the input o f the horn. The simulated and measured edge tapers corresponding
to 13.65° illumination angle have been presented in Table 4.3. The measured and simulated
cross-polarization have been presented in Table 4.4. This measurement has been done to
compare the radiation performance of the horn with pure TEy mode excitation to that of
excited with the multi-frequency OMT, where performance may degrade at higher
frequency bands due to higher-order mode coupling.
Table 4.3
Simulated and measured illumination taper in dB of the horn ( pure TEi i).
Frequency in
Simulated
Measured
GHz
Taper(dB)
Taper(dB)
E-Plane
H-Plane
E-Plane
-8.2
6.6
-8.6
■
00
H-Plane
-8.4
10.65
-11.7
-11.9
-10.8
-10.2
18.00
-15.4
-14.0
-14.2
-14.5
21.00
-16.0
-16.1
-15.9
-16.4
70
Table 4.4
Measured and simulated cross-polar radiation performance with pure
TEn mode excitation.
Frequency
Measured
Simulated
(GHz)
Cross-polarization(dB)
Cross-polarization(dB)
H-plane
E-plane
D-plane
H-plane
E-plane
D-plane
(Diagonal-
(Diagonal-
plane)
plane)
6.6
-40.0
-38.7
-38.0
-38
-37.2
-33.5
10.65
-27.3
-33.6
-27.6
-25.4
-32.0
-25.6
18
-28.2
-29.2
-26.6
-25.8
-27.4
-24.2
21
-28.8
-28.5
-27.1
-27.4
-27.8
-23.0
The photograph of the four frequency corrugated horn [86], [88], [89], is shown in Figure
4.3.
Figure 4.3 The photograph of the developed four frequency corrugated horn.
71
The measured and simulated radiation performance of the horns excited with pure TEn
mode transitions are shown in Figures 4.4 (a)-(d).
-60 :
-60:
m-jQ \i 1111111111111 in u.Jj.,i.ulu i i.l.i.u 11111111n 111n i
-50 -40 -30 -20 -10
0
10 20 30 40 50
Theta(Degree)
-50 -40 -30 -20 '-10
0
10 20 30 40 50
Theta(Degree)
(a) 6.6 GHz
(b) 10.65 GHz
Theta(Degree)
Theta(Degree)
( c)
Figure 4.4
_yQU,i„u,] 11 ii l.i.i,j.i.11t i l l,i,i i,i h,u.ii.i.,u i.l i i i i I m .ili.i-u -
(d) 21 GHz
18 GHz
The measured and simulated radiation performance o f the horns excited with
pure TEn mode transitions at (a) 6.6 GHz. (b) 10.65 GHz. (c) 18 GHz and
(d) 21 GHz.
The horn gave optimum performance in terms of pattern symmetry and cross-polar
performance and a good agreement between the experimental and theoretical radiation
patterns has been observed (see Figure 4.4). The slight deviations in numerical values of
72
measured and simulated patterns may be attributed to the measurement accuracy and
fabrication tolerance error.
4.1.4 Horn Radiation Patterns with Multi-frequency OMT
The corrugated horn yielded good pattern symmetry (see Figure 4.4) and cross-polar
performance when excited with transitions giving pure dominant TEn mode at the horn
input. This hom was further tested with the 8-port OMT presented in chapter-3 at all the
four frequency bands. The measured co-polar and cross-polar radiation patterns o f the hom
fed with the 8-port OMT are presented in Figure 4.5(a)-(d) for one polarization (vertical
pol.) and in Figure 4.6 (a)-(d) for orthogonal polarization ( horizontal p o l.).
(a) 6.6 GHz
(b) 10.65 GHz
(c) 18 GHz
Figure 4.5
(d) 21 GHz
The measured co-polar and cross-polar radiation patterns of the hom
fed with an 8-port OMT for one polarization (v-port).
73
The measured patterns at 21 GHz showed slight asymmetry due to larger ratio of higherorder modes to dominant mode power as compared to 18 GHz. This is due to the higherorder mode coupling in the OMT due to presence of lower frequency ports which act as
discontinuity. Larger ratio of higher-order mode to dominant mode power is due to the
poor isolation o f 21 GHz with 18 GHz port.
T h e ta(d e g re e )
Theta(d eg ree)
(a) 6.6 GHz
(b) 10.65 GHz
-10
0
-
E -p la n e C o -p o l
-
E - p l a n e C r o s s - p o l.
-
H -p la n e C o -p o l
-
H -p !a n e C ro s s -p o l
10
Theta(degree)
(c) 18 GHz
(d) 21 GHz
Figure 4.6 The measured co-polar and cross-polar radiation patterns o f the
hom fed with an 8-port OMT for orthogonal polarization (h-port)
74
The photograph of the four frequency corrugated horn integrated with 8-port 4-frequency
OMT [86] is shown in Figures 4.7.
Figure 4.7 The photograph of the developed 8-port OMT integrated with
four-frequency corrugated horn.
To see the utility of the four frequency feed and OMT, an offset reflector was illuminated
with the feed excited with the four frequency OMT. The offset angle of the reflector was
selected as 43.32 degree to achieve incidence angle of approximately 50° on the earth for
radiometric application. The reflector focal length to diameter (f/d) ratio was elected as 1.8.
Secondary radiation patterns were measured after integrating the composite feed with the
offset reflector. After performing the secondary pattern measurements computations were
carried out for the beam efficiency and cross polarization for three dimensional pattern.
Formulation used for computation of beam efficiency is described in [36]. Maximum beam
efficiency (>92%) was achieved at 18 GHz frequency band. It was of the order of 90 % at
10.65 and 21 GHz frequency bands. The beam efficiency was of the order of 90 % at all the
frequency bands except at 6.6 GHz where it was of the order of 85%. It was due to the
lowest edge taper in the primary pattern which resulted into back lobe level of -23 dB in the
secondary pattern. The measured secondary cross-polar radiation was of the order of -20 dB
all the frequency bands. The measured 3-dB beam widths for both polarizations are of the
75
order of 3.8°, 2.4°, 1.42° and 1.26° against the simulated values ot 3.7°, 2.4°, 1.4° and 1.2°
at 6.6,10.85, 18 and 21 GHz, respectively. The measured secondary radiation along with
computed patterns are shown in Figures 4.8 (a)-(d).
-------- E-Plane Co. (C om puted)
—
-
H -Plane Co. (Com puted)
E-Plane Co. (M e a su re d )
a - a- a
o o o H -Plane Co. (M easured)
+ -+ H -Plane C ro ss.(M e a su re d )
o
ro
Power (dB)
o
CM
x x E-Plane C ro s s .(M e a s u re d )
o
t
in
o
r\j
cn
o
CO
-15
-10
-5
0
5
20
25
Theta (Degrees)
(a) Radiation pattern at 6.6 GHz.
-------- E-Plane Co. (C om puted)
—
-
x x x
H -P lane Co. (C om puted)
E-Plane C ro ss. (M easured)
c— i— t- H -Plane C ro s s .(M e a s u re d )
Power (dB)
o o o E-Plane Co. (M e a su e rd )
a
-10
-5
0
a
a
H -Plane Co. (M e a su re d )
5
Theta (Degrees)
(b) Radiation pattern at 10.65 GHz.
76
20
25
-------- E-Plane Co. (Computed)
--------H-Plane Co. (Computed)
E-Plane Cross. (M easured)
h— i— i-
H-Plane C ross. (M easured)
o
E-Plane Co. (M easured)
Power (dB)
x x x
o
o
* -v H-Plane Co. (M easured)
-25
-20
-15
-10
-5
0
5
10
Theta (Degrees)
(c) Radiation pattern at 18.0 GHz.
-------- E-Plane Co. (Computed)
—
-
H-Plane Co. (Computed)
x x x
E-Plane C ross. (M easured)
-i— i— h H -PlaneC ross. (M esaured)
Power (dB)
o
o
o
a a a
-10
-5
0
5
Theta (Degrees)
E-Plane Co. (M easured)
H-Plane Co. (M esured)
10
(d) Radiation pattern at 21 GHz.
Figure 4.8
Measured and computed secondary radiation performance at
(a) 6.6 GHz; (b) 10.65 GHz; (c) 18 GHz; and (d) 21 GHz.
77
4.2 Feed for Three Frequency Bands
A new tri-band horn at 18.7, 23, and 36.5 GHz has been designed and developed based on
higher-order mode coupling at the input of the horn using a groove discontinuity. Simulated
and measured results o f the horn excited with three frequency mode transducer are
presented.
4.2.1 Design Approach
The radiometer sensor in conjunction with an altimeter sensor generally uses a prime focal
reflector antenna. The reflector antenna with a lower focal length to diameter ratio
(F/D<0.5) is preferred as it facilitates lesser accommodation in the limited space on the
satellite deck. The feed radiation patterns for reflectors o f low F/D ratio, have been found to
exhibit increased frequency sensitivity for the required maximum to minimum frequency
ratio o f 2:1. The radiation patterns from conventional design o f corrugated horns [35]-[51]
become too narrow at the highest frequency to provide the required amplitude taper at the
reflector edge. A new technique was used to overcome the narrowing o f the patterns at the
highest frequency in which TMn and TEu modes are introduced additionally apart from the
TEn mode at the input o f the corrugated horn. This was realized by providing a groove
discontinuity at the input of the hom. The groove discontinuity at the input o f the
cylindrical corrugated hom couples power in the higher-order modes which in turn was
used to optimize amplitude taper and symmetry o f radiation patterns at the highest
frequency without affecting the performance at lower frequency bands.
4.2.2 Design and Simulation
The hom has been designed at 18.7 ± 0.2 GHz, 23.8 ± 0.3 GHz and 36,5 ± 0.5 GHz. An
important parameter o f the feed design is the amplitude taper. In order to achieve
specifications on secondary pattern symmetry, side lobe levels and beam-widths, the
amplitude taper of the primary patterns o f the feed should lie within -1 2 to -18 dB at the
reflector edges for all the frequency bands. The F/D ratio of the parabolic reflector was
78
selected as 0.5, requiring ± 50° reflector edge illumination angle. The narrowing o f the
patterns at 36.5 GHz has been overcome by introducing TMn and TEn modes additionally
at the input of the corrugated hom using a groove discontinuity at the input o f the horn. The
horn aperture, corrugation depths and width to pitch ratio of the corrugation have been
selected for best radiation performance at 23.8 GHz and to achieve the bandwidth ratio of
1.6:1 i.e., from 18.5 to 30 GHz. Approximately, 6.3 corrugations per wavelength at 23.8
GHz have been taken. Pitch of the corrugations is 2 mm and width is 1.5 mm. Hom consists
of total 18 corrugations. But, these dimensions o f aperture size and corrugation depths
yielded very narrow main-lobe (main-beam) at 36.5 GHz. Even the side-lobes started
appearing within the illumination angle of the parabolic reflector at this frequency.
A new technique has been used to overcome the narrowing of the patterns at 36.5 GHz in
which TMu and TE12 modes are introduced additionally apart from the TEn mode at the
input of the corrugated hom. This is realized by providing a groove discontinuity at the
input of the hom. The depth and width of the groove discontinuity in the presence of
corrugations and cascaded input waveguides have been optimized using TICRA’S
CHAMP/FEED program to get symmetry as well as the amplitude taper. In the presence of
groove at 36.5 GHz, the computed amplitudes of TEn, TMu and TE12 modes at the input
of the corrugated hom are 0.84, 0.48 and 0.20 respectively. The Tables 4.5 and Table 4.6
show the modal amplitudes of higher-order mode at the hom input and also at the hom
aperture in the presence of groove discontinuity. Table 4.7 shows the modal amplitude at
hom aperture in the absence of groove discontinuity. The HEn mode (hybrid mode) which
is an in-phase combination TEn and TMn modes is supported in a corrugated waveguide.
The modal analysis results presented in the Table 4.7, show that at 36.5 GHz, there is no
power in the TMn mode at the hom aperture. This means that hybrid mode is not generated
at this frequency. This is due to the fact that the corrugation depths in terms of wavelength
becomes half wavelength at 36.5 GHz and the corrugations surface becomes equivalent to
that of a circular waveguide without corrugations. When the groove is introduced at the
input it couples power in the higher-order modes at the input o f the hom. The modes at the
aperture of the hom with groove are shown in Tables 4.8 and 4.9. By optimizing the groove
geometry, proper amplitude and phase was obtained at the hom aperture which gives
79
patterns equivalent to that of hybrid-mode. The multi-frequency corrugated feed employing
groove discontinuity at the input of corrugations and the tri-frequency mode transducer
feeding the horn is shown in Figure 4.9. This horn along with tri-frequency mode transducer
has been fabricated and tested for its radiation pattern which are presented in Section 4.2.3.
Table 4.5 Modes at the aperture o f mode transducer in the presence o f groove
at 36.5 GHz.
Mode
TEin
TMin
no.
n
Amplitude
Phase (degree)
Amplitude
Phase (degree)
1
0.83628
-90.675
0.4788
-141.035
2
0.191627
-73.909
0.0395
-137.971
Table 4.6 Modes at the aperture o f the horn in the presence o f groove at 36.5 GHz.
Mode
TMIn
TEln
no.
n
Amplitude
Phase (degree)
Amplitude
Phase (degree)
1
0.8838
-168.18
0.3946
-34.593
2
0.1777
-129.89
.015790
-155.155
Table 4.7 Modes at the aperture of the horn (horn output)without groove at 36.5 GHz.
Mode
TEln
TMin
no.
n
Amplitude
Phase (degree)
Amplitude
Phase (degree)
1
0.985
-164.8
.02570
-4.738
Table 4.8 Modes at the aperture of the horn with groove at 18.7 GHz.
Mode
TEln
TMin
no.
n
Amplitude
Phase (degree)
Amplitude
Phase (degree)
1
0.979
-17.0
0.22139
-27.2
80
Table 4.9 Modes at the aperture of the hom with groove at 23.8 GHz
Mode
TEi„
TMia
no.
n
Amplitude
Phase (degree)
Amplitude
Phase (degree)
1
0.93
-5.32
0.2548
-173.37
The hom input diameter and the groove dimensions are chosen in such a manner that other
higher order modes are not supported at the input of the hom except the desired propagating
mode TE ji mode at 18.7 and 23.8 GHz. The simulated return loss o f the hom in the
presence of groove discontinuity slightly deteriorates at lower frequency bands. It comes 26 dB at 36.5GHz, -15.1 dB at 18.7GHz and -12.5 dB at 23 GHz. The simulated cross­
polarization of the hom in the diagonal plane is -27.4 dB at 36.5GHz, -36 dB at 18.7 GHz
and -31.4dB at 23.8 GHz. The amplitude tapers are of the order of -1 2 dB at lower
frequency bands and -20 dB at higher frequency bands.
36 5 GHz port
23 8 GHzport
Figure 4.9 Schematic of the multi-frequency corrugated feed with a groove discontinuity.
The hom is fed with the multi-frequency mode transducer.
81
4.2.3 Measured Radiation Performance of Horn
The measured co-polar radiation patterns w ith groove discontinuity at 18.7 G H z and 23.8
G H z are clo sely matching w ith the predicted patterns as show n in Figure 4.10 and Figure
4.11, respectively. The radiation patterns w ith and w ithout groove are found to be identical
at 18.7 and 23.8 G H z and therefore patterns without groove are not included in Figures 4.10
and 4 .1 1 . The measured radiation patterns [90] w ith and without groove at 36.5 G H z are
show n in Figures 4.12(a) and (b). A s show n in Figure 4.12, the measured patterns without
groove are very narrow and patterns w ith groove are wider.
A lthough, the measured
patterns w ith groove at 36.5 G H z do not m atch closely w ith the com puted patterns, these
patterns exhibit definitely the beam broadening effect due to the groove. The m ism atch can
be attributed to the fact that the horn and pow er coupling w aveguides could not be
fabricated as a single piece. The w orst case measured cross polar pattern at 23.8 G H z, in the
diagonal plane is show n in Figure 4.11. The technique described above to generate T M n
and TE 12 m odes using groove at the input o f corrugations is very effective for m icrowave
o
i\ j
w
o
•-plane predicted
o
■k
P o w er (dB)
-h
o
o
radiometer feeds for prime focal parabolic reflectors for m ulti-frequency operation.
- H-pIane predicted
V'
-® E-plane measured
-50
\ /
H-plane measured
t /
-60 I i .„i.1 1 1 1.i. i . 1 1 1
-180 -150 -120
-90
- lL
-60
-30
0
30
60
90
T h e ta (D egrees)
Figure 4.10 M easured and predicted far-field radiation patternis v
82
120
150
180
Pow er (dB)
-50
-60 '■ i i i\ l i h i i I i i i i I i I i i 1 i i I i I i I I I I I
-180-150-120 -90 -60 -30 0
i i
i Ii i i i Ii
30
60
i
i
i 1 i < i
iIi
90 120 150 180
Theta (Degrees)
Figure 4.11 Measured and predicted far-field radiation patterns with groove at 23.8 GHz.
Theta (D egrees)
Figure 4.12 (a) The measured radiation patterns with and without groove at 36.5 GHz (E-plane).
83
Power (dB)
0
-60 -30 0 30 60
Theta (Degree)
120 150 180
Figure 4.12 (b) The measured radiation patterns with and without groove at 36.5 GHz (H-plane).
The photograph of the developed three frequency corrugated horn [90] integrated with 3port 3-frequency mode transducer is shown in Figures 4.13.
Figure 4.13 The photograph of the tri-frequency horn.
84
4.3 Conclusion
Multi-frequency mode transducers in the form of corrugated horns have been presented in
this chapter. Simulated co-polar and cross-polar performance of the four frequency (6.6,
10.65, 18 and 21 GHz) horn excited with pure TEn mode are in close agreement with the
measured results. The radiation characteristics o f the horn excited with four frequency
' OMT also showed satisfactory performance at all the frequency bands. The measured crosspolar radiation performance and pattern symmetry o f the horn [86] meet fairly with the
desired goals. The secondary radiation performance o f a reflector antenna illuminated with
the four frequency hom and OMT system has also been presented. Primary and secondary
radiation characteristics of the composite feed and antenna system give enough indication
that the developed multi-frequency feed system can be successfully utilized for radiometer
antenna. Optimum radiation performance o f another corrugated hom [90] at 18.7, 23.8 and
36.5 GHz has also been achieved all the three frequency bands. The slight deviation of the
i
measured data from simulated data may be attributed due to fabrication tolerances and
minor assembly and alignment errors.
85
Chapter 5
Multi-mode Transducers for Radiation Pattern Control
It was shown in the Section 2.3 of Chapter 2 that the circular waveguides joined with
tapered waveguide sections with large taper angle can be used as mode transducers to
couple power in the higher-order TEin and TMin modes. A few mode transducers exciting
these modes have been realized in this chapter in order to achieve shaped radiation patterns.
This chapter presents multi-mode transducer feeds for improving the efficiency of reflector
antennas for space-borne scatterometer and altimeter sensors. The techniques of shaping the
primary radiation pattern using multiple modes at feed aperture to improve the efficiency of
reflector antenna have been investigated. This technique has been applied to develop novel
type of elliptical multi-mode transducer feeds for reflector antenna of space-borne
scatterometer payload. The multi-mode transducer feeds for a nadir-looking altimeter
sensor is also presented. The measured efficiency of the reflector is of the order of seventy
percent when kept at the focus of the reflector. The measured and simulated primary and
secondary radiation patterns are presented.
5.1
Elliptical Multi-mode Transducer Feeds for Scatterometer Antenna
Pencil beam scatterometer [3] is a very useful microwave sensor used to retrieve the near
surface ocean wind speed and direction. The radiation pattern requirement o f pencil beam
scatterometer antenna is to realize two squinted high gain inner and outer beams having low
cross polarization and low side lobe level. In order to achieve squinted or angularly spaced
beams, the feeds have to be laterally displaced in the focal plane o f the reflector. But the
displacement o f the feeds results into rising o f the side-lobe level and scan loss which
reduces the overall gain o f the reflector antenna.
The rise in side-lobe levels can be
overcome by designing elliptical feeds with larger amplitude taper in the plane of
*
displacement (offset plane) of feeds. The reduction in gain due to scan loss can be
compensated by designing the feeds to yield sector-shape primary patterns which enhances
the spillover and illumination efficiency of the reflector antenna. Sector shape pattern can
be achieved with multi-mode feeds where power is distributed in several modes at the feed
86
aperture in such a way that resultant far-field patterns becomes sector-shape. Such a feed is
actually a type o f mode transducer which transforms a single dominant mode at feed input
to the multiple modes at the feed aperture. Coaxial feed geometry as described in [61] has
been preferred due to its compact size and weight as compared to dual hybrid mode
corrugated feeds for providing sector-shape patterns. In order to realize asymmetric sectorshape patterns o f the feeds for scatterometer antenna, the earlier concept o f circular coaxial
rings [61] has been extended to elliptical feeds with elliptical rings.
5.1,1 Design and Simulation
The reflector antenna for scatterometer has to be illuminated with two laterally displaced
elliptical feeds designed at 13.73 GHz ± 50 MHz to yield the inner and outer beam spacing
o f ±2.75° from the reflector axis, secondary gain o f 42.5 dB, 3-dB beam widths o f 1.17° and
1.40° in the E and H-planes respectively, side lobe level o f -16 dB and cross-polarization
level o f -22 dB. The elliptical multimode transducer feed has been designed by introducing
ellipticity in the aperture o f the single ring coaxial feed. In order to get sector shape far field
patterns, the feed aperture distribution for circular multi-ring coaxial feed is given by [61].
f(2n;pA )
= 2 Ji(27tp sin Go A)/2np sin Go/k
= Ai (2 np sin GoA );
(5.1)
where, p is the aperture radius in cylindrical coordinates, Go is the half angle at -10 dB o f
the sectoral pattern o f the feed.
The main aperture surrounded by the inner wall o f the single ring coaxial feed will yield the
whole main lobe and the position o f the outer wall o f the ring will produce the first lobe o f
the Ai function. Therefore, the ring’s inner wall position pi will correspond to the first zero
o f the Ji(x) function (Bessel’s function o f order 1) i. e., Xi = 3.85. Then we have; 2n pi sin
GoA = xj =3.85; Similarly, the second zero o f the Jflx) function i. e., X2 = 7.02 will give
the position o f the ring’s outer wall o f the single ring coaxial feed. Therefore, 2% p2 sin Go
A = X2 - 7.02. Initially, the dimensions pi and p2 o f the single ring feed were computed at
the design frequency o f 13,73 GHz, corresponding to the -1 0 dB beam-width o f the order
87
of 64°, which is the required edge illumination angle of the reflector. The depth o f the
choke was chosen as quarter wavelength. The computed initial values of pi and
pz
are 14.9
mm and 27 mm, respectively for circular aperture. The circular aperture of radius 27 mm
supports higher-order TEmn and TMmn modes at 13.73 GHz.
A shaped pattern can be realized by using combination of higher-order modes at the
aperture of the radiator. Since, the fields o f the circular waveguide TEmn and TMmn modes
form a complete orthogonal set, all possible radiation patterns can be synthesized from
these modal fields. As mentioned in [63], the source function at horn aperture can be
expressed in terms of the fields of cylindrical waveguide TEmn and TMmn modes as,
M ,N
(5.2)
m =0
n=l
where, amn and bmn are modal amplitudes of TEmn and TMmn modes normalized with respect
to the modal amplitude of TEn mode. In Equation (5.2), the sum o f the squares o f the
modal amplitudes is unity.
The far field radiation pattern of the above source function (equation 5.2) is given [63] as,
(5.3)
(5.4)
(5.5)
where 8mn and emn are the roots of Equations ( 5 . 4 ) and (5.5), respectively.
88
Using the expressions o f the far-field from Equation (5.3), radiation pattern has been
synthesized to yield shaped radiation pattern for a circular aperture of radius 27 mm which
supports TE h , TE 12, TMn and TM u modes. The values o f a,nn and bmn o f equation 5.2, are
varied to get the desired shaped pattern which should give -1 0 dB amplitude taper at 64
degree. The values o f amn and bn,n (m =1, n = 1,2) are 1.0, 1.1, and 1.5, 0.4 respectively.
These values corresponding to shaped patterns o f Figure 5.1(a) and Figure 5.1 (b) are
converted to modal amplitudes which are presented in Table 5.1. The sum o f squares o f the
modal amplitudes (or sum o f powers) should be unity. The pattern of Figure 5.1(a) shows
larger value (-12dB) o f null in the bore-sight direction o f the radiation pattern. For this
pattern, all the modes are in same phase. This null value should be reduced to get better
efficiency of a reflector antenna. It is seen that by changing only the phase of TE 12 mode,
the null depth can be reduced in the pattern. The phase value o f 45 degree in the TE 12 mode
brings the null depth below -6 dB as shown in Figure 5.1(b). This means that proper choice
of modal amplitude and phase at the feed aperture can yield sector shape radiation patterns.
Table 5.1 Modal amplitude and phase to synthesize shaped radiation patterns.
Mode
Shaped pattern of Figure 5.0 (a)
Shaped pattern o f Figure 5.0 (b)
No.
TEin
modes
TMin modes
TEin modes
TMin modes
n
Amp.
Phase Amp.
Phase
Amp.
Phase
Amp.
Phase
1
0.47
0.0
0.70
0,0
0.47
0.0
0.70
0.0
2
0.50
0.0
0.20
0.0
0.50
45
0.20
0.0
89
H*
O
U*
A
tb
©
©
&
U*
Relative Power (dB)
,
Ui
o
o
bi
Relative Power (dB)
$$>
-35
-40.
0
-35
10
20
30
40 50 60
Theta (degree)
70
80
-40.
90
0
10
20
30
40
50
60
70
80
90
Theta (Degree)
0>)
(a)
Figure 5.1 The synthesized shaped radiation pattern (a) all modes in same phase.
(b) TE21 mode with 45 degree phase and rest o f the modes in same phase.
The plots presented in Figure 5,1 verify the fact that the proper modal distribution at the
aperture o f circular waveguide can give a shaped radiation pattern. The next problem is to
find out the values o f pi and P2 which can provide shaped radiation patterns o f Figure 5.1(a)
and 5.1(b) respectively. The computed initial values o f pi and p2 are 14.9 mm and 27 mm,
respectively. These computed values o f radii yield 2Ji(x)/x distribution at the aperture in
which the choke size is not sufficient to couple enough power into higher-order modes to
get the required sector-shape patterns.
Although, the dimensions based on above design approach (based on equation 5.1) give
less power coupling to the higher-order modes, these dimensions have been taken as initial
design parameters to optimize the dimension o f the highly coupled choke. The required
weighting o f the main lobe (beam) has been achieved through coupling o f power into
higher-order modes by increasing die surface o f the first choke i.e., decreasing the position
pi o f the choke. Asymmetry was introduced in the aperture shape by increasing H-plane
dimension o f the feed for one polarization and E-plane dimension o f the feed for other
polarization. Finally, aperture asymmetry, choke size and choke depth o f the elliptical feed
were optimized to get maximum coupling in the higher order modes in order to achieve the
required pattern asymmetry, VSWR and cross polarization level. Corresponding to inner
90
and outer beams of scatterometer antenna, the amplitude taper of the radiation patterns of
the elliptical feeds should be -10 dB and -16 dB in the principal planes. The schematic of
the optimized elliptical feeds is shown in the Figure 5.2. Two elliptical multi-mode feeds
were developed using the optimized dimensions (see Figure 5.3). Using HFSS, the
computed modal amplitudes and phases in the dominant TEn mode and higher-order
modes i.e., TMn, TE12, TM12 modes at the aperture of the feed for both vertical and
horizontal excitation of the feed are presented in the Table 5.2.
Table 5.2 Amplitudes and phases of TEin and TMin modes at the aperture
of the elliptical multi-mode feed.
M ode
Horizontal P o la riz a tio n '''-—
Vertical Polarization
No.
n
$
T Ein
Amp.
modes
Phase
t
T M in modes
TEin modes
Amp.
Amp.
Phase
Phase
T M in modes
Amp.
Phase
1
0.4988
-6.01
0.7236
0.12
0.56430
-135.8
0.5892
49.1
2
0.4618
-1.65
0.1367
38.6
0.5445
-147.8
0.1543
92.8
Figure 5.2 The schematic of the optimized elliptical feed. (a=2.56?t, b=2Al'k, c=1.18X, d=1.09^,
al=2.27X, b l= 2 .m , cl=0.89k, dl=0.80X, e=0.77A., 11=0.1 IX, 12=0.71 A, 13=2.75X).
91
Figure 5.3 Developed elliptical multi-mode feeds.
The developed elliptical feeds were integrated with a parabolic reflector of diameter 1.2
meter.
Three spars of 20 mm diameter were used to hold the two laterally displaced
elliptical feeds in the focal plane of the reflector. The two feeds were displaced from each
other across the focal point in the focal plane by 55 mm to get two squinted high gain
pencil beams at ±2.75° .
Figure 5.4 shows the schematic diagram of the antenna including feeds, reflector, inner and
outer beams and antenna scanning axis. The secondary gain and 3-dB beam widths depend
on the size of the reflector. Corresponding to the inner and outer secondary beams, the
primary radiation amplitude taper of both the elliptical feeds should be -16 dB at the
reflector edge in the plane of the offset of feeds and -10 dB in the other plane (orthogonal
plane) in order to achieve different 3-dB beam widths for secondary beams in the principal
planes. This has been verified through simulations using GRASP8W software of TICRA. It
is also found from the simulated results that the elliptical feeds should be displaced laterally
by ±27.5 mm across the focal point in the focal plane of the reflector in order to achieve
two squinted pencil beams at ±2.75° with respect to reflector axis, meeting the
requirements of side lobe level, gain and beam width.
92
Figure 5.4 Schematic diagram of the antenna with reflector, feeds, inner-outer beams and
scanning axis.
5.1.2 Simulated and Measured Results
Hie two displaced elliptical feeds are linearly polarized with one feed having vertical
polarization while the other is horizontally polarized. The measured radiation patterns for
vertical polarization show that 10 dB beam-widths of the elliptical feed are 68° in E-plane
and 52° in the H-plane, respectively. In other words, amplitude tapers of the feed are -10.1
dB in the E-plane and -15.8 dB in the H-plane as required to illuminate the reflector with
edge illumination angle of ±64°. The comparison o f measured and predicted patterns o f the
elliptical feed [91], [92] for vertical polarization excitation is presented in Figure 5.5. The
measured H-plane pattern of the elliptical feed is in fairly good agreement with the
predicted patterns obtained from HFSS software. The elliptical multimode feed patterns
have also been measured for the horizontal polarization. In this case the measured
amplitude tapers of the feed are slightly narrower than that o f the vertical polarization i.e.,
-10.8 dB in the E-plane and -16.9 dB in the H-plane, corresponding to the reflector edge
93
illumination angle o f ±64°. This narrowing of the primary pattern slightly broadens the
secondary beams, thereby increasing the 3 dB beam widths by 0.04° for horizontal
polarization as compared to the feed with vertical polarization.
The measured return loss of the elliptical feed is of the order of -25 dB and cross­
polarization level is better than 22 dB over a bandwidth of 500 MHz for both the
P o w e r(d B )
polarization.
-60
-20
20
60
A n g le (D e g re e )
Figure 5.5 Measured and simulated (HFSS) E- and H-plane primary radiation
patterns of the elliptical feed for vertical polarization.
For displaced elliptical feeds, the measured value o f reflector gain at 13.73 GHz was found
to be of the order o f 42.5 dB. In other words, overall efficiency o f the order o f 60 % has
been achieved for the reflector antenna for squinted beams. The measured 3-dB secondary
beam widths in the principal planes have been found as 1.15° and 1.38° respectively, which
are very close to the specified values o f 1.17° and 1.40°. When the feed was kept at the
focal point the measured secondary gain was found to be o f the order o f 43 dB. This means
that the gain loss in the squinted secondary beam due to the feed displacement is o f the
order of 0.5 dB. The measured side lobe and cross-polarization levels of the secondary
94
squinted beams were found to be -15.2 dB and -25.2 dB, respectively at the center
frequency. Measured parameters of secondary radiation pattern for vertical polarization are
presented in Table 5.3.
Table 5.3 Measured parameters o f secondary radiation pattern for vertical polarization.
Freq.
Plane
(GHz)
3-dB
3-dB
Side Lobe
Side
Beam
Beam
Level
Lobe
Width
Width
Computed
Level
Computed Measured
(°)
13.67
E-plane
1.20
o
1.18°
Gain
Gain
Computed Measured
(Db)
(dB)
Measured
(dB)
(dB)
-18.7
-17.64
42.60
42.29
(11=57 40%)
13.73
H-plane
1.41
1.38
-15.4
-14.5
E-plane
1.17°
1.15°
-18.5
-17.5
42.80
42.50
(11=59.74%)
13.79
H-plane
1.40°
1.38°
-16.0
-15.20
E-plane
1.18
115°
-18.2
-17.21
42.65
42.30
(ip 56 55%)
1.44
1.42°
-16.84
-15.97
c n o o i o a t o o i o t n o
Power(dB)
H-plane
-10 ■9 -8 -7 -6 -5 -4 -3 - 2 - 1 0 1 2
3 4 5 6 7 8 9
10
Angle(Degree)
Figure 5.6 Secondary radiation patterns when elliptical feed at the focus.
95
CN
CO
Power(dB)
CM
o
CO
-45
-50
-
1 0 -9 -8 -7 -6 -5 -4 -3 -2 -1
0
1 2
3
4
5
6
7
8
9 10
Angle(Degree)
Figure 5.7 Secondary radiation patterns of displaced elliptical feed in the focal plane.
The measured and computed secondary radiation patterns for the elliptical feeds [92] kept
at the reflector focus as well as laterally displaced at ±27.5 mm from the focus are
presented in Figure 5.6 and Figure 5.7, respectively. The measured results show that the
squinted beam peaks are at ±2.75° corresponding to ±27.5 mm lateral shift of the feed in
the focal plane. Therefore, for the center to center distance of 55 mm between the displaced
feeds, the angular spacing between the two squinted secondary beams has been found to be
5.5° as required. The photograph of the lab model of the reflector antenna integrated with
the displaced elliptical feeds is shown in the Figure 5.8.
Figure 5.8 Reflector antenna with two displaced elliptical feeds.
