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Feasibility of incorporating a low profile di planar inverted cone antenna and a microwave amplifier in the design of a broadband E-field probe

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University of Nevada, Reno
Feasibility of incorporating a low profile di Planar Inverted Cone Antenna and a
microwave amplifier in the design of a broadband E-field probe
A Thesis submitted in partial fulfillment of the requirements for the degree of Master of
Science in Electrical Engineering
By
Vijayendar Reddy Yelaka
Dr. Indira Chatterjee/Thesis Advisor
August 2007
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UMI N um ber: 1448334
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THE GRADUATE SCHOOL
University o f Nevada, Reno
We recommend that the thesis
prepared under our supervision by
VIJAYENDAR REDDY YELAKA
Entitled
Feasibility O f Incorporating A Low Profile Di Planar Inverted Cone Antenna And
A Microwave Amplifier In The Design Of A Broadband E-Field Probe
be accepted in partial fulfillment of the
requirements for the degree of
MASTER OF SCIENCE
Dr. Indira Chatteijee, Ph.D., Advisor
Dr. James Henson,Ph.D., Committee Member
Dr. Gale Craviso,Ph.D., Graduate School Representative
Marsha H. Read, Ph. D., Associate Dean, Graduate School
August, 2007
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i
ABSTRACT
The goal of this thesis is to perform a feasibility study for the design of a broadband
Electric field (E-field) probe to measure E-fields in the 1 - 6 GHz frequency range,
specifically inside a microwave anechoic chamber. The E-field probe incorporates a low
profile di Planar Inverted Cone antenna (LPdiPICA) and a microwave amplifier.
An E-field probe is a device that is used to measure E-fields in different indoor or
outdoor environments. It typically consists of the following basic elements: a dipole
antenna which has an omni-directional pattern, a detector mounted across the gap that
separates the two arms of the dipole for rectifying the measured signal, a transmission
cable connecting the detector output with a remote observation site, and the ability to
measure accurately a wide range of field strengths over a wide bandwidth o f frequencies.
The E-field probe designed in this thesis incorporates a LPdiPICA as the receiving
element instead of the commonly used dipole antenna. The LPdiPICA is selected due to
its broadband performance in terms of impedance and radiation pattern bandwidth. The
effect o f reducing the LPdiPICA dimensions to a quarter of its original size so that it is of
reasonable physical size for use in an E-field probe is investigated. However, this
decreased the impedance bandwidth at the lower frequency side. Several techniques
including 1. Increasing the relative dielectric constant and thickness of the substrate, 2.
Increasing the width of the antenna while maintaining the length constant and, 3. Wire
loading the antenna, are investigated as a possible means of increasing the bandwidth.
These results are presented and discussed.
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In addition, a microwave amplifier has been designed that will increase the
sensitivity of the E-field probe in situations where the E-fields are low. It is designed to
operate at the center frequency of 3.5 GHz with a bandwidth of 1 - 6 GHz. The design is
simulated and the results are presented.
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iii
ACKNOWLEDGEMENTS
I would like to express my appreciation and gratitude to my thesis advisor, Dr.
Indira Chatterjee for her guidance, support, and help in this thesis. This thesis would not
have been completed in such a short time without her help and constant encouragement. I
would also like to appreciate her patience and willingness to assist me during editing and
time spent completing my thesis. She is the best teacher I have had until now.
I would like to thank Dr Jim Henson of the Electrical and Biomedical Engineering
Department and Dr Gale Craviso of the Department of Pharmacology, members of my
thesis committee, for their efforts in the completion of this work.
I wish to express my heart felt gratitude to my parents Papi Reddy Yelaka and
Pushpalatha Yelaka for their constant support and encouragement all these years. I could
not have completed my Master’s without their hard work and sacrifice.
I would also like to acknowledge my fellow graduate students Todd Hagan and
Jihwan Yoon for their help with the XFDTD software.
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TABLE OF CONTENTS
Table of C on ten ts.................................................................................................................. iv
List of F ig u res........................................................................................................................ vi
List of T ab les......................................................................................................................... ix
C hapter 1 ................................................................................................................................. 1
In tro d u ctio n .............................................................................................................................1
1.1:
References................................................................................................................5
C hapter 2 .................................................................................................................................8
Background and L iterature S earch ....................................................................................8
2.1: Introduction..............................................................................................................8
2.2: Definition of Broadband Monopole antenna......................................................... 8
2.3: Broadband Antenna Theory.................................................................................. 10
2.4: Evolution of the Tear Drop antenna..................................................................... 11
2.5: Planar Inverted Cone antenna (PICA)..................................................................11
2.6: diPICA (di Planar Inverted Cone Antenna)..........................................................14
2.7: LPdiPICA (Low Profile diPICA)......................................................................... 15
2.8: References...............................................................................................................17
C hapter 3 ............................................................................................................................... 19
Amplifier
3.1: Introduction............................................................................................................19
3.2: Scattering Parameters............................................................................................20
3.3: Transistor.................................................................................................................22
3.4: Impedance Matching Networks............................................................................ 25
3.5: Stability................................................................................................................... 26
3.6: Simultaneous Conjugate M atch............................................................................ 27
3.7: Bias Network......................................................................................................... 29
3.8: References............................................................................................................. 29
C hapter 4 ...............................................................................................................................30
Amplifier D esign.................................................................................................................. 30
4.1: Introduction.............................................................................................................30
4.2: Microwave Transistors..........................................................................................31
4.3: Stability Factor........................................................................................................31
4.4: Stability Circles.......................................................................................................33
4.5: Simultaneous Conjugate Match Coefficients...................................................... 35
4.6: Impedance M atching.............................................................................................. 37
4.7: Microstrip L ines..................................................................................................... 38
4.8: Matching N etw ork................................................................................................. 41
4.9: Transistor Biasing.................................................................................................. 43
4.10: References.............................................................................................................48
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V
C hapter 5 ...............................................................................................................................49
Results and Discussion.........................................................................................................49
5.1: Introduction............................................................................................................ 49
5.2: Software.................................................................................................................. 50
5.3: diPIC A .................................................................................................................... 50
5.3.1: diPICA with feed w ire ................................................................................. 56
5.3.2: Comparison of results for various heights of the feed wire below the
bottom surface of the substrate.................................................................. 60
5.4: LPdiPICA............................................................................................................... 62
5.4.1: LPdiPICA without the ground plane........................................................... 65
5.5: LPdiPICA with dimensions reduced by h a lf....................................................... 69
5.5.1: HLPD antenna ( e r = 10.2, thickness = 1.59 m m )..................................... 74
5.6: Quarter LPdiPICA (QLPD)...................................................................................79
5.6.1: QLPD ( s r = 2.33, thickness = 0.795 m m ).................................................80
5.6.2: QLPD ( s r = 37.28, thickness = 0.795 m m )............................................... 84
5.7: Investigation o f various methodsfor the extension of impedance
bandwidth for the Q LPD ......................................................................................88
5.7.1: Increasing the width of the QLPD patch.....................................................89
5.7.2: Wire loading the QLPD patch..................................................................... 92
5.7.3: Loading the patches of the Q LPD ............................................................... 95
5.8: Comparisons...........................................................................................................97
5.8.1: Effect of decreasing the length of the antenna........................................... 97
5.8.2: Effect of varying the relative dielectric constant of the substrate
(thickness = 0.795 m m )............................................................................. 100
5.8.3:
Effect of varying the thickness of the substrate ( e r = 2.33)....................102
5.9: References............................................................................................................. 104
C hapter 6 ............................................................................................................................. 106
Conclusions and Future W o rk .........................................................................................106
6.1: Conclusions........................................................................................................... 106
6.2:
Future w o rk .........................................................................................................108
A ppendix..............................................................................................................................109
Appendix A ...........................................................................................................................109
Appendix A ...........................................................................................................................I l l
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vi
LIST OF FIGURES
Figure 2.1:
Figure 2.2:
Figure 2.3:
Figure 2.4:
Figure 3.1:
Figure 3.2:
Figure 3.3:
Figure 3.4:
Figure 3.5:
Figure 4.1:
Figure 4.2:
Figure 4.3:
Figure 4.4:
Figure 4.5:
Figure 4.6:
Figure 4.7:
Figure 4.8:
Figure 4.9:
Figure 4.10:
Figure 4.11:
Figure 4.12:
Figure 4.13:
Figure 4.14:
Figure 4.15:
Figure 5.1:
Figure 5.2:
Figure 5.3:
Figure 5.4:
Figure 5.5:
Figure 5.6:
Figure 5.7:
Evolution of the tear drop antenna from a tapered
coaxial transmission lin e .................................................................................12
Various forms of the PIC A ............................................................................ 13
Two-circular-hole diPICA ............................................................................. 15
Geometry of the LPdiPICA............................................................................ 16
Block diagram of a microwave amplifier...................................................... 19
Schematic of a two-port network.................................................................. 20
Bipolar Junction Transistors........................................................................ 23
BJT with BE junction forward biased and BC junction reverse biased
24
A basic block diagram for a microwave amplifier....................................... 27
Diagram showing the simulation setup in ADS for finding