96
5.2 Circular Multimode Transducer Feeds for Reflector Antenna of
Altimeter
Space-bome altimeter sensor consists o f a nadir-looking fixed antenna at Ku-band. This
type of antenna is generally realized from a focal point fed parabolic reflector antenna. The
primary feed horn should illuminate the reflector uniformally in order to yield high gain
secondary beams. The circular multi-mode feeds having sector-shape radiation patterns can
yield high overall gain of the altimeter antenna.
5.2.1 Simulation and Design
The reflector antenna for altimeter
has been designed at 13.48 GHz to yield secondary
beam maximum gain requirement of 43.0 dB, 3 dB symmetric beam width of 1.2°, side
lobe level better than
-17 dB and cross-polarization level better than -22 dB. The
bandwidth requirement was ± 150MHz. The reflector diameter was 1.2 m. The F/D ratio of
the circular parabolic reflector was 0.4, requiring ± 64° reflector edge illumination angle.
The amplitude taper o f the radiation patterns of the multimode transducer (single-ring)
feed has been chosen as -11 dB at the reflector edges. The initial feed dimensions have
been computed in the same maimer as presented in Section 5.1.1 for elliptical feeds. Then
the feed was modeled on CHAMP software of TICRA as well as HFSS software. The feed
dimensions were optimized to get the required pattern shape. The schematic of the feed
with optimized dimensions is given in the Figure 5.9.
L1
m
Figure 5.9 The schematic of the optimized multimode circular feed. ( a = 0.8X, b = 0.99X,
97
The feed was modeled on HFSS and simulated amplitude taper of the best optimized feed
was obtained as -10.5 dB in the principal E- and H planes of the feed corresponding to
the reflector edge illumination angle of 64.0°. The return loss is better than 21 dB over full
band. The worst case simulated cross-polarization is -25.0 dB in the diagonal plane.
Amplitudes and phases o f TEin and TMin modes at the aperture o f the single ring coaxial
multi-mode feed are computed using TICRA’S CHAMP/FEED software based on mode
matching and CHAMP/FIELD program based on method of moments technique.
CHAMP/FIELD program takes care of the outer wall currents. The computed amplitude
and phase o f coupled higher-order modes at the aperture o f the feed, which resulted into
the required sector shape pattern is presented in the Table 5.4.
Table 5.4 Amplitudes and phases o f TEinand TMjnmodes at the aperture
o f the single ring coaxial multi-mode feed
Mode number
N
Vertical Polarization
TEin
Amp.
modes
Phase
TMjn modes
Amp.
Phase
1
0.468
-19.0
0.71
165.0
2
0.522
-19.0
0.19
26.90
3
0.160
-14.50
.013
-171.2
5.2.2 Simulated and Measured Results
The measured and computed primary radiation patterns are presented in Figure 5.10. The
measured edge illumination taper o f the order o f -11.5 dB is achieved which corresponds
to edge illumination angle of 64°. The comparison of measured and predicted patterns of
the single ring coaxial multimode feed is presented in Figure 5.10. The measured patterns
o f the feed axe in fairly good agreement with the predicted patterns obtained from CHAMP
98
and HFSS software. The measured return loss of the feed was better than 20 dB and cross­
polarization level is better than 22 dB over a bandwidth of 500 MHz.
The multi-mode feed has been integrated with a parabolic reflector of diameter 1.2 meter.
Three spars of 20 mm diameter were used to hold the feed at the focus o f the reflector. The
comparison of measured and predicted secondary patterns of the reflector with single ring
multimode feed is presented in Figure 5.11 The measured value o f reflector gain at 13.48
GHz was found to be 43.25 dB. In other words, an overall efficiency o f the order o f 73.65%
was achieved for the reflector antenna for the altimeter. The measured 3-dB secondary
beam widths in the principal planes have been found as 1.19° and 1.17° respectively which
are very close to the specified values of 1.2°. The measured side lobe and cross-polarization
levels of the secondary squinted beams are found to be -17.2 dB and -22.0dB respectively
at the center frequency. The secondary cross-polarization level is better than 20 dB over
full band. The measured parameters o f secondary radiation pattern for altimeter antenna
consisting o f single ring feed and a reflector o f diameter 1.2 m, is presented in Table 5.5.
Table 5.5
Measured parameters o f secondary radiation pattern for Altimeter antenna for
single-ring feed
Freq.
Plane
(GHz)
13.33
E-plane
3-dB
3-dB
Side Lobe
Side Lobe
Beam
Beam
Level
Level
Width
Width
Computed Measured
Computed
(°)
Measured
(dB)
(dB)
(dB)
-18.5
-16.83
43.20
1.20
Gain
Gain
Measured
Computed (dB)
(°)
1.21°
42.85
11=68 69%
13.48
H-plane
1.18
1.19
-18.5
-17.02
E-plane
1.18°
1.19°
-18.7
-17.10
43.64
43.25
il=73 65%
13.63
H-plane
1.16°
1.17°
-18.7
-17.28
E-plane
1.21
1.22°
-18.9
-17.80
43.5
43.12
t]=69.92%
H-plane
1.18
1.18°
-18.9
99
-17.81
The developed feed is presented in Figure 5.12. The photograph o f the lab model o f the
reflector antenna integrated with the single ring coaxial feeds [93], [94] is shown in the
P o w er(d B )
Figure 5.13.
E - P la n e C o - p o l( C H A M P )
H - P l a n e C o - p o l( C H A M P )
to
O
E - P la n e C o - p o l( H F S S )
H - P la n e C o - p o l( H F S S )
o
CD
' E - P la n e C o -p o l( M e a s u r e d )
1 H - P la n e C o -p o l( M e a s u r e d )
•
- 1
-180
I
I
I
D ia;id -P la n e C r o s s -p o l{ H F S S )
i
-140
-100
i
r
1 1 1 1 1 1 1 1 1
-60
-20
1 1 1
20
60
100
140
180
A n g le (D e g re e )
Figure 5.10 Measured and simulated (on HFSS and CHAMP) E and H-plane primary
radiation patterns o f the single ring coaxial multi-mode feed.
o
O
o
CO
o
N o rm a liz e d P o w e r(d B )
-10
-50
-60
-10
-8
-6
-4
-2
0
2
4
6
8
10
A n g ie (d e g re e )
Figure 5.11 Secondary radiation patterns with single-ring feed at focus.
100
Figure 5.12 Single ring coaxial multi-mode feed.
Figure 5.13 The photograph of the lab model of the reflector antenna
integrated with the single-ring coaxial feed.
101
5.3 Circular Multimode Transducer Feed (Dual-ring) for Reflector
Antenna of Altimeter
This section presents the design o f a circular multi-mode transducer (dual-ring) feed for
reflector antenna for altimeter. The feed has been optimized to get sector-shape radiation
patterns in order to enhance the over all efficiency of the altimeter antenna. The simulated
and measured primary and secondary radiation performance are presented.
5.3.1 Design and Simulation
The reflector antenna for altimeter
has been designed at 13.6 GHz to yield secondary
beam maximum gain of 40.5 dB with a given parabolic reflector o f diameter 910 mm,
secondary 3 dB symmetric beam width of 1.6°, side lobe level of -17 dB and cross­
polarization level of -22dB. The bandwidth requirement is ±150 MHz. The F/D ratio o f the
circular parabolic reflector is 0.36, requiring ± 69.55° reflector edge illumination angle. The
amplitude taper of the radiation patterns of the multimode transducer (two ring) feed has
been chosen as -11.0 dB at the reflector edges. The initial feed dimensions have been
computed in the same manner as presented in Section 5.1.1 for elliptical feeds. The feed
has been modeled on CHAMP software o f TICRA to optimize primary radiation patterns.
The feed dimensions are optimized to get the required pattern shape.
The schematic of the feed with optimized dimensions is given in the Figure 5.14. The
simulated amplitude taper of the best optimized feed is obtained as -11.5 dB in E-plane
and -12 dB in H-plane corresponding to the reflector edge illumination angle of 69.55°.
The return loss is better than -2 0 dB over full band. The worst case simulated cross­
polarization is -21.6 dB in the diagonal plane.
102
£
Figure 5.14 The schematic o f the optimized multimode circular feed (dual-ring). (a=0J6k,
b = 0 m , c=2.16X, d=2.23X, e=3.11X, f= 3 .m , g=0.1 IX, h=0.76X, p=0.49X, j=0.Q5X,
Amplitudes and phases o f TEjn and TMin modes at the aperture o f the two ring coaxial
multi-mode feed are computed from the TICRA’S CHAMP/FEED and CHAMP/FIELD
codes based on mode matching and moment method respectively. The computed amplitude
and phase o f coupled higher order modes at the aperture o f the optimized feed, which
resulted into the required sector shape pattern is presented in the Table 5.6.
Table 5.6 Amplitudes and phases o f TEjn and TMja modes at the
aperture of the two ring coaxial multi-mode feed.
Mode number
N
Vertical Polarization
TEln
Amp.
modes
TMin modes
Phase
Amp.
Phase
1
0.29
-26.0
0.45
-162.0
2
0.456
14.0
0.56
-158.0
3
0.41
20.7
0.20
74.0
4
0.14
27.0
0.01
74.0
103
5.3.2 Simulated and Measured Results
The measured and computed primary radiation patterns are presented in Figure 5.15. The
measured edge illumination taper o f the order of -12 dB in the E-plane and -1 4 dB in the
H-plane has been achieved which corresponds to reflector edge illumination angle of
69.55°. The measured patterns [93], [94] o f the feed are in fairly good agreement with the
predicted patterns obtained from CHAMP/FEED software. The measured return loss of the
feed better than 18 dB and cross-polarization level is better than -20 dB over a bandwidth
of 320 MHz.
Figure 5.15 The measured and computed primary radiation patterns.
The computed primary radiation patterns at different frequencies are presented in Figure
Power(aB)
5.16 (a) and Figure 5.16 (b).
13 60 GHz
13 90 GHz
05
14 70 GHz
-80
-180
fiiii
-140
-100
-60
-20
20
Angle(Degree)
.t.i.1.i i
60
100
140
180
Figures 5.16 (a) The computed primary radiation patterns at different
frequencies in E-plane.
104
Power(dB)
10c
-20
20
Angle(Degree)
Figure 5.16 (b) The computed primary radiation patterns at different
frequencies in H-plane.
The feed is integrated with the parabolic reflector o f diameter 910 mm. Three spars o f 20
mm diameter are used to hold the feed at the focus o f the reflector. The measured value of
reflector gain at 13.6 GHz is found to be of the order of 40.68 dB. In other words overall
efficiency of the order of 70% has been achieved for the reflector antenna. The measured 3dB secondary beam widths in the principal planes have been found as 1.58° and 1.6°
respectively which are very close to the specified values of 1.6°. The measured side lobe
and cross-polarization levels of the secondary squinted beams are found to be -17.1/21.6 dB
and -19.5dB respectively at the center frequency. The secondary cross-polar radiation is
better than -19 dB over full bandwidth o f 320 MHz. Measured parameters o f secondary
radiation pattern for altimeter antenna for two ring coaxial feed are presented in Table 5.7.
105
Table 5.7
Measured parameters o f secondary radiation pattern for altimeter antenna
with 2- ring feed.
Freq.
3 ~dB
3-dB
Side Lobe
Side Lobe
Beam
Beam
Level
Level
Width
Width
Computed
Measured
Computed Measured
Computed
Measured
(dB)
(dB)
(dB)
(dB)
(°)
(°)
E-plane
1.61°
1.63°
-18.0
-16.83
40.86
40.50
H-plane
1.59°
1.60°
-18.9
-17.4
Plane
(GHz)
13.44
Gain
Gain
11=68.50%
where, r| is
efficiency
13.6
13.76
E-plane
1.57°
1.58°
-18.6
-17.1
H-plane
1.59°
1.60°
-21.0
-21.6
E-plane
1.59°
1.60°
-18.5
-17.0
H-plane
1.58°
1.59°
-20.0
-18.5
41.15
40.68
11=69.6 %
40.94
40.55
il=66.0 %
The comparison o f measured and predicted secondary patterns o f the reflector with two
ring multi-mode transducer feed is presented in Figure 5.17. The two ring coaxial feed is
presented in Figure 5.18.
106
O
O
------- H-Plane (Computed
v v y E-Plane(Measured)
O
i
CO
i
i
O
O
NJ
o o o H-Plane(Measured)
-N
Normalized Power (dB)
i
—^
------- E-Plane (Computed
-50
-10
l ■■. . in ■. ......................
-8
-6
-4
-2
0
1 I I I I I » »
2
111II
4
6
8
10
Angle(Degree)
Figure 5.17 The comparison of measured and predicted secondary patterns of the
reflector with two ring multimode feed.
Figure 5.18 Two ring coaxial multi-mode feed.
107
5.4 Conclusion
Elliptical [92] and circular [93] multimode transducer feeds have been designed to
illuminate the parabolic reflectors of scatterometer and altimeter sensors to yield high
efficiency. The efficiency is better than 70% when feeds are at the focal point of the
reflector. The measured primary patterns of feeds and secondary radiation patterns of
reflector antenna closely match with the simulated performance.
Based on the design technique of the elliptical multimode feeds, a flight model antenna for
scatterometer sensor has been developed. This antenna meets all the electrical requirements
in terms of gain, cross-polar radiation, beam width and side lobe level. The photograph of
the flight model elliptical multi-mode transducer feeds and the reflector antenna illuminated
with these feeds are shown in Figure 5.19 and Figure 5.20 respectively.
Figure 5.19 Flight model elliptical feeds.
Figure 5.20 Parabolic reflector with elliptical
feeds.
108
Chapter 6
Mode Transducers for Circularly Symmetric Modes
The mode transducers presented in Chapters 3-5 are based on excitation o f non-axissymmetric TEi„ and TMin modes in circular waveguide. This chapter presents excitation
of higher-order axis-symmetric modes such as TMoi and TEoi in circular waveguide.
Simulation, modal analysis and design o f the mode transducers to excite TMoi and TEoi
modes in circular waveguide from rectangular waveguide TEio mode have been carried
out. The modal power in the desired modes have been maximized with very negligible
power in the undesired modes by properly configuring the mode transducer geometry and
optimizing the electrical performance in terms o f return loss and insertion loss. The
circular waveguide cross-sectional dimension is chosen so as to support both the TMoi
and TEoi modes. The optimization of electrical parameters for the mode transducer o f one
channel has been carried out in the presence of the mode transducer of the other channel.
Simulated and measured data on the RF performance of the rotary joint have been
presented with rotation.
6.1 Excitation of TM0i Mode in the Circular Waveguide
The mode configuration of TMoi mode in circular waveguide is shown in Figure 6.1. This
mode is generally excited in a circular wave guide using a coaxial probe, although there
are other mechanisms of excitation also.
109
--------H
--------
Coaxial
(a)
(b)
Figure 6.1 (a) Field configuration o f TMoi mode in circular waveguide.
(b) Scheme o f TMOI mode excitation in circular waveguide using axial
probe from the end o f the waveguide.
The requirement o f rotary joint output ports to be rectangular waveguide makes the
design o f transitions from rectangui ar-to-coaxial-to-circular waveguide very complex and
challenging. The following sections elaborate the methods to realize this mode transducer
transition.
Figure 6.2 shows a mode transducer to excite TMoi mode in a circular waveguide from a
rectangular waveguide propagating the dominant TEio mode. This mode transducer
consists of a door-knob transition in which a central coaxial rod protrudes in the circular
waveguide from a rectangular waveguide. This method is selected because this coaxial
rod can produce only radial and longitudinal electrical field components. In other words,
it can produce only the transverse magnetic field components and can not excite any o f
the undesired modes. The impedance offered to the coaxial probe is transformed by the
doorknob at the interface o f rectangular and circular waveguide to that o f rectangular
waveguide. A short is provided in the rectangular waveguide at a distance of quarter
guide wavelength and fine tuning is carried out by changing the location o f the short. In
this configuration the axis of circular waveguide is kept perpendicular to the axis of
110
rectangular waveguide from which the coaxial probe protrudes in the circular waveguide
to excite the mode.
The analysis and design has been presented in Ku-band with center frequency of 13.7
GHz. The diameter of the circular waveguide has been selected as 34 mm which is
oversized for TMoi so as to supports the next higher order circular symmetric mode TEoi
mode to realize finally a dual channel rotary joint at Ku-band. This diameter will also
support the undesired modes TEn, TE21 and TMn in circular waveguide along with the
desired mode TM 01. Thus, TM 01 mode has to be excited with minimum power transfer in
the supported undesired modes TEn, TE21 and TMu.
WR-75 rectangular waveguide (19 mm X 9.5 mm) has been used as input port o f the
mode transducer. The length o f circular waveguide is taken as 175 mm. The computed
guide wavelength for TM 01 mode in the circular waveguide is 25 mm. The diameter of
the coaxial probe is selected as 3.3 mm. The length o f the coaxial section from which the
probe protrudes in the circular waveguide is taken 3.2 mm. The doorknob transformer
and length o f the axial probe is optimized for maximum coupling of power in the desired
TM 01 mode and rejection of higher order modes. The optimized probe length which gives
the required return loss and power coupling is 16.5 mm. The doorknob is modeled using
HFSS in the form o f an incremental step transformer which follows the profile o f a semi­
sphere section o f radius 5.2 mm. The optimized plunger/short distance in the rectangular
waveguide which gives optimum return loss is 19.65 mm. The cross-sectional dimension
o f the coaxial section between rectangular and circular waveguide has been designed so
as to support only TEM mode.
Ill
Coaxial Probe
Figure 6.2 Schematic of TMoi mode transducer.
The modal amplitude was computed for various modes to see the mode purity o f the
TMoi mode and the rejection of the other modes. The results of the analysis are shown in
Figure 6.3. From Figure 6.3, it is clear that most of the power is confined in the TMoi
M o d a l A m p litu d e ( d B )
mode and rejection of other higher order modes is better than -22 dB.
F re q u e n c y (G H z )
Figure 6.3 The simulated modal amplitudes for different modes in
the circular waveguide for TMoi mode excitation.
112
Two mode transducers of Figure 6.2 were put back to back in order to realize a rotary
joint (see Figure 6.4). This rotary joint [95] geometry was modeled on HFSS to predict
return loss, insertion loss performance and their variation with 360 degree rotation of the
movable part with respect to the fixed part of the joint.
Input port
Rotating Joint
Output port
Figure 6.4 Single channel rotary joint with doorknob transition for TMoi
mode excitation in the circular waveguide.
The simulated insertion loss and return loss performance with rotation of the single
channel rotary joint is shown in Figure 6.5 and Figure 6.6, respectively.
F re q u e n c y (G H z )
Figure 6.5 Simulated insertion loss of the single-channel rotary joint
with rotation.
113
0
(aphis
0 Degree
- - 45 Degree
■90 Degree
o- a -e 180 Degree
* - * - * 270 Degree
_1__ «_ 1
13.60
13.65
13.70
13.75
L
13.80
13.85
13.9C
Frequency(GHz)
Figure 6.6 Simulated return loss of the single-channel rotary joint
with rotation.
The measured return loss and insertion loss have been presented for rotation o f 0,90,180
and 270 degrees as shown in Figures 6.7 and 6.8 respectively.
O
V
M
> O
7
tf)
^
O
^
IO
O
(BP)US
T
-35
-40
-45
-50
13.6013,6313.6613.6913.7213.7513.7813.8113.8413.8713.9C
F req u en cy(G H z)
Figure 6.7 Measured return loss o f the single-channel rotary joint with
rotation.
114
o
o
R> o
^
£> o
bo b
o
o
S 2 1 (d B )
0 D e g re e
-k
90 D e g re e
to
1 80 D e g re e
a-a-a 2 7 0 D e g re e
-1 .4
* - • * - * 3 6 0 D e g re e
-
1.6
-
1.8
-
2.0
1 ■ ■■
i
■ 1 1 ■ i ■ ■■ ■
i
■■■ 1 1 ■■ ■■
i
■ ■■■ i ■■1 ■
i
1 3 .6 0 1 3 .6 3 1 3 .6 6 1 3 .6 9 1 3 .7 2 1 3 .7 5 1 3 .7 8 13.81 1 3 .8 4 1 3 .8 7 13.9C
F re q u e n c y (G H z)
Figure 6.8 Measured insertion loss o f the single-channel rotary joint
with rotation.
The schematic o f the other possible configuration o f TMoi mode exciter is shown in
Figure 6.9. In this configuration rectangular waveguide axis and circular waveguide axis
are oriented in the same direction unlike the previous configuration of doorknob
transition in which both waveguide’s axes are transverse.
Figure 6.9 Rectangular to circular waveguide transition for exciting
TMoi mode in circular waveguide.
115
6.2
Excitation of TE0i Mode in the Circular Waveguide
Figure 6.10 (a) Field configuration o f TEoi mode in circular waveguide.
(b) Scheme o f TEoi mode excitation in circular waveguide using four slots.
The next higher order circularly symmetrical mode in a circular waveguide is TEoi mode
which may be used for realizing single or dual-channel rotary joints. The modal
configuration of TEoi mode is shown in Figure 6.10(a).
Since, the TEoi mode of a circular waveguide is a higher-order mode, the size o f the
waveguide selected to support this mode will automatically support four lower-order
modes which are TEn, TM0i, TE2i, TMn, respectively. In the Section 2.4 o f Chapter 2,
the simulation of a slot coupled oversized circular waveguide showed that sufficient
power couples in the lower-order modes along with the desired circularly symmetrical
higher-order TEoi mode. It was also shown that the lower-order modes can be suppressed
and the purity of the TEoi mode can be achieved by using four slots. Any unbalance in
116
the excitation o f the slots may excite undesired lower order modes and the presence of
these modes may not allow to achieve the goal of uninterrupted transmission of power
with rotation in rotary joints.
In order to excite pure TEoi mode, schematic o f the transition described in [68] as shown
in Figure 6.11(b) may be used. However, in [68] the exact philosophy of excitation of the
four slots with equal amplitude and phase is not very much clear. In order to study and
prove the concept of TEoi mode excitation in a circular waveguide using four slots on its
periphery, the schematic o f Figure 6.11 (a) may be used in which a four way equal power
divider is used to couple power in TEoi mode o f circular waveguide through the 4 axial
slots.
(a)
(b)
Figure 6.11 TEoi mode excitation in the circular waveguide using (a) 4-way power
divider, (b) Ring waveguide surrounding circular waveguide.
A proof o f conceptual model of a dual channel rotary joint has been designed and
realized using the configurations o f Figure 6.11(a) to excite TEoi mode and Figure 6.9 for
TMoi mode.
117
For TEqi mode excitation, a 4-way power divider which yields four equal amplitude and
phase output signals was realized using WR-75 waveguide. The amplitude and phase
imbalance over 1.0 GHz bandwidth was ± 0.25 dB and ± 5° dB respectively.
y - A circular waveguide o f diameter 31.5 mm and fed through 4 slots by the four-way
power divider has been modeled and simulated on HFSS. The location o f the short
position in the circular waveguide from center o f the slots and slot dimensions are
optimized to couple maximum power in the TEoi mode in circular waveguide. The
optimized slot length and width are 11.5 mm and 2 mm respectively, the position of the
short ( end walls of the circular waveguide) with respect to slot is 9.35 mm.
The simulated modal amplitudes for different modes show that the maximum power is
confined in the TEoi mode and the rejection for other undesired mode is better than 30
dB. Simulated return loss (-17 dB) bandwidth is 125 MHz for this transducer.
The other configuration as shown in Figure 6.11(b) to excite TEoi mode in circular
waveguide through 4-slots from ring rectangular waveguide was also modeled and
simulated on HFFS. The diameter, slot dimension and short locations of the circular
waveguide were optimized for balanced excitation o f the four slots to couple four slots.
The optimized diameter o f the circular waveguide is 30.6 mm. The optimized slot length
is 10 mm and width is 1.5 mm. The slot thickness is 2 mm. Its location from the input end
wall of the circular waveguide (from the short) is 10.9 mm. A triangular cone was used at
the periphery of the circular waveguide at the output location for impedance matching.
The height o f the cone is 9.7 mm, length is 6.5 mm and the length o f the base o f the cone
around the periphery is 9 mm. The simulated modal amplitudes for different modes in
the circular waveguide for this configuration show that the maximum power is confined
in the TEoi mode and the rejection for other non desired modes is better than 30 dB.
118
6.3 Excitation of TM0i and TE0j Modes in a Common Circular
Waveguide to Realize a Dual-channel Rotary Joint
The individual mode transducers to excite TMoi and TEoi modes in circular waveguide
from rectangular waveguide TEio were presented separately in Sections (6.1) and (6.2)
respectively. The two types of mode transducers shown in Figure 6.9 and Figure 6.11(a)
are combined to design a dual-channel rotary joint. Therefore, modal analysis has been
carried out for the configuration which incorporates both the transducers to excite TMoi
and TEoi modes in a common circular waveguide. Two common modes transducer to
excite TMoi and TEoi modes, placed back-to-back with an air gap may be utilized to
realize a dual channel rotary joint having choke joint and bearing mechanism.
The dual channel rotary joint was simulated on HFSS to compute return loss, isolation
between two channels and power coupled to the required modes. Simulated results show
that the maximum power is coupled in the TMoi and TEoi modes. A rejection better than
60 dB is obtained for non desired modes for TMoi channel and better than 30 dB for TEoi
channel at 13.5 GHz.
The photograph of the dual channel rotary joint [96] is shown in Figure 6.12.
TMoi
Channel
TEoi
Channel
Figure 6.12 The photograph of the dual channel rotary joint.
119
The measured return loss and insertion loss of the channel -1 (TMoi channel) is shown in
Return Loss(dB)
i>
lb o oi
<n o oi
Figure 6.13(a) and in Figure 6.13(b), respectively.
-45
-50
13 40
Figure 6.13
Figure 6.13
13 45
13 50
Frequency(GHz)
13 55
13 6C
(a) Measured return loss at the input port of channel-1 ( TMoi channel).
(b) Measured insertion loss of channel-1 ( TMoi channel).
The measured return loss and insertion loss o f the channel-2 (TEoi channel) is shown in
Figure 6.14(a) and in Figure 6.14(b) respectively. Measured isolation between channel-1
and channel-2 is shown in the Figure 6.15.
120
R eturn loss (dB )
/
0
o c\i
in (O
o to
o
(O Tj-
(N
:
:
~
“
-4 5
i-
~
:
-5 0 :—i—
13 40
Degree
Degree
Degree
Degree
+ + + 360 Degree
------ 0
------ 90
o o o 180
& a & 270
° v
i—-j— i— 1— i_i__i__i__1__i__i__i__i__1__i__i__i__i__
13 5 0
13 4 5
13 55
1 3 6C
F re q u e n c y (G H z)
Figure 6.14
(a) Measured return loss at the output port of channel-2 ( TEoi channel).
(b) Measured insertion loss of channel-2 ( TE qi channel).
h
o
O
<7\
Channel Isolation(dB)
Figure 6.14
121
6.4 Compact Design of Dual Channel Rotary Joint
The configurations of Figure 6.9 for TM0i mode excitation and Figure 6.11(b) for TEoi
mode excitation have been combined to design a compact dual channel waveguide rotary
at Ku-band. Two such dual-mode transducers are placed back to back to develop a
compact dual channel rotary joint as shown from its HFFS model in Figure 6.16.
x
Figure 6.16
Solid model of the compact dual channel rotary joint with TMoi and TEoi mode
excitation in the circular waveguide.
In the presence of one channel the RF performance of the other channel has been
simulated with different angular orientations of one part with respect to the other part of
the rotary joint. The critical geometries of TMoi and TEoi mode transducers of the rotary
joint have been optimized to achieve return loss better than 19 dB. insertion loss less than
0.1 dB and isolation between channels better than 40 dB with 360° rotation for minimum
bandwidth of 50 MHz. Probe length, height and location of the step transformers have
been optimized for TMoi channel. Slot length and location of slots from the end walls of
the circular waveguide have been optimized for TEoi channel. The optimized slot length
and width have been found to be 10 mm and 1.5 mm. respectively. The location of the
slot from the end walls is 10.9 mm. A triangular cone is used at the periphery of the
circular waveguide at the output location for impedance matching. Based on the RF
design and simulation, a dual channel rotary joint was fabricated and tested. The
simulated and measured performance of this compact dual-cannel rotary joint are
presented in the next section.
122
6.4.1 Simulated Results of Compact Dual-Channel Rotary Joint
The complete geometry of compact dual-channel rotary joint mode transducer was
modeled on HFSS to compute the power coupled to various modes in the circular
waveguide from rectangular waveguides to see the mode purity o f TMoi and TEoi modes.
The Figures 6.17(a) and 6.17(b) show the modal amplitude o f fundamental and higherorder modes for the optimized mode transducers for TMoi channel (channel-1) and TEoi
channel (ehannel-2), respectively. The Figures 6.17(a) and 6.17(b), show that the
maximum power is coupled in the TMoi and TEoi modes in the circular waveguide and a
rejection better than 30 dB is obtained for non-desired modes over the frequency band.
13 30
13 35
13 40
1345
13 50
13 55
13 60
13 65
13 7C
F re q u e n c y (G H z )
Figure 6.17 (a) Modal amplitudes of fundamental and higher order modes for the
optimized mode transducer for channel-1 (TMoi channel).
CO
-O
X5
3
Q.
O
2
13 20 13 25 13 30 13 35 13 40 13 45 13 50 13 55 13 60 13 65 13 TC
F re q u e n c y (G H z )
Figure 6.17
(b) Modal amplitudes of fundamental and higher order modes for the
optimized mode transducer for channel-2 (TEoi channel).
123
The simulated results for return loss, insertion loss and isolation between channels is
presented in Figure 6.18(a). The orientation of rotary joint ports for which the simulation
has been performed is shown in Figure 6.18(b). In this figure, the orientation between the
rotor and the stator parts of rotary joint is assumed as zero degree. The performance has
been optimized around the center frequency of 13.515 GHz. The simulated return loss
performance is better than 19 dB over the desired bandwidth of 50 MHz i.e., from 13.49
to 13.54 GHz for both the channels of rotary joint. The simulated insertion loss is 0.1 dB
over desired 50 MHz, 0.15 dB over 100 MHz, and 0.65 dB over 200 MHz as shown in
the Figure 6.18 (a). -17 dB return loss bandwidth around the center frequency is 100
MHz for TEoi Channel and 110 MHz for TMoi channel. The simulated isolation between
both the channels is better than 68 dB.
TEoi
channel i/p
TEoi
channel o/p
Frequency (GHz)
(a)
Figure 6.18
(b)
(a) The simulated return loss, insertion loss and isolation between two
channels of dual-channel rotary joint.
(b) The orientation of rotary joint ports. Here, i/p stands for input and
o/p for output.
124
6.4.2 Simulated Performance with 360 degree Rotation:
Modeling and simulation has been performed to predict the electrical performance of the
rotary joint when one half part is rotated with respect to the other half part. Initially, the
performance with rotation is predicted for individual channels in the absence o f the other
channel. The return loss performance for 0°, 90°, 180° and 270° rotations o f the rotating
part of TMoi channel in the absence of TEoi channel is shown in Figure 6.19. Similarly,
the return loss performance for 0°, 90°, 180° and 270° rotation o f the rotating part of
TE0i channel in the absence o f TMoi channel is shown in Figure 6.20. It is seen that
return loss performance is very stable for TMoi channel with rotation but varies slightly
for TEoi channel with rotation.
Figure 6.19 The return loss performance
o f TMoi channel in the absence
o f TEoi channel.
Figure 6.20 The return loss performance of
TEoi channel in the absence of
TMoi channel.
When both channels are present simultaneously, the return loss, insertion loss and
isolation performance for 0°, 90°, 180° and 270° rotations o f the rotating part with respect
to stationary part is shown in Figure 6.21 for TMoi and TEoi channels. It is seen that in
the presence of both TMoi and TEoi channels, electrical performance varies with rotation
for both channels. But the simulated performance is within acceptable limits for both the
channels.
125
is
R e tu rn L o s s (d B )
tt>
(b) TEoi Insertion loss.
i
R e tu rn L o s s (d B )
(a) TMoi Insertion loss.
' 180 deg
' 1 80 deg
-5 0
-5 0
i 2 7 0 deg
-6 0
1340
■ l
I,
1344
13 4 8
1352
.
13 56
■
1 3 6£
-6 0
13 40
» • « 270 deg
................
_L
1344
13 4 8
F r e q u e n c y (G H z )
13 52
13 56
13 6(
F re q u e n c y (G H z )
(c) TMoi Return loss.
(d) TEoi Return loss.
(e) Isolation between TE0i and TMoi channels.
Figure 6.21 Simulated performance with rotation in presence o f both channels simultaneously.
(a) Insertion loss for TMoi channel, (b) Insertion loss for TEoi channel, (c) Return loss
for TMoi channel, (d) Return loss for TEoi channel, (e) Isolation between TMoi
and TEoi channels.
126
6.4.3 Measured Results of Compact Dual-channel Rotary Joint
Various parts of the compact rotary joint have been fabricated and assembled. Proper
jigs, fixtures and dowels have been used to align coaxial probes protruding in the upper
and lower half of the cylindrical cavity for TMoi channel. An angular contact ball bearing
has been assembled between upper and lower half of the cylindrical cavity for the
implementation o f rotation between fixed and rotating parts o f the rotary joint. The
measurement for the compact dual-channel rotary joint (see Figure 6.25) has been
performed on a PNA series network analyzer (E 8363 B) for return loss, insertion loss
and isolation between channels with respect to 360 degree rotation at the interval o f 90
degree. The measured return loss and insertion loss with rotation is shown in Figure 6.22
for TMoi channel and in Figure 6.23 for TEoi channel. The isolation between channels
with rotation is shown in Figure 6.24.
It is clearly seen from Figure 6.22(b) and Figure 6.33(b) that the measured variation of
insertion loss is within ±0.1 dB with rotation at the edge o f the frequency band and it is
within ±0.05 dB near the center frequency at 13.515 GHz. The return loss performance is
nearly 17 dB for TMoi channel and better than 15.6 dB for TEoi channel over 50 MHz
bandwidth. The isolation between channels is better than 39 dB over the frequency band.
The nature o f measured electrical performance is similar to the simulated results, except
slight shift of resonance frequency. Various plots show that the purity o f excited circular
symmetric modes has been achieved which was the main objective o f the design o f rotary
jo in t The slight deviation in the values o f return loss and isolation from simulated results
could be attributed to achieved fabrication tolerance and assembly and alignment errors.
127
;
Insertion Loss (dB)
o
CVt
------ 0 Degree
-
o
-
— - 180 Degree
;
o o o
b
o 90 Degree
270 Degree
O
b.
o
CO
o
-60
13 49
13 50
13 51
13 52
Frequency (GHz)
13 53
13
-2 5 ' .. »„„>
13 49
5*
(a) Measured return loss at the input port
o f channel-1 (TM0i channel).
Figure 6,22
t
1 f
1 1 » i 1.....t ....I „, l i 1
13 51
13 52
13 53
Frequency (GHz)
1 1__ L_.1...1 t
13 50
t
II.,
13 5-
(b) Measured insertion loss o f channel-!
. (TMoi channel).
Measured performance o f the compact dual channel rotary joint.
(a) Return loss at the input port o f channel-1(TMoi channel).
(b) Measured insertion loss of channel-1(TMoi channel).
O
O
Ol
<h
iuaa aa e e a u e a n e w i B t a e a a a a f l a g a B B B a -B^ uaagHBi
Insertion Loss (dB)
8§§g8g§8ggggggg§ggggaggaga8fl8aflaaMaffl>a
—— 0 Degree
h
— - 90 Degree
o o o 180 Degree
■
_L
i ....
13 50
13 51
13 52
Frequency (GHz)
o
-60
13 49
a 270 Degree
— i_l_i_i— i— i
13 53
13 5*
(a) Measured return loss at the input port of
channel-2 (TEoi channel).
Figure 6.23
— - 90 Degree
o o o 180 Degree
o o D 270 Degree
cv
an
( 3%
Return Loss (dB)
Return Loss (dB)
M m ********
-2 5
13 49
13 50
13 51
13 52
Frequency (GHz)
13 53
(b) Measured insertion loss o f
channel-2 (TEoi channel).
Measured performance o f the compact dual-channel rotary joint.
(a) Return loss at the input port of channel-2 (TEoi channel).
(b) Measured insertion loss of channel-2 (TEoi channel).
128
13 5*
------- 0 Degree
K)
o
o
CO
i 270 Degree
o
j*
Isolation (dB)
— - 90 Degree
-60
13.49
Figure 6.24
o- e -© 180 Degree
13.50
13.51
13.52
Frequency (GHz)
13.53
13.5*
Measured isolation between channel-1 and channel-2 for the
compact dual-channel rotary joint.
The photograph of the compact dual channel rotary joint is shown in Figure 6.25.
Figure 6.25 The photograph of the compact dual-channel rotary joint.
129
6.5 Conclusion
The mode transducers to excite TMoi and TEoi modes in a circular waveguide have been
presented in this chapter. This investigation finally led to the development of a compact
dual channel rotary joint. The measured results of the compact dual channel rotary joint
closely meets the requirement of insertion loss, isolation and return loss parameters with
360 degree rotation. This rotary joint has been successfully developed as flight model to
be used for the scan mechanism of pencil beam scanning scatterometer antenna for
Oceansat-2 mission which is aimed for remote sensing applications. The developed flight
model rotary joint as shown in Figure 6.26 meets the specifications of insertion loss,
return loss and isolation of 0.35 dB, -19 dB and 40 dB respectively with 360 degree
rotation. The measured results of the rotary joints presented in this chapter are in close
agreement with the simulated results for most of the configurations. Slight deviations for
a few configurations may be attributed to fabrication and assembly errors, as the devices
were not fabricated as a single piece but in different pieces due to their complex
configurations.
Figure 6.26 The photograph of the compact dual-channel rotary joint (flight model).
130
Chapter 7
Summary Conclusion and Future Scope
7.1 Summary and Conclusion
Electromagnetic modeling followed by the design and development o f a new multi­
frequency ortho-mode transducer (OMT) operating at four widely separated frequency
bands was presented. In this mode transducer cascaded circular waveguide sections have
been used as main-arm, rectangular waveguides as side-arms and coaxial line fed probes as
coupling elements. Major effort was put to find out an optimized design which confines
maximum power in the dominant TEn mode in the outer most section o f OMT at all the
four frequency bands in the presence o f multiple discontinuities in the form o f waveguide
junctions and coaxial probes. The analysis results for post [78], probe [97] and step junction
discontinuities in circular waveguide (Chapter 2) showed that the probes o f reduced depth
(Figures 2.13,2.15 and 2.16) and the waveguides o f small taper angle result into improved
return loss and low power coupling (Figures 2.23) into higher-order modes. Therefore,
coupling o f the incident power into the higher-order TMin (n >0) and TEin (n > 2) modes
was minimized by taking smaller flare angle o f the tapered waveguide sections between
cylindrical waveguides o f the multi-frequency mode transducer. Coupling o f incident
power into higher-order TMmn and TE^, (m ^ 1, n > 0) modes was minimized by taking
reduced depth probes in the lower frequency sections. The incident higher frequency
signals showed more coupling (Table 3.2) with the lower frequency probes. This coupling
was minimized by designing new rectangular to circular waveguide transitions for the
lower frequency sections. Ridged waveguide step transformers were used in the rectangular
waveguides in order to achieve impedance matching between the rectangular waveguide
and the coaxial line from which the probe protrudes in the circular waveguide. The location
o f the onset o f the step transformers in the rectangular waveguides were optimized to
achieve isolation o f higher frequencies with lower frequency coupling probes (Table 3.3).
The return loss performance at various frequency bands was achieved by optimizing the
probe depth, its location from the cut off taper and the height o f the steps in the step
transformer. The complete geometry o f the common mode transducer was modeled and
131
optimized on HFSS to achieve optimum performance at all the four frequency bands o f the
ortho-mode transducer [86].
The simulated and measured return loss, isolation between ports and insertion loss (Figures
3.6-3.12) at all the frequency bands were presented for the developed multi-frequency
OMT (Figure 3.13). Slight deviation in simulated and measured return loss and isolation
parameters of 8-port, four frequency OMT may be attributed to fabrication, assembly and
probe alignment errors.
A mode transducer operating at 18.7,23.8 and 36.5 GHz frequency band was also designed
and developed (Figure 3.20). For this mode transducer various configurations having
different relative positions (Figure 3.14) o f power coupling ports were studied in terms o f
return loss, power distribution in various modes, isolation o f orthogonal ports and isolation
of polarization matched ports. A configuration yielding optimum result was selected,
fabricated and measured for its electrical performance. Simulated and measured results
(Figures 3.15-3.19) were in close agreement.
Design o f a corrugated horn [86], [88], [89] fed by the above mentioned 4-frequency OMT
was carried out using the technique of harmonic operation o f corrugation depth to operate
at all the four frequency bands (6.6,10.65,18 and 21 GHz). The horn geometry was
optimized in order to yield symmetric far-field co-polar patterns and low level o f crosspolar radiation at all the frequency bands. The horn (Figure 4.7) was tested with separate
transitions [88] at each frequency at its input and also with the developed 4-frequency OMT
[86] at its input. Optimum radiation performance o f the horn excited with multi-frequency
ortho-mode transducer was achieved at all the four frequency bands for both the
polarizations (Figures 4.5 and 4.6). To see file utility o f the four frequency feed and OMT,
an offset reflector was illuminated with the integrated feed and OMT system. The measured
secondary radiation performance (Figure 4.8). showed that the antenna can be successfully
used for microwave radiometer application for multi-frequency operation. The modal
analysis based design approach presented for this 4 frequency OMT may be applied to the
design o f multi-frequency ortho-mode transducers and horns at other frequency bands.
132
A common aperture three frequency hom was also designed, simulated and tested with the
developed three frequency common mode transducer at 18.7,23.8 and 36.5 GHz. A groove
discontinuity was used at the input of the hom to couple power in the higher order TMn
and TE12 modes at 36.5 GHz to achieve symmetric radiation patterns without affecting the
performance at lower frequency bands at 18.7 and 23.8 GHz. The developed hom [90] was
tested for its radiation performance using the three frequency mode transducer at its input.
The measured and simulated performance (Figures 4.10-4.12) o f this feed system are in
close agreement.
New elliptical multi-mode feeds (Figure 5.3) for achieving high efficiency for reflector
antenna were presented at Ku-band. In order to obtain better efficiency of a reflector
antenna, feeds yielding sector shape radiation patterns have been designed. The sector
shape radiation pattern was obtained using higher-order modes with proper amplitude and
phase at the feed aperture. The measured radiation patterns (Figure 5.5) o f elliptical feeds
[92] closely met the simulated radiation patterns. To prove the utility o f these multimode
feeds, the feeds were integrated with reflector antennas and the radiation characteristics
were measured for gain, side lobe level, beam-width and cross-polar radiation. The
measured results for secondary radiation patterns closely met the simulated results (Figure
5.5). A flight model (Figures 5.19 and 5.20) antenna for scatterometer sensor was
developed based on the design technique o f the elliptical multi-mode feeds meetings the
requirements o f gain, cross-polar radiation, beam-width and side-lobe level. The multimode
single mid dual-ring coaxial feeds (Figures 5.12 and 5.18) having circular aperture [93],
[94] were also designed and developed for altimeter antenna which is a fixed nadir-looking
antenna. These feeds were integrated with parabolic reflector antenna and the overall
efficiency of the order o f 70 % was achieved.
Mode transducers supporting circularly symmetric TEoi and TMoi modes [95], [96] in a
circular waveguide were successfully demonstrated based on the design using modal
analysis approach to develop a dual channel rotary at Ku-band. The purity o f both the
modes was established by observing invariance o f RF parameters with rotation o f rotating
part of the rotary joint with respect to stationary part for full 360° rotation. The measured
results (Figures 6.22 and 6.24) of the compact dual channel rotary joint (Figure 6.25)
133
closely met the desired and simulated return loss (> 17 dB), insertion loss (< 0.35 dB) and
isolation (40 dB) between two channels with rotation. Slight deviations in the electrical
performance of the rotary joints may be attributed to fabrication, assembly and alignment
errors between different parts of the device. A flight model rotary joint (Figure 6.26) was
developed based on the approach o f exciting TEoi and TMoi modes in circular waveguide
meeting the desired electrical specifications.
7.2 Future Scope of the Work
The formulation and analysis of single post and probe discontinuities presented in Chapter
2 can further be extended to two, three and multiple post discontinuities. Post analysis can
be utilized in the design o f tri-mode or matched feeds [77] which are used to obtain reduced
level o f cross-polar radiation in an offset reflector antenna. Theses feeds are based on
coupling o f power in TEn, TMn and TE21 modes. The TE21 mode can be excited by using
post discontinuity in circular waveguide [78]. The modal content can also be adjusted using
post the height. The analysis of symmetric discontinuity can be used in the generation of
TM n mode along with the incident TEn mode for the tri-mode matched feeds. A
waveguide filter can also be designed using multiple posts.
The 4-frequency otho-mode transducer presented in Chapter 3 consisted o f probe coupling
mechanisms at different frequency bands. Theses probes were used to couple power in
cascaded circular waveguides sections which were terminated at their input end with
tapered waveguide sections. The size o f the tapered waveguides sections were selected so
as not to allow the signal coupled by the probe to propagate towards higher frequency
waveguide sections. The rigorous formulation and analysis of coaxial line fed probe in the
presence o f a tapered waveguide section may be attempted in future, talcing the probe as a
coupler and also as a discontinuity [97] in cylindrical waveguide. The technique o f probe
discontinuity analysis presented in chapter 2 can be further extended to discontinuity with
tapered waveguide. The results presented in Chapter 3 showed slightly poor isolation
between closely spaced frequency bands, particularly the isolation o f 21 GHz with the 18
GHz port In order to get better isolation between polarization matched ports, further
134
investigation may be attempted by putting appropriately designed filters at the waveguide
ports of the lower ftequency bands.
At millimeter and sub-millimeter wave frequency bands, the design in terms o f controlling
the power in the desired modes, isolation between frequency bands and polarization would
be a challenging task apart from mechanical realization o f the devices. The design
methodologies presented in the current research work can be successfully utilized to design
the devices at millimeter wave frequency bands. The current technology on antennas for
millimeter-wave radiometer operating at 57, 89, 110, 183 GHz uses different feeds at
different frequencies. The concept presented in this thesis may be extended to explore the
feasibility of common aperture multi-frequency feeds at these frequencies. Multi-frequency
mode transducers using slot coupling instead o f probe coupling can also be attempted at
other frequency bands. The multi-mode feeds giving shaped radiation patterns and their
application for remote sensing antennas can also be attempted at higher frequency bands.
In Chapter 6, coaxial probe coupling was used to excite TMoi mode in a circular waveguide
for realizing rotary joints. The technique o f exciting TMoi mode using slot coupling instead
of probe coupling can also be explored.
In the thesis, some novel designs were presented for achieving mode purity o f fundamental
mode (Chapter 3 and 4), for achieving combination o f fundamental and higher-order mode
(Chapter 5) and also for achieving mode purity of higher-order axis symmetric modes
(Chapter 6). Utilizing these designs, different devices were developed for the antenna
systems for microwave sensors such as radiometer, scatterometer and altimeter. The design
techniques presented in the thesis can also be used to develop mode transducers for multi­
frequency, dual-polarized feed systems for communication satellites and earth station
antennas. The work carried out in the thesis will be very useful as a tool and guideline to
optimally design waveguide devices at different frequency bands using the modal analysis
approach presented in the thesis.
135
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[ 73 ] D. A. McNamara and L.T. Hildbrand, “Fullwave analysis o f non-contacting
rotary joint choke sections using the generalized scattering matrix(GSM)
approach”, Proc. IEE Microwave Antennas Propagat., vol. 150, no. 1, pp. 5-9,
Feb. 2003.
[ 74 ] Rambabu and Jens Bomemann, “ Compact single channel rotary joint using
ridged waveguide sections for phase adjustment,” IEEE Trans. Microwave
Theory Tech., vol. 51, no. 8, pp. 1982-1985, Aug. 2003.
[ 75 ] K. M. Prasad and Lotfollah Shafai, “Improving the symmetry o f radiation
patterns for offset reflectors illuminated by matched feeds,” IEEE, Trans.
Antenna Propagat., vol. 36, no. l,p p . 141-144, Jan. 1988.
[ 76 ] Keyvan Bahadori and Yahya Rahmat-Samii, “A tri-mode hom feed for
gravitationally balanced back to back reflector antennas” in IEEE, AP-S, Int.
Symp. Antennas Propagat, pp. 4397-4400,2006.
[ 77 ] S. B. Sharma, Dhaval Pujara, S.B. Chakrabarty, and V. K. Singh. “Performance
comparison of a matched feed hom with a Potter feed hom for an offset
parabolic reflector,” in IEEE A P S, Int. Symp., Antennas Propagat., July 2008.
[ 78 ] S. B. Sharma, Y. K. Singh. Ranajit Dey, and S.B. Chakrabarty, “Analysis of
post discontinuity in an oversized circular waveguide,” IEEE Trans. Microwave
Theory Tech, submitted fo r publication.
[ 79 ] Baisuo Wang, “ Mutual Impedance between probes in a waveguide,” IEEE
Trans. Microwave Theory Tech, vol. 36, no.l, pp. 53-59, Jan. 1988.
[ 80 ] B.-S. Wang, “ Mutual impedance between probes in a circular waveguide,”
IEEE Trans. Microwave Theory Tech, vol. 37, no. 6, pp. 1006-1012, June
1989.
[ 81 ] B. N. Das and G. S. Sanyal, “Coaxial to waveguide transition (end launcher
type),” Proc. IEE, vol.l23,no. 10, Oct. 1976.
[ 82 ] Samuael Hopfer, “Design of Ridged Waveguides,” IRE Trans. Microwave
Theory and Tech., pp. 20-29, Oct. 1955.
[ 83 ] Tsung-Shan Chen, “ Calculation o f Parameters of Ridge Waveguides,” IRE
Trans. Microwave Theory Tech, pp. 12-17, Jan. 1957.
[ 84 ] Wolfgang, J. R. Hoefer, and Miles N. Burton, “ Analytical expressions for the
parameters o f finned and ridged waveguides,” IEEE Trans Microwave Theory
T e c h - S IGEST,pp. 311-313, 1982.
[85]
M. Jaimal Ahmed, “Impedance transformation equations for exponential,
cosine squared, and parabolic tapered transmission lines,” IEEE Trans.
Microwave Theory Techniques, vol. MTT-29, no. 1, pp.6768, Jan. 1981.
141
[ 86 ] S. B. Sharma, V. K. Singh, and S B Chakrabarty, “Multi-frequency waveguide
orfhomode transducer,” IEEE Trans. Microwave Theory Tech., vol. MTT-53,
no. 8, pp. 2604-2609, Aug. 2005.
[ 87 ] V. K. Singh. R. M. Makwana, R. K. Malaviya, P. D. Ramavat, S. B. Sharma,
“Model analysis of cascaded circular waveguide sections o f 8-port ortho-mode
transducer for multi-frequency operation o f horns”, in National Symp.
Advances in Microwaves and Light waves, Mar. 25-28, 2000. pp. 153-156.
[ 88 ] S. B. Sharma and V. K. Singh. ” Design o f common aperture hybrid mode
corrugated horn for multifrequency scanning microwave radiometer,” IETE
Technical Review, vol. 16, no.l, Jan.-Feb. 1999, pp. 47-52.
[ 89 ] V. K. Singh, S. B. Chakrabarty, S. B. Sharma, and Arun Kumar, “Evaluation
o f common phase center o f multi-frequency feed for radiometric applications,”
in Proc. Int. Conf. Antenna Technologies (ICAT2005), Space Applications
Center (ISRO), Ahmedabad, India, pp. 279-283, Feb. 2005.
[ 90 ] S.B. Sharma and V. K. Singh. “Multifrequency corrugated feed with groove
discontinuity at input,” Electron. Lett., vol. 37, no. 18, pp. 1121-1122, Aug.
2001.
[ 91 ] V. K. Singh. R. M. Makwana, R. K. Malaviya, K. P. Bhalsod, S. B. Sharma, “
High gain elliptical coaxial feed”, in National Symp. Advances in
Microwaves and Lightwaves, Mar. 25-28,2000. pp. 95-98.
[ 92 ] S. B. Sharma and V. K. Singh. “Parabolic dish antenna with offset elliptical
multi-mode feeds for space-borne remote sensing application,” Microwave Opt.
Technol. Lett., vol. 39, no. 2, pp. 138-141, Oct. 2003.
[ 93 ] V. K. Singh and S. B. Sharma, “Sudoor samvedan upyogi aadhunik
sukshmtarang antenna neetbhar,” in Hindi Conference, Space Applications
Center, Ahmedabad, India, Mar. 2002.
[ 94 ] V. K, Singh and S. B. Sharma, “Sudur samvedanopyogi antenna kaa aadhar
stumbh:Vidyut chumbkiya vidhayen (electromagnetic modes),” in Takneeki
Hindi Seminar, Space Applications Centre, Ahmedabad, India, Jan. 2003.
[ 95 ] S.B. Chakrabarty, V. K. Singh. S. Kulshrestha, G. Upadhyay, and S. B.
Sharma, “TMoi mode transducer using circular and rectangular waveguides, ” in
Int. Conf. Microwaves, Antenna Propagation and remote sensing, ICRS,
Jodhpur, India, Feb. 2008.
[ 96 ] V. K. Singh. S.B. Chakrabarty, Anil Solanki, R. Dey, Ila Agnihotri, and S. B.
Sharma, “Mode Transducers for Ku-band dual-channel microwave rotary
joint,” in Int. Conf. Microwaves, Antenna Propagation and Remote Sensing,
ICRS, Jodhpur, India, Feb. 2008.
[ 97 ] S. B. Sharma, V. K. Singh, Ranjit Dey, and S.B. Chakrabarty, “Analysis of
coaxial probe discontinuity in an oversized circular waveguide,” submitted for
publication.
142
Appendix A
A.1
Coaxial Probe Coupling in Circular Waveguide with Perfect Short
The coaxial probe excitation of a circular waveguide having a perfect short at input is shown in
Figure A .l. Maximum power is coupled to the circular waveguide from the coaxial line fed probe
when the real part of the impedance seen by the probe in the circular waveguide matches with the
characteristic impedance o f the coaxial line and the reactive part becomes zero.
A
u
Figure A .l Coaxial probe excitation of a circular waveguide with perfect short at
input and output terminated in matched port.
Detailed expressions are given in [28] to find out the input impedance of a coaxial line fed probe in
circular waveguide. Those expressions have been used presently to find out the probe parameters for
impedance matching. As described in [28] the expression for impedance offered to the coaxial probe
in circular waveguide is given as,
= T j \ \ \ \ \ m - G p(r ,r ,).J {r')ds'ds
/
s'
(A.1)
s
where Gp(r,f') is the radial component of the electric dyadic Green's function and J(r) is the
current density on the coaxial probe, p, <j>,z is the cylindrical co-ordinate system for the circular
waveguide. The expressions for Green’s function [28] are,
143
G
P
0 ,r’)=
-JCOfi
2
m
_
,2 . — r sinh[«mn(z' + /)] Jm(ymnp ) J m(y'„p)
II
^^m 6)mn7mna mnPP
m=l n=l
.
00
(z+/) cos(w{(j>-(j))) + ~~ ~
e
00
2-sin h [a m„(z' + 0] A ( J m(rmnp ’))
S
™=0 "=1
—
(
dp
QP
“™(z+,) COS(m(0- 0'))
J m(YmnP))e
\ Z> z
(A.2)
G (r,r’)=
P
60
2
00
/w
- e~a™iz'+l)
J m(ym„p ) J m(ymnp) sinh[amn(z + /)]
^ S0m&ma7mna mnPP
B )= l » = 1
cos(i»(*-*))+ —7
£ £
'l(O B w=0n=1
e -“™(z,+/)
A C A O ™ /? ))
3p
K S o m ^ m n ’/ m n
_d_
d ( ^ ( r m„ /2 ))sin h [a mfl(2 + 0 ] cos(»i(^-^ ))
dp
:-l<2T < Z
(A.3)
The current density on the probe is,
J =
2m
,
where, r is the radius of the probe and I ( p) = I m— — - —
‘ sin(/eft)
— is the assumed
current distribution on the probe. In this expression of current, h is the probe depth, a is the radius of
circular waveguide, k is the free space propagation constant and l is the distance of probe from the
location of the perfect short.
Equation (A .l) can be expressed as,
Z„ =
i
£ ( + jar' - ) + f , i
m-\ n-1
m-1 n~\
(*„. + J X „ )
(A.4)
where, Rmn + J X mn are the input impedance due to TEmn mode, while Rmn •+• JX mn are due to TMmn
mode. The cross-sectional dimension of the circular waveguide only allows TEn mode to propagate.
Thus, all Rmn, Rmn vanish except R u which is a real part of impedance offered to probe due to
propagating TEn mode in circular waveguide. The expressions for real and imaginary parts of
impedance are given in [28]. If the real part of the impedance offered to the probe have to be matched
144
with the characteristic impedance ( Z0 ) of the coaxial line, then in this condition the reactance part of
Zmshould be zero. The design dimensions of the coaxial probe for impedance matching can be found
from the expressions,
2
(A.5)
(A.6)
Equations (A.5) and (A.6) give unknowns such as height lh ’ of probe and the position T of the
probe from the perfect short for matching where real part o f the impedance matches with the
characteristic impedance of the coaxial line and the reactance due to all modes vanishes.
Using the expressions o f equations (A.5) and (A.6) as described in [28], the input impedance and the
return loss as can be computed. A circular waveguide of diameter 32.54 mm, excited with a probe of
diameter 1.6 mm was analyzed. The diameter of inner and outer conductor of coaxial line was
selected as 1.6 mm and 6.5 mm respectively. The distance o f the perfect short from the probe and the
probe depth were varied and it was found out that a short distance of 19 mm from the probe position
gave optimum matching at 6.6 GHz. The return loss was o f the order of -30 dB at 6.6 GHz and the 10 dB return loss bandwidth was o f the order of 12 %. This distance o f the perfect short from the
probe is nearly quarter o f the guide wavelength which is equivalent to 90 degree phase. Also, probe
height of 11 mm (nearly quarter of the wavelength) was found to be exactly matching with the
coaxial line TEM mode impedance (83 Ohms). Thus the analysis for probe coupling shows that
impedance matching for maximum coupling can be obtained for a particular depth of coaxial line fed
probe and its location from the short.
A.2 Coaxial Probe Coupling in Circular Waveguide with Tapered Short
In case of multi-frequency mode transducer (see Figure 2.1), the probe depth and its location with
respect to the tapered section should also be determined for maximum power coupling to the circular
waveguide. Since, the tapered waveguide section provides a virtual short to the coaxial probe signal,
145
the probe depth can be taken as that computed from equations A.5 and A.6. For this depth of probe,
approximate location o f the probe for impedance matching can be found out. Figure A.2, shows a
circular waveguide o f radius r0 terminated to a cut off waveguide o f radius r, through a tapered
waveguide section. The maximum power from the coaxial probe can be coupled in the circular
waveguide if the probe is located such that the direct power coupled to circular waveguide is in phase
with the power reflected from the tapered section. To find out the location of the probe, the phase
contribution by tapered section of waveguide should be known.
Port -1
Port-2
Figure A.2
Coaxial probe excitation o f a circular waveguide
with tapered waveguide section at input.
Let the location of the probe with respect to cutoff position is given by Xt +XS where, Xt is the
distance in tapered section and is Xs the distance in straight waveguide section.
Corresponding to these distances total phase can be given as
Total phase = f ^
d x + ^ -X s
o A'g (x)
Xg (x)=
(A.7)
U[l- {VXc(x)}2] 1/2
Xc (x)=2.7cr(x) / 1.841 = 3.41 r(x)
r(x) = rc + x tan(6),
where,
146
Ig (x) is the guide wavelength in the tapered section and Xc (x) is the cutoff wavelength in the tapered
section. Xg is the guide wavelength of straight waveguide section in which probe is protruding. rc is
the cut off radius for TEn mode in the tapered section. r(x) is the radius of waveguide in the tapered
section, x is the distance from cut off location and 0 is the taper angle. To achieve maximum
coupling in the waveguide with a tapered section, the total phase computed from equation (A.7) can
be taken as
2
A circular waveguide of diameter 32.54 mm and a probe o f depth 11.6 mm was taken. Circular
waveguide was terminated at its input with a tapered waveguide section o f taper angle 5.7°. The
probe was kept at a location where the total phase becomes 90 degrees with respect to the cut off
diameter (26.8 mm at 6.6 GHz) in the tapered section o f waveguide. Taper angle of 5.7° yielded a
distance of 28 mm between the cut off diameter and the coaxial probe for achieving a total phase of
90 degrees as computed using equation (A.7). The complete geometry was simulated on ansoft
HFSS. With tapered short, the probe location for optimum coupling (or impedance matching) has
been found to be 28.4 mm in simulation against the computed value o f 28 mm from equation (A.7).
For tapered short, the simulated return loss was o f the order o f -25 dB at 6.6 GHz and the -10 dB
return loss bandwidth was of the order of 5 %. This simulation showed that the return loss and
coupling performance of a circular waveguide terminated with a tapered section can be obtained if
the height of the probe is taken as same as that computed for a perfectly shorted circular waveguide
and the probe location computed using equation (A.7).
A.3 General Expression of Dyadic Green’s Function
The expressions for dyadic Green’s functions Gel,Gml,Ge2 and Gml for cylindrical waveguide [33]
are,
Ge2(R ,R ') = ~ z z 5 ( R - * ' ) + £
A
n,m
0.1 (R, R') = ~ & 6 ( R ~ R') + £
*
Gml(R,R’) =^
(±*„ )N'lrtl (**„ ) + cxM enX(±kx )M'mX(+kx )
(±*„
) + cxNmX(±kx)N'mX(+kx)
n.m
ot,M m,{ ± k p) N ' m M o xN ^ ( ± k x) M U m x)
n jn
,zKz’
Gm2{ R , R ' ) ^ k c„N mi, (±A„ W L G k J + cxM mX (±kx )N'S„XQfkx )
147
,z[z'
(A.8)
(A.9)
(A. 10)
(A-11)
The dyadic Green’s functions in equations A.8 to A.11, have been expressed in terms o f cylindrical
vector wave functions M mfl and N enXas
o
o
cos
M ^ ( / 0 = Vx J„(/ur )
n(f> e 'tez
(A. 12)
sin
COS
— V x V x J„(Xr)
o
Kx
where a =
a
(A. 13)
ntj> e,hzz
sin
and X =
a
k \ = X2 + h2 and k \ = pi1 + h2
k\ = k 2 - X 2
k \ = k 2 - fi2
The general expressions given in equations A.8 to A.11, for Gel,Gml,Ge2 and Gml , the different
components o f dyadic Green’s function in circular waveguide have been derived.
A.4 Expression for Components of Green’s Function
The derived expressions for Gn ,Gn , Gr?s, Gzr, G ^ , Gzz, Gzi>, G# , G# are as follows.
(a) Component o f Gel for computing electric field in circular waveguide due to electric current J on
the post or probe
G„(r,r') = I dCf
ikxdJ„{Xr)
,k
— — —— -cos ntpe *
dr
A
nm
(A. 14)
ikxdJ( Xr ' )
2)
,
— -— —— -cos ntb'e 1
dr’
(b) Component o f Gml for computing magnetic field in circular waveguide due to electric current J
on the post or probe
1 \ - i k Mn J H( f t r ) .
A
G ^ r ,r ') = ^ k C M — j -----if----------- sm n<pe "
K,
ip
k CJ x
+ z — ran
^ X
L
dJn{Xr)
cos n^e 'M
dr
nJn(nr')„x
sin nm e
(A. 15)
■ikxdJn(Xr')
cos n<j>'e
dr'
1 f/iV„(//r)
,
I \ - n J n{fir') .
—
- - cos n<pe * H ------ - sm n p e
1
k„
148
tk „ z '
“
(A. 16)
(c) Component of Gmlfor computing electric field in circular waveguide due to magnetic current M
in coaxial aperture (i.e., due to coaxial aperture field)
1 ( - n J (/lit) .
t \ \ i k nJn{fxr') .
*
— J----- 2 — srnn^e *
— ------sm n f e "
<?*(r.O = Z * C , K„
ikxdJn(Xr )
cos n<j>e
dr
■rp kC,
+ E —A
K,
U ... ^
: >
(A. 17)
cos
1 f - nJ (fur) .
,
\
Gl,( r ,r ') = 2 ACA — j ----- ”v^ sm nfa " X ——
±< -&„*
—cos n f e '
(A. IS)
(d) Component of Ge2 for computing magnetic field in circular waveguide due to magnetic current
M in coaxial aperture (i.e. due to coaxial aperture field)
G J r , / ) = ~±zzS(R - R ’) + £ c j
nm
I ^
^
cosh^
j
lkMnJ„(fir')
1 J /iV .O /r )
-------sm nme “
cos n^e'k“z u
1
/c
Gz/ r , r ' ) = X C
ra n
G^(r,r') = X c ,
1 f - i k unJ„({ir)
* JJ rk^nJ^ftr') t
-sinn^e
-smnme "
A T,,
- a /„ ( A r )
nm
•i
^
(A.20)
(A.21)
G^r,r') = ^ C u
4~
(A. 19)
dr
cos nfe
■dJJXr')
, ..
B
-cos ndte 1
dr'
(A.22)
A.5 Mode Matching Technique for Step Junction Discontinuity in Circular
Waveguide
A schematic o f step junction between two uniform circular waveguide sections as shown in Figure
A.3 has been taken into consideration to explain the mode matching technique. In this technique, the
149
total modal field is matched at the junction between uniform waveguide sections. The amplitudes of
separate modes at the output of junction are computed in terms of the modes at the input o f the
junction. These amplitudes are expressed in the form o f a scattering matrix.
Incident mode
Z=Q
Figure A.3 Step junction between two smooth-walled waveguides o f different radius.
Let the transverse electric and magnetic modal functions [35], [42] corresponding to M modes on the
left side of the junction are represented byeral, hml and corresponding to N modes on the right side of
the junction are represented by en2, hn2. The transverse electric and magnetic fields on the left side
are represented as [35].
_
M
= X iA m
z)
+ B m expOmZ ) p ml
(A.23)
m=l
M
__
h x= Y jR
_
. exP(~ rmz) - Bmexp (ymz)}hml
(A.24)
m=1
where, Amand Bmare the forward and reflected amplitude coefficients of mode m on the left-hand
side o f the junction.
The fields on the right side are,
_
N
E2 = X
eXP(~YnZ) + Dn eXP(lnZ)^n2
(A-25)
exP (-r„ z) - Dn exp(y„z)^„2
(A.26)
n=l
_
N
H 2
=Z
M—1
where CHand Dnare the forward and reflected amplitude coefficients o f mode n on the right-hand
side o f the junction.
Matching the total transverse fields across the junction at z = 0 , gives
150
M
X (4n + A.)ewl
_
M
(A.27)
S (C » + C » fe
n=l
J»=l
N
£ (A --9.)*.,= £(c,+ f,fe
(A.28)
»=1
J»=l
The continuity of the fields and the orthogonality relationship between modes results into a pair of
simultaneous equations,
[i> ]p ]+ [£]]= f e l c ] + [£>1
(A.29)
(A.30)
where [A] and [S] are M-element column matrices in the section on the left-hand of the junction
containing the unknown modal coefficients Al to Au and Bx to Bu . Similarly, [C] and [.D] are Nelement column matrices on die right-hand side o f the junction containing the unknown modal
coefficients
C, to C^and Dl to DN. [P] is an N X M matrix whose elements are integrals
representing the mutual coupled power between mode i on the left-hand side and mode j on the right
hand-side. [P]T is transpose of [P], i.e., rows and column are interchanged. [Q] is an N X N diagonal
matrix whose elements are integrals representing the self coupled power on the right hand-side o f the
junction. [R] is an M X N diagonal matrix whose elements are integrals representing the self coupled
power on the left hand-side of the junction. The elements o f these matrices are given as [35], [42].
Pmn =
(A.31)
Si
& ,= J f c x A .iW ,,
s2
'
Rmm = j(emlX K l ) - d sl
sl
(A.32)
(A.34)
where st and s2are the cross-sectional areas of the waveguides of radius a, and a2respectively.