stability factor K ............................................................................................. 32
Simulation Setup for plotting the stability circles in ADS..........................34
Plot showing the stability circles generated using A D S .............................35
Simulation setup to find simultaneous match coefficients using A D S
36
Matching networks that will be used to match the transistor.................... 37
Geometry of a microstrip lin e ......................................................................39
A typical window of ‘LineCalc’ in ADS used to calculate
the lines and widths of the microstrip lines................................................. 40
Block diagram in ADS containing the input and
output matching circuits................................................................................ 42
The gain (S21 ) of the amplifier with the input and output
microstrip matching networks generated using A D S ................................. 42
The input return loss (Si 1) and output return loss (S22 )
of the amplifier with the input and output microstrip
matching networks generated using A D S ................................................... 43
A self bias network.......................................................................................45
Setup for finding the resistor values for the self bias netw ork................. 45
The bias network used for the transistor NE 29801, designed in A D S 46
Circuit schematic containing the bias network and
matching circuits in A D S ............................................................................. 47
The gain (S21 ) of the amplifier with the microstrip
matching networks and the bias circuit generated using A D S ................. 48
Geometry of the diPICA antenna................................................................51
diPICA impedance as a function of frequency calculated
using XFDTD and compared to results in [5.1]..........................................52
XFDTD computed VSWR plot of diPICA...................................................53
XFDTD computed radiation patterns of the diPICA
at various frequencies in the range 1 - 8 G H z............................................. 55
XFDTD computed maximum gain for the diPICA...................................... 55
Geometry of diPICA with the feed points..................................................... 56
XFDTD computed impedance of the diPICA with
height of the feed wire below the bottom surface of the
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Figure 5.8:
Figure 5.9:
Figure 5.10:
Figure 5.11:
Figure 5.12:
Figure
Figure
Figure
Figure
5.13:
5.14:
5.15:
5.16:
Figure 5.17:
Figure 5.18:
Figure 5.19:
Figure 5.20:
Figure 5.21:
Figure 5.22:
Figure 5.23:
Figure 5.24:
Figure 5.25:
Figure 5.26:
Figure 5.27:
Figure 5.28:
Figure 5.29:
Figure 5.30:
Figure 5.31:
Figure 5.32:
substrate equal to 1m m ...................................................................................57
XFDTD computed VSWR of the diPICA with
height of the feed wire below the bottom surface of the
substrate equal to 1m m ...................................................................................58
XFDTD computed radiation patterns of the diPICA with
height of the feed wire below the bottom surface of the
substrate equal to 1m m ...................................................................................59
XFDTD computed maximum gain of the diPICA with
height of the feed wire below the bottom surface of the
substrate equal to 1m m ...................................................................................60
Real part of impedance as a function of frequency
for different heights of feed wire below the bottom
surface of the substrate...................................................................................61
Imaginary part of impedance as a function of frequency
for different heights of feed wire below the bottom
surface of the substrate...................................................................................61
Geometry of the LPdiPICA...........................................................................63
XFDTD computed LPdiPICA antenna impedance..................................... 64
XFDTD computed VSWR plot for LPdiPICA............................................ 64
Impedance as a function of frequency LPdiPICA antenna
without ground plane....................................................................................66
XFDTD computed VSWR plot for LPdiPICA
without the ground plane............................................................................. 66
XFDTD calculated radiation patterns for LPdiPICA
without the ground plane............................................................................. 68
XFDTD computed maximum gain for the LPdiPICA
without the ground plane............................................................................. 68
Geometry of the H LPD ................................................................................. 70
Impedance as a function of frequency for LPDH ( e r = 2.33 )
calculated using XFDTD............................................................................. 70
XFDTD
computed VSWR plot for HLPD ( s r = 2.33 ) .........................71
XFDTD computed radiation patterns for HLPD ( s r = 2 .3 3 ).................... 73
XFDTD compute gain for the HLPD ( s r = 2 .3 3 )...................................... 73
Impedance as a function of frequency for HLPD antenna ( s r = 1 0 .2 )..... 76
XFDTD computed VSWR plot for HLPD ( e r = 10.2)...............................76
XFDTD computed radiation patterns for HLPD ( s r = 1 0 .2 )..................... 78
XFDTD computed gain for the HLPD with ( s r = 1 0 .2 ).............................78
Geometry of the Q LPD ................................................................................. 79
Impedance as a function of frequency for QLPD antenna ( s r = 2.33)
computed using X FDTD.............................................................................. 82
XFDTD
computed VSWR plot for HLPD ( e r = 2.33 ) ......................... 82
XFDTD computed radiation patterns for HLPD ( e r - 2 .3 3 ).................... 83
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Figure 5.33: XFDTD computed gain for the QLPD ( s r = 2 .3 3 ).................................... 84
Figure 5.34: Impedance as a function o f frequency for
QLPD antenna ( e r = 3 7 .2 8 )......................................................................... 85
Figure 5.35: XFDTD computed VSWR plot for HLPD ( s r = 3 7 .2 8 )............................86
Figure 5.36: XFDTD computed radiation patterns for the HLPD ( e r = 37.28 ) ............87
Figure 5.37: XFDTD compute gain for the QLPD ( s r = 3 7 .2 8 ).................................... 88
Figure 5.38: Geometry of the wider Q LPD ....................................................................... 89
Figure 5.39: Wider QLPD mesh generated in XFDTD.................................................... 90
Figure5.40: XFDTD computed impedance for wider QLPD
and compared with Q LPD ........................................................................... 91
Figure 5.41: XFDTD computed VSWR for wider QLPD
and compared with Q LPD ........................................................................... 91
Figure 5.42: Geometry of the wire loaded Q LPD ............................................................. 93
Figure 5.43: XFDTD computed impedance for the wire loaded QLPD
and compared with Q LPD ........................................................................... 94
Figure 5.44: XFDTD computed VSWR for the wire loaded QLPD
and compared with Q LPD ........................................................................... 94
Figure 5.45: Geometry of the loaded Q LPD .....................................................................95
Figure 5.46: XFDTD computed impedance for the loaded QLPD.
The results for the QLPD are also plotted for comparison.........................96
Figure 5.47: XFDTD computed VSWR for the loaded QLPD.
The results for the QLPD are also plotted for comparison.........................97
Figure 5.48: Real part of impedance as a function of frequency
for different antennas (full (LPdiPICA), half (HLPD),
and quarter (QLPD)).....................................................................................98
Figure 5.49: VSWR as a function of frequency
for different antennas (full (LPdiPICA), half (HLPD),
and quarter (QLPD))....................................................................................99
Figure 5.50: Comparison of the real part of impedance as a function of
frequency for different relative dielectric constants of the
substrate used in the QLPD (thickness of substrate = 0.795 m m ).......... 101
Figure 5.51: Comparison of VSWR as a function of frequency for
different relative dielectric constants of the substrate used
in the QLPD (substrate thickness = 0.795 m m )........................................ 102
Figure 5.52: Comparison of impedance as a function of frequency
for different thicknesses for the QLPD (full, half, quarter)..................... 103
Figure 5.53: Comparison of VSWR as a function of frequency
for different thicknesses of the QLPD (full, half, quarter)...................... 104
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List of Tables
Table 4.1:
Table 4.2:
Table 4.3:
Table 4.4:
Table 4.5:
Table 4.6:
Table 4.7:
Table 4.7:
Stability factor over the specified frequency range
generated using A D S .......................................................................................33
S-parameters at the center frequency of 3.375 GHz
obtained using A D S .........................................................................................35
Simultaneous match coefficients TMS. and YML at the
center frequency 3.375 G H z........................................................................... 37
Electrical lengths of the shorted stub and series lines
for the input and output matching circuits..................................................... 38
RT/ Duroid 5880 characteristics [4.3].............................................................39
Widths and lengths of the short circuited stub and series
transmission line for the input matching network calculated
using ‘LineCalc’ .............................................................................................. 40
Widths and lengths of the short circuited stub and series
transmission line for the output matching network calculated
using ‘LineCalc’ .............................................................................................. 41
Resistor values used in the bias network........................................................ 46
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1
CHAPTER 1
INTRODUCTION
An electric-field (E-field) probe is a device that is used to measure or monitor Efields in indoor or outdoor environments. A need was created for improved
electromagnetic (EM) field measurements in both free space and material media, when
concern arose in the 1970s over the possible health hazards to humans of nonionizing EM
radiation [1.1]. Also with the advances in wireless communications there arose the
necessity to develop EM field probes that operate at microwave frequencies, have
broader bandwidth, smaller size, and at the same time are highly sensitive and accurate
[
12] .
An E-field probe generally consists of the following basic components: a dipole
antenna which has an omni-directional pattern, a detector mounted across the gap that
separates the two arms of the dipole for rectifying the measured signal, a transmission
cable connecting the detector output with a remote observation site, and the ability to
measure accurately a wide range of field strengths. Three mutually perpendicular
antennas may be combined in a closely spaced array to construct an E-field probe with an
isotropic response [1.1, 1.3]. Commonly used detectors are diodes. Thermocouple
detectors are used for obtaining time-averaged data in the case of high peak-power
modulated fields [1.1]. The transmission cable may consist of highly resistive
transmission lines or optical fibers with a suitably modulated light source [1.2].
E-field probes can be implemented in a variety of ways. Standard probes used earlier
were an electrically short dipole, a resistively-loaded dipole, a half-wave dipole, an
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2
electrically small loop, and a resistively-loaded loop. A single-turn loop designed for
simultaneous measurement of the electric and magnetic components of near-fields and
other complex electromagnetic environments was also used. Each type of antenna
presents a different compromise between broadband frequency response and sensitivity
[1.1, 1.4, 1.5].
The operation of the E-field probe can be explained as follows. When a continuous
wave o f certain frequency is incident on a dipole, it produces an oscillating voltage across
the detector terminals. A signal with dc component proportional to the square of the
amplitude o f the incident field is developed at the detector due to its nonlinear
characteristics. This dc component is then conveyed over the transmission line to the
monitoring instrumentation. Thus, a signal proportional to the square of the amplitude of
the incident E-field is measured [1.1].
Generally, three orthogonal dipoles are used for obtaining an isotropic response. The
detector in the probe is usually a Schottky barrier diode or a thermocouple junction. A
highly resistive (high resistance per unit length) transmission line used as a transmission
cable has several advantages: 1) The direct reception of the incident E-field by the line is
minimized 2) The scattering of the incident E-field by the line is reduced, and 3) It
suppresses the transferring of interference to the detector and monitoring instrumentation
by behaving as a low-pass filter.
There are several applications for E-field probes, one of these being the
measurement of E-fields to which humans are exposed for the assessment of nonionizing
radiation hazards. Another application is for the measurement of E-fields for EM
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3
compatibility [1.1], [1.3], for example in the monitoring of the E-fields in the proximity
of electronic devices which are susceptible to radio frequency interference [1.1].
The main objective of this thesis is to design a small broad band ( 1 - 6 GHz) E-field
probe for measuring the E-fields in an anechoic chamber. Even though many types of Efield probes have been designed to date, most of them use dipole probes as their receiving
element [1.1], [1.2], [1.4], [1.6], [1.7]. But dipole antennas have the inherent
disadvantage of being narrowband, which makes E-field probes that incorporate them
also narrow band. There have been attempts to increase E-field probe bandwidths, via
changes made to a dipole (e.g. tapered resistive dipoles [1.4], resistively loaded dipoles
[5.6], etc.). In this thesis, the feasibility of using a special type of patch antenna as the
receiving element in a broadband E-field probe is explored. The patch antenna used is a
Low Profile di Planar Inverted Cone Antenna (LPdiPICA) [1.8], [1.9], [1.10]. This is a
wide band antenna and therefore can be used for a broad range of frequencies. It also has
an omni directional radiation pattern. The size of the antenna would be small, so that it
can be used in small spaces.
In order to improve the sensitivity of the E-field probe, an amplifier is designed for
placement in front of the detector [1.2]. This would help to amplify the received signal
and increase the sensitivity o f the probe, which in turn would allow the measurement of
low level fields. The amplifier is designed using the discrete transistor amplifier method,
which provides greater design flexibility in terms of gain, bandwidth, and power output
requirements [1.11], [1.12], [1.13].
Although E-field probes are available commercially, they are expensive, large in
size or not available in the frequency range required for this project, which is 1 - 6 GHz.
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4
One such probe is the EF-105 (ENPROBE, Berlin, Germany) [1.15]. It has extremely
small dimensions (5 mmx 5 mm x 5 mm) and a frequency range of 1 MHz - 1 GHz.
Another probe PS-400 (Com-Power Corporation, California, USA) [1.16] has a
frequency range of 20 MHz - 2 GHz. It has dimensions of 9.9 cm x 1.52 cm. The HI6105 Electric Field Probe (ETS-Lindgren, IL, USA) [1.17] has an operating frequency
range o f 100 kHz - 6 GHz and dimensions of 32 mm x 32 mm x 32 mm, housed in a 43
mm sensor protection cap. Although this probe has the ideal frequency range for our
application, the probe dimensions are rather large.
Chapter 2 in this thesis will present relevant background information on broadband
antennas and examples of several broad band antennas. Specifically information on the
evolution of the teardrop antenna will be discussed, since this antenna forms the basis for
the Planar Inverted Cone Antenna (PICA) and di PICA (diPICA) that are the antennas
chosen in the design of the E-field probe. The evolution of the low profile diPICA
(LPdiPICA) is also presented.
Chapter 3 explains the relevant theory pertaining to the design of microwave
amplifiers. Scattering parameters are explained, as they are critical for the selection of
transistors as well as the Bipolar Junction Transistor, impedance matching networks,
stability of the transistor, simultaneous match coefficients and bias networks.
Chapter 4 explains the actual procedure for designing of a microwave amplifier. The
results of the designed amplifier are provided in this chapter. Chapter 5 contains the
computed results for the impedance, VSWR and radiation patterns of the diPICA,
LPdiPICA, and LPdiPICA without a ground plane, Half LPdiPICA (HLPD), and Quarter
LPdiPICA (QLPD). Results are also provided for the various methods that have been
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5
implemented to increase the impedance bandwidth of the QLPD on the low frequency
end of the bandwidth. The final section contains comparison plots for various antennas.
The parameters that are used for comparison include the length of the antenna, and the
relative dielectric constant and thickness of the various antennas. The conclusions and
future work will be discussed in chapter 6.
1.1 References
[1.1]. H. I. Bassen and G. S. Smith, “Electric Field Probes - A Review,” IEEE Trans.
Antennas and Propagation, Vol. AP-31, No. 5, September 1983, pp. 710-718.
[1.2]. A.Glassmachers, “Active Miniature Radio Frequency Field Probe,” Advances in
Radio Science 2003, pp. 161-164.
[1.3]. H. I. Bassen, “Electric Field Probes for Cellular phone Dosimetry,” IEEE
Proceedings - 19th International Conference- IEEE/EEMBS Oct.30 - Nov.2, 1997
Chicago, IL.USA, pp. 2492-2495
[1.4]. M. Kanda and L. D. Driver, “An Isotropic Electric-Field Probe with Tapered
Resistive Dipoles for Broad-Band Use, 100 kHz to 18 GHz,” IEEE Trans. Microwave
Theory and Techniques, Vol. MTT-35, No. 2, February 1987, pp. 124-130.
[1.5]. M. Kanda, “Standard Probes for Electromagnetic Field Measurements,” IEEE
Trans. Antennas and Propagation, Vol. 41, No. 10, October 1993, pp.1349-1364
[1.6]. K. Pokovic', T. Schmid, and N. Kuster, “Millimeter-Resolution E-Field Probe for
Isotropic Measurement in Lossy Media between 100 MHz and 20 GHz,” IEEE Trans, on
Instrumentation and Measurements, Vol. 49, No. 4, August 2000, pp. 873-878
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
6
[1.7]. Z. Harasztosi, “High Frequency E-field Probe,” 24th International Spring Seminar
on Electronics Technology, May 5-9,2001, Calimanesti-Caciulata, Romania, pp. 172-174
[1.8]. S-Y. Suh, “A comprehensive investigation of a new planar wide band antenna,”
Ph.D. Dissertation, Virginia Polytech. Inst. State Univ., Blacksburg, VA, July 2003.
[1.9]. S-Y. Suh, W. L. Stutzman, W. A. Davis, “A new ultrawideband printed monopole
antenna: the planar inverted cone antenna (PICA),” IEEE Trans. Antennas and
Propagation, Vol. 52, No. 5, May 2004, pp. 1361-1365.
[1.10]. S-Y. Suh, W. L. Stutzman, W. A. Davis, A. Waltho, J. Schiffer, “A novel
broadband antenna, the low profile dipole planar inverted cone antenna (LPdiPICA),”
IEEE Antennas and Propagation Soc. Int. Symposium, 2004, Volume 1,20-25 June 2004,
pp. 775 - 778.
[1.11]. S. N. Talbot, “Development of a Step-by-Step Procedure for the Design of a
Discrete Buffer Amplifier Operating between 11.8 GHz and 12.5 GHz,” Master’s Thesis,
Univ. of N evada, Reno, NV, August 2001.
[1.12]. G. Gonzalez, Microwave Transistor Amplifiers - Analysis and Design, 2nd
edition, Prentice Hall, Inc., New Jersey, 1997.
[1.13]. D. M. Pozar, Microwave Engineering, Addison- Wesley Publishing Company,
Reading, Massachusetts, 1990.
[1.14]. W. L. Stutzman, G. L. Thiele, Antenna Theory and Design, 2nd edition, John
Wiley & Sons, Inc., New York, 1998.
[1.15]. “Preliminary Technical data,” http://www.enprobe.de
[1.16].
“Near
field
probe
set
for
EMI
/
EMC
testing,”
http://www.com-
power.com/nfprobes.htm
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
7
[1.17]. “HI-6105 Datasheet,” http://www.ets-lindgren.com
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
8
CHAPTER 2
BACKGROUND AND LITERATURE SEARCH
2.1 Introduction
A broadband antenna is one which operates over a frequency range greater than 25
% of the operating center frequency. If the operating center frequency is in the GHz range
this entails a large bandwidth. So narrowband antennas like thin wire dipoles and
microstrip antennas which operate over 10 % of the operating center frequency cannot be
used for broadband E-field probes. Although classic antennas like horn antennas and
spiral antennas [2.1] are broadband, their dimensions make them impractical for use in Efield probes that are usually required to be small in size.
In this chapter the definition of broadband antenna is presented first. Also examples
o f several broadband antennas are presented. Then the theory behind broadband antennas
is presented. The evolution of the tear drop antenna which forms the basis for the Low
Profile di Planar Inverted Cone antenna (LPdiPICA) used in the E-field probe is
discussed. Finally, the PICA, di Planar Inverted Cone antenna (diPICA), and LPdiPICA
are discussed and theory behind them is presented.
2.2 Definition of Broadband Monopole antenna
A broadband E-field probe requires a broadband antenna to measure E-fields over a
wide bandwidth. The main challenge in broad band antenna design is achieving a wide
impedance bandwidth while maintaining high radiation efficiency. The bandwidth o f an
antenna according to IEEE standard [2.4] is defined as “the range of frequencies within
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9
which the performance o f the antenna, with respect to some characteristics, conforms to a
specific standard.” The characteristics can be impedance, radiation pattern, gain, etc. The
bandwidth as a percent of center frequency can be defined as [2.5, pp. 225]:
^ x 100%
Bp = £ u
(2 .1)
fc
where f , and f L are the upper and lower frequencies respectively over which
satisfactory performance is obtained and f c is the center frequency.
Bandwidth can also be defined as a ratio Br [2.5, pp. 225]:
(2 .2)
The impedance bandwidth is defined for a Voltage Standing Wave Ratio (VSWR)
less than 2. It indicates the bandwidth for which the antenna is sufficiently matched to its
input transmission line such that 10% or less of the incident signal is lost due to
reflections [2.1]. Pattern bandwidth is a little difficult to define and is taken as the
frequency range over which the radiation pattern is satisfactory for a specific application.
According to the IEEE Standard [2.4], an antenna radiation pattern (or antenna pattern) is
defined as “a mathematical function or a graphical representation o f the radiation
properties o f the antenna as a function of space coordinates. In most cases, the radiation
pattern is determined in the far-field region and is represented as a function of the
directional coordinates. Radiation properties include power flux density, radiation
intensity, field strength, directivity phase or polarization.” Three dimensional radiation
patterns are typically measured in a spherical coordinate system indicating relative
strength of radiation power in the far field spherical region surrounding the antenna.