Equations (A.29) and (A.30) can be rearranged into the scattering matrix [S] formulation as,
(A.35)
[F] = [S][X]
where,
[s„] [s„r
[s] =
(A.36)
151
[7] =
[X] =
B
D
~A
C
The elements of [S] in terms of matrices [R], [P],[Q] are described in [35] and given as,
[*„]= N+t^ner^fh-iriferN
[s„]=4*]+[j»rEsrdpJ"t^r
(a j *)
f e ] = 2 l a l + M W ''W r r w
(a .40)
fej- -te]+M W M fteHd WW]
(A.4i)
Cascading of Scattering Matrices
A mode transducer geometry having tapered waveguide section between two uniform waveguides of
different cross-sections is shown in Figure A.4. The tapered section is approximated as series of
incremental step junctions. Scattering matrix for incremental straight waveguide section between two
step junctions should be known. This scattering matrix will be an N X N matrix having only diagonal
elements as Vim = e x p , where / is the length o f the incremental length of waveguide between
junctions. The scattering matrix due to step junction discontinuities and due to the incremental
lengths is cascaded progressively to obtain an overall scatter matrix for the geometry shown in Figure
A.4.
Corneal section
replaced with —' '
2=0
Injunctions
Figure A.4
^ ---------------
Smooth wall conical waveguide approximated by incremental step
junctions to apply mode matching using cylindrical modes.
152
If there are two scattering matrices [sa] and [s ^corresponding to two step junctions, then the
expressions for cascaded scattering matrix [sc ] are [35],
\scn] [Sc,2]'
h
M
M
<A -4 2 >
where,
[s e„ ] = [San J / ] - [Shn Jsra22
[ s \ , Is’a2. ]+ [.S'0,, ]
(A.43)
(A.44)
1 4 - S a22_ S > 4 ' S° 2,]
(A.45)
14-
(A.46)
S C2 , ’
S L22
II
[«'.,]=[sr-„I/]- [s‘,.Is-r, J- [s*„]
=
5*2,'
S fl22
s ‘„
r
S fl2 2 ] S fc1 2 ] + [ s ft2 2 ]
Similar to cascading of two matrices, one can cascade number o f scattering matrices corresponding to
different junctions in order to obtain resultant scattering matrix [S]. From the resultant matrix [S] the
characteristics of any conical horn can be found out from,
\M\
(A.47)
where, [A] and [B] are column matrices containing the forward and reflected coefficients of all the
mode looking into the horn from source side. [C] and [D] are column matrices containing the forward
and reflected coefficients of all modes looking into the aperture of the horn from the outside. The
reflection coefficient of the horn is [B] = [Sn][A]. The transmission coefficient of the horn is [D] =
[S21] [A], where, [A] is the matrix corresponding to incident mode which is assumed to be TEn mode
of circular waveguide.
153
HARD COPY OF INTERNATIOAL
PUBLICATIONS
IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES. VOL 53. NO. 8, AUGUST 2005
2604
Multifrequency Waveguide Orthomode Transducer
Shashi Bhushan Sharma, Vijay Kumar Singh, and Soumyabrata Chakrabarty
Abstract—This paper presents the design and development of
a multifrequency probe-coupled orthomode transducer (OMT)
using a circular waveguide as the primary waveguide and a
rectangular waveguide as the secondary waveguide. Design is pre­
sented for a common OMT operating at 6.6,10.65,18, and 21 GHz
using four cascaded circular waveguide sections with different
cross-sectional dimensions. An innovative design technique is used
to minimize the inter-port coupling and to maximize the power in
the dominant mode to get the required radiation performance at
all the frequency bands using a common radiating aperture. The
simulated and measured parameters of the OMT and the horn fed
by this OMT have been presented.
In this paper, a novel configuration for the OMT is presented,
which gives optimum performance in terms of mode purity, re­
turn loss, inter-port isolation, and radiation characteristics for
multifrequency band operation. This technique has been em­
ployed to develop a single OMT to operate at four frequency
bands at 6.6, 10.65, 18, and 21 GHz. Numerical data on simu­
lated modal amplitudes and comparison of simulated and mea­
sured return loss, isolation between ports, the radiation pattern
of corrugated hom [3] fed by the multiffequency OMT have
been presented.
Index Terms—Cascaded waveguide, corrugated horn, multifre­
quency orthomode transducer (OMT), probe coupling.
I. I n t r o d u c t io n
ICROWAVE radiometers operate in the receive mode at
widely separated frequency bands, which are sensitive
to geophysical parameters. A single aperture antenna operating
at all the frequency bands is preferred for radiometers since in­
dependent antennas for each frequency band will require larger
satellite space and weight. For scanning microwave radiome­
ters, an offset parabolic reflector antenna is generally used with a
corrugated hom, which is designed to operate optimally at mul­
tiple frequency bands [ 1]—[3]. For desired radiation patterns of
the multifrequency hom, an orthomode transducer (OMT) must
provide dominant mode purity at each frequency band at the
input of the hom. Higher order mode generation and coupling
between different frequency ports are major problems for the
design of a multifrequency OMT. Though OMTs have been in
use for a long time, the literature elaborating the analysis and de­
sign is limited. Design of dual-band OMTs and the techniques
for bandwidth enhancement are reported in the literature [4],
[5], To the best of the authors’ knowledge, the design of the
OMT for multifrequency operation for more than two frequency
bands is not available in the literature. For a common OMT op­
erating at four frequencies, the different waveguide sections cor­
responding to different frequencies have to be cascaded. As a re­
sult of cascading of waveguide sections with different cross-sec­
tional dimensions, the lower frequency waveguide sections be­
come oversized for higher frequencies and supports higher order
modes generated due to discontinuities in the form of junc­
tions (step or taper) between successive sections [6], [7] and
power-sensing probes or slots on the walls of the primary wave­
guide [8], [91.
M
Manuscript received October 21, 2004; revised January 18,2005.
The authors are with the Microwave Sensors Antenna Division, Antenna
Systems Group, Space Applications Centre, Indian Space Research
Organization, Ahmedabad 380 015, India (e-mail: drsbs@sac.isro.org).
Digital Object Identifier 10.1109/TMTT.2005.852754
II. D e s ig n
and
A n a l y s is
The design goals for this multifrequency OMT was to achieve
—23 dB or better isolation between two orthogonal ports,
- 1 7 dB or better return loss, and minimum insertion loss at the
frequency bands 6.6 GHz±125 MHz, 10.65 G H z±150 MHz,
18 G H z±200 MHz, 21 G H z±200 MHz. Additionally, higher
frequencies should be decoupled with the lower frequency
ports by —18 dB or better for the same polarization. In OMT,
coaxial probes [8] or slots [9] are used for power coupling.
Maximum power is coupled when a short termination is used
at a distance of \ g / 4 from the location of the probe, and the
depth of probe is chosen so as to match the impedance seen
by the probe to the characteristic impedance of the coaxial
line [8]. This configuration is not suitable in the case when
a common aperture corrugated hom is to be operated for a
number of frequency bands. For multifrequency OMT, different
waveguide cross sections, which correspond to the dominant
mode propagation at that frequency band, have to be cascaded
such that the cross-sectional dimensions at higher frequency
bands are at cutoff for the lower frequency bands. The wave­
guide sections for lower frequency bands become oversized at
higher frequencies and support higher order modes, which are
excited because of structural discontinuities. Apart from this,
the higher frequency dominant mode signal gets coupled to
the lower frequency power-sensing ports, thereby increasing
the insertion loss of the device. In the current case, the higher
order modes are generated because of: 1) transition in the form
of step or tapered discontinuity between two waveguides of
different cross sections and 2) a probe that senses power at a
lower frequency band acts as a radial discontinuity for higher
frequency signal. Since the design goal is to ensure dominant
mode purity at each frequency band, the higher order modes
have to be suppressed and all the frequency ports have to be
decoupled. The dominant mode purity at each frequency band
of the OMT will ensure the desired radiation patterns of the
corrugated hom antenna. Hence, it is worthwhile to estimate the
modal amplitude of different higher order modes generated be­
cause of the discontinuities, as discussed above. Finite-element
method (FEM)-based electromagnetic (EM) software [Ansoft’s
0018-9480/$20.00 © 2005 IEEE
SHARMA etal MULTIFREQUENCY WAVEGUIDE OMT
Fig 1
I
2605
M ultifrequency waveguide sections jcm ed w ith step junctions
High Frequency Structure Simulator (HFSS)] has been used to
estimate power of the different higher order modes and the EM
modeling o f the transitions and to am ve at an optimum design.
The design steps for the development o f a multiffequency mode
transducer are explained below.
A. Modal Analysis of Step Junctions
Fig 1 shows four straight circular waveguide sections A s,
B S,C S, and D„ jomed together to form stepped waveguide tran­
sitions When a pure T E n mode is incident in section A s. B x,
Cs, and D s corresponding to 21, IS, 10.65, and 6 6 GHz, re­
spectively, it is o f interest to evaluate the modal power in the
output waveguide section D s , which is oversized for 2 1 ,1 8 , and
10 65 GHz and supports the higher order modes generated due
to step junctions between waveguide pairs A s, B s, and B s, Cs,
and <7S, D s
For the three-dimensional (3-D) model o f the step junctions
used in HFSS, the diameters o f sections As B s, C„, and I ) ,
are chosen as 9 4 ,1 1 ,1 9 , and 32 54 mm for the propagation of
the dominant T E n mode at 2 1 ,1 8 ,1 0 .6 5 , and 6 6 GHz, respec­
tively The lengths o f the individual sections have been selected
as 3 4 ,5 3 , 54, and 78 mm, respectively The higher order propa­
gating modes supported at the waveguide section D s that feeds a
corrugated horn are T M oi, T E 21, T E 0i, T M u , T E 31> T M 2i,
T E 41, T E 12, T M 02, and T M 31 at 18 GHz Along with these
modes, additional propagating higher order modes at 21 GHz
are T E 51, T E 22, T E 02, and T M 12 A t 10.65 GHz, T M 0i and
T E 2i are the higher order propagating modes m section D s
The step junction discontinuities generally couple power in the
higher order T E ln.(n > 1) and TMxn (n > 1) modes From the
modal analysis results, it is found that the dominant mode pu­
rity is not achievable m section D s and almost half of the power
gets coupled to higher order modes (T M u and T E 12) at 18 and
21 GHz Additionally, step discontinuity also causes reflection
o f the input power
A corrugated horn fed by the mode transducer o f Fig 1
yields poor radiation performance The cross-pol level at 18
and 21 GHz degrades to —13.5 dB, as compared to the case
o f pure T E n mode, giving a cross-pol level o f the order o f
—27 5 dB In order to minimize reflected power and the power
coupled to higher order modes at higher frequencies, the step
junctions have to be replaced by gradual tapered junctions
Section II-B deals with design and modal analysis o f different
waveguide sections joined by tapered sections
B Waveguide Sections Cascaded With Tapered Sections
Fig 2 shows four circular waveguide sections At , B t, Ct . and
D t jomed together by a tapered section between two successive
waveguide sections The dimensions o f the straight waveguide
sections are same as mentioned above for Fig 1
The taper angle and length o f the tapered sections between
waveguide sections At , Bt (6 i,A i),B t, Ct (02, A2) and Ct ,D ts
( 63 , A3) have to he optimized m order to minimize the power in
the higher order modes and maximize the power m the desired
dominant T E n mode A' 3-D model o f the structure has been
inputted to Ansoft’s HFSS with the initial taper angle and length
o f the taper between two successive waveguide sections, and
optimization was earned out to minimize power m higher order
modes The optimum flare angles for the geometry are between
3 ° -6 °
j
The modal power was computed at the output waveguide sec­
tion (D t ) havmg the largest cross-sectional dimension consid­
ering a unity power incident at the input waveguide sections at
each frequency. It is found that, for optimum flare angles, the
power m the desired T E n mode is o f the order o f —0 044 dB
at 18 and 21 GHz and better at 10 65 and 6 6 GHz for the opti­
mized transitions. The power coupling in the higher order modes
is negligible and the reflected power is less than —21 6 dB at all
the frequencies The radiation pattern o f a corrugated horn fed
with the geometry o f Fig 2 exhibits symmetrical patterns and
cross pol better than —27 dB at all the four frequency bands
Thus, the desired radiation performance o f a corrugated horn
can be achieved at each frequency band if the horn is fed by
waveguide sections jomed with tapered sections, ensuring T E n
mode purity
C. Effect of Coaxial Probes
For exciting the T E n mode in the circular waveguide section,
a coaxial probe [8] is used Since a common aperture OMT is to
be used for all the frequency bands to excite the horn antenna,
the waveguide sections for individual frequency bands cannot
be short terminated for maximum power couplmg A s seen in
Fig 2, the waveguide section for the 6 6 -GHz frequency band
is terminated by waveguide section (Ct ) at 10 65 GHz through
a tapered transition, which is at cutoff for 6 6 GHz Similarly,
an 18-GHz section (B t) is at cutoff for a 10 65- and 21-GHz
section (A t) is at cutoff for 18 GHz In this configuration, the
location o f the probe from the cutoff region, which is m the form
o f a tapered transition, can be optimized for a particular depth o f
the probe for maximum power coupling to or from the primary
circular waveguide
Modal analysis using Ansoft’s HFSS was earned out at
21 GHz m the presence o f coaxial probes in 6 6-, 10 65-, and
18-GHz waveguide '•actions to con fu te the cower coupled
to the higher order in-vies in die on-nut s> -on Dt . Probe or
IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL 53, NO 8, AUGUST 2005
2606
TABLE I
Power (in D ecibels) in Dominant and H igher O rder M odes
in Section Dt for T apered S ections
In p u t
sig n al
freq u e
ncy
H ig h er-
TEn
21
18
10 65
ord er
m ode
GHz
GHz
port
GHz
66.
GHz
p o rt
p o rt
-2 83
-15 6
-25 9
-4 12
-18 2
p o rt
m odes
(G H z)
21
-9 56
-6 09
18
-8 55
-4 37
-2 2 0
10 65
-1 2 35
-1 36
< -99
< -99
66
< -4 0
-0 002
< -9 9
< -9 9
-7 2 9
< -9 9
post discontinuities generally couple power in the higher order
TEon, TM0„, (n > 1), and T E „i, T M „i(n > 1) modes.
The analysis results are shown in Table I for all frequencies.
The Table I shows that the power is coupled to higher order
modes and also to the lower frequency ports, which effectively
reduces the power m the desired T E n mode The return loss
also deteriorates to the order of —10 dB at 18 and 21 GHz due
to the presence of coaxial probes at 6.6 and 10 65 GHz.
In the presence of probes, the cross-polar performance of
a corrugated horn at 18 and 21 GHz deteriorates to around
—11 dB, as compared to -2 7 dB for the configuration of Fig. 2
where no probes are considered at lower frequency bands.
It has been found through simulation and also through an­
tenna pattern measurement that the cross-polar performance at
18 and 21 GHz gets improved if the depth of the probe at 6 6
and 10 65 GHz is reduced from its optimum value for maximum
power coupling and impedance matching Radiation pattern per­
formance is further improved if the higher frequency and lower
frequency ports of same polarization are decoupled However,
with the reduction of the depth of the probes, the impedance
matching gets deteriorated at 6 6- and 10 65-GHz ports, though
there is an improvement of cross-polar performance at 18 and
21 GHz Thus, the design challenge for this type of multifre­
quency mode transducer is to ensure mode purity in the output
section (Dt) at all the frequency bands and at the same time
to achieve optimum power coupling, impedance matching, and
port-to-port isolation. The overall design of the multifrequency
OMT is presented in Section E-D
D. Design o f Multifrequency OMT
The current design of the mode transducer is based on
coupling from primary cascaded circular waveguide sections to
output rectangular waveguides WR-137 for 6 6 GHz, WR-75
for 10 65 GHz, and WR-42 for 18 and 21 GHz The schematic
of the mode transducer (a circular-to-rectangular waveguide
end launcher) at 6 6 GHz is shown m Fig 3
The orthogonal ports at the same frequency band have been
separated by an axial distance of Xg/2 and the angular spacing
of 90° to achieve the desired isolation between the two ports
As described in Section E-C, the reduction of the depth of the
probes m the lower frequency waveguide sections from their
resonant depths (quarter-wavelength) improves the cross-polar
performance at higher frequency bands due to reduced power m
the higher order modes
The probe depths were reduced from resonant depths from
11 6 to 7 5 mm in the 6 6-GHz section, from 7 to 4.2 mm in
the 10.65-GHz section, and from 3 6 to 2 5 mm in the 18-GHz
section The undesirable effect of the reduction in the depths
of the probes is that the real part of the impedance seen by the
coaxial probe is reduced with a reactive impedance, which re­
sults in the deterioration of return loss at that frequency For
example, the simulated return loss with reduced depth probe is
only —4 5 dB, as compared to a full-depth probe, where it is
better than —17 dB at 6.6 GHz. The real part of the impedance
seen by the coaxial probe of reduced depth is transformed to the
rectangular waveguide impedance by multisection ridge wave­
guide sections [10], [11] by properly optimizing the heights and
widths of the ndge sections. The reactance due to the reduced
depth probe was cancelled by using a stub pin m the coaxial
section, shorting the inner and outer conductor of the coaxial
section (like a single stub), as shown in the Fig. 3 The shorting
pins at 18 and 21 GHz were not required in the coaxial sections
of the mode transducer The location of the steps of the ndges
in the rectangular waveguide with respect to the coaxial section
have been found to significantly affect mter-port isolation For
example, a displacement of 0 25 mm of the step from its op­
timum position of 0.5 mm from the onset of the coaxial section
reduced the isolation of the 18-GHz signal with a 6 6-GHz port
from —41 to —10 8 dB Step locations were optimized for best
isolation between lower and higher frequencies
Modal power distribution and coupling of power to other
ports have been computed in the presence of optimized mode
transducers consisting of optimized step transformers and lower
depth probes giving a best return loss at 6 6 and 10 65 GHz
The simulated results for the optimized mode transducers are
presented in Table E, which shows that the maximum power is
confined m the dominant T E n mode at all the frequencies The
return loss at 18 and 21 GHz with optimized mode transducers
also improved to the order of —15 dB, as compared to —10 dB
for the case of full depth coaxial probes present at lower fre­
quencies, as described in Section E-C The return loss at 6 6
and 10 65 GHz was optimized for better than —17 dB. Table E
shows improved port-to-port isolation and reduced coupling to
higher order modes than shown m Table I
At 18 GHz, the simulated radiation patterns of a horn fed
by the OMT of optimized step transformers and reduced depth
probes in the lower frequency sections are given in Fig. 4 Sim­
ulated results show 9 dB better cross-polar performance of the
SHARMA el a/.: MULTIFREQUENCY WAVEGUIDE UMT
2607
TABLE II
Power ( in D ecibels) in Dominant and Higher O rder Modes
in S ection D , in the Presence of Mode T ransducers
Input
signal
freque
ncy
(GHz)
Higher
modes
(dB)
21
-13.03
TE„
mode
(dB)
21
GHz
port
(dB)
-1.55
18
GHz
port
(dB)
10.65
GHz
port
(dB)
6.6
GHz
port
(dB)
-7.0
-22.0
-27.5
-18.0
-41.0
18
-13.01
-0.441
-21.7
10.65
-26.38
-0.068
<-99
<-99
6.6
-36.0
-0.005
<-99
<-99
-19.1
<-99
Fig. 4 Patterns of corrugated horn at 18 GHz with optimized mode transducers
at 6.6 and 10.65 GHz.
Fig. 5 Return loss for 6.6-GHz circular-to-rectangular waveguide mode
transducer for both orthogonal ports.
horn fed with the OMT of reduced depth probes than the full
depth probes in the lower frequency sections. This improvement
is due to the higher isolation with lower frequency ports and less
coupling to higher order modes.
The simulated and measured return loss and isolation be­
tween orthogonal ports is presented in Fig. 5 at 6.6 GHz.
The measured isolation between orthogonal ports at 6.6 GHz
is better than —36 dB at the specified bandwidth of 250 MHz.
At 10.65 GHz. —15-dB return-loss bandwidth of 300 MHz
is achieved by using circular-to-ridged rectangular wave­
guide mode transducer. Measured decoupling of —18 dB was
achieved for the 10.65-GHz signal with the 6.6-GHz coaxial
probe. An isolation of better than —29 dB was achieved be­
tween orthogonal ports over the band.
The measured results for an 18-GHz OMT are shown in
Fig. 6. The measured isolation between orthogonal ports at
Fig. 6
Return loss and isolation for 18-GHz OMT.
Fig. 7
Photograph and drawing of the eight-port OMT with orthogonal ports.
18 GHz is of the order of - 2 5 dB over the band. The measured
isolation of the 18-GHz signal is better than —30 and - 2 0 dB
with 6.6- and 10.65-GHz ports, respectively, for same polariza­
tion.
At 21 GHz, with the probe depth of 3.1 mm, -15-dB re­
turn-loss bandwidth obtained was 360 MHz. The measured
isolation between orthogonal ports is of the order of —25 dB
over the band. The isolation of the 21-GHz signal with 6.6
and 10.65 GHz was better than —20 dB over the band. The
measured isolation of the 21-GHz signal with the 18-GHz port
was only from —"7to —10 dB over the band, which could not be
improved due to the comparable size of the OMT at 21 GHz to
that of 18 GHz. The poor isolation adds to increased insertion
loss at 21 GHz. The measured insertion loss of the OMT is 0.5,
0.7, 1.1, and 1.6 dB at 6.6, 10.65, 18, and 21 GHz, respectively.
The photograph and drawing of the developed eight-port OMT
with orthogonal ports at all the frequency bands is shown in
Fig. 7.
A common aperture conical corrugated horn [3] yielding
good pattern symmetry and cross-polar performance when
excited with a pure dominant T E n mode was tested with the
current OMT at all four frequency bands. The horn [3] was
designed to feed an offset parabolic reflector of focal length to
a diameter ratio of 1.8, requiring an edge illumination angle
of ±13.65°. The measured co-polar and cross-polar radia­
tion patterns of the horn fed with this OMT are presented in
Figs. 8-11 for one polarization. Similar patterns are achieved
for orthogonal polarization The measured patterns at 21 GHz
showed slight asymmetry du< o a larger ratio of higher order
modes to dominant mode power, as or.mared to 18 GHz. A
IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL 53, NO 8, AUGUST 2005
2608
m . C o n c l u s io n
Fig 8
Radiation patterns of the horn at 6 6 GHz
A novel design of four frequency-band OMT to feed a
common corrugated horn has been presented. In the multi­
frequency environment, the methods of controlling power in
the higher order modes and improving isolation of higher
frequencies with lower frequency ports has been described
Modal analysis has been performed to estimate the effects of
symmetrical step, taper, and asymmetrical probe discontinuities
in the mam waveguide, particularly at higher frequencies An
optimum configuration of a multifrequency OMT yielding
a desired isolation of orthogonal ports, isolation of higher
frequencies with lower frequency ports of the same polariza­
tion, and maximum power in the dominant T E n mode has
been obtained Optimum radiation performance of the horn
excited with the presented OMT has been achieved for all four
frequency bands for both polarizations. It was not possible to
fabricate the OMT device as a single piece This was fabricated
in a number of pieces and assembled to make the eight-port
device. The sEght deviation of the measured data from simu­
lated data may be attributed to fabrication tolerances and minor
assembly and alignment errors The modal-analysis-based
design approach presented in this paper may be appEed to the
design of multifrequency OMTs at other frequency bands
Thetaldagree)
Fig 9
A cknow ledgm ent
Radiation patterns of the horn at 10 65 GHz
The authors thank Dr K N Shankara, Space Applications
Centre (SAC), Ahmedabad, India, for his support The authors
also acknowledge and are thankful for the help provided by the
Engineers of Microwave Sensors Antenna Division, Antenna
Systems Group, SAC.
References
Fig 10
Radiation patterns of the horn at 18 GHz
[1] E G Njoku, I M Stacey, and F T Barath, “The seasat scanning
multi-channel microwave radiometer (SMMR) Instrument description
and performance," IEEE J Ocean E n g , vol. OE-5, no 2, pp 100-115,
Apr 1980
[2] S B Sharma, “Antenna system for the multi-frequency scanning mi­
crowave radiometer MSMR," IEEE Antennas Propag. Mag., vol 42,
no 3, pp 21-29, Jun 2000
[3] S B Sharma and V K Smgh, “Design of common aperture hybrid mode
corrugated hom for multifrequency scanning microwave radiometer,”
IETF. Tech R ev, vol 16, no l,p p 47-52, Jan-F eb 1999
[4] J Uher, J Boememann, and U. Rosenberg, Waveguide components
fo r antenna feed systems Theory and CAD Norwood, MA Artech
House, 1993
[5] S J Skinner and G L James, “Wide band orthomode transducers,”
IEEE Trans Mtcrow Theory Tech , vol 39, no 2, pp 294-300, Feb
1991
[6] W J English, “The circular waveguide step discontinuity mode trans­
ducer,” IEEE Trans Mtcrow Theory Tech, vol MTT-21, no 10, pp
633-636, Oct 1973
[7] K Tomiyasu, “Conversion of T E n by a large conical junction,” IEEE
Trans Mtcrow Theory Tech, vol MTT-17. no 5, pp 277-279, May
1969
[8] W W S Lee and E K N Yung, “The input impedance of a co-axial
line fed probe m a cylindrical waveguide," IEEE Trans Mtcrow Theory
Tech., vol 42, no 8, pp 1468-1473, Aug 1994
[9] S. B Sharma, S B Cbakrabarty, and V K. Smgh, “Moment method
analysis o f a slot coupled circular waveguide orthomode transducer,”
Microwave Opt Technol L e tt, vol 34, no 4, pp. 285-289, Aug 30,
2002
larger ratio of higher order mode to dominant mode power is
due to the poor isolation of 21 GHz with the 18-GHz port
[10] T -S Chen, “Calculation of parameters of ridge waveguides,” IRE Trans
Mtcrow Theory Tech , vol MTT-5, no 1, pp 12-17, Jan. 1957
[11] S Hopfer, “Design of ndged waveguides,” IRE Trans Mtcrow Theory
Tech, vol MTT-3, no 10, pp 20-29, Oct 1955
SHARMA et al.: MULT1FRRQUENC . WaVRGUIDE v. V V
Shashi Bhushan Sharm a was bom in Moradabad, India, in 1947. He received the B.E. degree
electronics and communication and M.E. degree
in microwave engineering from the University
of Roorkee, Roorkee, India, in 1970 and 1972,
respectively, and the Ph.D. degree in microwave
engineering from Gujarat University, Ahmedabad,
India, in 1987.
He possesses over 32 years of academic and di­
versified research and development experience in the
design and development of antenna systems for satel­
lite communication and remote sensing. He is currently the Group Director ot
the Antenna Systems Group (ASG), Space Applications Centre (SAC), Indian
Space Research Orgainzation (ISRO), Ahmedabad, India. He has authored or
coauthored over 100 publications.
Dr. Sharma was the recipient of the 1992 Dr. Vikram Sarabhai Research
Award in the field of electronics, telematics, and automation for his outstanding
contributions to the development of various types of antenna systems for ground,
airborne, and spacebome systems.
Vijay K um ar Singh was bom in Bahraich Dis­
trict, Uttar Pradesh, India, on August 21, 1967.
He received the B.Tech. degree in electronics and
telecommunication engineering from the Jhuggilal
Kamlapati Institute of Applied Physics and Tech­
nology, Allahabad University, Allahabad, India, in
1990, the M.Tech. degree in electronics engineering
(microwavesi from the Institute of Technology,
Banaras Hindu University, Varanasi, India, in 1992,
and is currently working toward the Ph.D. degree at
Gujarat University, Ahmedabad, India.
Since, 1993, he has been with the Antenna Systems Group (ASG), Space Ap­
plications Centre (SAC), Indian Space Research Orgainzation (ISRO), Ahmed­
abad, India. Working as Project Manager for Radar Imaging Satellite (RISAT),
as well as Oceansat-II missions, he is currently involved in the design and devel­
opment of spacebome active phased-array antennas and scanning scatterometer
antennas, respectively. His area of interest is multimode couplers, transducers,
wide-band multifrequency feeds, reflectors and dual-polarized microstrip an­
tennas for satellite remote sensing application.
2609
Soum yabrata O n krabarty was bom on January
3, 1966, in the Karimganj District, Assam, India. He
received the B E. degree in electronics and telecom­
munication engineering (with honors) from Gauhati
University, Guwahati Assam, India, in 1988, the
M.E. degree in electronics and telecommunication
engineering from Jadavpur University, Calcutta,
India, in 1992. and the Ph.D. degree in engineering
from the Indian Institute of Technology, Kharagpur,
India, in 1996.
He is currently with the Antenna Systems Group
(ASG), Space Applications Centre (SAC), Indian Space Research Orgainzation
(ISRO), Ahmedabad, India, as Senior Scientist/Engineer and Deputy Divisional
Head of the Microwave Sensors Antenna Division, where he has been involved
in the development of antennas related to microwave remote sensing. His area
of interest is computational electromagnetics, microwaves, and millimeter-wave
antennas.
Analysis of a Post Discontinuity in an Oversized
Circular Waveguide
Shashi Bhushan Sharma, Senior Member, IEEE, Vijay Kumar Singh, Ranajit Dey,
Soumyabrata Chakrabarty
Abstract— This paper presents the analysis of scattering
characteristics of a radial post in circular waveguide using
Method of Moments (MoM). Electric type dyadic Green’s
function has been used to compute scattered field in the
circular waveguide considering one dimensional current in the
axial direction of the post. The point of observation has been
taken on the surface of the post as a line. Simulated data on
return loss and power coupling in the dominant mode and
higher order modes have been compared with the data
computed using Ansoft HFSS. The data on return loss as a
function of frequency has also been compared with
experimental data.
Index Terms—Circular waveguide, Green’s function, higher
-order modes, method of moments, multi-frequency mode
transducer, post discontinuity.
I.
I n t r o d u c t io n
Different configurations of symmetric as well as
asymmetric waveguide discontinuities are utilized to realize
a number o f passive microwave components. Asymmetric
discontinuities such as radial posts in waveguides are used
in a variety o f microwave filters, tri-mode matched horn
feeds [1], [2] and mode transducers [3]. Higher-order TE2i
mode in circular waveguide is generally excited using radial
posts [2] in the horn feed to obtain better cross-polar
performance o f an offset parabolic reflector antenna [1] by
matching the cross-polarization component o f the reflector
focal-field distribution. The mode transducers capable of
operating at number o f widely separated frequency bands
[3] use cascaded sections o f probe or slot coupled
waveguide junctions with each junction supporting
dominant mode at a particular frequency band. The probe at
lower frequency band acts like a post discontinuity and
generates a number o f higher-order modes. Since, the
waveguide junction at lower frequency band is oversized at
higher frequency bands, this will support some o f the
higher-order modes generated at the post discontinuity.
These propagating higher-order modes have special
radiation characteristics which influence the overall
radiation pattern o f the feeds excited by the multi-frequency
mode transducer. It is therefore, worthwhile to investigate
the scattering characteristics o f a post loaded circular
waveguide to get an insight about the behavior o f higherorder modes which in turn provides more insight into the
Manuscript submitted for publication in IEEE Transactions on Microwave
Theory and Techniques (IEEE MTT), August, 2008.
The authors are with Antenna Systems Area, Space Applications Centre
(SAC), Indian Space Research Organisation, Ahmedabad- 380 015, India,
e-mail: drsbs@sac.isro.gov.in.
design o f multi-frequency mode transducers and matched
feeds.
The available literature on the analysis o f a post in a
circular waveguide is very much limited. X. H. Zhu et. al
[4] have presented the analysis o f a pair o f metallic post in a
circular waveguide using multi-strip current representation.
In [4], data on equivalent susceptance of frosts has been
presented. Simulated and experimental results for the
reactance of the post discontinuity in circular waveguide are
presented in [5], The literature [4], [5] present the analysis
o f post discontinuity in circular waveguide supporting only
the dominant TEU mode.
To the best o f authors’
knowledge, no other literature deals with the higher-order
mode scattering properties o f metallic post in circular
waveguides.
In the present paper, a post discontinuity in a circular
waveguide has been analyzed using the Galerkin’s MoM
considering the entire domain basis functions. Dyadic
Green’s function for the radial current has been derived
using the approach as given in [6], The moment method
formulation has been employed by approximating the
induced current on the post as a line current and also taking
the testing point on the surface o f the post as a line. Return
loss characteristics and the power coupled to higher-order
modes have been found out for various heights o f the post.
The data on the scattering parameters computed by the
present method have been compared with HFSS to justify
the validity o f the present analysis. Experimental data on
return loss o f the dominant TEU mode have been compared
with the data computed by the present method. Close
agreement has been observed between the experimental and
computed data o f the return loss, r
II. A n a l y s is
The geometry to be analyzed is shown in Fig. 1.
Fig. 1 A circular waveguide loaded with a post discontinuity.
2
It consists o f a circular waveguide with a radial post
discontinuity. The incident TE A mode polarized in the
direction o f the post induces electric current on the post.
The induced current on the post generates infinite modes in
TE and TM configuration in both the directions Depending
on the size o f the waveguide some modes will be
propagating while the other modes will be evanescent The
From equations (3)-(5), the expression for the required
Green’s function can be written as
G p p > (p J > z ,p \< P ,z ') =
-JCOfl
ZZ
™=1 B=1
2
m
'2xe»ma>mnymna m,pp
■J m & m n P ) Jm(Ym
„P)
mnr
tangential components o f total electric field E' at the
surface o f the post is zero. An electric field integral
equation can be developed from this boundaiy condition as,
COS(»J#)COS(m#’)
00 CO
+- J
2m
E l
2 7te0ma>mny mn
»=0«=1
8_
E mc + E S = E ‘ = 0
E mc = - E s
(i)
dp
dp
(6)
z> z
■cos(m $)cos(m 0)
Es represents scattered field from the post and is given by
E(fi4,z) =
■J(p)dfi
(2)
G on'(P ’ 0>s’ P,’ fi> z') ~ - ~ r L
2
pp
Where, G^ip^z^p,<j>, £ ) is the dyadic Green’s function
which has been derived following the approach given in [6]
In [6], the Green’s function is derived with one end o f the
waveguide shorted and the other end terminated at a
perfectly matched load. But in the present case the Green’s
function is derived considering both ends o f the waveguide
terminated with matched loads.
Considering all the TEn,n and TMmn modes o f circular
waveguide, the radial component o f electric type Green’s
function ( G^.) for z > z can be written as [6],
1
30
00
G pp. { p j , z , p ' ^ , z ' ) = - — Y 2
,
,
m
^ K S nm0 im nY mna m n P P
Jm(j'nmp ') J m(rmnP) e<lm"Z cos(m0)cos(mdi )
. J
^
a.
XX
2 cos W*=0
•A ( J m ( r m„ p y ) ^ ( J m(YmnP ) ) eC
Bp
Bp
.c o s ( m 0 ) c o s ( m 0 ')
Cmn(P
XX
s t r
; z< z
(?)
EP m=l n=1
y mn, a mn are the cutoff wave numbers and phase constants
cos(m0) J m(ymnp ) & **'”
*
°0 05
XX
m=0 n=1
+
respectively for TEmn modes and represented by
Cmn(P ><l>'’ Z ')
y
COS
.
4 mn
(3)
dp
The expression for radial component o f the electric type
Green’s function for z < z may be obtained by changing the
sign o f argument o f the exponential terms in (3)
X
-S S L
a
rln
_____
a rm= jfimn~^Yan~k
Where
X mn
is
the
m - 1 ,2, 3 . .a n d n - 1 ,2 ,3 . .
nth root
of
J m(x)
=0.
Similarly y mn, a tm are the cutoff wavenumbers and phase
where, c mn( p ,<f>',z') and Cmn ( p
have been
constants respectively for TM™, modes and represented by
derived by following the approach given in [6].
c mn( P , f t , z ') =
■— —— T — f - Gm(>m„P))
m(°mnltmna mn &P
co s ( m $ ‘)e <w
(4)
m
Jm(r'm»P)
2
^ P .m ^ m rP m n P
a mn = jP nrn = - J / L ~ ^
> m =0,1 ,2 ,3 ,...... and
n=l,2,3,
where, Xmn is then* root o f J m( x ) = 0 .
.c o s ( m < f ) e am,z
(5)
The unknown surface current J ( p ) o f equation (2) on the
post can be expressed in terms o f basis functions as
3
HI
(8)
• /(p )= £ / , / »
p=i
where
fp(p) is entire domain basis function given by
s m ( p k ( p - a + h))
fp
, p = 1, 2 N
(9)
sm (kh)
Taking the inner product o f the equation (1) with testing
function f q (same as the basis function-Galerkin’s
technique), we have
<f g, ES>=<f q, ~ E mC>
where
sm(qk(p - a + h))
sm (kh)
fq
l EJg(p)dp
(10)
,q = 1,2,
N
=-\ E lncf q{p)dp
( 11)
(12)
p
p
Using equations (2), (8) and (10), we get
z')fg(P)dpdp’
J j X / p /p (P ') Gv ( P > <M > P
p p'p->
= - f EmJg(P )dp
(13)
p
11
p=1
(p ')Gpp.(p,<l>, *, p ’A
fp
W
) f g
(P)4>4p
p p'
=~1^/,( pMp
(14)
P
The above equation can be expressed in matrix form as
[z ][/H f ]
(15)
where the elements o f the matrix [Z] and matrix [V] are
zm
=11
as)
pp
Vq = - \ E acf g(p)dp
(17)
P
where £
—_
cos(<»-f1( ^u-p)
P7i(*u) VnKx’, , ) 2 - ! )
-fin*
w h ere,
x lt = 1 .8 4 1
The integration limits for both p and p r are from (a-h)
to a Matrix [I] contains unknown coefficients o f the
current distribution on the post Solution o f matrix
equation (15) w ill give the unknown coefficients (Ip) and
putting these values o f coefficients m equation (8), the
current j(p') on the post surface can be computed Once
the current is known, the scattered field corresponding to
different modes and the other electrical parameters o f
interest can be found out
RESULTS AND DISCUSSION
Using the above formulation a computer program has
been developed using MATLAB
D ie scattering
parameters have been computed for a circular waveguide o f
diameter 32 54 mm with a circular cylindrical post o f
diameter 1 6 mm 16 pomt Gaussian integration has been
used to solve the integral expressions given in equations
(17) and (18) Sixteen TE and TM modes have been taken
to ensure converged solution. Return loss for the mcident
TEn mode m the circular waveguide is shown in Figure 2
The return loss has been plotted for different heights o f the
post As shown in these plots, the return loss becomes poor
when the post height is increased At 10 GHz, it becomes 16 dB for a post height o f 11 mm as compared to -54 dB
when there is no post
Ripple like behavior has been
noticed in the return loss plot over the 7 to 14 GHz
frequency band The plot has dips at 9 GHz 12 4 GHz
indicating improved return loss performance These dips
occur independent o f the height o f the post for a fixed size
o f waveguide. The dips show frequency sensitivity only
when the size o f the waveguide is changed as shown in
Figure 3 For larger size waveguide, the response and dips
move towards lower frequency and for lower waveguide
size they m ove towards higher frequencies
The
frequencies where dips occur can be selected as higher
frequency bands for a multi-frequency mode transducer so
that they are least affected due to the presence o f post at
lower frequency
The power carried forward in the
dominant TEU mode is shown m Figure 4 This plot also
shows that maximum power is confined m the dominant
TE h mode where dips occur in the return loss plot Above
7 GHz, the waveguide becomes oversized and supports
higher-order modes The power coupled to higher- order
TMjn, and TE^, modes have been computed and it has been
found that the power couples significantly to higher- order
asymmetric TMoi, TE2 1 , TE3! modes and it shows
negligible coupling in the TM]n and TE]n modes The
power coupled to TMoi mode for different heights is shown
in Figure 5. The power in TE 2 1 and TE31 modes is shown
in Figure 6 and 7 respectively. The results for higher-order
modes show that a particular higher-order mode gets
coupled only at a frequency where the waveguide size
becomes above cut o ff for that mode The power in higherorder modes increases with post height As shown in
Figures 2 to 7, the results computed from the present
method are m close agreement with HFSS results In order
to verify the simulated results, the appropnate hardware
has been developed (Figure 8) The measurements were
earned out for the post height o f 11 mm in the frequency
range o f 7-9 GHz and the results are plotted in Figure 9
As shown m Figure 9, the measured and the simulated
results are m close agreement Slight deviation above 8 4
GHz may be attnbuted due to the fact that WR-137 works
up to 8 2 GHz, w hile the measured values are presented up
to 9 GHz
o 8 g
4
PostTi i ’ight 11mm (Prese i iM etfiod^
x x x Post
11mm (HFSS)
------- Post Height 7mm (Present Method)
Post Height 5mm (Present Method)
w v *r Post Height 3mm (Present Method)
a a a
S11 (dB)
» Post Height 3mm (HFSS)
• -• No post
-40
-50
■K. Jt
-60*1
9
^N '?‘t-Tr^T~TT
h m
10
11
Frequency (GHz)
12
13
14
Fig. 2 Return loss performance for a post discontinuity in a circular
waveguide.
7
8
9
10
11
Frequency (GHz)
12
13
14
Fig. 3 Return loss performance for different sizes of the waveguide with post
discontinuity.
Fig. 6 Modal power in TE:] mode as function of frequency for post height as
parameter.
12.50
12.75
13.00
13.25
13.50
Frequency (GHz)
13.75
14.0C
Fig. 7 Modal power in TE3i mode as function of frequency for post height as
parameter.
5
4
Post
» Post
( Post
V Fost
Post
3
Height
Height
Height
Height
Height
11mm (Present Method)
11n*n (HFSS)
7mm (Present Method)
5mm (Present Method)
3mm (Present Method)
-
£>
S21 (dB)
2
■2
-3‘
-5 -
8
9
10
11
12
13
14
Frequency (GHz)
Fig. 8 Hardware of circular waveguide with post discontinuity.
Forward Power in TM01 mode (dB)
Fig.4 Forward power for a post discontinjity in a circular waveguide.
y y v Pos' Height 11mm (Present M ethod |
-------- Pos Height 11mm (HFSS)
O 0 -0 Pos Height 7mm (Present M elhoc)
-------- Pos H ag ht 5mm (Present M elhoc)
X X K Pos H ag ht 3mm (Present M elhoc)
Frequency GHz)
Fig. 5 Modal power in TM(,i mode as function of frequency for post height as
parameter.
Fig. 9 Simulated and measured values of return loss for post height of
11mm.
IV. Cosci a
s io n
MoM technique using line current approximation for the
induced current on post has been used to find out the
scattering parameters in the circular waveguide. The effect
o f the post height on the reflection, transmission and
coupling to higher order inodes was analyzed. The analysis
shows that these parameters are very sensitive to the post
height. Computed data from the present method show close
agreement with the data computed using An soft HESS and
experimental data. The analysis presented in this paper can
be used in the design of multi-frequency orthomode
transducers, tri-ntode or matched feeds, tracking feeds and
mode couplers.
A i k n o w i r n iix iH N T
The authors thank Dr. R. R. Navalgund. Director SAC.
Ahmedabad for encouragement and support. The authors
also tiiank Prof. Dhaval Puja-a o f Minna University and the
Engineers o f Microwave Sensors Antenna Division.
Antenna Systems Area, SAC. Ahmedabad for extending
the help and the necessary support.
R h f i; r k m , t : s
[ i|
[2]
[3]
[4 j
j5 ]
[ 6j
K. M. Pra.saJ and Lotfbilah Shalai. "Im proving the symmetry o f
radiation patterns for offset reflectors illum inated by matched feeds.'’
/
f r unsi h lions on antenna and Propagation . vol. 30. no. 1.
pp. 141-144. January 1988.
Keyvan Bahadnri and Yahya Rahmat-Samh. " A tri-mode hunt feed
for gravitationally balanced hack to back reflector antennas." IEEE
International Symposium on Antenna and Propagation tAP S). pp.
43<>7-j400. 2000.
S. B. Shamtu. V. k . Singh, and S B Chakrabarty "M ulti-frequency
waveguide orthomode transducer." IE E E Trans. Stic row. Theory
Tech., vol. 53. no. 8. pp. 2604-26U9. August 2005.
X. il . Zhu. D. / . Chen, and S. J. Wang. " A m ultistrip nxmient method
technique and its application to die post problem in a circular
waveguide." IEEE Trans. Microw. Theory Tech., vol 39. no 10. pp.
1762-1765. O d I W I .
Qian ('. Xiui. Allan <i. W illiumson. and Michael J. N c\e. "Reactance
o f posts in circular waveguide " IH liii Irons. Microw. Thvon Tedi..
\u l. 55. no. 8, pp. 1685-1688. Aug. 20<>7.
Wilson W. S. I ee and I;. K.
Yung. "The input impedance of a co­
axial line fed probe in a cylindrical waveguide.” IEEE Trans.
M icrow. Theory Tech., vol. 42. no. 8. pp. 1468-1473. August 1094
Shashi Bhushan Sharma was born in
Moradubad, India in 1947. He received
B. E. in Electronics & Communication.
M. E. in Microwave Engineering, both
from the University of Roorkee in 1970
and 1972 respectively and Pli. D.
degree in Microwave Engineering in
1987 from Gujarat University. Dr. Sharma has more than
72 years o f
academic and diversified research and
development experience in t ie design and development of
antenna systems for satellite communication and remote
sensing. He has about lit ) publications to his credit. He
was honored in 1992 w ith Dr. Vikram Sarabhai Research
Award and Astraunautical Society o f India Award.2003
for Ins outstanding contributions to the development of
various types of antenna systems for ground, airborne and
spacebornc systems. Dr. Sharma is presently Deputy
Director. Antenna Systems Area (ASA). Space Application
Center. ISRO. India.
Vijay Kumar Singh was born on 2 1’1
August 1967 in Bahraich District of
Uttar Pradesh. India. He received B.
Tech.
in
Electronics
and
Telecommunication
Engg.
from
Allahabad Uimersttv m 1990 and M.
Tech, in Electronics Engg. from
Institute o f Technology. Benaras
University in 1992. Since. 1993. he has been with the
Antenna Systems Group in Space Applications Centre.
ISRO. Ahmedabad. He is involved in die design and
development of space-borne microwave antennas for
R1SAT and Scatterometer antennas. His area of interest is
mode transducers, multi-frequency feeds, -eflectors. beam
wave guides and microstrip antennas for satellite remote
sensing application. Currently he is pursuing Ph. D.
a
i
Ranajit Dey was Born in Kolkata.
India
in
1981.
Graduated
in
Electronics & Telecomm. Engg. from
Kalyani University, Kalyani in 2(3)3
and did his M E from Jadavpur
University
in
Electronics
&
Telecomm. Engg with specialization
in microwave Engg
in 2005.
Presently he is working in Space Applications Centre.
ISRO. His present areas o f research are computational
electromagnetics and spacc-borne antenna design.
Soumyabrata Chakrabarty was born
on 3,J January I960 iti Karimganj
District o f Assam. He obtained his B.
E. (Hons) degree from Gauhati
University in 1988. M. E. from
Jadavpur University m the year 1992
both
in
Electronics
and
t
Telecommunication Engineering and
Ph. D. degree in Engineering from Indian Institute of
Technology, Kharagpur in the year 1996. He is currently
working in Antenna Systems Area. Spa;e Applications
Centre. Ahmedabad as senior Scientist/Engineer and
divisional Head, microwave Sensors Antenna Division and
involved in the development o f antennas related to
Microwave remote sensing. His area of interest is
computational
Electromagnetics.
Microwave
and
Millimeter wave Anten
REFERENCES
1. K.L. Wong. Planar antennas for wireless communications, Ch. 3, Wiley,
New York, 2003.
2. F.S. Chang and K.L. Wong, Folded meandered-patch monopole antenna
for low-profile GSM/DCS dual-band mobile Phone, Microwave Opt
Technol Lett 34 (2002), 84-86.
© 2003 Wiley Periodicals, Inc.
PARABOLIC DISH ANTENNA WITH
OFFSET ELLIPTICAL MULTI-MODE
FEEDS FOR SPACE-BORNE REMOTE­
SENSING APPLICATIONS
S. B. Sharm a, V. K. Singh, and S. B. C h akrab arty
Antenna Systems Group
Space Applications Centre, ISRO
Ahmedabad, India
Received 14 March 2003
ABSTRACT: This paper presents the design and development o f a pen­
cil-beam scanning parabolic reflector antenna with new multi-mode el­
liptical feeds for space-borne scatterometer application. The feeds have
been laterally displaced in the focal plane o f the reflector in order to
achieve two squinted elliptical beams with the required angular spacing.
The asymmetry in the secondary beams has been realized by illuminat­
ing the reflector with elliptic sectoral patterns o f the elliptical feeds.
Sectoral patterns have been synthesized by coupling power into higherorder modes at the feed aperture. Using this new type o f feed, a gain
improvement on the order of 0.7 dBi has been achieved, as compared to
the reflector antennas illuminated by elliptic feeds o f nonsectoral pat­
terns. The computed and measured data on primary and secondary radi­
ation patterns have been presented. The desired gain, beam widths,
beam asymmetry, angular spacing between the beams, side-lobe level,
and cross-polarization level have been achieved. © 2003 Wiley Periodi­
cals, Inc. Microwave Opt Technol Lett 39: 138-141, 2003: Published
online in Wiley InterScience (www.interscience.wiley.com).
DOI 10.1002/mop. 11150
Key words: parabolic dish antenna; antenna feeds; remote sensing
1. IN T R O D U C TIO N
The scatterometer is a very useful microwave payload employed to
retrieve near-surface ocean-wind speed and direction in the field of
microwave remote sensing. The antenna subsystem of the payload
plays a very important role in deciding the overall performance of
Figure 1 Schematic diagram of the antenna with reflector, feeds, innerouter beams, and scanning axis
Figure 2 The schematic of the optimized elliptical feec (a = 2.567.
b = 2.47A, c = 1.18A. d = 1.09A. a , = 2.27A. b, = 2.18A, c, =
0.89A, d , = 0.80A. e = 0.77A. /, = 0.11 A. /, = 0.71A. /, = 2.75A)
the system. The pencil-beam scanning scatterometer antenna is
preferred over the fixed fan-beam scatterometer antenna because
of its advantages of high directional accuracy, continuous swath
with no nadir gap, simplified model design, smaller size, and easier
signal processing, as mentioned in the literature [1], The radiation
pattern requirement of the pencil-beam scatterometer antenna is to
realize two squinted high-gain inner and outer elliptical beams
with lev cross polarization and low side-lobe level. In order to
achieve squinted or angularly spaced beams, the feeds have to be
laterally displaced in the focal plane of the reflector. However, the
displacement of the feeds results in an increase of the side lobe
level and scan loss, which reduces the overall gain of the reflector
antenna. The gain of the reflector antenna can be increased by
using multi-mode feeds yielding sector-shaped patterns, such as
dual hybrid-mode corrugated feeds and multi-ring circular coaxial
feeds [2]. But these feeds yield symmetrical sectoral patterns and
almost symmetrical secondary radiation patterns for the required
offset of the feeds in the focal plane. Although the feed displace­
ment slightly broadens the secondary beam in the feed displace­
ment plane, that is not sufficient to meet the beam asymmetry
requirement. To meet the requirements of asymmetric secondary'
beams, generally elliptical reflectors illuminated by elliptical feeds
are used [3-5]. However, the radiation patterns of these feeds are
not sector shaped, as required to uniformly illuminate the reflector
to enhance the antenna gain. Moreover, the size of the elliptic
reflector with these feeds needs to be increased in order to meet the
required gain and beam widths, which was not permitted due to the
fixed size of the reflector on satellite deck. This necessitated the
development of a new elliptical feed for the parabolic reflector to
Figure 3
Developed elliptical feeds
r
' ‘’ Finite Element Method Baaed HFSS Simulator
Vertical Polarization
TE, n Modes
Mode Humber N
Horizontal Polarization
TE, n Modes
TM,n Modes
TM1N Modes
Amp
Phase
Amp
Phase
Amp
Phase
Amp
Phase
04988
04618
-601
-1 6 5
0 7236
01367
012
386
056430
0 5445
-1 3 5 8
-1 4 7 8
0 5892
01543-
49 1
92 8
achieve elliptical beams with the required gain and beam asym­
metry
In the present paper, the elliptical feeds have been designed to
yield different edge illumination tapers m the principal planes The
feeds have been displaced laterally m the focal plane of the circular
parabolic reflector m order to obtain two squinted inner and outer
secondary beams Since the lateral offset of the feed increases the
side-lobe level of the secondary pattern, the feeds have been
designed to provide larger edge taper in the offset plane so that
even after their displacement, the secondary beam side-lobe re­
quirement is met The feed yielding the inner beam is horizontally
polarized and the feed yielding the outer beam is vertically polar­
ized The elliptical feeds presented in this work consist of elliptical
rings similar to the concept of circular coaxial feeds The elliptical
feeds were modeled on a high-frequency structure simulator (Agi­
lent HFSS 5 6) based on the finite-element method (FEM) The
parameters of the feeds have been optimized to obtain the required
amplitude and phase distribution m the dominant and higher-order
modes m order to synthesize the sector-shaped elliptical radiation
patterns The secondary patterns, corresponding to the simulated
and measured primary sectoral patterns, were simulated using
GRASP8W software (TICKA)
A comparison of measured and simulated results for the pri­
mary patterns is presented The simulated and measured secondary
radiation patterns for displaced feeds, as well as feeds at the focus,
are also presented
2. DESIGN
The reflector antenna has been designed at 13 73 GHz to yield
inner and outer beam spacmgs of ~2 IS* from the reflector axis, a
gam of 42 5 dB, 3-dB beam widths of 1 17° and 1 40° m the E and
H planes, respectively, a side-lobe level of - 1 6 dB, and a crosspolanzation level of —22 dB Figure 1 shows the schematic
diagram of the antenna, including feeds, reflector, inner and outer
beams, and antenna scanning axis The bandwidth requirement
was ±50 MHz The secondary gam and 3-dB beam widths depend
on the size of the reflector Within the allowed space on the
satellite deck, a reflector diameter of 1 2 m was selected The F/D
ratio of the circular parabolic reflector was selected as 0 4, requir­
ing a ±64" reflector-edge illumination angle A larger F/D ratio
would have resulted m less scan loss due to feed displacement, but
an F/D greater than 0 4 increases the lengths of the spars to hold
the feeds, which was not permitted due to the fixed satellite
envelope The amplitude1taper of the radiation patterns of the
multimode elliptical feed! should be —10 dB in the E plane and
—16 dB in the H plane, respectively, at the reflector edges in order
to achieve different 3-dB secondary beam widths m the E and H
planes for the respective squinted beams This was verified by
using TICRA’s GRASP8-W software It was also found from the
simulated results that the elliptical feeds should be displaced
laterally by ±27 5 mm across the focal point m the focal plane of
the reflector m order'to j achieve two squinted pencil beams at
± 2 75° with respect to the reflector axis, thus meeting the require­
ments of side-lobe level and beam width
As reported in the literature [2], the gam of the reflector antenna
can be increased by illuminating the reflector using feeds with
sector-shaped far-field radiation patterns The sector-shaped radi­
ation patterns can be achieved by distributing power into dominant
and higher-order modes with proper amplitude and phase at the
aperture of the feed
;
The multi-ring coaxial feed is the simplest feed to meet this
requirement The number of coaxial rings and their size decide the
number of modes excited and the amount of power coupled to the
various modes, respectively In order to achieve the ideal sector­
shaped illumination pattern of the reflector, a feed with innumer­
able coaxial rings would be required, which is not practically
feasible More than two; rings in the feed increase the blockage
loss Generally, one or two rings are sufficient to closely approx­
imate the sector-shaped1pattern The single nng coaxial feed is
light m weight and size and has been found to meet the required
secondary performance Therefore, m the present work, the ellip­
tical feed has been designed by introducing asymmetry or elhpticity m the aperture of the smgle-nng coaxial feed [2] As men­
tioned m [2], to obtain sector-shaped far-field patterns, the feed
aperture distribution for the circular multi-rmg coaxial feed, must
be of the following type
/(2-rrp/A) = 2J[(2-trp sin 0o/A)/2irp sin 0<A
= A,(2irp sin 0O/A),
Figure 4 Measured and simulated (HFSS) E- and H-plane primary
radiation patterns of the elliptical feed for vertical polanzanon
where p is the aperture radius in cylindrical coordinates, 0o is the
half angle at - 1 0 dB of the sectoral pattern of the feed
The mam aperture surrounded by the inner wall of the smglenng coaxial feed will yield the whole mam lobe, and the position
MICROViiAVE AND OPTICAL TECHNOLOGY LETTERS / Vol 39, No 2, October 20 2003
l
139
TABLE 2
Measured Parameters of Secondary Radiation Pattern for Vertical Polarization
Freq (GHz)
Plane
Computed 3-dB
Beam Width (°)
13 67
E-plane
H-plane
E-plane
H-plane
E-plane
H-plane
120
141
1 17°
140°
1 18
144
13 73
13 79
Measured 3-dB
Beam Width
f)
I 18°
1 38
1 15°
1 38°
1 15°
1 42°
of the outer wall of the ring will produce the first lobe of the A,
function Therefore, the ring's inner wall position p, will corre­
spond to the first zero of the J x(x) function, that is, x x = 3 85
Then we have 2irp,sm G0/A — x x = 3.85, similarly, the second
zero of the J x(x) function, x2 = 1 02, will give the position of the
nng’s outer wall for the smgle-nng coaxial feed Therefore,
27rp2sin 0O/A = x2 — 7 02
Initially, the dimensions p, and p2 of the smgle-nng feed were
computed at a design frequency of 13 73 GHz, corresponding to
th e ..10-dB beam width on the order of 64°, which is the required
edge-illummation angle of the reflector, and the depth of the choke
was chosen as quarter of a wavelength But this design approach
gives 2J x(x)/x distnbution at the aperture where the choke size is
not sufficient enough to couple power in the higher-order modes to
obtain the required sector shape patterns
The dimensions based on the above design approach, which
yield less power coupling to higher-order modes, have been used
as initial parameters to optimize the dimension of the highly
coupled choke by using HFSS The required weighting of the mam
lobe was achieved by coupling the power into higher-order modes,
which was m turn achieved by increasing the surface of the first
choke, that is, by decreasing the position p, of the choke Asym­
metry was introduced in the aperture shape by increasing the
H-plane dimension of the feed Finally, the elliptical feed’s aper­
ture asymmetry, choke size, and choke depth were optimized in
order to obtain maximum coupling m the higher-order modes and
thus achieve the required pattern asymmetry, VSWR, and crosspolanzation level
The schematic of the optimized elliptical feed is shown m
Figure 2 The developed elliptical feeds based on these optimized
dimensions are shown m Figure 3
Secondary Patterns w ith Elliptical Feed at Focus
Computed
Side-Lobe
Level (dB)
-1 8 7
-1 5 4
,
-1 8 5
-1 6 0
-1 8 2
- 1 6 84
140
Secondary radiation patterns when the elliptical feed is kept at
Computed
Gam (dB)
Measured
Gain
(dB)
42 60
42 29
42 80
42 50
42 65
42 30
- 1 7 64
-1 4 5
-1 7 5
-1 5 20
- 1 7 21
- 1 5 97
The computed modal amplitudes and phases m the dominant
TEn mode and higher-order modes, namely, the TM U, TE12,
and TM,2 modes at the aperture of the feed for vertical and
horizontal excitation of the feed at its input, are presented m
Table 1
3. RESULTS AND DISCUSSIONS
The two displaced elliptical feeds are linearly polarized and one
feed is vertically polarized while the other is horizontally polar­
ized The measured radiation patterns for vertical polarization
show that the 10-dB beam widths of the elliptical feed are 68° m
the E plane and 52° in the H plane, respectively In other words,
the amplitude tapers of the feed are —10 1 dB m the E plane and
—15.8 dB m the H plane, as required to illuminate the reflector
with an edge-illumination angle of ±64°
The comparison of measured and predicted patterns of the
elliptical feed for vertical polarization excitation is presented m
Figure 4 The measured H-plane pattern of the elliptical feed is in
fairly good agreement with the predicted patterns obtained using
HFSS software The elliptical feed patterns have also been mea­
sured for horizontal polarization In this case, the measured am­
plitude tapers of the feed are slightly narrower than that of the
vertical polarization - 1 0 8 dB in the E plane and —16.9 dB in the
H plane, corresponding to the reflector edge-illummation angle of
±64°. This narrowing of the primary pattern slightly broadens the
secondary beams, thereby increasing the 3-dB beam widths by
004° for horizontal polarization, as compared to the feed with
vertical polarization
The measured return loss of the feed is on the order of 25 dB
and the cross-polanzation level is better than —22 dB over a
bandwidth of 500 MHz for both polarizations
Secondary Patterns w ith Elliptical Feed O ffset ay 27 5 m m m the Focal Plane
Angle(Degree)
Figure 5
focus
Measured
Side-Lobe
Level (dB)
Angle(Degree)
Figure 6 Secondary radiation patterns of the displaced elliptical feed in
the focal plane
MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol 39, No 2, October 20 2003
dB, which is a 0.7-dB improvement over the reflector antenna
illuminated by dominant-mode elliptical feeds or rectangular
feeds. This antenna meets the requirement of a pencil-beam scatterometer antenna and can be successfully employed for remotesensing applications.
ACKNOW LEDGM ENTS
The authors thank Dr. K. N. Shankara, Director, Space Applica­
tions Centre (SAC) and Dr. Arun Kumar and Shri R. K. Malaviya
of the Antenna Sensors Group, SAC, Ahmedabad, for their con­
stant support and encouragement. The authors also would like to
acknowledge the help and support provided by the engineers of
AMD and MSAD of SAC, Ahmedabad.
REFERENCES
Figure 7
Developed reflector antenna with two displaced elliptical feeds
The feeds were integrated with the parabolic reflectcr of diam­
eter 1.2 m. Three spars of 20-mm diameter were used to hold the
two laterally displaced elliptical feeds in the focal plane of the
reflector. The two feeds were displaced from each other across the
focal point in the focal plane by 55 mm to obtain two squinted
high-gain pencil beams at ±2.75°. For displaced elliptical feeds,
the measured value of reflector gain at 13.73 GHz was found to be
on the order of 42.5 dB. In other words, overall efficiency on the
order of 60% has been achieved for the reflector antenna’s
squinted beams. The measured 3-dB secondary beam widths in the
principal planes were found to be 1.15° and 1.38°, respectively,
which are very close to the specified values of 1.17° and 1.40°.
When the feed was kept at the focal point, the measured secondary
gain was found to be on the order of 43 dB. This means that the
gain loss in the squinted secondary beam due to the feec displace­
ment is on the order of 0.5 dB. The measured side-lobe and
cross-polarization levels of the secondary squinted beams were
found to be —15.2 dB and —25.2 dB. respectively, at the center
frequency.
Measured parameters of secondary radiation pattern for vertical
polarization are presented in Table 2.
The measured and computed secondary radiation patterns for
the elliptical feeds kept at the reflector focus, as well as laterally
displaced at ±27.5 mm from the focus, are presented in Figures 5
and 6, respectively. The measured results show that the squinted
beam peaks are at ±2.75°, corresponding to a ±27.5-nm lateral
shift of the feed in the focal plane. Therefore, for the center-tocenter distance of 55 mm between the displaced feeds, the angular
spacing between the two squinted secondary beams has been found
to be 5.5°, as required. A photograph of the lab model of the
reflector antenna, integrated with the displaced elliptical feeds, is
shown in Figure 7.
4. C O N C L U S IO N
The reflector antenna has been designed and developed at 13.73
GHz to achieve a beam squint of ±2.75° from the reflector axis, a
squint-beam gain of 42.5 dB, 3-dB beam widths of 1.15° in the E
plane and 1.38° in the H plane, a squinted beam side-lobe level of
—15.2 dB and a cross-polarization level of —22 dB, which are in
close agreement with those specified. An elliptical coaxial multimode feed, giving sector-shaped elliptical radiation patterns, was
realized. It was shown that the measured primary patterns of the
elliptical feed closely match the predicted patterns. Measured
secondary patterns are also fairly well matched with the simulated
results. The measured gain was found to be on the order of 42.5
1. M.W. Spencer, C. Wu, and D.G. Long, Tradeoffs in the design of a
spaceborne scanning pencil beam scatterometer: Application to sea
winds, IEE Trans Geosci Remote Sensing 35 (1997), 115-126.
2. P. Brachat, Sectoral pattern synthesis with primary feeds, IEEE Trans
Antennas Propagat 42 (1994), 484-491.
3. E. Lier, Broadband elliptical beamshape horns with low cross polariza­
tion, IEEE Trans Antennas Propagat 38 (1990), 800-805.
4. E. Lier and S. Rengarajan, Radiation from elliptical hybrid-mode
waveguide, IEE Proc H (1990), 417-419.
5. E. Lier, Y. Rahmat-Samii, and S. Rengarajan, Application of rectangu­
lar and elliptical dielcore feed horns to elliptical reflector antennas,
IEEE Trans Antennas Propagat 39 (1991), 1592-1597.
© 2003 Wiley Periodicals, Inc.
A DUAL-BAND CHEBYSHEV
IMPEDANCE TRANSFORMER
G. C a s ta ld i,1 V. Fiu m ara,2 and I. M . Pinto1
1 Wavesgroup
University of Sannio at Benevento
Benevento, Italy
2 University of Salerno
Dipartimento di Ingegneria dell'lnfornazione ed Ingegneria Elettrica
via Ponte don Melillo 1
84084 Fisciano (Sa), Italy
Received 18 March 2003
ABSTRACT: This paper presents a simple extension o f the Chebvshev quarter-wave multisection transformer synthesis to dual-band
operation. The method is a variation o f the classical Chebyshev
transformer design procedure, using a suitable 2nd-order trigonomet­
ric polynomial as the argument o f the Chebyshev polynomial. As
compared to a single-band Chebyshev transformer encompassing
both required passbands, the proposed design yields significantly bet­
ter performance. © 2003 Wiley Periodicals, Inc. Microwave Opt
Technol Lett 39: 141-145, 2003: Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.l 1151
Key words: dual-band; impedance transformer; Chebyshev polynomial
1. IN T R O D U C TIO N
Impedance matching is a classical topic in microwave engineering,
which arises in a wide variety of microwave systems [1, 2]. In
many cases of practical interest, including dual-band mobile tele­
phony, impedance matching over two separated frequency bands is
required. Developing new design methods to synthetize dual-band
(or even multi-band) impedance transformers is thus a topic of
renewed interest [3],
MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 39, No. 2, October 20 2003
141
M u ltifre q u e n c y c o rru g a te d fe e d w it h
g ro o v e d is c o n tin u ity a t in p u t
S B Sharma and V.K. Singh
The design of a multifrequency feed system for the microwave
radiometer for Ocean Sat-II satellite covering 18 7, 23 8 and
36 5 GHz frequency bands is leported A groove discontinuity is
introduced at the input of the corrugated horn to optimise
amplitude taper and the symmetry of pnmary patterns at the
highest frequency without affecting the performance at lower
frequency bands Computed and measured radiation patterns are
compared at all the frequencies
Intioduction Multifrequency operation is often necessary for
space-borne microwave radiometers Commonly, prime focal-fed
parabolic reflectors havmg lower focal length-to-diameter ratio are
used owing to the constraints of the dynamic envelope on the sat­
ellite bus The feed radiation patterns for such reflectors exhibit
mcreased frequency sensitivity for the specified maximum-to-mmimum frequency ratio of 2 1 The feed patterns become very nar­
row at the highest frequency, rendering undesired secondary
radiation characteristics A conventional corrugated horn cannot
cover all frequency bands since it offers best performance only for
the 161 frequency ratio [1, 2] Dual-depth corrugated horns [2]
also have limitations in maintaining horn characteristics if the two
frequency bands aie separated by more than the 1 6 1 ratio The
ring loading of corrugated horns [1, 3] can meet the frequency
ratio of 2 1, however, the radiation patterns with this feed become
too narrow at the highest frequency to provide the required ampli­
tude taper at the reflector edges In this Letter a new technique is
described which is used to provide beam broadenmg as well as
pattern symmetry at 36 5 GHz without affecting the radiation pat­
terns at lower frequencies
§-20
Io
c o r ru g a tio n s
1 8 7 G H z p o rt
-10
to ta l n u m b e r = 1 8
a- - 3 0
2 3 8 G H z p o rt
c ir c u la r
w a v e g u id e
s e c tio n s
-4 0
X
-1 8 0
-1 0 8
-3 6
36
108
180
th e ta , d e g
3 6 5 G H z p o rt
[
g ro o v e
d is c o n tin u ity
Schematic dtagiam o f imdttfiequenct cotiugatedfeed with gioove
discontinuity
F ig
to
o
o
t | 11 I I T"t t I
.T
18mm, n d = 1 5m m, p t = 2 0m m , u = 6 3mm, d = 1 8mm, D\
14 4m m , D2 = 10 1 mm, Z>3 = 81 mm D4 = 5 4 m m
i
I
o
.£»
6
p o w e r, d B
-
1
o
IIII|
D
-1 8 0
-1 0 8
-3 6
36
108
180
theta, deg
1901/21
Computed and measwed tadiation patterns with gioove at
IS 7 GHz
F ig .