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10
An antenna is classified as a broadband antenna if the impedance and radiation
f
pattern characteristics do not change significantly over an octave ( — = 2) [5.5]. The
II
classic broadband antennas are the spheroidal antenna, biconical antenna, spiral antenna,
circular disc antenna, trapezoidal antenna, and teardrop antenna [2.2], [2.5], [2.6], [2.7].
All these antennas provide a bandwidth that is larger than 2:1.
2.3 Broadband Antenna Theory
The theory behind the broadband characteristics of these antennas is based on the
fact that a thicker wire dipole antenna provides wider impedance bandwidth than a thin
wire dipole antenna. This can be explained from the fact that most of the electromagnetic
energy is stored within a few wire radii of a thin dipole. Therefore, the fields are most
intense around the wire radius and can be approximated by a TEM transmission line
model, which corresponds to high Q resonance. However, as the dipole wire radius
becomes thicker, the TEM transmission line model approximation breaks down and a
lower Q resonance is obtained. Thus, thickening a dipole spreads the energy throughout
the dipole and lowers its resonant Q value. Since Q is inversely proportional to the
bandwidth, a lower Q resonant value results in increased bandwidth [2.5], [2.8].
Bandwidth versus length to diameter (1/d) ratios of antennas have been presented in [2.5,
pp 172]. The results show that as the diameter of the thin wire dipole increases the
bandwidth also increases. Thus, ultra wide band (UWB) performance can be achieved by
appropriately modifying the wire antenna by introducing planar shapes such as circular
and elliptical discs as well as square plates. Circular and elliptical disc planar monopole
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11
antennas have potential for obtaining ultra wide bandwidths [2.9]. Square planar
monopole antennas are able to achieve an overall impedance bandwidth of 1.2 - 5.2 GHz
[2.10] that is narrower than that obtained for circular (2.25 - 17.25 GHz) [2.11] or elliptic
planar monopole antennas ( 1 .2 - 1 2 GHz) [2.6].
2.4 Evolution of the Tear Drop antenna
An antenna may be defined as a structure associated with the region of transition
between a guided wave and free space, or vice versa. The transmission line acts as a
guide for a plane wave and it has constant impedance over a broad band of frequencies.
As explained above, the bandwidth of a dipole antenna can be increased by using a thick
wire. If this concept is extended and a coaxial transmission line is flared out while
maintaining the ratio of the conductor diameters D/d constant as in Figure 2.1 (a), the
characteristic impedance of the line is kept constant along the transmission line [2.2]. If
the taper is gradual and D is large where the line ends, this device radiates with little
reflection over a very wide bandwidth (Figure 2.1 (b)). The teardrop antenna shown in
Figure 2.1 (c) can be designed by shaping the top part of Figure 2.1 (a). The bandwidth
can be further enhanced by tapering the ground plane of the tear drop antenna.
2.5 Planar Inverted Cone antenna (PICA)
The PICA is a wide band monopole antenna with a ground plane perpendicular
to the radiating element as shown in Figure 2.2 (a). The radiating element is etched on a
dielectric substrate. The PICA was invented by Seong-Youp Suh at Virginia Tech. and is
presented in [2.2]. He worked extensively on various wideband antennas. These include
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12
(a) Flared coaxial transmission line [2.1]
(b) Wide band antenna [2.12]
(c) Tear drop antenna [2.1]
Figure 2.1: Evolution of the tear drop antenna from a tapered coaxial transmission line.
the PICA, diPICA and low profile diPICA (LPdiPICA). The diPICA is explained in the
next section. The diPICA and LPdiPICA evolved from the PICA which itself was
evolved from the monopole circular disc and tear drop antennas.
The PICA can be regarded as a circular disc with its top part trimmed to the shape of
a planar inverted cone. A circular disc antenna as described in section 2.2 has a very large
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bandwidth (1.2 - 5.2 GHz) [2.11]. This is because, the resonant modes of the circular
resonator are characterized by the roots of the Bessel function rather than sine or cosine
functions that tend to describe the fields of rectangular resonators. This results in the
resonant modes being much more closely spaced than those of other antenna
configurations, which leads to less variation in impedance bandwidth and hence larger
bandwidth. Also the tapering of the top part of the antenna further increases the
bandwidth. This follows from the theory that adding sharp comers to a thick dipole
antenna adds current nulls at antiresonant frequencies. This leads to lower standing wave
length ratios at those frequencies resulting in a broader bandwidth [2.5].
z
x
L-5UV4
L=Xl/4
(a) PICA
(b) Two circular hole PICA
Figure 2.2: Various forms of the PICA.
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14
In the case of PICA, there is no requirement for a tapered ground plane as in the case
of the tear drop antenna for obtaining a wide impedance bandwidth. This is because the
radiating element has a round shape at the bottom of the element to compensate for the
gradually tapered ground plane [2.2]. This is the most important factor in determining the
impedance bandwidth. The length of the antenna is X, / 4 where XL is the wavelength at
the lowest frequency. The ratio of L1/L2 as shown in Figures 2.2 (a) and 2.2 (b) is 1.609,
which is close to the golden ratio (or sacred section) of 1.618 [2.13]. The PICA provides
outstanding impedance bandwidth and pattern performance. The impedance bandwidth is
more than 10:1 and the pattern bandwidth is more than 4:1. In addition, the pattern
bandwidth can be increased by creating two holes in the patch radiating element as shown
in Figure 2.2. This improvement increases the pattern bandwidth to 7:1 without degrading
the impedance bandwidth. This is due to the fact that the holes control the flow o f the
current in the metal plate so that the frequency response of the element is improved
without deteriorating the impedance performance [2.2], [2.13].
2.6 diPICA (di Planar Inverted Cone Antenna)
The diPICA is a dipole version of the monopole PICA antenna [2.1]. It basically
consists of two PICA elements which are of the same size as the monopole PICA. The
two-circular-hole diPICA shown in Figure 2.3 is a dipole version of the two-circular-hole
PICA. It is fed at the center at the two feed points as shown in Figures 2.3(a) and (b)
[2.14]. The diPICA provides excellent antenna performance in both antenna impedance
and radiation patterns. It has an impedance bandwidth of 10:1 and a radiation pattern
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15
bandwidth o f 8:1. The radiation pattern is similar to that of a wire dipole which is omni­
directional.
Feed
Penis
(a) Top view
(b) Side view
Figure 2.3: Two-circular-hole diPICA.
2.7 LPdiPICA (Low Profile diPICA)
The radiation pattern of the diPICA is omni directional [2.14]. Some applications
require a unidirectional radiation pattern. The standard method o f obtaining a
unidirectional pattern is to back the antenna with a ground plane parallel to and A/4
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16
behind the antenna. The low profile diPICA as shown in Figure 4.4 is obtained by
introducing a ground plane parallel to the diPICA at a height o f A,/4 below the diPICA.
The diPICA patch is placed on a dielectric substrate. It has an excellent impedance
bandwidth of 10:1 and radiation pattern bandwidth of 2.2:1.
MetaSzadoo
Foam
Coaxial Feed <
Ground Plane
(a) Side view
DO.
oo
Patch
Substrate
(b ) Top View
Figure 2.4: Geometry of the LPdiPICA.
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17
The antennas described in this chapter are designed and characterized in this thesis for
designing an E-field probe that will operate in the frequency range 1 - 6 GHz.
2.8 References:
[2.1]. J. D. Kraus, Antennas, McGraw Hill, New York, 1950, pp. 9, Chap 1.
[2.2]. S-Y. Suh, “A comprehensive investigation of a new planar wide band antenna,”
Ph.D. Dissertation, Virginia Polytech. Inst. State Univ., Blacksburg, VA, July 2003.
[2.3]. S. Honda, M. Ito, H. Seki and Y. Jinbo, “A disc monopole antenna with 1:8
impedance bandwidth and omni-directional radiation pattern,” Proc. ISAP ’92 (Sapporo,
Japan), pp. 1145-1148, Sep. 1992.
[2.4]. Antenna Standards Committee of the IEEE Antennas and Propagation Society,
“IEEE Standard Definitions of Terms for Antennas, IEEE Std,” 145-1993, The Institute
of Electrical and Electronics Engineers, Inc, New York, 1993.
[2.5]. W.L. Stutzman and G. A. Thiele, Antenna Theory and Design, 2nd edition, John
Wiley & Sons, Inc., New York, 1998.
[2.6]. N. P. Agrawall, G. Kumar, and K. P. Ray, “Wide-band Planar Monopole
Antennas,” IEEE Transactions on Antennas and Propagation, Vol. 46, No. 2, pp.294-295,
Feb. 1998.
[2.7]. J. A. Evans and M. J. Ammann, “Planar Trapezoidal and Pentagonal monopoles
with impedance bandwidth in excess of 10:1,” IEEE International Symposium Digest
(Orlando), Vol. 3, pp. 1558-1559, 1999.
[2.8] C.A. Balanis, Antenna Theory and Analysis, 2nd ed., Wiley, New York, 1997.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
18
[2.9]. M. J. Ammann, “Impedance Bandwidth of the Square Planar Monopole,”
Microwave and Optical Technology Letters, Vol. 24, No. 3, pp. 185-187, Feb. 5 2000.
[2.10]. X. N. (Jerry) Qiu, H. M. Chiu and A. S. Mohan, “Techniques to improve ultra
wide band performance of planar monopole antenna,” IEEE/ACES International
Conference on Wireless Communications and Applied Computational Electromagnetics,
pp. 186-190,2005.
[2.11]. P. P. Hammoud and F. Colomel, “Matching the input impedance of a broadband
disc monopole,” Electron. Letters, Vol. 29, pp. 406-407, Feb. 1993.
[2.12]. Radio Research Laboratory (U.S.), “Very High-frequency Techniques,” McGraw
Hill, New York, 1947, pp.1-25, Chap 1.
[2.13]. S-Y. Suh, W.L. Stutzman, W.A. Davis, “A new ultra wideband printed monopole
antenna: the planar inverted cone antenna (PICA),” IEEE Trans. Antennas and
Propagation, Vol. 52, No. 5, May 2004, pp. 1361-1365.
[2.14], S-Y. Suh, W.L. Stutzman, W.A. Davis, A. Waltho, J. Schiffer, “A novel
broadband antenna, the low profile dipole planar inverted cone antenna (LPdiPICA),”
IEEE Antennas and Propagation Soc. Int. Symposium, 2004, Volume 1,20-25 June 2004,
pp. 775 - 778.
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19
CHAPTER 3
AMPLIFIER
3.1 Introduction
An amplifier is a device that is used to increase a signal level. It forms an important
building block in microwave communication systems. A microwave amplifier consists of
the following blocks: 1) A transistor, 2) input matching network, and 3) output matching
network as shown in Figure 3.1, where Z s is the source impedance and Z , is the load
impedance [3.1, chapter 2].
500
T ra n sisto r
Input
M atching
N etw ork
Zs
O u tp u t
M atching
N etw ork
ZL
Figure 3.1: Block diagram of a microwave amplifier [3.1, chapter 2].
Although not explicitly shown in the block diagram, the transistor block also
contains the bias network to correctly bias the transistor. The bias network plays an
important role in the functioning of a transistor.
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20
3.2 Scattering Parameters
Scattering parameters (S-parameters) are a set of parameters which are used to
characterize the behavior of two-port networks at microwave frequencies. They are
defined in terms of traveling waves. S-parameters can be used to characterize microwave
networks containing a multiple number of ports. The popularity of S-parameters
increased due to availability of network analyzers that can be used to easily measure Sparameters. S-parameters are also used to characterize microwave transistors [3.1].
►
50ft
Two-port
Network
<
Vi
< -----
X
s ,12
v *2
50ft
v:
5”2i S 22
Figure 3.2: Schematic of a two-port network.
Figure 3.2 shows a schematic of a two-port network. Here Vx+ is the amplitude of the
incident wave at port 1, Vt~ is the amplitude of the reflected wave at port 1, V2 is the
amplitude o f the incident wave at port 2, and V2 is the amplitude of the reflected wave at
port 2 [3.2, chapter 4].
For a two-port network,
v;=suvx++snv2+
v2-=s2]v:+s22v2+
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(3.1)
(3.2)
21
where the S y represent the S-parameters of the network, i, j = 1, 2
1
+
1
1
1
1
1
These equations can also be written in matrix form:
(3.3)
1
1
<N
N1
<
Co
1
Sa '
Then the S-parameters are defined as follows:
(Input reflection coefficient with output port
terminated with a matched load)
^S2 1
“
(Forward transmission coefficient with
v;
v+=o
output terminated with a matched load)
12
(Reverse transmission coefficient with
y+
2
input terminated with a matched load)
(Output reflection coefficient with input port
Kj+ =0
terminated with a matched load)
The S-parameters for various microwave devices are usually specified in decibels
(dB):
l^n \da ~ 201°g|Sn |
(3.4)
\dB = 20 log|S'211
(3.5)
|S12|<B=201og|512|
(3.6)
= 201og|S'22|
(3.7)
1^21
1*^22 \dB
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22
If the two-port network in Figure 3.2 represents a transistor, then it should be
properly biased. Therefore the S-parameters for a transistor are given at the Q (quiescent)
point, under small signal conditions [3.1, chapter 2]. Small signal modeling is a common
analysis method used in electrical engineering to describe nonlinear devices in terms of
linear equations. A nonlinear device is one that does not have a linear input / output
relationship. For example, in a transistor, current and voltage do not have a linear
relationship. So, small signal conditions are obtained by writing the voltages and currents
of a transistor in terms of linear equations and solving them. The Q point is the operating
point of a transistor. It provides the correct bias or dc voltage that must be applied to the
transistor to get the desired response. Also, since they change with frequency, Sparameters for the whole frequency range over which the transistor operates satisfactorily
is provided by the manufacturers [3.3].
S-parameters can be used to calculate many of the important characteristics of
transistor amplifiers. These include the gain, stability factor, and matching circuits for the
input and output impedances.
3.3 Transistor [3.4,3.5]
A transistor is a three-terminal semiconductor device that performs one of the most
fundamental functions in the design of electronic circuits, which is amplification of a
signal. Two common types of microwave transistors are bipolar junction transistors
(BJT’s) and gallium arsenide field effect transistors (GaAS FET’s). The BJT is a current
controlled device which is typically used below 4 GHz and the FET is a voltage
controlled device which is used at frequencies above 4 GHz. But BJT’s are preferred at
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23
lower GHz frequencies since they provide very good gain compared to FET’s at these
frequencies.
A BJT is manufactured by using NPN silicon technology. It is formed by joining
three sections of semiconductor material, each with a different doping concentration. The
three sections can be either a thin n region sandwiched between p + and p layers, or a p
region between n and n+ layers, where the superscript plus indicates a more heavily
doped material. The resulting BJT’s shown in Figures 3.3 (a) and 3.3 (b) are called PNP
and NPN transistors, respectively. For amplification purposes, NPN BJT’s are commonly
used.
Collector
CoBector
B
Base -
K
B
Base
n+
Emitter
(a) PNP transistor and its circuit symbol
Emitter
(b ) NPN transistor and its circuit symbol
Figure 3.3: Bipolar Junction Transistors.
The operation of the NPN BJT may be explained by considering the transistor as
consisting o f two back-to-back PN junctions. An NPN transistor is said to be biased if
the base-emitter (BE) junction is forward-biased and base-collector (BC) junction is
reverse biased as shown in Figure 3.4. In forward bias, the positive terminal is connected
to the P type material and negative terminal to the N type material. Reverse bias is
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24
exactly opposite that of forward bias. A transistor is needed to be biased to make it
function as an amplifier [3.4, 3.5]. When the BE junction is forward biased, the electrons
from the emitter cross into the base layer and some will combine with the holes in the
base. The remaining charges will give rise to a net flow of current from base to emitter.
This is because conventional current flow is opposite to the direction of electron flow.
5 1 l.
Ib
1
B
n+
Figure 3.4: BJT with BE junction forward biased and BC junction reverse biased.
Subsequently when the BC junction is reverse biased the electrons emitted by the
emitter with the BE junction forward-biased reach the very narrow base region, and after
a few are lost to combination with the holes in the base, most of these electrons are
collected by the collector. This is possible because the base region is very narrow and the
electron would have gathered enough electric energy to cross the base collector junction.
The result is that there is a net flow of current from collector to emitter. The electron
current flowing into the collector through the base is substantially larger than that which
flows into the base from the external circuit. From Figure 3.4 it can be observed that
Ie = Ib + Ic
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(3.1)
25
Thus by keeping the BE voltage positive with respect to the BC voltage, the collector
current can be controlled. We can also say by controlling the base current the collector
current which is the output current, can be controlled. The higher the BE voltage, the
higher is the collector current. Thus the most important parameters for a NPN BJT are the
BE voltage and the collector current. These two are usually specified in transistor
specifications by manufacturers.
3.4 Impedance Matching Networks
Impedance matching networks play a very important part in the design o f amplifiers.
For amplifiers to deliver maximum power to the load or to reduce the losses in an
amplifier, they must be properly terminated at the input and output ports.
The basic procedure is to transform the impedance of the transistor on the input and
output sides to the impedances of the source and load respectively. This involves the
design o f matching networks to ensure that maximum power is delivered to the load and
losses in the amplifier circuit are kept minimal [3.1, chapter 2].
As shown in the Figure 3.1, for the transistor to deliver maximum power to the 50 Q.
load, the transistor must have terminations Z s and Z L. The input matching network must
be designed to transform the generator impedance (50 Q ) to the source impedance Z s
and the output matching network must transform the 50 Q termination to the load
impedance Z L.
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26
There are several methods that can be used to design matching networks for a
microwave amplifier: Ell sections, single stub tuning and double stub tuning [3.1, chapter
2], [3.2, chapter 5].
3.5 Stability
An important consideration in the design of an amplifier is the stability or resistance
of the transistor to oscillate. The stability can be determined from the S-parameters, the
matching networks, and the terminations. Oscillations occur in a two-port network, when
either the input port or output port present a negative resistance.
A transistor can either be unconditionally stable or potentially unstable. An
unconditionally stable transistor has the real parts of the input and output impedances
greater than zero for all passive load and source impedances. A potentially unstable
transistor has input and output impedances with negative real part (negative resistance)
for some passive load and source impedances.
The conditions for a two-port network to be unconditionally stable are [3.1, chapter
3]:
A <1
(3.8)
K>1
(3.9)
or
where
2
K =
(3.10)
and
(3.11)
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27
3.6 Simultaneous Conjugate Match
A two-port device is said to be a unilateral network if a load at the output does not
affect the input and conversely a load at the input does not affect the output. A device is
unilateral ifS 12 = 0. If not, the device is bilateral i.e. ifS^ * 0.
Transducer gain is defined as the ratio of power delivered to the load to the power
available from thesource. It isone of the power gains that is used in the design of
microwaveamplifiers. The conditions required toobtainmaximum transducer gain are
[3.1, chapter 3]:
r s = r *iN
(3-12)
r\ = K u r
(3.13)
and
These conditions are illustrated in Fig.3.5 and are called simultaneous conjugate
match conditions.
50
Vs
n
Input
Matching
Network
Output
Matching
Network
Transistor
r1 S
r1 IN
rL OUT
r1 L
Fig 3.5: A basic block diagram for a microwave amplifier.
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In order to match a unilateral device, the simultaneous conjugate match conditions
must be satisfied. The input and output simultaneous match coefficients, Ts and Y , , have
to be calculated first to determine the conjugate match conditions.
The values of Ys and Y, required for a simultaneous conjugate match are referred to
as Tms andTMi, and are calculated using equations (3.14) and (3.15):
2C,
(3.14)
and
r1 MS =
2C.