901/4 |
Computed and measwed ladiatton patterns with and without
gioove at 36 S GHz
F ig .
2
— -—
E-plane computed
--------- H-plane computed
—• — E-plane measured
—V —~ H-plane measured
- measured cross-polarisation
ELECTRONICS LETTERS
30th August 2001
Vol. 37
4
— —— E-plane computed
--------- H-plane computed
—• — E-plane measured
—V-— H-plane measured
—■ — E-plane measured without groove
— + — H-plane measured without groove
- - • — measured cross-polansation
Design The multifrequency prune focal feed was designed at
18 7+0 2, 23 8+0 3 and 36 5±0 5 GHz to yield secondary sidelobe
levels and cross-polar radiation below -30 and -25 dB, respec­
tively The focal length-to-diameter ratio of the parabolic reflector
is selected as 0 5, requiring a +50° reflector edge illumination
angle To achieve required specifications of the secondary pattern
symmetry, sidelobe levels and beamwidths, the amplitude taper of
the primary patterns of the feed should he within -12 to -18 dB at
the reflector edges for all the frequency bands
Cascaded waveguide sections at different frequencies were
designed to give TEU mode punty at the mput of the corruga­
tions The power at each waveguide section was coupled through a
matched circular to a rectangular waveguide transducer The horn
aperture, corrugation depths and corrugation width-to-pitch ratio
were selected for best radiation performance at 23 8 GHz to
achieve the bandwidth ratio of 161, i e from 18 5 to 30 GHz,
however, this aperture size and the corresponding corrugation
depths give rise to a very narrow mam lobe at 36 5 GHz, and the
sidelobes start appearing within the illumination angle at this fre­
quency
The narrowing of the patterns can be overcome by introducingadditional TMii and TE12 modes at the mput of the corrugated
No. 18
1121
hom. This is realised by providing a groove discontinuity at the
input of the horn.
The depth and width of the groove discontinuity in the presence
of corrugations and cascaded input waveguides were optimised
using CHAMP software to obtain symmetrical as well as the
amplitude taper. In the presence of a groove, the computed ampli­
tudes of TE,,, TM || and TE,2 modes at the input of the corru­
gated hom are 0.84, 0.48 and 0.20, respectively, at 36.5 GHz. The
multifrequency corrugated feed employing a groove discontinuity
at the input of the corrugations is shown in Fig. 1.
Results and discussion: The measured co-polar radiation patterns
with a groove discontinuity at 18.7 and 23.8 GHz closely match
the computed patterns as shown in Figs. 2 and 3, respectively.
The radiation patterns with and without a groove were found to
be identical at 18.7 and 23.8 GHz and therefore patterns without a
groove are not included in Figs. 2 and 3. The measured radiation
patterns with and without a groove at 36.5 GHz are shown in
Fig. 4. As shown in this Figure the measured patterns without a
groove are very narrow and patterns with a groove are wider.
Although the measured patterns with a groove at 36.5 GHz do not
closely match the computed patterns these patterns clearly exhibit
the beam broadening effect due to the groove. The mismatch can
be attributed to the hom and power coupling waveguides not
being fabricated as a single piece. The worst case measured crosspolar patterns in the diagonal plane are shown in Figs. 2 - 4 .
Measured return loss at all the frequencies is shown in Fig. 5.
18.50
18.60
18.70
18.80
18.90
23.50
23.65
23.80
23.95
24.10
36.00
36.25
36.75
37.00
36.50
frequency, GHz
Fig. 5 Measured return loss at IS. 7. 23.8 and 36.5 GH: frequency bands
-
18.7GHz
36.5 GHz
- 23.8 GHz
Conclusion: The technique to generate T M n and TE12 modes
using a groove at the input of corrugations is very effective for
microwave radiometer feeds for prime focal parabolic reflectors
for multifrequency operation.
n i u i u i i i i d y e a D i e x m c K -T iim m i l l i m e t r e
metal-pipe rectangular waveguides
M.S. Aftanasar, P.R. Young, I.D. Robertson,
J. Minalgiene and S. Lucyszyn
A novel dielectric-filled metal-pipe rectangular waveguide h
been fabricated using photoimageable thick-film materials. T1
waveguides incorporate a new transition from CP\V-to-TFMS-t
MPRWG. Standard on-wafer measurement techniques, waveguii
STD calibration standards, demonstrated low attenuation aero
the 60 to 90 GHz frequency range.
Introduction: Metal-pipe rectangular waveguides (MPRWGs) hat
been used tor many decades as a low-loss guided-wave structur
However, at millimetre-wave frequencies they can be difficult t
manufacture with high precision using conventional machinin
techniques, and integration with planar circuitry can be difficult.
In recent years, several technologies have been investigated t
fabricate miniature MPRWGs. including bulk micromachining c
both silicon [1] and thick photoresist [2], However, these air-fille
structures require many processing steps and yield can be vei
poor [3]. An alternative approach is to use dielectric-fille
MPRWGs. In 1980. Hinken spray coated a dielectric rod wit
metal [4], In 1995. Lucyszyn et id. reported the first monolith
dielectric-filled MPRWG, by combining photolithography wii
simple multilayer mic; ^electronic fabrication processing [5. (
This experimental proof-of-concept suffered from unacceptab
attenuation due to (i) the design frequency being deliberately s
close to the cutoff frequency; (ii) the ultra-small height of tl
structure (4 pine): and (iii) the use of very lossy materials (polyin
ide dielectric and aluminium conductor) [7], Recently, a relative
lossy low-temperature cofired ceramic MPRWG was demoi
strated at microwave frequencies [8],
For volume manufacture of multichip modules [9], thick-fil
technology is attractive. Moreover, new photoimageable dielectr
and conductor pastes give improved edge definition and small
feature sizes, resulting in the same performance as thin-fil
processing [10] To this end, this Letter describes the use of phi
toimageable thick-film technology for the fabrication of millim
tre-wave MPRWGs.
Fabrication process: A summary of the simple multilayer thick-fill
fabrication process is as follows: (i) the first metal layer is screer
printed and fired; (ii) two dielectric layers are then screen-printed
patteined and fired; (iii) the second metal layer is screen-printei
patterned and fired. The sidewalls are formed using a long trenc
via by patterning, exposing and developing the photoimageabl
dielectric layer.
2.490mm th roug h line
(back-to-back transition)
4.010mm delay line
Acknowledgments: The authors thank Shri A.K.S. Gopalan. Direc­
tor, Space Applications Centre, Ahmedabad for providing encour­
agement and support. They also acknowledge the help provided
by the Engineers of the Sensors Antenna & Feed Group.
© I EE 2001
Electronics Letters Online No: 20010677
DO I: I0.1049/el:20010677
jy November 2000
two 1.245mm eff-set shorts
| 236/11
S B. Sharma and V.K. Singh (Space Applications Centre, ISRO
Ahmedabad. India)
References
1 Ja m e s , g .l .: Analysis and design ol TE,, to HE,, corrugated
cylindrical waveguide mode converter’, IEEE Trans. Microw.
Theory Tech., 1981, MTT-29, (10), pp. 1059-1066
2 c l a r ic o a t s , P.J.B., and o l v e r , a .d .: ‘Corrugated horns for
microwave antennas’ (Peter Perigrinus Ltd., London)
3 JAMES, G.L., and THOMAS. B.M.: "TE,| to HE,, cylindrical mode
converters using ring loaded slots’, IEEE Trans. Microw. Theory
Tech.. 1982, MTT-30, (3), pp. 278-285
1122
2.990mm delay line
Fig. t Photograph o f thick-film M PRW G on-wafer STD calibration
standards
Measurements: To demonstrate this technology, an E-band (60^ C H x ) MPRWG was designed. The dielectric has relative per
mittivity er — 9. The internal width and height dimensions of th<
3D structures were 1220 and 18pm, respectively. A novel transi­
tion is used to couple energy efficiently from the coplanai
waveguide (CPW) on-wafer measurement probe pads to the thinfilm microstrip (TFMS) feed line to the MPRWG, as shown it
Fig. 1. An alternative transition was recently presented by Des
landes and Wu 11], having a microstrip taper that abruptly meet;
an open-ended waveguide. This is likely to cause significant radia­
tion and possible coupling to surface wave modes. With our trail-
ELECTRONICS LETTERS
30th A ugust 2001
Vol. 37
No. 18
i
Analysis of coaxial probe as discontinuity in
circular waveguide
Shashi Bhushan Sharma, Senior Member, IEEE, Vijay Kumar Singh, Ranajit Dey,
Soumyabrata Chakrabarty
Abstract—This paper presents method of moments analysis
of scattering characteristics of dominant as well as higherorder modes in a circular waveguide excited by a coaxial
line fed probe. Dyadic Green’s functions for the electric
and magnetic fields in the circular waveguide have been
derived considering one dimensional electric current in the
axial direction of the probe and magnetic current over the
co-axial aperture at the base of the coaxial probe. Taking
incident TEu mode in the circular waveguide, return loss,
power coupling to the coaxial port, power in the dominant
and higher-order modes have been computed. The validity
of the analysis has been checked by comparing the
computed values from the present method with the data
computed using Ansoft HESS and also from
measurements.
found out for both the electric and magnetic current sources at
the locations of probe and the coaxial aperture.
In this paper, two separate equations are formed by applying
boundary conditions on the probe surface and over the surface
of the coaxial aperture In order to formulate the expressions
for the scattered field, dyadic Green’s functions have been
derived for the electric and magnetic current sources. The
integral equations are solved using method of moments
technique.
Computed data on return loss and power coupling in the
dominant and higher order modes from the present method
have been compared with the data computed using Ansoft
HFSS and from measurements
E. ANALYSIS
Index Term —Circular waveguide, coaxial probe, Green’s
function, higher-order modes, method of moments, multi­
frequency mode transducer.
I.
I n t r o d u c t io n
Coaxial line fed probes have been widely used in coupling
electromagnetic energy to a waveguide from a microwave
source through a coaxial line. The problem of determining the
input impedance of a coaxial line fed probe in a waveguide
which is short circuited at one end has been addressed by
many authors for rectangular as well as circular waveguides
[l]-[5]. However, there are cases in which different probe
excited waveguide sections are used in tandem to realize
multi-frequency mode transducers [6], it is necessary to
analyze the scattering parameters of die probe considering this
as an asymmetrical discontinuity in the waveguide
In order to analyze coaxial probe as a discontinuity, one has to
deal with two types of current sources, the electric current on
the probe and die magnetic current over the coaxial aperture.
Using these current sources, electric and magnetic field
integral equations have to be formulated applying proper
boundary conditions on the surface of the probe and over the
coaxial aperture respectively. In addition, expressions for
electric and magnetic type dyadic Green’s functions have to be
The geometry of a circular waveguide loaded with a coaxial
probe is shown in Fig. 1, where TEU mode has been assumed
to be incident at port-1. The incident TEu mode has the
electric field orientation in the direction of the probe. The
incident mode induces electric current on the probe and
magnetic current over the coaxial aperture. Depending on the
size of the waveguide these current sources may couple power
m the different modes corresponding to the incident mode.
Fig 1 A circular waveguide loaded with coaxial probe
Let IT1
®1* ," IP®1
’ be the incident electric and magnetic
me
me ,ur
Manuscript submitted for publication, September, 2008
The authors are with Microwave Sensors Antenna Division, Antenna
Systems Area, Space Applications Centre (SAC), Indian Space Research
Organisation, Ahmedabad- 380 015, INDIA, e-mail drsbs@sac isro gov in
fields corresponding to the dominant TEn mode in the circular
waveguide. Let the scattered electric and magnetic fields in
2
the circular waveguide due to electric current source j( R ') on
the probe are I T / ^ , W l cw and due to magnetic current
continuous across the coaxial aperture. This boundary
condition is expressed as,
source M(R') over the coaxial aperture areE f cw , H f cw ■
+H
nH s,cw T
n s,cw +
TH
n inc
Let the scattered electric and magnetic fields in the coaxial
waveguide due to magnetic current source over the coaxial
aperture are W ^cxiV , fT ^ iCm . Global cylindrical co­
H s, cxw
The unknown surface current on the probe can be expressed its
terms o f basis functions; as,
ordinate system is represented as r,<j>,z and local co-ordinate
system as rx,<f>x, zx respectively as shown in Fig. 1.
(!)
J(R ')d V
The electric field due to a magnetic current source
given as
£(fi)=_JJ pxG JR,R')\-M (RytS’
(?)
/>=>
where f p(r) is entire domain basis fimction.
In general, the electric field due to an electric current source
J (F ) is given [7] as,
=
(6)
m
(R') is
(2)
where, magnetic current m (R') is related to aperture field
Taking entire domain basis functions to expand the unknown
surface current (assumed as line current at the axis of the of the
thin cylindrical probe) as
, sin(pA:(r-a+/i))
p
sin(kh)
IP ~ 1 ,2...N
I
II
(8)
E(R') as M (R ')~ - n xE (R ’)
A TEM mode distribution has been assumed for the coaxial
aperture field (or magnetic current).
and Gti(R,Rr) is an electric dyadic Green’s function of 1st type
The expressions for field components have been derived as,
and (Jrf(^,^')is electric dyadic Green’s fimction of 2nd type.
The magnetic field due to the electric current source J ( R ’) is
given as
H ( R ) = m |v x Wtl (F,F')J J ( R ' ) d V '
(3)
VxG el = Gm2
I
C = |K ( n ^ W
H l,cw = - H i Sin 4 + H f cosfc
= ~ HGzr( r , r V (r') sin <j>xdr' + jjG ^ (r, r')J(r') cos <j>xdr'
where, Gm2( R , R ‘) is magnetic dyadic Green’s function of 2nd
type. The magnetic field due to a magnetic current source
M(R') is given as,
H( R ) = -jo>£ o g W ' i ( R, R') M(R')dS'
VxGc2
<9>
!
(10)
Es.cw = ~ I P * (?,?’)£„ cos<f>xrxdrxd<fix +
jjG„(r,/•')£„ sttbfxrxdrxd<l>x
(4)
(ID
^
H ^cm = I p v M E ^ d r M
(12)
where, Gml(R,R')i$ magnetic dyadic Green’s function of T*
type.
_____ ________
_
The general expressions for Gel,Ge2 and Gml ,Gm2 for
cylindrical and coaxial waveguide are given in [7]. From these
expressions the required components of the Green’s functions
for the given problem have been derived.
On the probe surface, the boundary condition is applied on the
tangential component of the total electric field. Assuming
probe to be a perfect conductor, the tangential components of
the total electric field E‘ at the probe surface should be zero.
This boundary condition is expressed as
E i.c r +
= £' = 0
(5)
Over the coaxial aperture, the boundary condition is applied
on the azimuthal component of the total magnetic field. The
azimuthal component of the total magnetic field should be
Hs,cw~ l p j r , r ^ rxsml>xrxdrx<fyx - \ p 2f( r ,c o v j > trxdrxd4>x
+ J J ^ (r,/0£„ smtpxrxdrxd<t>c - J|3w(r,r')£„ cos0xrxdrxdf>x
(13)
E™ = ^ 1 -C T E n cps</Ji(— p )-e l' M>rtm*)
pakcp
!
a
(14)
= - H r sin& + a y i cos&
= - JjG=.(r,r')/(r')sm ^i*-'+ jjC^ (r, r')J(r’) cos (f>xdr'
(15)
em r m +A2/ 1(4i)co^
l i ? =CTE—
im
H™ = CTEll
where,
=1.841
(16>
(17)
i
,
3
< \ ^ cw>= \pa(r ,^ s x ^ M < E II/d r d 4
CTEU- 1
2
•W i)
- Ipt^r^E,* ™ 4/xdrMrxdrxd<l>x+ jp^(r>rySrxsinf/xdb^/-xdrxd^
The equations (5) can be converted into matrix equation by
taking the inner of the same using testing functions same as
basis functions in the form o f ,
< /f >E t,a r ) + ( / , , E
) = - { /, , E Z % )
- l p d ^ a C04 > i ^ $ r A M
(26)
8)
<XHs.cw >= \ p J r , r Y \ sin£drtffcrxdrxd0x
Similarly equation (6) is converted to matrix equation by
taking the inner product using unity testing function
<1>HJs,cw } + ( l ,H Z ar ) +
where,
) = ( l,H la w )
- \ p ^ , r ’)E0c o s tM d fr A M + J J 7 (r,r')E0sm^xdr'%
d^xrxdrxd ^
- J|^ (r,r')£ '0cosfi.drxd<f>xrxdrxd</>x
(19>
(27)
<f q,Es,cw
The azimuth component of magnetic filed in coaxial region is
given as,
p=l
= t l p -Zn
(2°)
P=l
where,
< 1,H le w >= 2tt
(rz - r,)(r/ - r,*)/Z ,
(28>
<XH»ar > -<XH“aw >= j ^ ( r , r ) i ; Sm<j>'xdr'Mrdrd4> '
Z» = \\fp (r')G„. (r, r')/?(r)dr'dr
~
< f<,>Es,cw >= - | | G r(((r,r')£ „ c o s f c f q(r)rxdr^dfxdr
co4'xdr'Mrxdrxd<l>x + JJb* ( r / ) f , sin^ d ^ A M
~ lp # (r,ry ;ocos<fxdr'xd^xrxdrxd^>x- h f E f a -rt)(r* - i f )/Z0
+ JjG „ (r,r')£ „ s m f j q( r ) r 'd r ^ d r
(29
> -< l.< c « r >=E„ Z22 , where
In the coaxial waveguide,
z22= j p r . M ^ A W / A M
~
< f q,E^cw >= - fjGr,(r,r')£0cos^ f q{r)d r 'M d r
+ jp4'Xr,rism$dry<%r:'dr:dfc
~ \p J r,d )c o 4 xm z J r M - ^ { r 2-rX > i-^)IZ q
(22)
(30)
+ I K (r>r'^E‘ sm # / , (r)dKd€dr
< f q>Elcw >=E0 -Z\1
(23)
For the incident terms of the matrix
where
T, = < /,,£ “ >= K
/ ,( #
(31)
z n = ~~JjT-#(r>E) cos$*fq {r)dr’d$'xdr
where,
- Jfcfr-.r')sm$xf q{r)drxd$'xdr
> = -j
E'cw = - ^ - C T E Ucos^ / , K p )
pakcfi
a
(32)
V2 =<1
(33)
l K ( r , r ') ( X / pf f (r'))cost xdr'rsdrxd tx
(24)
V2 =< l ,f f * >= - J K M .s in ^ rW rW ^ rd r#
(34)
+
s.CW.6
> ~ y 'I n
. 1. cos <f)xr'dr’d<t>'rdrdtt>
E li
(25)
where
z i>^ \ p ir{ry)fp{rr)smj>xdr'rdr4+ J p ^ {r,r)fp{r)cv4xdr'r drity
Thus equation (7) and (8) can be written in the matrix form as,
Z12 7
-----i
|> .l
SsT1
___
z 22
‘
1obrj
< XH
>= I p r ^ .iy d r 'd ^ 'r d r d f
p4
(35)
v4
1 I
\
,i
- 7-1
"
;
K2 I
I
MK
J
i k ^ i f j r ')
A
— — ----- s m ^ fe M
The different components o f dyadic o f Green’s .function (for
z>?’) m circular wavegmde are derived using the g.’iicr.:!
expressions given m [7] as,
(41)
r
(a) Component o f Gel for computing electnc field m circular
k
G *(r,r')-£C ,
A
— i—•-------------sin n&e M
r
r K
(42)
t l A E L l l co
. 1
-cosfy<f)e
<7> > '') = 5 k
ik ^ n J n (f ir)
li
wavegmde due to electnc current J on the post or probe
1 \-ik MnJ„(/r)
dr'
ct
+^nm?K-x
(36)
(b) Component of
GmZ
-a/„(2r’)
cosrnfie^
SR
for computmg magnetic field m
(43)
circular waveguide due to electnc current J on the post or
probe
m.
&
.
(37)
G„(r,/)^Ykc„ 1 fftJnUr) cosnife'^
'>1 1
(38)
(c) Component of
Gmlfor computing electnc field m circular
waveguide due to magnetic current M in coaxial aperture (i e.
due to coaxial aperture field)
sin ntpe
Grf(r>r') =Z kc>
x r kC, W ik id J ^ X r )
> — 4,
1
1
kx
li
j *.*1
,mn<b'e~ p
t,
— z±— t-cosnde ** W------^ — -cos nd>e 1 \
Jl
dr
dr
J
sm H4e* A Ul L & I cos n fe -*s
G„(r,r') = 'ZkCi
(39)
(d) Component of G e2 for computing magnetic field in
circular waveguide due to magnetic current M m coaxial
aperture (i.e., due to coaxial aperture field)
( U r S > - ± Z S ( R - R ') +
2X
- i- J ^ M
C0S„ ^
] \ i ^ l cosn^
(40)
'Results and discussion
Using the formulation presented in this paper, a MATLAB
based computer program has been developed. The scattering
parameters have been ;computed for a circular waveguide
(diameter 32.54 mm) having a co-axial line fed probe of
diameter 1.6 mm. The diameter o f the inner and outer
conductors of the coaxial line were taken as 1.6 mm and 6.5
mm, respectively. 32-point Gaussian integration has been used
to solve the integral expressions. First twenty five TE and TM
modes have been considered for convergence o f the solution.
Return loss for the incident TEn mode m the circular
waveguide and the powpr coupled to higher order modes and
to the coaxial hne port have been computed and compared
with the data from HFSS. The return loss has been computed
for the different depths1of the probe. The computed data for
return loss is shown in Fig. 2. Return loss vanes with probe
depth (or height) in circular waveguide. For example at 7 GHz,
it becomes -10 dB for a probe height of 11 mm as compared to
-50 dB when there is no probe (probe height 0 mm). The
forward power earned by the dominant TEn mode is shown m
Fig. 3 It is observed that the power coupling to the dominant
TEn mode is increased when probe height is reduced. The
probe also acts as asymmetrical discontinuity m circular
waveguide exciting higher-order TMoi, TE2l, TE31 modes
above 7 GHz. The Fig 4 shows the power coupled into higher
order TMoi mode. The power coupled into higher order TE2i
mode is shown m Fig ,5 The power in higher order modes
increases with probe height The part of the incident power
gets coupled to the coaxial probe which is shown m Fig. 6
The hardware shown m Fig. 7 has been used to verify the
probe analysis results In this hardware ( Fig 7 ), a coaxial line
fed probe of height 11 mm was used m a circular waveguide
section Measured return loss for the incident TEn mode m the
circular waveguide is shown in fyg s 8 The measured power m
the forward TE11 mode and the power coupled to the coaxial
port with respect to incident TEn mode m the circular
waveguide are shown m Fig 3 and F k - re.j -c.cn .'dy ibe
\
5
results computed from the present method are in close
agreement with the data computed from HFSS and
measurements. In the absence of the probe, the measured
return loss of the transitions (put back-to-back) itself is of the
order of 21 dB having ripples of ± 3.0 dB up to 9 GHz ( Fig. 8
). This causes ripples in the measured return loss plot for the
probe discontinuity as shown in Fig. 8. The return plot of a
post discontinuity [8] is also included in Fig. 8 to compare
with probe discontinuity. Improved return loss (-10 dB) has
been observed at lower frequency for probe in comparison to
the return loss (-3.6 dB) for post discontinuity [8] of similar
height (11 mm). This may be due to the fact that probe couples
part (-3.8 dB) of the incident signal into the coaxial line unlike
that of post.
20
•
10
•
•
T E 2 1 - P o s t h e ig h t 1 1 m m
---------- T E 2 1 - P o s t h e ig h t 7 m m
----------
0
(H F S S )
(P r e s e n t M e th o d )
T E 2 1 - P o s t h e ig h t 3 m m
(P r e s e n t M e th o d
-----------T E 2 1 - P o s t h e ig h t 1 1 m m
( R e s e n t M e th o d
-10
- 20*
-30
-4 0
J____.___ .____ 1___ 1___ I— 1____ i____ .____,____L
-50
y.oo
9.2 5
9.50
9.75
Freque ncy (GHz)
Fig 5 Power in TE 21 mode
30
20
—
P ro b e H eight 11 m m (P re s e n t M ethod)
- -
P ro b e H eight 11m m (H FSS)
10
S31
i P ro b e H eight 0 m m (P re s e n t M e thod)
GO
O
M
O
S11 (dB)
* -e P ro b e H eight 3 m m (H F S S )
O
(d B )
v P ro b e H eight 3 m m (P re s e n t M e thod)
O
r -▼ P ro b e H eight 7 m m (P re s e n t M ethod)
-4 0
-5 0
-6 0
6 .3
7 .0
7 .5
8 .0
8 .5
9 .0
9 .5
6 8
7 .3
7 .8
8 .3
8 8
9 3
9 8
F reque ncy (GHz)
1 0 .0
F re q u e n c y (G H z)
Fig.6 Power coupling to the coaxial line.
Fig. 2 Return loss o f probe loaded circular waveguide.
— — — P ro b e H eight 11m m (H FSS)
P ro b e H eight 11m m (P re s e n t M e thod)
■ 9 - + - * P ro b e H eight 7 m m (P re s e n t M e thod)
o - » -e P ro b e H eight 3 m m (P re s e n t M e thod)
P ro b e H eight 11 m m (M e a s u re d )
S21 (d B )
---------
8 .0
8 .5
Fig.7 Hardware o f circular waveguide with co-axial
line fed probe discontinuity.
9 .0
F re q u e n c y ;G H z)
Fig.3 Forward power in the dominant TEj i mode.
——
P r o b e H e ig h t 11 m m ( P r e s e n t M e t h o d )
----------P r o b e H e i g h t 1 1 m m ( H F S S )
---------- P r o b e H e i g h t 1 1 m m ( M e a s u r e d )
20
■ TM 01- Probe height 11 mm (Present Method)
• TM 01- Probe height 11 mm (HFSS)
t TM 01- Probe height 7m m (Present M ethod)
0
i TM 01- Probe height 3 mm (Present M ethod)
W ith o u t P r o b e (M e a s u r e d )
►*
P o s t H e ig h t 1 1 m m
f
(8P) U S
10
• «> «
• -10
’ -20
-3 0
-4 0
6 .6
-5 0
6 .8
7 .0
7 .2
7 .4
7 .6
7 .8
3 .0
8 .2
8 .4
8 .6
8 .8
9 .0
F re q u e n c y (G H z )
-6 0
3 .0
8 .5
Freque ncy (GHz)
Fig. 4 Power in TM 01 mode.
9 0
Fig. 8 Measured and computed return loss for the incident
T E n m od e in the circular waveguide having a
probe o f height 11mm.
i\
JONCLUSKM
A circular waveguide loaded with a coaxial _ obe was
analyzed after deriving appropriate components of dyadic
Green’s functions corresponding to electric current on the
coaxial probe and the magnetic current over the coaxial
aperture. The computed results from the analysis show that the
probe deteriorates the return loss performance, couples the
part of incident signal and excites higher order modes at higher
frequencies. This study gives a good insight about the nature
of coupling and the higher order modes excited due to coaxial
probe discontinuity. This analysis may be useful :n the design
of multi-frequency orthomode transducers [6], where the
probe at lower frequency ports acts as asymmetrical
discontinuity, thereby affecting the performance of higher
frequencies.
A cknow ledgm ent
The authors thank Dr. R. R. Navalgund, Director SAC,
Ahmedabad for encouragement and support. The authors are
extremely thankful to Prof. S. N. Sinha, 1IT, Roorkee for his
valuable inputs and suggestions for formulating the problem.
The authors also thank the Engineers of Microv/ave Sensors
Antenna Division, Antenna Systems Area, SAC, Ahmedabad
for extending help and necessary support.
References
[1] Wilson W. S, Lee, and E. K. N. Yung, “The input impedance of a
co-axial line fed probe in a cylindrical waveguide,” IEEE Trans.
Microwave Theory Tech., vol. 42, No. 8, pp. 1468-1473, Aug.
1994.
[2] R. E. Collin, Field theory o f guided waves. 2nd ed tion, NY: IEEE
Press, 1991.
[3] A.G. Williamson and D. V. Otto, “Coaxially fed hollow cylindrical
monopole in a rectangular waveguide,” Electron. Lett., vol. 9, no.
10, pp. 218-220, May 1973.
[4] Le-Wei Li, Pang-Shyan Kooi, Mook Seng Leong, and Tat-Soon
Yeo, “The input impedance of a probe excited semi infinite
rectangular waveguide with arbitrary multilayered loads, ” IEEE
Trans. Microwave Theory Tech., vol. 45, no. 3, pp. 321-328, Mar.
1997.
[5] Hon-Tat Hui, K. N. Yung, and Xin-Qing Sheng, “ The complete
set o f dyadic Green’s functions for the parallel plate
chirowaveguide and the application to the coaxial-probe excitation
method,” IEEE Trans. Microwave Theory Tech., vol. 48. no.11,
pp. 1917-1925, Nov. 2000.
[6] S. B. Sharma, V. K. Singh, and S B Chakrabarty “Multi-frequency
Waveguide Orthomode Transducer,” IEEE Trans. Microwave
Theory Tech., vol. 53, no. 8, pp. 2604-2609, Aug. 2005.
[7] Chen-To Tai, Dyadic Green Functions in Electromagnetic Theory.
2lld Edition, New York, IEEE Press, 1994, pp. 81, 141 and 147.
[8] S. B. Sharma, V. K. Singh, Ranajit Dey, and SJ3. Chakrabarty,
“Analysis of post discontinuity in an oversized circular
waveguide,” IEEE Trans. Microwave Theory Tech., submitted fo r
publication.
Shashi Bhushan Sharma was bom in
Moradabad, India in 1947. He received
B. E. in Electronics & Communication,
M. E. in Microwave Engineering, both
from the University of Roorkee in 1970
and 1972 respe''” / - . A . D.
degree in Mn.. »-ave Engin:
> in
from •'•ujarat
University. Dr. Sharma has more than 32 years of academic
and diversified research and develo, mer.‘ *.■rience
in the design and development of antenna systems for satellite
communication and remote sensing. H° has about 110
publications to his credit. He was honored in 1992 with Dr.
Vikram Sarabhai Research Award and Astraunautical Society
of India Award,2003 for his outstanding contributions to the
development of various types of antenna systems for ground,
airborne and spacebome systems. Dr. Sharma is presently
Deputy Director, Antenna Systems Area (ASA), Space
Application Center, ISRO, India.
Vijay Kuniar Singh was bom on 21st
August 1967 in Bahraich District of
Uttar Pradesh, India. He received B.
Tech.
in
Electronics
and
Telecommunication
Engg.
from
Allahabad University in 1990 and M.
Tech, in Electronics Engg. from
Institute of Technology, B. H. U. in
■
| N:
1992. Since, 1993, he has been with
the Antenna Systems Group in Space
Applications Centre, ISRO, Ahmedabad. He is involved in the
design and development of space-borne microwave antennas
for RJSAT and Scatterometer His area of interest is mode,
transducers, multi-frequency feeds, beam wave guides and
microstrip antennas for satellite remote sensing application. He
is pursuing Ph. D.
Ranajit Dey was Bom in Kolkata,
India in 1981. Graduated in electronics
& Telecomm, engineering from Kalyani
University, Kalyani in 2003 and did his
M.E from Jadavpur University in
Electronics & Telecomm, engineering
with specialization in microwave
engineering in 2005. His present areas
of research
are computational electromagnetics and antennas for
microwave remote sensing.
Soumyabrata Chakrabarty was
bom on 3rd January 1966 in
Karimganj District of Assam. He
obtained his B. E. (Hons) degree from
Gauhati University in 1988, M. E.
from Jadavpur University in the year
1992 both in Electronics and
Telecommunication Engineering and
Ph. D. degree in Engineering from
Indian Institute of Technology, Kharagpur in the year 1996.
He is currently working in Antenna Systems Area, Space
Applications Centre, Ahmedabad as senior Scientist/Engineer
and divisional Head, microwave Sensors Antenna Division and
involved in the development of antennas related to Microwave
remote sensing. His area of interest is computational
Electromagnetics, Microwave and - ,'ii.c . s Antennas.
Proceedings of the International Conference on Antenna Technologies. ICAT 2005
EVALUATION OF COMMON PHASE CENTER OF MULTIFREQUENCY
FEED FOR RADIOMETRIC APPLICATIONS
V. K. Singh, S. B. Chakrabarty, S. B. Sharma and Arun Kumar
Space Applications Centre,
ISRO, Ahmedabad
India
A bs tract
In this paper, a method o f locating common phase center o f a corrugated horn operating at four
frequency bands is presented. The phase centers at different frequency bands have been computed by
fitting the fa r field phase data to a circle in a least square sense using an iterative procedure. The
common phase center representing all the frequency bands has been estimated fo r optimum
performance o f Multifrequency Scanning Microwave Radiometer antenna. The measured amplitude
and phase patterns o f the antenna are presented.
I.
Introduction
I he antenna presented in this paper employs an offset parabolic reflector illuminated by a single feed
horn operating at 6.6 GHz ± 125 MHz, 10.65 GHz ± 150 MHz, 18 GHz ± 200 MHz and 21 GHz ± 200
MHz. Phase center of illuminating feed must coincide with the focal point of the reflector for optimum
performance and it can be easily determined if the feed is designed for single frequency band. Since, the
leed has been designed to cover four widely separated frequency bands, the determination of the location
of common phase center becomes a guiding parameter to optimize reflector illumination at all the
trequency bands. The techniques for the estimation of phase center
have been reported inf 1]-[3].