(3.15)
where
Bx = i + |s n |2 - | s 22|2 - | a | 2
(3.16)
+ \s 22\2 - | s n |2 - | a | 2
(3.17)
b2
=
i
C, = S n - A S 22
(3.18)
(3.19)
Available gain is defined as the ratio of power available from the network to the
power available from the source. Maximum available gain for a bilateral transistor will
occur when the conditions for simultaneous conjugate match are satisfied, since under
simultaneous conjugate match conditions maximum transducer gain is equal to maximum
available gain [3.1, chapter 3]. This means that the input and output ports of a transistor
have to be terminated in YMS and YML respectively.
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29
3.7 Bias Network
As mentioned earlier, the transistor bias network plays an important role in the
design o f an amplifier. The main objective of the design of a bias network is to provide
proper DC bias to the transistor without affecting the RF portion of the amplifier
network. It also isolates the DC voltage from the RF signal. Coupling or blocking
capacitors and inductors constitute the DC bias network.
The main function of a transistor is to amplify the RF signal provided to its input
terminal. The DC voltage applied to the transistor controls the output voltage and current
of a transistor and hence the amount of amplification.
3.8 References
[3.1]. G. Gonzalez, Microwave Transistor Amplifiers - Analysis and Design, 2nd edition,
Prentice Hall Inc., New Jersey, 1997.
[3.2]. D. M. Pozar, Microwave Engineering, Addison- Wesley Publishing Company,
Reading, Massachusetts, 1990.
[3.3]. “2SA1977 Preliminary data sheet” NEC corporation, April 1996.
[3.4], S. Gibilisco, Basic Transistor Course, 2nd edition, Tab Books Inc., PA, 1984.
[3.5] G. Rizzoni, Principles and Applications of Electrical Engineering, 5th edition,
McGraw-Hill Inc., New Jersey, 2007.
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CHAPTER 4
AMPLIFIER DESIGN
4.1 Introduction
An amplifier can be used in an E-field probe to increase the magnitude of the
received signal if it is very low. The first step in the design of an amplifier is the selection
of an appropriate transistor.
Many considerations have to be taken into account when selecting a proper
transistor for a broadband microwave amplifier. The most important among these
considerations is the determination of the required specifications. These specifications are
usually driven by the role of the amplifier in a particular application. Once the
specifications are determined, the type of transistor can be selected and the data sheets of
potential transistors can be obtained from the manufacturers. The design specifications
for the broadband microwave amplifier required for amplifying the received signal of the
E-field probe are given below
Gain:
10 dB
Input VSWR:
<2:1
Output VSWR:
<2:1
Frequency of Operation: 1 - 6 GHz
Supply Bias
To be determined
Stability
Unconditional
The supply bias is typically specified as the collector current (Ic) and collector voltage
(V ce)-
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31
4.2 Microwave Transistors
Bipolar Junction Transistors (BJT’s) and Gallium Arsenide Field Effect Transistors
(GaAS FET’s) are the most common types of transistors used in microwave circuits.
BJT’s are typically used below 4 GHz and FET’s are used at frequencies above 4 GHz.
For this design, a NE29018 BJT manufactured by NEC Corporation [4.1] is selected. It
has a specified gain of 12 dB and its operating frequency range is above 6 GHz. Thus it
meets the required specifications.
As explained in section 3.5, one of the important factors in transistor selection is its
stability or the resistance of the transistor to oscillate. A transistor is said to be
unconditionally stable if the stability factor K > 1. Advanced Design System (ADS),
version 2006 A [4.2], a radio frequency/microwave design software from Agilent
Technologies, Santa Clara, California, was used for designing this amplifier. Everything,
from finding the stability to actually designing the circuit and getting the response can be
achieved with this software. Also, the chosen transistor can be directly accessed from the
software library in ADS without having to input the S-parameters of the transistor into
the software.
4.3 Stability Factor
The stability o f the transistor can be directly found by using the simulation set up
shown in Figure 4.1 using ADS. The transistor is terminated at the input and output
terminals with a standard 50 Q termination. A S-parameter simulation box is placed in
the setup to provide the S-parameters of the transistor required for calculating the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
32
stability factor. The frequency range is specified in this box. Then a stability factor box
‘StabFactl ’ is placed in the setup to find the stability factor.
Tt ehnota gy F i l e
1n e l u d a
&
Techlnclude_NEC_ACTIVELIBRARY
NEC_ACTIVELIBRARY_Lib
File=Nominal
s p_nec_N E21908_4_19940401
SNP1
Bias=”Bjt: Vce=8V lc=30mA"
Frequency=”{0.10 - 5.00} GHz”
SP
Term
Terml
Num=1
Z=50 Ohm
S-PARAMETERS
|
S_Param
SP1
Start=1 GHz
Stop=6 GHz
Step=500 MHz
Term
Term2
Num=2
Z=50 Ohm
Stab Fact
StabF actl
S tab F actl = stab Jac t(S )
Figure 4.1: Diagram showing the simulation setup in ADS for finding the stability factor
K.
A stability factor table as shown in Table 4.1 is obtained. The results in Table 4.1
show that the device is unconditionally stable for the entire range of frequencies specified
for this design. Hence we can say that the transistor is unconditionally stable. The
stability factor at the 3.375 GHz is 1.119.
The estimated maximum transducer gain (section 3.6) can be calculated using the
following method. At 3.375 GHz, S-parameters for the transistor are given below [4.1]:
S u = 0.652 , 5,2 =0.109, S21 = 2.130 , S 22 = 0.278
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
33
To estimate the gain available at the center frequency, the following simple formula can
be used [4.3]:
G a i n ^ = ^ - ( K - ^ K 2 - 1 ) = - ^ - ( 1 . 1 1 9 - V l . l l 9 2 -1 ) = 19.541 = 12.91 dB
^
Sn
0.109
Frequency (GHz)
Stability Factor(K)
1
1.151
1.5
1.130
2
1.099
2.5
1.065
3
1.134
3.5
1.121
4
1.074
4.5
1.067
5
1.087
5.5
1.124
6
1.182
(4.1)
Table 4.1: Stability factor over the specified frequency range generated using ADS
4.4 Stability Circles
Another method that can also be used to determine the stability of a transistor is by
plotting stability circles on a Smith chart. The regions outside these circles in the Smith
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34
chart are said to be stable. A Smith chart is a useful electrical engineering tool that can be
used for designing matching circuits.
It is a graphical aid which is used to analyze
matching circuits at microwave frequencies. Basically it is a plot of all passive
impedances in a reflection coefficient chart of unit radius [4.4].
The setup in ADS for plotting the stability circles is shown in Figure 4.2. The setup
is the same as that in Figure 4.1, except for the placement of a stability circle box
‘S StabCirclel’ instead of a stability box. The stability circle box is used for plotting the
stability circles.
©
Techlnclude_NEC_ACTIVELIBRARV
NEC_ACTlVELIBRARY_Lib
File=Nominal
S-PARAMETERS
S_Param
SP1
Start=0.75 GHz
Stop=6 GHz
Step=250 MHz
CalcNoise=yes
sp_nec_NE21908_4_19940401
SNP1
Bias=”Bjt: Vce=8V lc=30mA"
Frequency=”{0.10 - 5.00} GHz"
SP
Term
Terml
Num=1
Z=50 Ohm
SStabQide
S_StabCircle
S_StabCircle1
S_StabC ircle1=s_stab_circle(S ,51)
Term
Term2
Num=2
Z=50 Ohm
Figure 4.2: Simulation Setup for plotting the stability circles in ADS
After simulating the above setup the stability circles are plotted on the Smith chart.
As can be observed from Figure 4.3, the stability circles fall outside the Smith chart and
hence the load and source terminations can lie on any part of the Smith chart.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
35
O
indep(S_StabCircle1) (0.000 to 51.000)
Figure 4.3: Plot showing the stability circles generated using ADS
4.5 Simultaneous Conjugate Match Coefficients
As explained in section 3.5 of chapter 3, for a bilateral transistor to have maximum
gain the input and output of the transistor should be terminated with simultaneous match
coefficients TMS. and T ML. The S-parameters are obtained in ADS by using the same setup
as shown in Figure 4.1. The frequency in the simulation parameter box is set to the
frequency 3.375 GHz. The resulting S-parameters from the simulation, at the frequency
3.375 GHz are tabulated in Table 4.2.
Frequency
Sn
Sl2
S21
S22
3.375 GHz
0.652 Z 141.0U
0.109 Z 34.25°
2.130Z 34.25°
0.278 Z -99.5°
Table 4.2: S-parameters at the frequency of 3.375 GHz obtained using ADS.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
36
From Table 4.2, it can be observed t h a t ^ | = 0.109, which is not equal to zero, showing
that the transistor is bilateral.
The simultaneous match coefficients TMS. andTML can be found from equations
(3.14) to (3.19) in chapter 3 [4.3, chapter 3]. The calculations are included in Appendix
A. Alternatively, ADS can be used to find the simultaneous match coefficients. The setup
for finding them is shown in Figure 4.4. The stability box in Figure 4.1 is replaced by
source and load simultaneous match coefficient boxes, ‘SmGammal’ and ‘SmGamma2’
and are used to obtain Twv and TMI respectively. After running the simulation, TMS
and Y mi at the center frequency are obtained. They are shown in Table 4.3.
S-PARAMETERS
r * c h n o I o q y F11 ■
Inciudt
Techlnciude_NEC_ACTIVELIBRARY
NEC_ACTIVELIBRARY_Lib
File=N om inal
S _ P ara m
SP1
S tart= 3.375 GHz
S top= 3.375 GHz
Step=
■10
s p_nec_N E 2 1 9 0 8 _ 4 _ 1 9940401
SNP1
Bias="Bjt: Vce=8V lc=30m A"
Frequency= ”{0.10 - 5.00} GHz"
Term
T erm l
Num=1
Z=50 Ohm
SP
S n G a n ra l
Sm G am m al
Sm G am m al
S m G a m m a 1 = sm _ g a m m a 1 (S )
Term
T erm 2
N um =2
Z=50 Ohm
Sm G am m a2
Sm G am m a2
S m G a m m a 2 = sm _ g a m m a 2 (S )
Figure 4.4: Simulation setup to find the simultaneous match coefficients TMS and
using ADS.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ML
37
r1 MS
^ML
0.837Z -144.638°
0.677 Z 80.036°
Table 4.3: Simultaneous match coefficients TMS, and YML at the frequency 3.375 GHz.
4.6 Impedance Matching
The transistor should be terminated at the input and output with the simultaneous
match coefficients to obtain maximum available gain (section 3.6). Impedance matching
circuits are used for this purpose. There are several methods that are used for designing
the matching circuits. Matching circuits consisting of a short circuited shunt stub and a
series transmission line of appropriately designed lengths and widths are used in this
thesis [4.3, chapter 2]. The matching networks are shown in Figure 4.5.
Input Matching
Output Matching
SedesLine
Short
Stub
Short
Stub
Figure 4.5: Matching networks that are used to match the transistor.
The first step in the design of the matching circuits is to determine the lengths li, I2
and I 3 , 14 of the series transmission lines and shunt stubs respectively, needed to obtain the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
38
appropriate simultaneous matching coefficients, r MS and ^ ML , at the input and output of
the transistor. The matching networks are designed in ADS using a module called
‘SmithChart’. A two port network is created consisting of a short circuited shunt stub and
a series transmission line each with an electrical length of 0°. The electrical length of 0° is
equivalent to starting at the center of the Smith chart. The network consists of ideal
transmission lines. The length ‘li’ of the shunt stub is adjusted until the value on the
Smith chart is equal to |Tms. | . The length ‘h ’of the series line is adjusted until the angle is
equal to Z TMV. The same procedure is repeated on the output side. The lengths li, I2 , and
I3 , I4 needed to achieve the required TMS, and YML shown in Table 4.3 are provided in
Table 4.4.
Input matching network
Output matching network
li
I2
13
22.32 0
34.2°
28.8°
14
25.92
0
Table 4.4: Electrical lengths o f the shorted stub and series lines for the input and output
matching circuits.
4.7 Microstrip Lines
The shorted stub and series transmission lines used in the above section are ideal
transmission lines. They have to be converted into microstrip lines so that they can be
used in practical circuits. A microstrip line is a planar transmission line that is
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
39
commercially available. A conductor of width W is printed on a substrate of thickness d
and relative dielectric permittivity s r . A typical geometry of a microstrip line is shown in
Figure 4.6.
I
W
I
>\
I<-----i
--------- 1
Dielectric. s r
\
\
\
\
\
\
\
\
\
\
I
Figure 4.6: Geometry o f a microstrip line.
The microstrip line material used for the design of the amplifier is Rogers
Corporation RT / Duroid 5880 [4.4]. The specifications for this material are provided in
Table 4.5.
Material
RT / Duroid 5880
Relative Dielectric constant ( e r )
2.33
Dielectric Thickness (d)
0.757 mm
Conductivity (S/m)
4.1 x iov
Loss Tangent (tan 5)
0.0005
Foil thickness
70 pm
Table 4.5: RT/ Duroid 5880 characteristics [4.3]
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40
The length and width of the microstrip lines are then calculated using the ‘LineCalc’
calculator in ADS (Figure 4.7). The electrical specifications and the electrical lengths of
the ideal transmission lines have to be entered to obtain the lengths and the widths. The
lengths and widths of all four microstrip lines are calculated using LineCalc at the center
frequency and are provided in Tables 4.6 and 4.7 respectively.
i
I irtc( a l e / u n l i H c d
nto SkniaUon O ptkn
.
T . ^
H«fc>
D & 6 Si
Comport**
MUN
MUN: MUN_DEFAULT
Stitttrate P a anetett
id
Phpocd
- W [89737796
'A L
'496.386827
ig
Ei
[2200
iMu
[1.000
[H
[0787
Hu
[3.9e*34
T
[70.000
;Cond !4.1e7
<
ComponentPaanefea*
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E
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ZD 50000
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>
(GH* _~j
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H -TJ
1 _J
1” J
Anefc»
13
Ohm j-j
4*0
J
rrinfaMrinemii
K_E8.1.955
A
Be»plh
ao-ioQ.053ml
Sk.D
inO
jrri
[mi
Vjluot
Figure 4.7: A typical window of ‘LineCalc’ in ADS used to calculate the lengths and
widths of the microstrip lines.
Input Short Circuited Stub
Input Series Transmission Line
W (mils)
h (mils)
W (mils)
L 2 (mils)
88.737
155.04
88.737
237.56
Table 4.6: Widths and lengths of the short circuited stub and series transmission line for
the input matching network calculated using ‘LineCalc’.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
41
Output Shorted Circuit Stub
W (mils)
88.737
13
(mils)
200
Output Series Transmission Line
W (mils)
I4 (mils)
88.737
180
Table 4.7: Widths and lengths o f the short circuited stub and series transmission line for
the output matching network calculated using ‘LineCalc’
4.8 Matching Network
The values shown in Tables 4.7 and 4.8 are then used to design the input and output
matching circuits. The transistor is then terminated on the input and output with these
matching circuits and simulated in ADS. The setup in ADS with the input and output
matching circuits is shown in Figure 4.8.
The resulting plots in Figures 4.9 and 4.10 show S21 (gain), Sn (input return loss)
and S22 (output return loss) for the transistor. It can be observed from Figure 4.9, that the
gain S21 decreases with frequency. At the center frequency (3.5 GHz) S21 is 6.871 dB.
Although the amplifier has reasonable gain up to 4.5 GHz it does not meet the initial
specifications (gain: 10 dB, frequency range: 1 - 6 GHz).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
42
-----------------1
licnnolaBy
lneTu4«FIl«lI
Techlnclude_NEC_ACnVELIBRARY
NEC_ACTIVELBRARY_Lib
Fite=Nominal
S_F^ram
SP1
Start=1 GHz
Stop=6.0 GHz
Step=250NHz
MSubl
B=0.787 mm
Br=2.33
Mur=1
Cond=41E+7
Hu=3.9e+034 mil
T=70 um
TanD=0
Rough=0 mil
MLIN
TL3
Subst="MSub1"
W=88.737 nil
L=180 mi
IN
TL1
Subst=''MSub1"
W=88.737 mil
L=237.56 mil
MLEF
TL2
Subst="MSub1"
W=88.737 nil
L=155.04 mil
*1
MSub
S-PARAMETERSj
Term
Term2
Nunr=2
Z=50 Ohm
I
lprm
Terml
Num=1
Z=50 Ohm
MLEF
TL4
Subst="MSub1"
W=88.737 mil
L=200 mil
sp_nec_NE21908_4_19940401
SNP1
Bias-'Bjt: Vce=8V fc=30mA"
Frequency-'{0.10 - 5.00} GHz”
Figure 4.8: Block diagram in ADS containing the input and output matching circuits.
18—
16—
14-
ml
12-
ip
CN
U)
CO
n
freq=3.500GHz
dB(S(2,1))=6.472
10B-
ml
T
6—
420-2 - I
1.0
I M
|
1.5
I I I I | l
2.0
) )
I I
2.5
I I I I I ! I
3.0
I I |
I I I
3.5
I I I I
4.0
I I I I I I
4.5
I |
5.0
I I I I
I M
5.5
I I
6.0
freq, GHz
Figure 4.9: The gain (S21 ) o f the amplifier with the input and output microstrip matching
networks generated using ADS.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
43
0
-
“I--------------------------------------------------------------------------------
2-
-4 -
coco
-
6-
-
8—
co
T3Tco
3
-
10 -
-
12 -
-14—
*16—
1.0
i | | | | ||
1.5
i i | i i i ■i | i i i i | i i i i | i i | | | r r r T " [ " r i
2.0
2.5
3.0
3.5
4.0
4.5
m
| m
5.0
i i | i i m
5.5
6.0
freq, GHz
Figure 4.10: The input return loss (S n ) and output return loss (S22) of the amplifier with
the input and output microstrip matching networks generated using A D S.
4.9 Transistor Biasing
A bias network is required in an amplifier circuit to provide the correct dc voltage
and current to the transistor without interfering with the RF portion of the circuit. Also, it
blocks the RF signal from getting into the dc line, which if allowed causes noise in the
system.
Coupling capacitors are used for blocking the dc signal from entering the RF portion
o f the system. Since ideal capacitors act like open circuits at lower frequencies, they
effectively block the dc signal and hence are called dc blocks.
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44
Inductors (RF chokes) are used for blocking the RF signal from entering the dc line.
Since inductors act like open circuits at higher frequencies and short circuits at lower
frequencies, they are used for blocking the RF signal and they present a short circuit path
to the dc signal.
There is a provision for designing the bias network in ADS. A self bias circuit such
as shown in Figure 4.11 is used for biasing the transistor. The resistors R1 and R2 form a
potential divider and determine the base potential of the transistor and hence the base
current lb. Ib determines the output collector current Ic. Rc is the resistor across which the
output is taken. The inclusion of resistor Re helps in stabilizing the transistor against
temperature rise. As explained in section 3.3, the emitter current is a combination of the
collector and base current.
Ie = Ib+ Ic
(4.2)
If the collector current increases due to increase in the transistor temperature, from
equation 4.2 the emitter current also increases. This results in more voltage drop across
Re thus effectively reducing the base emitter voltage. This decreases the base current Ib
and hence the collector current Ic. The ‘DC Block’ are ideal blocking capacitors which
are used to block dc signals from entering the RF portion of the circuit. The ‘DC Feed’
are the ideal inductors used for blocking the RF signals from entering the dc line.