Nomographs have been given in [1] for the estimation of phase center of the aperture antennas. The
closed form expressions to compute phase centers of horn antennas are given in [2], But these methods
are not suitable, if the phase centers are required at different edge tapers of the feed pattern. Phase center
has been defined as the center of the best fit phase spheres in [3], but it is not evident how tc minimize the
leir.t square error in an iterative way. A Liest technique based on least square is described in [4] to fit a
•>phere in an iterative way. By using this method, the phase centers can be computed accurately only at
separate frequency bands but cannot be used to estimate the common phase center. Therefore, it is
worthwhile to carry out the analysis which leads to the estimation of the common phase center of the
mukitrequency feed as described above.
In the present work, the center of a circle has been found out which is fitted to the far field phase data by
n-rati\ e means. This technique is a special case of that reported in [4], After computing the phase centers
thi. different planes of the feed, the common phase center has been estimated which leads to
‘ulor-N Performance at all the frequency bands. The measured radiation patterns for which the phase
-•> .,?.\e been computed are presented.
Analysis
►
base center of an antenna, radiating electromagnetic waves at single frequency can be determined
279
[4] by Least Square Fitting o f the far-field phase data to a sphere or circle(CFM) using an iteratiy
procedure. Let the far field phase distribution data points in polar coordinates are (r,0, <j>). This data ca,
be converted into cartesian coordinates xd, yd, zd as
’
*
I
xa — rsind cos<j>; yd ~ r sinO sm<j>;
'
I
zd = rco sd
'
1
- J
where d = 1,2,3,,..,n > 3, n is the total no o f data points, r is equivalent to the far field phase data Le;
(A, B, C) be the unknown center, and let R be the unknown radius o f ;a sphere, (x-A)2 + (y-B)2 + (z-C)2~
R2 to be fitted to the far field phase data. The most natural fitting principle consists o f minimizing the sum
o f squared distances from the given data points to points on the sphere given by the intersection o f a
straight line through a data point and the center One formulation o f the objective function can be found
out if the parametric representation o f a sphere is used, i.e.
j
x =A + R cos u sm v
i
y = B+ R sm u sin v
j
z = C+ R cos u,
i
with 0 <u < k, 0 <v <2n
i
With the unknown parameter values (wd vj), d= 1,2, 3 , . corresponding to the intersection points, the
objective function becomes
]
S,(A, B, C, R, u], u2, ,un , vl, v2, , vlt)
1
n
( xr- A - R cos uj sin vt/)2
= ^
+ (y d- B - R sin udsin v</)2+ (zd- C - R
cos itj)'
d =i
For S\ to be minimum, the conditions are
a s, / a 4
=
dSi/dB=dSi/dC = dSi/dR = 0, 3Sx/dud = dSx/dvd - 0,d = 1 , 2 , ,n
These equations yields a 4 X 4 linear system o f equations which gives a matrix equation as, [a] [>']
= [6] -» [y] = [tf]'1 [i], where [a] is 4 X 4 matrix, [y] is a vector with unknowns A, B, C, R and [b] is
also a vector. First we get values o f udand vd. Consequently, these values o f ud and vd can be used to get
first iterative values o f the center as A, B, C, R and this process can be repeated until best fit center is
obtained with minimum value o f least square error parameter Si. If we'delete all the functions showing
dependence on ^ as well as deleting either o f the x and y coordinates we will get center o f the best fit
circle corresponding to a fixed plane o f the antenna
!
i
The phase centers at different frequency bands should be symmetrically located in terms o f wavelengths
with respect to the focal point o f the reflector for optimum performance o f the antenna If the phase
centers corresponding to extreme frequency bands centered at 6 6 GHz and 21 GHz are properly located,
the location o f phase centers at 10.65 GHz and 18 GHz are expected to yield optimum performance. As
shown in Fig. 1, the common phase center is located at X- distance from the aperture o f the horn. The
value o f X can be found by taking common phase center point to bei equally displaced in terms o f
wavelength, from the extreme phase centers at 6.6 GHz, 21 GHz which can be represented by the
following equations
1
( 1)
X, = K X S6 = X - P C 66and X2 = K X 2, = X - P C 21
Where X, and X2 are distances from common phase center to the phase centers at 6 6 GHz and 21 GHz
respectively PC66 and PC2, are locations o f phase center from the aperture o f the horn. K is a constant.
Xfi6 and A.2i are wavelengths at 6 6 and 21 GHz In order to get optimum performance at 6 6 and 21 GHz,
the required condition should be
,
(2)
X, = X 2; this gives, K= ( PC21 - PC66)/{X2I+X66)
i
280
!
X can be computed using equations (1) and (2) as
X = (K X 6 6+PC 66)
(3)
X gives the location of common phase center with respect to the horn aperture.
' Phase Center o f 10 65 GHz
Phase Center
Fig. 1 Location of common phase center and the phase centers at individual
frequencies in the feed horn
III.
Computed Results
The measured radiation patterns are given in the Fig 2 and 3. Phase centers have been computed using
the least square fitting method from the phase patterns measured in the planar near-field test facility.
Measured phase pattern at 6.6 GHz is shown in the Fig. 4.
• 21 GHz
■ 18 GHz
CQ
-a
Q-
CO
' 1065 GHz
• 66GHz
s *
/it
»/
»y
//./
R e la tiv e P o w er*
S
U
R e lative Power<
/
/
h
']'!
/'I
'
/
,
'/
1
I
•!
1
\\
'A
vv \ \\ \
V ;\\
v ,.\
\/ V
- to
to
A n g le ( d e g )
Fig. 2 Measured H-plane Patterns
Fig. 3 Measured £-piane Patterns
281
In the different planes, the values of the computed phase centers at the Required edge taper are shown in
the Table 1,
:
Table 1 Phase Center Values at Different Frequencies at the Rlequii ed Edge Tapers
Frequency
Required Edge Taper (dB)
Computed Phase Centers(mm) at the
in GHz
Required Edge Taper
H Plane
E Plane
45°
Plane
H Plane
E Plane
45° Plane
66
-8 60
-8 36
-8 50
-122.00
1-108 90
-113 6
10 65
-11 68
-11 92
-11 80
-297 00
-247.00
-272.0
18.00
-15 36
-14.00
-14.72
-423.00
i-3 7 3 .5 0
-407.0
21 00
-15 99
-16.05
-16.00
-421.40
-387.30
-403.7
The negative values of the phase center in the above table imply that the phase centers are located inside
the hom, when the horn aperture is taken as reference plane. The phase center at the centre frequency
can be taken as the average of the phase centers in the different planes. It comes -114.83 mm, -272 mm, 401.166 mm and -404.13 mm at 6.6GHz, 10,65GIIz, 18GHz and 21GHz respectively. If the values of
phase centers at 6.6 GHz and 21 GHz are put in equation(2), the value qf K is obtained as 4 84. This
means that the phase centers at 6 6 and 21 GHz must be located at 4.84 times their respective wavelengths
from the common phase center or the-focus of the reflector. This value of K when substituted in equation
(3) gives X= -335 mm. It means that the location of common phase center is 335 mm inside the horn.
The position of phase centers at 10 65 GHz and 18 GHz are at 3.96 Xjoes and 2.24 X!8 respectively from
the location o f the common phase center. The location of the common phase center and the phase centers
at different frequencies are shown in the Fig, 1.
VI.
Conclusions
■
i
The feed was integrated with the offset reflector m such away that its focal point coincides with the
location of the common phase center computed from the method discussed in this paper. This gave
optimum performance at all the frequency bands justifying the validity of the analysis.
282
Acknowledgement
The authors express sincere thanks to Dr, K N Shankara, Director, Space Applications Centre for
providing encouragement and support. The authors are also thankful to the engineer of Microwave
Sensors Antenna Division for necessary help.
References
[1]
I. Ohtera and H. Ujiie, "Nomographs for Phase Centers of Conical Corrugated and TE) 1 Mode
Horns," IEEE Trans, on Antennas Propagat., No. 12, Nov. 1975, pp. 858-859.
[2]
E. I. Muehldorf, "The Phase Center of Horn Antennas", IEEE Trans. Antennas Propagat., Vol. 18,
No.6. Nov. 1970, pp. 750-760.
[3]
V. T. Rush and Porter, Analysis o f Reflector Antennas, New York: Academic Press 1970
[4]
H. Spath, "Least Square Fitting with Spheres," Journal of Optimization Theory and Applications,
Vol. 96, No. 1, lan. 1998, pp. 191-199.
283
;TE Technical Review
ol 16, No I, January-February
1999, pp 47 - 52
Design of Common Aperture Hybrid Mode
Corrugated Horn for Multifrequency
Scanning Microwave Radiometer
S B SHARM A
and
V K S IN G H
M ic ro w a v e S e n so rs A n te n n a , D ivisio n of S pa ce A p p lica tio n s C entre, Ind ian S pa ce R esearch
O rg a n is a tio n , A hm e da ba d 380 053, India.
The paper presents an innovative design m ethodology for m ultifre qu ency dual polarised common
aperture conical corrugated horn which meets the specifications In term s of cross-pol, pattern symmetry,
side-lobe levels, beam w idth at all frequency bands of Interest for bandw idth ratio up lo 3.3:1. It Is shown
th a t the h y b rid mode c h a ra c te ris tic s of corru ga te d con ica l horn can be o p tim ize d to give low
crossp olarize d radiation and good pattern sym m etry over widely separated frequency bands.
'i HE Multifrequency Scanning Microwave Radio- meter payload to be flown with 1RS-P4 in 1998
ng a dual polarised radiometer system is capable of
imating a number of geophysical parameters related
land, ocean and atmosphere. In order to assure the
tired performance of the payload, the antenna assumes
ater importance as the performance of the payload
ically depends upon the antenna characteristics. The
enna for MSMR payload forms the most vital
system because of the critical requirement of very
' overall cross-polarization, high beam efficiency
pattern symmetry over very large bandwidth of the
er of two octaves (6.475 GHz - 21.2 GHz, bandwidth
0 1:3.3). MSMR antenna consists of an offset
ector of FID ratio of 1.8, offset angle of 43.32 degree
a projected aperture of 80 cm which results into an
illumination cone angle of 13.65 degree. This
ector is to be illuminated by a multifrequency dual
trized feed system which must be designed to give
s-pol level better than 23 dB at all frequency bands
1 good pattern symmetry.
performance of the horn was optimised over a frequency
band from 5.7 GHz to 10.8 GHz with best performance
at 5.9 GHz to 7.2 GHz. Since, the performance of the
horn will repeat at its odd harmonics, it is expected that
the horn will depict satisfactory performance over the
frequency band 17.7 to 21.6 (odd harmonics of5.9 to 7.2
GHz).
A comparison of the simulated and measured pat­
terns of the horn has been presented. A good agreement
between the experimental and theoretical radiation pat­
tern has been observed.
THE DESIGN PHILOSOPHY
The basic conical corrugated horn has been illus­
trated in Fig 1.
The design requirement of the MSMR antenna sys­
tem is to achieve good pattern symmetry, low cross­
polarisation level (< -23dB), high beam beam effi­
ciency (better than 90% at -10 dB point and low return
loss at the input of the horn at all the frequency bands.
'"he electrical design of this type of antenna is very
cult because of the requirement of common radiataperture to be used to accommodate the limited
e available on the satellite.
In order to meet the above requirements of the
MSMR antenna, the feed horn has to be designed for
better performance in terms of cross-pol. because the
offset reflector itself deteriorates the cross-pol perfor­
mance of the overall antenna system.
The available literature^l-5' on the feed reveals that
maximum achievable bandwidth is of the order of
2 by using ring loaded corrugated horn. Therefore,
came necessary to evolve a new innovative design
ic corrugated horn which meets '.he MSMR antenna
irement of very low cross-polarization at all widely
rated frequency bands.
Following design considerations have been applied for
the design of the horn.
•
•
•
The paper presents tiie design of conical corrugated
based on the concept of harmonic operation. The
•
No 19-F: Copyright © 1999 by the 1ETE.
47
Size based on minimum beamwidihs at all frequen­
cies to get high beam efficiency
Continuous as well as harmonic band operation
Minimum input diameter to avoid higher order mode
generation
Optimum 5-6 corrugations per wavelength at high­
est frequency
48"
IETE TECHNICAL REVIEW, Vol 16, No 1, 1999
This equation gives the depths of the corrug;
corresponding to balanced hybrid mode condition*'
is also applicable for corrugated conical horns of n;
flare angle (less than 15 degree) of the waveguide,
the above equation a closed form expression fo
depth of corrugation for hybrid mode condition is
as*6*
!
4
^ 2.5ka J
I he quantities a, b, d0, d^ etc are shown in F
•
Corrugation depths based on capacitive reactance
generation to meet hybrpd mode condition at all
frequencies
GENERAL ANALYSIS
The characteristic of the horn-aperture field is de­
termined by the admittance as seen from the entrance of
the corrugation slot and the improvement of the aperture
field is achieved over the frequency range in which the
slot admittance is between large capacitive reactance
and small inductive reactance which results into mini­
mum surface current. The expression for the slcl reac­
tance is given as under*3)
XZ= ~S
J (.k a) Y (kb) - Y. (k a) J. (kb)
— ---------------- *---------------------!----------------!-------------
(
1)
J \ ,ka) Y, (kb) - Y \ (ka) 7, (ka)
8 = ratio of slot width to pitch
k = free space wave number
a - inner corrugations radius,
b = outer corrugations radius
d j = depth of corrugations,
dQ = width of corrugations
J | = Bessel function of order 1,
The number of corrugations per wavelength
been selected so that it offer high impedance anc
surface current on the walls of the corrugations red
to minimum. For this criteria to be met, the reqi
number of corrugations per wavelength have been t
as 5-6 corrugations at highest frequency i.e. 21 C
Even 5-6 corrugations result into very fine corrugat
having pitch equal to 2.5 mm and the width of the t
equal to 0.5 mm to get an anisotropic surface.
In order to improve the performance of the hoi
all frequency bands, the corrugation depth, pitch
were optimised based on frequency harmonic corn
and varying depth of corrugations to achieve a cr ,
polarisation level better than 23.0 dB over the freque
band from 5.7 GHz to 10.8 GHz which depicts
performance over the frequency band from 5.9 to
GHz and a cross-polarisation level better than 30.0
was achieved over this frequency band. Since the [
formance at corrugation depth of AM and 3A/4
similar because of harmonic periodicity, the satisi
tory performance of the horn over the band 5.9 to
GHz will repeat over the frequency band 17.7 to 2
GHz. It has been found theoretically that a cro
polarisation level betle- than 25.0 dB was obtained at
GHz (3rd harmonic of 6 GHz) and at 21 GHz (
harmonic of 7GHz).
The aperture diameter, length and the flare an
for conical corrugated horn are selected based on
narrow radiation pattern requirement and to ensure l i
phase of the radiated field at the aperture is close
uniform. Moreover, higher order modes amplitude
the input of the horn arc controlled so that the radian
pattern is not degraded. The depth of corrugations ;
varied from the throat to the horn aperture to achic
7'j = Derivative Bessel function of order I
Yj = Neumann function of order 1,
Y', = Derivative Neumann function of order 1
When X —»
which is a condition for hybrid
mode generation, the above equation reduces to the
form
J j' (ka) Yj [&(a + id\)} = Y|' (ka) J ( [k(a + r/()]
Fig 2 Corrugation geometry of the horn of Fig I
SHARMA & SINGH . C ommon A perture H ybrid M ode C orrugated H orn
49
Harmonic operation of Corrugation
best input match and good pattern symmetry
Another important param eter which has to be con­
sidered in the design o f the feed is the edge taper ot feed
taper This param eter characterise the effects o f the feed
element pattern on the far-field pattern o f reflector.
The size o f the feed is governed by the satellite
space available and illum inating cone angle at the reflcttor and finally the si/.c o f the feed is limited by the
lowest operating frequency (6 6 GHz) The size limita­
tion of the feed resulted into the lowest edge taper at 6 6
GHz
6
7* k
X
f
g (it, A) +
7
1_
y »k
'I
P
)
l
h (u, A) cos 2 p
(8. P)
7* k
(3)
h (it, A) sin 2$
(4)
The co-polar patterns computed based on expres­
sion given by (3) at frequencies 6 6, 10.65, 18 and 21
GHz has been presented in Fig 4
Figures 5 to 12 presents the numerical data on
primary radiation patterns as a function of angle at both
0
rdr
3 = a2/2L, where L is the slant length from apex to edge
>f 'he aperture of the horn, e x p :- j k A r 2) is the spherical
vave phase error term Under balanced hybrid condition
1 ‘>nd jUk -> 1 and Ka = 2 405, where k is the free
pace wave num ber and K is the transverse wave propaation constant
IUMERICAL RESULTS AND DISCUSSION
COMPUTED rR iilA A T PATTERNS AT 8 6 10 6$ H 421 GHz l a
t
DOMINANT,MEu;MODE
■10
P ow er(dB )
h(u. A) = P0 J 2 (Kar) J 2 (ur) exp ( - j k A r 2)
30
given by equation (3) and (4) It is worthwhile to men­
tion that the semi angle 15° was achieved in two steps
of 6° and 9° tn the throat region to avoid power splitting
into EH (n modes which are responsible for the deterio­
ration of cross-pol at higher frequencies.
where u = ka sin 6 and r = p/a, p corresponds to horn
aperture co-ordinate frame (p, p, z) a = radius of the
horn aperture,
rdr
74
Fig 3 Corrugation slot reactance as a function of frequency
Fx (8, ip), E (8, p) correspond to the co-polar and crosspolar radiation pattern respectively
g(«. A) = Jq S0 (F a r) J Q (ur) exp (-jkAr 2)
18
o
1+
1?
o
The far field radiation pattern of a narrow flare
anglj corrugated conical horn for dominant hybrid mode
is given b y ^
F. (8, <P) =
8
F f« q u * n c y In C H j
Far Field Pattern of Corrugated Feed Horn
Angie(deg)
Fig 4 Co-planar pattern computed based on dominant hybrid
mode propagation
The edge tapers corresponding to horn aperture size
220 mm and 15° sem i angle of the horn corresponding
the illum ination cone angle o f ±13.65° o f the rcflechave been com puted using the field expressions
AntpliludCiJQ)
6SGHz E-Plane
Using equation (1), the slot reactances has been
omputed for a co rru g a tio n depth o f 15 mm and
■aveguide radius o f 17 5 mm The numerical data on
ot reactance as a function of frequency is shown in Fig
From Fig 3, it ts evident that slot can provide capaci-e reactance in continuous band from 6 0 GHz to 11 0
Hz as well as in harm onic band ranging from 18 GHz
21 GHz Therefore the depths of all the corrugations
the horn must be optim ised to get large capacitive
actance over both bands, which is responsible for low
,s-polarization and pattern sym m etry of the horn.
-20
20
A.'iglel'.leg)
Fig 5
Co-planar measured and simulated E-plane pattern at
6 6 GHz
IETE TECHNICAL REVIEW, Vol 16, No 1, 1999
Amplnuoe{dB)
50
oO
23
20
Angte{D*;g J
Fig 6 Co-planar measured and simulated H-plane pattern at
6 6 GHz
‘
18.00 GHz H-PJans (primary)
Amplitude^}
10 65 GHz E-Plana (pnra- )
Fig 9 Co-planartmeasured and simulated E-plane pane
ISO 0 GHz
I
im
60
i
Fig 7 Co-planar measured and simulated E-plane pattern at
10 65 GHz
:o
:o
€o
Anjic(d.J9)
Fig 10 Co-plana'r measured and simulated H-piane pnu>
18 0 GHz
21 GHz £-Plans {pnrrsry)
A ntphiudc{dB )
10 65 GHz H-Plane
Fig 8 Co-planar measured and simulated H-plane pattern at
10 65 GHz
Fig 11 Co-planar measured and simulated E-plane pats
21 0 GHz
i
E and H plane for frequencies 6 6 GHz, 10 65 GHz 18
transitions were designed at all Irequencics The
plete horn along with tapcied waveguide nans
has been modelled on a standaid soltwaie pa*
(CHAMP) to give the optimum edge tapeis at a!
quencies The simulated and measured edge t
corresponding to 13 65° illumination angle have
picsentcd in Table I
and 21 GHz.
It is not possible to have dominant mode purity
simultaneously at all frequencies at the' input of the
horn which will finally result into other higher order
hybrid modes To ensure dominant mode pur ty at the
input of the horn at all frequencies tapered waveguide
51
SHARMA & SINGH : C ommon A perture H ybrid M ode C orrugated Horn
TABLE 1 Simulated and measured illumination taper in
dB of MSMR feed
21 G H z
H * P :a n e ( p r im a r .)
/
\
1
Frequency
Simulated
Measured results
- 16
------ U E A S .
____ SIM U.
1
1
GHz
H-plane
E-plane H-plane
E-plane
a
oz
*21
6.6
-8.6
-8.36
-8.43
-8.20
10.65
-1 1.68
-11.92
-10.77
-10.2
18.0
-15.36
-140
-14.23
"14.54
|
1
1
1
i
_
,w
/
•100
21
-15.99
-16.05
-15.92
r
i A /V
i/ V
V 1
\l
20
-60
20
CO
iv.'O
A n g ie (ce g )
-16.44
Fig 12 Co-planar measured and simulated H-plane pattern at
21.0 GHz
TABLE 2 Measured and simulated cross-pol
IS O
21.0
Measured
E-plane
D-plane
H-plane
-38.0
-25.4
-25.8
-27.4
-37.2
-32.0
-27.4
-27.8
-33.5
-25.6
-24.2
-23.0
-40.4
-27.3
-28.2
-28.8
Simulated
E-plane
38.7
33.6
29.2
Lyi
6.6
10.65
H-plane
to
CO
Frequency
GHz
D-plane
-38.0
-27.6
-26.6
-27.1
D-plane as designated in the above table corresponds to diagonal pla
This software computes modal powers in all modes
at the aperture and predicts the farfield radiation pat­
terns using Kirchhoff-Huygcn’s aperture integration
technique. Iterations on CHAMP software were per­
formed to optimise the simulated cross polarization
ilevels. The measured and simulated cross-polarisation
have been presented in Table 2.
I he deviations in numerical values of measured and
»iin u1ated cross-pol may be attributed to the measurenent inaccuracy of the order of ±1.5dB at -30dB and
:!dB at -23 dB. Further in order to compare the meaured 3nd simulated pattern, the probes at all other ports
rere removed at the time of measurement. The holes on
to waveguide were covered by metallic tape but still
lose portions of the waveguide where holes were drilled
thibit discontinuities which are finally responsible to
■grade the cross-pol performance.
MSMR antenna system. The bread-board and engineer­
ing models based on the above design have been already
tested have been found to meet all the specifications.
ACKNOWLEDGEMENT
The authors thank Dr George Joseph, Director, Space
Applications Centre, Ahmedabad for constant encouragement
and s pport. The authors also wish to acknowledge the support
provided by Shri RK Malaviya Project Manager MSMR
antenna, Ramji M Makwana and PD Ramavat, Engineers of
Microwave Sensors Antenna Division.
REFERENCES
1.
P J B Clarricoats & A D Olver, Corrugated Homs for
Microwavce antennas, Peter Peregrinus Ltd., London,
UK.
2.
F Takeda & Tsutoinu •Hashimoto, Broadbanding ot Cor­
rugated Conical Horns by means ol ring loaded corru­
gated waveguide Structure, IEP.E Transaction on An­
tenna and Propagation, vol, 24, no 6, pp 786-792,
November 1976.
3.
G L James, Analysis and design ot TE|( to HEn corru­
gated cylindrical waveguide mode converter, IEEE on
MTT, vol 29, no 10, pp 1059-1066, October 1981.
4.
G L James, TE -to-HE,, Mode Converters tor Small
Angle Corrugated Horns, IEEE Transaction on Antennas
and Propagation, vol AP-30, no 6, pp 1057-1062, No­
vember 1982.
The figures of cross-pol as shown in table 2 assures
jondary pattern cross polarization levels better than
3 dB at all frequencies as offset geometry itself giving
>ss-pol level o f -30 dB corresponding to FID ratio of
The optimized corrugated cor.ical horn along with
ered waveguide OMT has been fabricated and tested,
ce, the horn based on the above design is giving best
formance in terms of VSWR and cross-pol, the same
been considered for,.the MSMR antenna system.
> horn.has been finalized as final flight model for
Mode Transducers for Ku-band Dual Channel
Microwave Rotary Joint
V. K. Singh, S. B. Chakrabarty, Anil Solanki, Ranajit Dey, Ha Agnihotrii, S. B. Sharma
Antenna Systems Area, Space Applications Centre, Ahmedabad-15
Abstract— This paper presents the design and development of a dual-channel microwave rotary joint using
circular waveguide as primary waveguide and rectangular waveguide as the secondary waveguide. Design is
presented at Ku-band using dual channel mode transducers exciting TM0, and TE0i modes in the circular
waveguide. Rectangular to circular waveguide transitions employing probe and slot coupling are used to
excite TMot and TE0j modes respectively. The simulated and measured parameters of dual-channel rotary
joint (DRJ) have been presented.
Index Terms—Circularly symmetric modes, dual-mode transducer, probe coupling, rotary joint, slot
coupling.
I. INTRODUCTION
Scanning type of antennas require microwave rotary joints to transport microwave energy from stationary
part to the rotating part of the antenna. The design of device becomes challenging in terms of achieving
isolation and mode purity if it has to support more than one channel. Earlier efforts to design single and
dual channel microwave rotary joints for the scanning antennas are reported in [l]-[5]. The uninhibited
power transmission with rotation requires special types of mode transducers which can excite circularly
symmetric modes in the main waveguide. TMoi and TEoi modes of a circular waveguide can be used for the
design of rotary joint. None of the existing papers give the design details of the mode transducers for such
device. In this paper, design and development of a dual channel rotary joint is presented which gives
optimum performance in terms of mode purity, return loss, inter-port isolation and minimum variation of
theses parameters with the rotation of the device. Purity of TMoi and TEoi modes of a circular waveguide is
achieved in order to realize the rotary joint. Ansoft HFSS based on Finite Element Method technique has
been used for modeling and analysis of the device. The simulated results for TE01 -TM01 dual channel rotary
joint are presented for return loss, insertion loss, isolation between channels, mode coupling behavior,
variation of return and insertion loss with 360 degree rotation.
II. DESIGN AND SIM ULATION
The design goals for this rotary joint are to achieve 17 dB return loss, 0.5 dB insertion loss, 40 dB isolation
between two channels and the variation of insertion loss less than 0.1 dB with 360 degree rotation of the
rotating joint over 50 MHz bandwidth by excitmg two orthogonal TMoi and TEoi modes of a circular
waveguide. In the dual mode transducer, TMoi mode channel has been realized by axial excitation of the
circular waveguide by a coaxial probe using new configuration. In this new configuration rectangular
waveguide axis and circular waveguide axis are oriented in the same direction. The coaxial probe is
connected to a metallic post in the rectangular waveguide and the post’s bottom surface is in contact with
the bottom wall of the rectangular wavegude, forming a loop in the plane of narrow wall of rectangular
waveguide. Required return loss, insertion loss and mode purity is achieved over the band by optimizing the
geometry of the mode transducer. Other channel of the dual mode transducer, which is a TEoi mode channel
has been realized by exciting a circular waveguide through four axial slots at its periphery. A four way Eplane waveguide power divider is designed to couple power in the circular waveguide to excite TEoi mode
through four equally spaced slots at the periphery of the circular waveguide. Power divider is optimized for
equal amplitude and equal phase at its output ports to excite four slots on circular waveguide to excite TEoi
International Conference on Microwaves, Antenna Propagation and Remote Sensmg, Jodhpur, India, Feb 2008
mode. The end wall ot the circular waveguide from which coaval \ robe t .on:;ae a_*r TMoi mode
excitation has been used as short to couple power through slots for TEoi mode excitation. Modal analysis
technique is used to predict the power coupled to the required TMoi and TEoi modes in the circular
waveguide. The diameter of the circular waveguide has been chosen such that it propagates both the
required TMoi and TEoi modes. The diameter of the circular waveguide has been selected as 31.5 mm,
which is 15.3 % above the cut off diameter which is 27.3 mm at 13.402 GElz for TE0i mode. Cut off
diameter for TM0i mode in circular waveguide comesl7.13 mm. The selected diameter of the circular
waveguide allows the propagation of TMn mode which is a degenerate mode with TEoi mode and also the
next higher order mode TE . Apart from this the lower order modes TEu, TM0i and TE2i will inherently
propagate [1], Out of these lower and higher order modes only TM0i and TE0i are the required modes for
the design of dual channel rotary joint, therefore, proper excitation mechanism is needed to couple power in
only these two modes corresponding to two channels. The dimension of the rectangular waveguides
exciting the circular waveguides through coaxial probe for TMm mode has been taken as 19 mm X 9.5 mm.
The dual mode transducer has been modeled on HFSS based on FEM technique and the dimensions of the
circular waveguide and the coupling elements for TE0i to TMoi mode transducer are optimized in terms of
return loss, insertion loss and mode purity of TMoi and TEoi modes. The solid model of the of the dual
mode transducers connected back to back to excite two modes for dual channel rotary joint are shown in the
Figure 2.0. This figure shows the model from HFSS consisting of coupling through 4-slots for TEoi mode
and coaxial probe coupling for TMoi mode.
3 1
The Table 1.0 shows the simulated modal amplitude of fundamental and higher-order modes for the
optimized mode transducers for both the channels. This table shows that the maximum power is coupled in
the TMoi and TEoi modes and a rejection better than 40 dB is obtained for non desired modes.
TE, i
TMnl
t e 2,
TE0,
TMn
t e 31
-0.123
-71.05
-78.47
-74.79
-77.37
-61.057
-79.314
-49.266
CO
O
-0.168
-72.04
-51.98
•70
13.30
Figure 1.0
13.34
13.38
13.42
Frequency(G H z)
13.46
13.51
The simulated return loss, isolation between
two channels with radiation boundarv
------- Return loss ( TE01 C h a n n e l)
Isolation Betw een TE01 a nd TM01 channels
------- Return loss ( TM01 C h a n n e l)
Insertin loss ( TE01 C h a n n e l)
» ■ ■ Insertion lo s s T M O l C h |n n e l) ^
S
M agnitude(dB )
1
2
3
4
5
6
channel)
-73 817
iO
(TMoi
Modal
amplitude in
Channel-2
(TEoi channel)
8 8 i 8
Number
Modal
amplitude in
Charnel-1
M a g nitude(dB )
Mode
Name
‘
Mode
N.
C
Table 1.0 Modal Amplitudes in the circular waveguide
for TMoi and TE0i channels at 13.402 GHz.
Channel-1
_9 0 h . . 1 1. i . . 1 . . . 1 1 . 1 1 . 1 . .
. I i i i i l i i . i l . i i i i i i i i l i . i i l
13.20 13.24 13.28 13.32 13.36 13.40 13 44 13 4 8 13.52 13.56 13.6C
Frequency(G H z)
Figure 2.0 HFSS solid model o f the dual channel rotary
joint
Figure 3.C The simu'iUd return loss, insertion loss and
isolation oc-.i-v- *vo ch riels
International Conference on Microwaves, Antenna Propagation and Remo. V using Jodhpr India, Feb. 2008
The simulated isolation is better than 58 dB between channel-1 and channel-2 and return loss is better than
17 dB for both TMoi and TEoi channels at 13.402 GHz ,with radiation boundary,. The simulated return loss
and isolation between two channels with radiation boundary are shown in the Figure 1.0
Two dual mode transducers were connected back to back to make a dual channel rotary joint. The complete
geometry was modeled on HFSS to compute return loss and insertion loss of the model. HFSS solid model
of the dual channel rotary joint with TMoi and TEoi mode excitation in the circular waveguide is shown in
Figure 2.0.
The simulated return loss, insertion loss and isolation between two channels of the dual-channel rotary
joint are shown in the Figure 3.0.
In the rotary joint the electrical parameters should ideally be invariant with 360 degree rotation of the
rotating part of the joint with respect to the stationary part. It was observed from simulation that with
rotation the power variation in the two channels is within 0.05dB and the return loss variation is within ldB
III MEASURED RESULTS
The measured return loss TMoi channel of the dual channel rotary joints ( see Figure 2.0) is shown in
Figure 4.0. Measured insertion loss of TMoi channel is given m Figure 5.0. Theses results are taken with
respect to 360 degree rotation of moving part with respect to stationary part.
Figure 4 0 Measured return loss TM01 Channel
Figure 5.0 Measured insertion loss o f TMni Channel
1
Jr
• fr o ig S IlM V
U
©
IO
u
cn ©
r
l
--------
0 Degree
SODegree
-40 r
• • • 160 Degree
a a a 270 Degree
•4 5
■ ■ ■ 360 Degree
Si
:
6
Return loss(dB)
i-
■ ■ i
13 30
....
13 35
t
•
....
13 4 0
i
■.
13 4 5
13 50
13 5 5
13 60
Frequency(G H z)
Frequency(GHz)
Figure 6.0 Measured return loss o f TE0| channel
Figure 7 0 Measured insertion loss o f TE0i channel
International Conference on Microwaves, Antenna Propagation and Remote Sensing, Jodhpur, India, Feb 2008.
The measured return loss ot TEoi channel is given in Figure 6.0 and i.’.ir'tion ' • ot i l ot clnunel is given
in Figure 7.0. Measured isolation between TEoi and TM0i channels is shown in the Figure 8.0.
o
u
o
l
o
t!n
o
A
o
s
o
a
o
Channel Isolation(dB)
ro
o
-10
-90
•100
13
...
„
. .
Fieure 8. : Measured isolation between
Figure 9.0: The photograph of the dual channel microwave rotary
. .
loint.
The photograph of the developed hardware of the dual channel rotary joint with different views is shown in
Figure 9.0.
IV CONCLUSION
Dual channels of the rotary joint were realized by designing rectangular waveguide TE|0 to circular
waveguide TMoi mode transducer and rectangular waveguide TEm to circular waveguide TEoi mode
transducer respectively. The measured insertion loss of the order of 0.7 dB and return loss better than -15
dB achieved for the dual channel rotary joint for both the TEoi and TMoi channels. The measured isolation
of 50 dB between the two channels is achieved. The variation of measured return loss, insertion loss and
isolation parameters with 360 degree rotation is very small thereby proving that the purity of circularly
symmetric modes has been achieved. Slightly more insertion loss than the desired value of 0.5 dB in the
dual-channel rotary joint can be attributed to fabrication and assembly errors since the device was not
fabricated as a single piece but in parts.
References:
[1] H. P. Raabe, “ A rotary joint for two microwave transmission channels of the same frequency
band”, IRE Transsactions-Microwave Theory and Technique, pp.30-41, July 1955.
[2] Tomiyasu K., “ A new annular waveguide rotary joint “,pp. 548, Proc. IRE, vol. 44, 1956.
[3] P. H. Smith and G. H. Mongold, 11 A high-power rotary waveguide joint,” IEEE Transactions
on Microwave Theory and Techniques, pp. 55-58, Jan. 1964.
[4] S. Boronski, “A multichannel Waveguide rotary joint,” Microwave Journal, vol. 8, pp. 102-105,
1965.
[5] O.M Woodward, “A dual-channel rotary joint for high average power operation,” IEEE
Transactions on Microwave Theory and Techniques, Vol., MTT-18, no.12,, pp.1072-107, Dec.
1970-71.
International Conference on Microwaves, Antenna Propagation and Rei.u.ic
i.-.v,, JodintuIndia, Feb. 200
1
TMoi Mode Transducer Using Circular and
Rectangular Waveguides
S. B. Chakrabarty, V. K. Singh, S. Kulshrestha, G. Upadhyay, S. B. Sharma
Antenna Systems Area, Space Applications Centre, Ahmedabad-380015, India,
email:soumya@sac.isro.gov.in
Abstract — This paper presents a technique to excite TMoi mode in circular waveguide from a
rectangular waveguide propagating the dominant TEn mode. Impedance matching between
the two dissimilar waveguide is achieved using a door-knob transition. The power in the
asymmetrical mode TEn is minimized by properly designing this transition. The analysis and
design has been presented in Ku-band with center frequency at 13.7 GHz. The purity o f the
TMoi mode has been checked by simulation and also through RF measurement o f TMoi
exciter assembly formed by placing two similar sections back to back through a choke joint
and one section is rotated when the other section is stationary. The purity o f the mode has
further been tested by computing the far-field radiation pattern o f the open-ended waveguide
supporting the TMoi mode. Simulated and experimental data on scattering matrix parameter
o f the propagating mode has been presented.
Index Terms—Mode transducer, rotary joint, doorknob, coaxial probe
I. INTRODUCTION
Excitation of dominant modes in circular waveguides is preferred for most of the applications for
guiding electromagnetic waves. The excitation of higher-order modes like TMoi, TE21 and TE01
m circular waveguide is also needed for certain applications. As for example, TMoi and TE01
which are higher-order modes in circular waveguides are used in motional joints that provide
continuous rotation in either direction about an axis without deteriorating the electrical
performance The circular symmetricity of these modes ensures the invariance of amplitude and
phase of the desired modes. The methods described in these literature require a complex
transitions and mode filters to achieve the purity of modes. The excitation of TMoi mode in
circular waveguide using a probe coaxial with the circular waveguide has been described in [1].
However, no details of this mode transducer as well as its matching section is elaborated in [1].
This paper presents the details of analysis and design of circular waveguide TMoi mode
transducer which has been realized by axial excitation of the circular waveguide by a coaxial
probe. The impedance seen by the axial coaxial probe is matched to rectangular waveguide by
using coaxial to rectangular waveguide mode transducer with doorknob transition [1], The mode
transducers has been modeled to achieve the punty of the desired TM0i mode in circular
waveguide and the suppression of undesired mode TEn. Ansoft HFSS, a Finite Element Method
International Conference on Microwaves, Antenna Propagation and Remote Sensmg, Jodhpur, India, Feb 2008
I
based EM simulator has been used for electromagnetic modeling and computation o f scattering
parameters o f different modes supported m the circular waveguide: Measured and simulated
results on RF performance o f the device have been presented.
i
EL SIMULATION AND DESIGN
Figure 1 shows the schematic o f the TM0i mode transducer. The cross-sectional dimension o f
the circular waveguide has been chosen so as to support the TMoi mode with cutoff wavelength
^c=2rca/2.405, ‘a’ is the radius o f the circular waveguide. The center frequency is 13.7 GHz
(A.=21.9mm), The cutoff diameter o f TMoi mode at this frequency is approximately 16.8mm.
The diameter o f the waveguide is chosen as 19mm which is around 14% higher than the cutoff
diameter o f TMoi mode and 12% less than the cutoff diameter o f next higher order mode TE2 1 .
This diameter will also support the dominant TEn mode in circular waveguide which is
asymmetric. Thus, TMoi mode has to be excited with minimum power transfer in the dominant
TEn mode. In the configuration shown in Fig. 1, there is perfect circular symmetry o f the mode
launcher so that no TEn mode may be excited unless some asymmetric discontinuity is
introduced in the circular waveguide.
!
In the configuration o f F ig.l, the transition consists o f a coaxial rod with doorknob in the center
o f the cylinder, protruding through a hole in the bottom and using a shorted rectangular
waveguide stub for tuning mismatch. This method is selected because this coaxial rod can
produce only radial and longitudinal electrical field components. In other words it can produce
only the transverse magnetic field components and can not excite any o f the undesired modes.
The impedance offered to the coaxial probe is transformed by the doorknob at the interface of
rectangular and circular waveguide to that o f rectangular waveguide. A short, is provided in the
rectangular waveguide at a distance o f quarter guide wavelength and fine tuning is earned out by
changing the location o f the short to arrive at its optimum position. In this configuration the axis
o f circular waveguide is kept perpendicular to the axis o f rectangular waveguide from which the
coaxial probe protrudes in the circular waveguide to excite the mode. 1
Rectangular waveguide WR-75 with dimensions 19mmX 9.5 mm was used. The length o f
circular waveguide is taken as 175 mm which is the multiple o f guide wavelength (25.09mm) for
TMoi mode. The device was modeled on Ansoft HFSS to optimize it: to get maximum power m
the required TMoi- The optimized probe length which yielded the required return loss and power
coupling was 16.5 mm. The radius o f the doorknob which gave optimum performance was
5.2mm. The diameter o f the coaxial probe was 3.3 mm. The length o f the coaxial section from
which the probe protrudes m the circular waveguide was 3.2 mm. The inner and outer diameters
o f the coaxial section are chosen 3.3 mm and 6.5 mm respectively to avoid propagation o f other
modes except TEM mode at 13.7 GHz. The optimized plunger/short distance in the rectangular
waveguide which gave optimum return loss was 19.65 mm.
Inlemationa1 Confcicnoeou Microu aves, Antenna Propagation and ~
■■S'1;
,7odbr ,r T-adia, FA 2008
3
m.
SIM ULATED AND M EASURED DATA
The modal amplitude was computed for various modes to ascertain the mode purity o f the TMoi
mode and the rejection o f the other modes. The results o f the analysis are shown in Fig. 2. From
these plots it is evident that m ost o f the power is confined in the TMoi mode and rejection o f
other higher order m odes is better than 22 dB. Two m ode transducers o f Fig. 1 were put back to
back. The simulation as well as RF measurement was performed with one part stationary while
the other part is rotating.
0i
jp
“P
-10
-90
-100
132
133
134
135
136
137
138
139
140
F re q us n c y tG H z )
Fig. 2 Modal amplitudes for different modes m the
circular waveguide
Fig.l Schematic of TMoi mode transducer
The simulated and measured return loss and insertion loss have been presented for rotation o f 45,
90, 180 and 270 degrees as shown in Fig. 3 and 4. Fig. 5 shows the far field radiation pattern o f
an open-ended waveguide supporting TMoi mode. The hardware developed is shown in Fig. 6.
(OP! a p n iiid u iw
A m p litu d e (dB )
0 Degree
— — • 90 Degree
180 Degree
* - * - « 270 Degree
t » » 380 Degree
X X X 0 Degree
a a a so Degree
o o o 180 Degree
□ □ □ 270 Degree
-50
13 60
•
13 65
13 70
13 75
13 80
13.85
13 90
Frequency(G H z)
Fig. 3 Simulated Return loss and insertion loss
-50 <
13.60
■ ■ «
i
* »
13.65
■ ■ i
» « »
13 70
» i
13.75
13.80
13.85
13 90
FrequencyfG H z)
Fig. 4 Measured Return loss and insertion loss
International Conference on Microwaves, Antenna Propagation and Remote Sensing, Jodhpur, India, Feb 2008
4
IV. C onclusion
Normalized Pattern Magnitude(dB)
The measured results show that the return loss and insertion loss performance does not change
with the rotation. This validates the design of the mode transducer to excite TMoi mode in the
circular waveguide. The validity of the analysis has further been justified through the
computation of radiation pattern of the open-ended waveguide supporting TMoi mode. The
radiation pattern shown in Fig. 5 shows a difference pattern which is yielded by an circular
aperture with TMoi mode field pattern on the aperture. The slight frequency shift towards lower
side is observed. This can be attributed to the fabrication tolerance, alignment of coaxial probes
in the circular waveguide.
Fig. 5 Radiation pattern of open-ended
waveguide supporting TMoi mode
Fig. 6: The photograph of the developed mode
transducer
A cknow ledgm ent
The authors thank Director, Space Applications Centre, Ahmedabad, India for support and
encouragement. The authors also thank Engineers of Microwave Sensors Antenna Division for
their help and support.
R eferen ces
[1] G. L. Ragan, Microwave Transmission Circuit., MIT Radiation Laboratory Series, vol.9,
New York: McGraw-Hill, 1948
[2] H. P. Raabe,” A rotary joint for two microwave transmission channels of the same
frequency band,” IRE Trans. Microwave Theory Tech., pp.30-41, July, 1955,.
[3] Y. H. Chong, “Wideband tmoi-mode travelling wave coupler”, IEE Proc., Microwaves,
Antennas Propagation, vol. 144, no.5, pp. 315-320, Oct. 1997
International Conference on Microwaves, Antenna Propagation an4 Remote Sens’
to d 'v r . IrVia, Feb. 2008.
14 V Krasnopolsky, W Gemmtll, and L, Breaker, A neural network
niultiparameter algorithm for SSM/I ocean retrievals Comparisons
and validations, Remote Sens Environ 73 (2000), 133-142
15 P Cipollint, G Corstm, M Diant, and R Grasso, Retrieval of sea
water optically active parameters from hyperspectral data by means of
generalised radial basis function neural networks, IEEE Trans Geosci
Remote Sens 39 (2001), 1508-1524
© 2002 Wiley Periodicals, Inc
MOMENT-METHOD ANALYSIS OF A
SLOT-COUPLED CIRCULAR
WAVEGUIDE ORTHOMODE
TRANSDUCER
S. B. Sharma, S. B. Chakrabarty, and V. K Singh
A ntenna and Feed G roup
S pace A pplications C entre
Indian S pace Research Organisation
A h m edabad 380015, India
Received 28 Januan 2002
ABSTRACT: An analysts o f a slot-coupled cucitlai to rectangular
waveguide oithomode transducei (OMT) 's presented A set o f font cou­
nted integi odifferentta! equations ate obtained ft am the enforcement of
the continuity conditions o f tangential magnetic fields a! the slot-apei tine interfaces The method o f moments, with entn e-domain sinusoidal
basts functions and Galerlan testing, is used to solve the coupted-mte%ra! equations, with finite wall thickness taken into account Mutual
.oupling between the two aperture slots, winch plays a major tole in
solaling the orthogonal ports, is property accounted fo r Resonant
ength o f the slots and reflection coefficient ard coupling between ports
ire computed A compattson between the experimental and computed
lata by the present method as well as HFSS is piesented © 2002 Wiley
’enodicals, Inc Microwave Opt Techno! Lett 34 285-289, 2002,
’ubhshed online m Wiley InterScience (www interscience wiieycom)
)OI 10 1002/mop 10439
Cej words: moment methods, ctuulai waiegwde oithomode Hons­
hu ei
ular geometry with a suitable numerical technique like the method
o f moments, closed-form expression can be derived easily and it is
not necessary for the whole geom etiy to be meshed For the
method o f moments, only the source region must be meshed into
subsections In addition, the number o f unknowns is extremely
small, so the computational effort to obtain an accurate solution is
negligible as compared to general 3D implementation using FEM
and FDTD, as in HFSS- and CONCERTO-like softwaie Thus, it
is worthwhile to develop analysis methods for complex geom etnes
like OMT
The present Letter presents a method-of-moinents analysis o f
an orthomode transducer consisting o f circular to rectangular
waveguide [3] To the best o f the authors’ knowledge, the present
Letter is one of the first to give a detailed method for analyzing a
cucular-waveguide OMT
The present authors reported the analysis o f a slot-coupled T
junction between circular and to rectangular waveguides [4, 5]
This work has been suitably modified and extended to slot-coupled
OMT by considering the electromagnetic interaction between the
two slots This analysis takes into account the effect o f finite wall
thickness by considering the slot as a cavity wheie the walls o f the
slot aie closed with perfect conductor and equivalent magnetic
walls on both the lower and upper interfaces [6] A set of coupled
integrodifferenttal equations are formed by enforcing the continu­
ity o f tangential components o f magnetic field at all the slot
aperture interfaces The method o f moments with Galerkin’s tech­
nique is employed to solve the coupled integral equations for the
accurate apeiture fields Entire-domain basis functions are used for
the estimation o f aperture field Mutual coupling between the slot
apertures m the common waveguide is properly accounted
The unknown field distribution m the slot aperture is found by
transforming the integral equations derived from the boundary
conditions for the tangential components o f the magnetic fields
into a matrix equation The elements o f the matrices are found by
considering the effect o f all possible higher-order modes in circu­
lar and rectangular and stub waveguides The field distribution on
both the slot interfaces is used to find the return loss at all ports and
coupling between different poits
A comparison o f measuied data to that computed by the present
method is presented Companson o f data computed by HFSS is
also presented
\
INTRODUCTION
)rthomode transducers (OMT) find wide application in antenna
red system m ground- and space-borne systems to facilitate
requency reuse [1] Two orthogonally polarized signals at the
ame frequency band are sensed by a common antenna feed
trough the use o f an OMT OMT’s are also used m radiometer
ntennas by which polarization-sensitive geophysical parameters
ke sea surface temperature, wind velocity, moisture content, etc ,
re estimated [2]
Although OMTs have been extensively used for dual-polarized
ansm ission and reception in communication and remote sensing
i'stems for the last several decades, the literature elaborating the
ssign o f OMTs employing electromagnetic modeling is very
luch limited Commercial software, such as HFSS, FIDELITY,
id CONCERTO, based on FEM and FDTD, are available for the
isign o f these 3D geometrical structures Unfortunately the softare often needs an enormous amount o f time to yield analysis
suits, and thus optimization o f design parameter is extremely
fficult and time consuming The commercially available softare, m general, use mesh for the whole 3D geometry and the field
[uations are solved numerically at each mesh point, known as a
ide. When electromagnetic modeling is performed for a partic­
2. GENERAL ANALYSIS
Figure 1 shows the schematic diagram o f the slot-coupled circularto-rectangular waveguide orthomode transducer (OMT) A com­
mon circular waveguide o f radius p0 is coupled to two other
rectangular waveguides o f dimensions a , X £>, and a 2 X b 2,
respectively To develop a generalized program the angular spac­
ing between the two slots is taken as $ 0 The signal is coupled
from one waveguide to the other through axial slots o f length and
width 2 L , and 2W%and 2 L2 and 2 W2, respectively The two slots
are separated by a distance 1 12 along the.r axis An expanded view
o f the slots is shown m Figure 2 The coupling slots are m the form
of curvilinear rectangles on the walls of the circular waveguide
The angular width 2 A<t>0 is assumed to be very small, so that the
curvilinear rectangle on the wall o f the circular waveguide can be
replaced by a planar rectangle for the purpose o f analysis [4. 5]
Because 2 pn A $ 0 is small as compared to the slot lengths 2Lt
(2 L 2), the electric-field intensity along the width o f the coupling
slot is assumed to be constant
If the equivalence principle is applied, the domain o f the
problem may be separated into three distinct regions [5, 6] as
shown in Figure 3, namely, (i) primary waveguide (circular
MICROWAVE AN D OPTICAL TECHNOLOGY LETTERS / Vol 34. N o 4, August 2 0 2 002
285
r
Figure 3 (a) Sectional view of the OMT (b) The equivalent models fo
Slot 1 (c) The equivalent ’models for Slot 2
i
Figure 1
A slot-coupled circular-to-rectangular waveguide OMT
waveguide) with equivalent magnetic currents M2, M}, (n) sec­
ondary waveguide (rectangular waveguide) with equivalent mag­
netic currents
MA, (in) cavity regions with equivalent mag­
netic currents [—Af,, —M, (slot 1) —M3, —Af4 (slot 2)]
As shown m Figure 2, the slot interfaces S, (/ = 1,2, 3, 4}
are closed with peifect electuc conductois and equivalent mag­
netic current pairs (M,, - M,) aie placed on eithei side This
ensures the continuity of the tangential component of the electric
field across the surfaces The electromagnetic field m the
waveguide is produced by the impressed sources, and the equiv­
alent magnetic currents are given by
Mr —Er X n
over the slot surfaces Here, Er is the electnc field on the i th slot
surfaces of the original pioblem. and « is the unit outward normal
to the slot surface
The analysis is carried out for the case when the signal is fed to
Port 1 and all other ports are assumed to be match teiminated
Ensuring the continuity of the tangential componer. of mag­
netic field (\ directed) across the four slot surfaces S u S2, 53, SA,
the following aie the foui mtegrodiffeiential equations
2H'mc +
( 1)
n
1+ h K - m 2) = Hl(M2) + Hl(M3),
I
HlJMi) +
«?(-M 3 ) + W-Md =
1
N
S4
t
1
Slot 2
Figure
286
(4;
|
r| = 1, 2, 3, 4 and p = 1,2,
!
, N,
,
(5)
*
|
where Vrp are the unknown complex coefficients and N is the
number of entire-domain basis functions
It has been shown by several authors [4-6] that the field
distribution along the length of the slot is approximately half
sinusoidal, and so the natural choice for the basis functions is the
entire-domain sinusoidal' functions
The basis functions used are given by [4-6]
,
l ptr
S \2Z^
K
HUM*)
j
M,= 2 vJrp,
P=i
S3
h~ 2l /- ~ I
(3;
In the above equations rw stands for rectangulai waveguide, cw —>
for circular waveguide, c for cavity region, and
and
H‘cvXMj) are the a-directed magnetic fields at the ith interface of
the rectangular and circular waveguide respectively, due to mag­
netic current at the jth slot interface H[(Mj) is the a-directed
magnetic field in the cavity region near the ith interface due to the
magnetic current at the/th interface H'lnc is the incident magnetic
field at Port 1
The above sets of equations are solved with the method of
moments In order to apply the method of moments, let us define
a set of basis functions f p for representing the magnetic current as
follows
|
t
I
;
-j-P
ii
a
+ -v) )■ ~ L>- A'- L"
2W j
u-
-Lj +.X|2<.X-£L2+.V|:
r = 3, 4
2 Expanded view of coupling slots
MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol 34, No 4, August 20 2002
'
(6 )
.
'..
A m » • • • ■-’* •
ubstituting (5) and (6) in (l)-(4 ) ar.d using the linearity of field
arameters, gives
2v
W
-X
-
2v # - /* ) = -2«L
(7)
£ VlpHH-fxP) + X V2PH2
A - f lp)
P
P
The method for the derivation of the expression for Yr" ,
and
E33 are given in [4, 5, 7]. The derivation of the expres­
sion for Y U and E32 requires the derivation of the magnetic field
in the circular waveguide at the slot interface due to magnetic
current at the interface of the other slot and vice versa.
First derive the expression for the magnetic field in the circular
waveguide at Slot 1 due to magnetic field at Slot 2, fr'2w(M 3). In
this case,
is expanded by the basis functions given by Eq. (6).
The expression for the magnetic field in Slot 1 due to magnetic
field at Slot 2 is derived as
= X v&x/v) + X v & o y (8)
~j(2W2) ^
,
HCVI(M}P) -
e„
\r<
X X o2vp2
„ nl0y„
—
.-0 - 1
X VlpHlvihn) + X v & u y
= XV}pH l(-f,p) +X V £ ( - / „ ) .
/>
cos n(<t> — <&o)
- n2l^„,„ ~ ^
XX£/>tL
(9)
+ (ptr/2L2)2
P
/>
■ (18)
X virHt(-U) + X V fl-/*) =X V M U Y 00)
r
p
p
The following matrix equation is generated by taking the inner
product of Eqs. (7)-(10) with the testing functions which are same
as the basis functions given by Eq. (6):
[ c - t f 1]
[E21]
[0]
[0]
[ - e; 2]
[E22 - E22]
[E32]
[0]
[0]
[ - E 2i]
[E” - E ” ]
W 3]
[0]
[0]
[ - e;j ]
[ e :j -
The expression for the elements of the submatrix [ Egfv] can be
derived by performing the inner product of the above expression
with the testing function and is expressed as
X —
yL
[ “ find
[0]
[0]
[ 0]
[V2p]
[Vv ]
[VVI
J
2-nplym„
coH
(k 2
+ M 2 £ i)2
1 - m/.tL
rL + {p^2LiY
+ 7L )( 2L2) \ 2 L i
.
(ID
(19)
Similarly, the expression for Hl„(M2) is expressed as
where
Y " = (u-,„ H ' M <r)),
- f (2 W'|) „ y,
e„
top " f ^ x2-irpiy,
YU = <w„. /& ,(/*)> .
l £ = <w.,. / & ( / * » •
E32 = <ns„ « - .(/> )),
02)
cos n(I>
1
"l - »r/.vL X X E? y [ n + (PTT/2LJ
E33. = <»■*. W»(/3,)>.
P
Ytt = <w2l, H U U ) ) ,
(13)
( ~ \ Y e yU)
X
Ei1 = <wls, H i(-/,p )).
E22 = <w,„ W2( - /2 ,» .
Y;' = <w,„ H2(-/„ )> ,
(14)
E32 = (w2s, H ] ( - f lp) \
(15)
After carrying out the inner product of the above equation with the
testing function, the expression for E3;, is found to be
E;3 = (W„,
(op
E;J = <w2, . / / 3( - / j„)>,
E*3 = (vi'2s, HA - f >,,)),
E44 = (ii'i,
« = (w,,, 2H]J.
(16)
cos(n<I»o)
-y(4VV,VE,)
E2
E33 = (w*,
( 20)
e: : = <wls, H'A-f2p)),
" y y
^
—
^ 2rrp57,n
1 - n2/£ .
STT
(k2 + ytrmJ \ 2 L J X 2L>
r„,„ + (pirl2L,y X Y„„ + (sirl2L,)-
(17)
X
Each of the submatrices of the 4 X 4 square matrix of Eq. (11) are
of size N X N, whereas each of the submatrices of the 4 X 1
column matrix is of size N X 1. The above matrix equations are
then solved for evaluation of accurate aperture field amplitude
coefficients.
(e~yL' - (-1 Ye*')
- y « * l x u + Lz)
X
(21)
The derivation of the above expression for / 'nc, Y‘J are given in [5,
6], respectively.
MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 34, Nc. 4, August 20 2002
287
b
3. EVALUATION OF REFLECTION, COUPLING
COEFFICIENTS
8
The reflection coefficient looking from Port 1 is defined as
Eb' = (V'{0T - e \ 0.
(23)
E'"c= (Vl0r-e^
(24)
b
k
where £ bs and £ mc are the dominant TE,0 mode electric field of
the back-scattered wave and the incident wave, respectively The
above electric fields are expressed tn term? of the modal voltage
and the modal vector functions as
S
(22)
2
.
A m p litu d e (dB )
- B m + £*"
r, = ~ g s —
-TO
•60
Frequency (GHz)
The expression of eet0 is given m [7, 8] Because tne modal
voltages of the incident wave is unity [8], the expression for the
reflection coefficient F , is given by
£ bs = -
1+ (F;0)b'
(25)
The expression for ( V*I0)b!* is given in [7]
The expression for the coupling coefficient from Pon . to Port
r (> = 2, 3, 4) is defined as
r
(v.,),
(26)
(v\rc
i = 0 for the rectangular waveguide port and i = 1 for the cuculnr
vaieguide port Because (V‘,0)mt is equal to unity the expiession
for the coupling coefficient is obtained from the dominant-mode
electnc field uavehng toward Ports 2-4 caused by the aperture
fields induced by the incident field and deriving the expression for
modal voltage from the dominant-mode electnc field
4. NUMERICAL RESULTS AND DISCUSSION
With the above-mentioned procedure, the return loss at Port 1 and
coupling between the ports are computed with a computer program
run on a SUN SPARC workstation The waveguide dimensions for
the circular waveguide are 16 8 mm diameter and 110 mm long
WR75 is used for the rectangular waveguide sectior The slot
dimensions aic 2£, = 2L2 = 10 95 mm and 2 IK, = 2 W2 - 1 5
—►-Return loss at port 1 (HFSS)
-•-C oupling from port 1 to 3 (HFSS)
«o
-♦“ Return loss at port 1 (Present Method)
fo
-^-Coupling from port 1 to 3;Present method)
o
(BP) opmilduiv
-•-Isolation between ports 1 & 2{HFSS)
-♦-•Isolation between ports 1 & 2(Present method^
!
o
Up
o.
N
13 6
mm, the distance betweenjslots x ,2 = 51 mm, and the waveguide
wall thickness = 2 mm :
The numerical data arethecked for convergence with respect to
the number of modes and jalso the number of basis functions It is
observed that a set of three basis functions and m
30 and n rs
30 is sufficient for convergence less than 0 19c of the final results
The analysis results aie presented consideung the case when the
signal is fed at Port 1 and other ports are match terminated
In order to compare the computed data by the piesent method
to that of other methods, the geometrical model shown in Figure 5
was analyzed with the useiof Agilent HFSS (veision 5 6) In HFSS,
circular geometry is approximated by polygons, the angle per
segment was chosen to be| 10° Tne minimum angle per segment is
5°, which Agilent HFSS 5 6 can handle For the present problem
the minimum angle per segment (5°) could not be used because of
memory limitation A comparison of the data computed by the
present method and that by HFSS is presented in Figure 4
One OMT was fabricated with the above parameters Measure­
ments were conducted on this work model with the HP8510C
vector netwoik analyzer The experimental results on return loss at
Port 1 and coupling coefficients to the other ports are plotted in
Fig ,te 5 The computed parameters are also presented m the same
figure
1
It is seen from Figure 4 that there is a very good agreement
between the data computed by HFSS and the piesent method,
except for a slight shift of the tesonant fiequency Because HFSS
takes a polygon approximation of the circular boundary, the slot
resonant frequency will,' be different from that of the circular
canonical case, and the 'difference will reduce as the angle per
segment of polygon is reduced
The fairly good agreement between the computed and experi­
mental results also justifies the validity of the analysis The vari­
ation between the computed and experimental results may be
attributed to (a) fabrication tolerance or (b) in the analysis, the
signal is fed at one pori, and the other ports are assumed to be
match terminated, but m'practice perfect match termination is not
possible These are the factots that impart a slight vanation be­
tween the theoretical and experimental data
l
13 9
Frequency (GHz)
Figure 4
Figure 5 Comparison of data between experimental and computed data
by the present method
J
Comparison of data between HFSS and the present method
ACKNOWLEDGMENT
|
The authors thank Director SAC(ISRO) for necessary support anc
encouragement The authors also thank Professor B N Das, INS/*
288 ‘ ' ' -MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol 34, No 4, August 20 2002
Senior Scientist (Hon.), Department of E and ECE, IIT Kharagpur,
India, for his valuable advice and guidance.
REFERENCES
I. J Uher, J. Borncmnnn, anti Uwe, Waveguide components for antenna
feed systems: Theory and CAD, Artcch House, Boston, 1984.
j 2. S.B. Sharma, Antenna system for multifrcquency scanning microwave
radiomcter:MSMR, IEEE Mag Antennas Propagat 42 (2000), 21-29.
3. R.E. Harrington, Field computation by moment methods, McMillan,
New York, 1968.
4. S.B. Sharma, S.B. Chakrabarty, and B.N. Das, Analysis of a slot
coupled circular to rectangular waveguide T-junction between. IEEE
Trans Microwave Theory Tech MTT-46 (I99S), 1173-1176.
5. S.B. Sharma and S.B. Chakrabarty, S-matrix of a slot coupled circular
to rectangular waveguide T-junction. Int J Electron 87(2000). 591-603.
i 6. R.W. Lyon and A.J. Sangster, Efficient moment method analysis of
radiating slots in a thick walled rectangular waveguide, Proc Inst Elect
i
Eng Pi H 128 (1981). 197-205.
7. B.N. Das. A. Chakrabarty. and N.V.S.N. Sarnia, S-matrix of a slotcoupled T-junction between rectangular waveguides, IEEE Trans Mi­
crowave Theory Tech M'lT-38 (1990), 779-781.
8. R.F. Harrington, Time harmonic electromagnetic fields. McGraw, New
York. 1961.
[ © 2002 Wiley Periodicals. Inc.
TIME-DOMAIN CFIE FOR THE
ANALYSIS OF TRANSIENT SCATTERING
FROM ARBITRARILY SHAPED 3D
CONDUCTING OBJECTS
Baek Ho Ju n g ' and Tapan Kumar Sarkar2
Department of Information and Communication Engineering
Hoseo University
Asan 336-795, South Korea
2 Department of Electrical Engineering and Computer Science
Syracuse University
Syracuse. New York 13244
Received 5 February 2002
ABSI RACT: .4 time-domain combined field integral equation ICF'E) is
presented to obtain the transient scattering response from arbitrarily
shaped three-dimensional f 2D i conducting bodies. This formulation is
based on a linear combination of the time-domain electric field integral
equation lEFIE) with the magnetic field integral equation IMFIE). The
time derivative of the magnetic vector potential in EEIE is approximated
svitli the use of a central finite-difference approximation for the deriva­
tive. and the scalar potential is averaged over time. The time-domain
CFIE approach produces results that are accurate and stable when
solving for transient scattering responses from conducting objects. The
incident spectrum of the field may contain frequency components, which
may correspond to the internal resonance of the structure. For the nu­
merical solution, hath the explicit and implicit schemes are considered
an<l two different kinds of Gaussian pulses are used, which mas or mas
not contain frequencies corresponding to the internal resonance. Sinnerteal results for [lie EFIE. MFIE. and CHE are presented ami compared
"i'll those obtained from the inverse discrete Fourier transform tlDFTl
of the frequency-domain CFIE solution. © 2002 Wiley Periodicals. Inc.
Microwave Opt Technol Lett 34: 2S9-296. 2002; Published online in
Wiley InterScience (www.interseience.wiley.com). DOI I0.l002/mop.
10440
Key words: transient: integral equation: EFIE: MFIE; CFIE
1. INTRODUCTION
I lie analysis of electromagnetic scattering from arbitrarily shaped
conducting and/or dielectric bodies in the frequency domain has
been of considerable interest. The integral equations based on
electric and magnetic fields are termed the EFIE and MFIE,
respectively. However, in the analysis of closed conducting bodies,
frequencies, which correspond to the internal resonance of the
structure, may produce spurious solutions for both the EFIE or
MFIE. One possible way of obtaining a unique solution for closed
bodies at an internal resonant frequency is to combine the ERE
with MFIE in a linear function. This combination results in the
combined field integral equation. Although the CFIE formulation
has been extensively used for conducting and dielectric bodies in
the frequency domain [1-3], only a few researchers have applied
it to the analysis of transient scattering by two- and three-dimen­
sional bodies [4, 5], In [5], a modulated Gaussian pulse, which has
a narrow spectrum of frequency, is used as the incident wave.
In recent years, several formulations have been presented for
the solution of the time-domain integral equation to calculate the
electromagnetic scattering from arbitrarily shaped 3D structures
with the use of triangular patch modeling techniques [6]. In EFIE,
there is a time derivative of the magnetic vector potential. By
differentiating all the terms in the EFIE with respect to time, this
magnetic vector potential term is approximated by second-order
finite difterences, and an explicit solution is presented in [7], But
the results become unstable for late times. The late-time oscillation
could be eliminated by approximating the average value of the
current [8). In this method, the incident field is also differentiated.
The disadvantage of this procedure is that an impulse or step
function for the incident field cannot be used as an excitation. In
addition, to overcome this problem, a backward finite-difference
approximation for the magnetic vector po ential term has been
used tor the explicit technique [9], Many numerical results using
the explicit method with forward and backward difference
schemes have been shown in [6, 9, 10]. Recently an implicit
scheme has been proposed to solve two- or three-dimensional
scattering problems [11-15]. When one uses an explicit method,
the time step becomes very small and the computed time-domain
response becomes unstable. This is due to the accumulation of
numerical error and it takes much computation time. When an
implicit method is used, the time step is larger than that for the
explicit case. Therefore numerical error due to the approximation
of a time derivative with the use of finite difference is :ncreased.
In this Letter a central finite-difference methodology, which is
more accurate and provides stable solutions, is used.
It is well known that the solutions to both EFIE and MFIE in
the frequency domain are not unique when the incident field
includes internal resonant modes of the scatterer. Also, similar
problems are expected to arise in the time domain. In this work, the
time domain EFIE and MFIE are extended to a CFIE formulation.
The resulting EFIE and MFIE are then converted into matrix
equations and a combined EFIE and MFIE is then solved for CFIE
solution. The goal is to find that the CFIE gives a unique solution
of transient scattering problems when the incident wave includes
resonant frequencies of the scatterer. Tne solution technique de­
veloped in this work is capable of handling either an explicit or
implicit scheme of the EFIE. MFIE. and CFIE.
This Letter is organized as follows. In the next section, the
lime-domain EFIE. MFIE, and CFIE formulations are described.
Section 3 shows the numerical results for three-dimensional con­
ducting structures, and the results are compared with the inverse
Fourier transform of the frequency-domain CFIE solution. Last,
some conclusions based on this work are presented.
MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 34, No. 4, August 20 2002 .
289
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