The setup for finding the resistor values for the bias network in ADS is shown in
Figure 4.12. The setup needs the collector to emitter voltage Vce, collector current Ic and
the supply bias Vce. Vce and Ic are provided in the transistor data specification sheets by
the manufacturer. After simulating the network in ADS, the bias network shown in
Figure 4.13 is obtained.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
45
Rc
Vcc
DC_Feed
DC_Feed3
D C_Feed
DC_Feed2
DC_Block
DC_Block1
DC_Block
SP
DC_Block2
R2
Re
sp_nec_NE21908_4_199404C
DC_Feed
DC_Feed4
SNP1
Bias="Bjt Vte=8V lc=30mA"
Frequency=”{0.10 - 5.00} GHz
Figure 4.11: A self bias network in ADS.
Vcc
B
DA_BJTBia!>1_BiasCHt
DA BJTBiasI
SP
sp_nec_NE21908_4_19940401
SNP1
Bias-'B jt: Vce=8V lc=30mA"
Frequency="{0.10 - 5.00} GHz"
Figure 4.12: Setup for finding the resistor values for the self bias network in ADS.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
46
R
j
tL
Rc
R = 33.33 Ohm
R
R1
R = 886.343 Ohm
VJDC
SR
SRC1
V d c= 1 0 V
D C _F eed
DC F e e d 3
D C _F eed
DC F e e d 2
DC_Block
DC Blockl
SP
Pa,
R
R2
R = 113.8 Ohm
D C _F eed
DC F e e d 4
DC_Block
DC Block2
R
Re
R = 32.92 Ohm
sp _ n e c _ N E 2 1 9 0 8 _ 4 _ 1 9940401
SNP1
Bias="Bjt: V ce=8V lc=30m A"
Frequency="{0.10 - 5.00} GHz"
Figure 4.13: The bias network used for the transistor NE 29801, designed in ADS.
Resistor Values for the bias network (O)
R1
886.43
R2
113.8
Rc
33.33
Re
32.92
Table 4.7: Resistor values used in the bias network.
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47
The circuit containing the bias network and the matching circuits is shown in Figure
4.14. The circuit is then simulated in ADS to obtain the frequency response (Figure 4.15)
M Sub
S -P A R A M E T E R S
3
S_Param
SP1
Start=1 GHz
Stop=6.0 GHz
Step=250 MHz
T e c h ln c lu d e _ N E C _ A C T IV E L IB R A R Y
V_DC
SRC1
Vdc=10 V
R
R1
R =886.343 Ohm
R=33
NEC_ACTIVELIBRARY_Lib
Fite=Nominal
MLEF
TL2
Subst="MSub1"
W=88.737 mil
L=155.04 mil
MLIN
TL1
Subst="MSubt
W=88.737 mil
L=237.56 mil
MLIN
TL3
Subst="MSubr
W=88.737 mil
L=180 mil
DC_Feed
DC Feed2
MSUB
MSubl
H=0.787 mm
Er=2.33
Mur=1
Cond=4.1E+7
Hu=3.9e+034 mil
T=70 urn
TanD=0
Rough=0 mil
DC_Block
DC Block 1
Term
Term2
Num=2
Z=50 Ohm
DC_Block
DC Bk>ck2
T erm l
Num=1
Z=50 O
R=32.92 Ohm
R=113.8 Ohm
DC_Feed
DC Feed4
MLEF
TL4
Subst="MSub1"
W=88.737 mil
L=200 mil
-=T
sp_nec_N E21908_4_ 19940401
SNP1
Bias="Bjt: Vce=8V lc=30mA"
Frequency =“{0.10 - 5.00} GHz"
Figure 4.14: Circuit schematic containing the bias network and matching circuits in
ADS.
From Figure 4.15, it is observed that the gain is fairly constant up to 5.0 GHz.
However, beyond 5 GHz the gain decreases sharply. Hence the designed amplifier can be
used with the antenna to increase the signal strength up to 5 GHz. Beyond 5 GHz, a
separate amplifier would have to be designed and a switch implemented in the E-field
probe to switch between frequency ranges 1-5 GHz, and 5 - 6 GHz.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
48
8
m.............................................................................................
ml
1
^............
freq=3.500GHz
dB(S(2,1))=5.654
|dB(S(2,1))=5.654
7_
ml
T
▼
.
54-
&
C/3
3-
m
■a
2—
1-
0-
-
1-
1—i n
m —im
—im
—|—
r"i ii—
p m —m
- 1—i ii n
i l—p
i—m
m—
—p
m —m
pi m
p m —mrnj—r
i i—p
—
pm—
—
ri"n
—
pm—
mp—
—
pi—
mm
pm
—
mpi
mm
m pm—
mrnj—
r m
-2
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
—
6.0
freq, GHz
Figure 4.15: The gain (S21 ) of the amplifier with the microstrip matching networks and
the bias circuit generated using ADS.
4.10 References
[4.1] “NE 21908 Data Sheet,” NEC Corporation, California,
[4.2] “ADS 2006 A,” Agilent technologies, 5301 Stevens Creek Blvd, Santa Clara,
California 95051.
[4.3] G. Gonzalez, Microwave Transistor Amplifiers - Analysis and Design, 2nd edition,
Prentice Hall, Inc., New Jersey, 1997.
[4.4] “RT / Duroid 5880 Data Sheet,” Advanced Circuit Materials Division, 100 S.
Roosevelt Avenue, Chandler, AZ 85226.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
49
CHAPTERS
RESULTS AND DISCUSSION
5.1 Introduction
The goal of this work is to design a broadband E-field probe in the 1 -
6
GHz
frequency range. The antenna used in the probe should be able to operate in this
frequency range and also have small dimensions so as to measure detailed distributions of
E-fields in an anechoic chamber. This thesis focuses on reducing the size of the chosen
antenna to acceptable dimensions and still be able to provide the desired operating
frequency range. The results of this work are provided in this chapter.
The chapter is organized as follows: Section 5.2 discusses the software used for
conducting the numerical simulations. In section 5.3, results for a diPICA which is a
replica of the antenna designed by Suh [5.1] are presented in order to validate the
numerical simulations. In section 5.4, results for the low profile diPICA (LPdiPICA) are
presented. The diPICA is backed with a substrate and a ground plane to obtain the
LPdiPICA. Section 5.5 describes the results for the Half LPdiPICA (HLPD), whose
dimensions are half those o f the LPdiPICA. Also, in this section the dielectric constant
and thickness of the substrate are varied to observe their effect on the antenna impedance
and radiation patterns. In addition, results are presented for the Quarter LPdiPICA
(QLPD) whose dimensions are one fourth those of the LPdiPICA, for different dielectric
constants and thicknesses o f the substrates. In the final section, comparison plots for
impedance and VSWR are presented. The parameters that are used for comparison
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
50
purposes include the length o f the antenna, the substrate relative dielectric constant and
thickness.
5.2 Software
The antenna geometries were created using the CAD software package SolidWorks,
version 2005 (SolidWorks Corporation, Concord, Massachusetts) [5.2] and imported into
the Finite Difference Time Domain software package XFDTD, version 6.3.8.3 (Remcom
Corporation, State College, Pennsylvania) [5.3]. XFDTD was used for computing the
impedance, gain and radiation patterns of the antennas.
5.3 diPICA
In this section the results for the diPICA described by Suh [5.1] are duplicated. The
dimensions of the diPICA shown in Figure 5.1 are those designed in [5.1]. The height and
width o f each PICA element are 76.2 mm which is XIA (X = free space wavelength) at the
lowest frequency of the band for which it is designed. The gap between the two patch
elements is 1.27 mm. The circular holes in the patch are of radius 10.16 mm. The antenna
is fed at the center similar to a dipole.
The Yee cell dimensions used in XFDTD were 0.5 mm x 0.5 mm x 1.27 mm.
XFDTD requires a minimum cell size that is at least 1/10 of the minimum wavelength.
The minimum cell size is calculated using equation (5.1) [5.2].
c _ 3xl Qn
Zmm = 7 7 T~ 7 = i a i A . ^.9 = 3 m/M
l O x / ~ 10x10x10s
r
V
J
A
iU
where,
c = velocity of light and, f = highest frequency of the band.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(5.1)
51
A cell size o f 0.5 mm which is 1/6* of 3 mm is taken in the X and Y directions to
accurately mesh the antenna. A cell size of 1.27 mm is taken in the Z-direction which is
the size of the gap between the two patches.
►Y
10.16
153.67
1.27
Feed
Points
76 .2
Figure 5.1: (a) Geometry o f the diPICA
(all dimensions are in mm).
(b) diPICA mesh
generated in XFDTD.
The impedance computed using XFDTD is presented in Figure 5.2 together with the
results from [5.1]. Good agreement was obtained for the real and imaginary parts of
impedance at frequencies below 5.5 GHz. The discrepancy at higher frequencies may be
due to the difference in the method of feeding of the antennas. The antenna simulated in
XFDTD was fed at the gap between the two patch elements with the feed provided in the
software; whereas the diPICA in [5.1] was fed using a coaxial cable at the feed points
that are shown in Figure 5.1 (a). The feed used in XFDTD is a discrete source that is a
cell edge on which the electric field is modified by the addition of some type of input
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
52
waveform. The cell edge can be modified to behave like a voltage or current source [5.3].
Also, a Gaussian waveform is used as input to the discrete source, since it allows
calculations over a broad range of frequencies. The same feed is used for feeding all the
antennas used in this thesis.
200
150
100
50
0
R e a l- X F D T D
-50
Imaginary - X F D T D
Real - [1]
Imaginary - [1 ]
-100
2
3
4
5
6
7
8
9
10
Frequency (GHz)
Figure 5.2: diPICA impedance as a function of frequency calculated using XFDTD and
compared to results in [5.1].
The XFDTD computed VSWR is shown in Figure 5.3. The impedance bandwidth
can be clearly observed from the VSWR plot. It is computed for VSWR less than 2. The
impedance bandwidth, as can be observed from the graph is almost 1 - 1 0 GHz. At lower
frequencies the VSWR is slightly above 2, but it can still be taken as an acceptable result.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
53
The XFDTD calculated radiation pattern results are shown in Figure 5.4. They are
plotted for ^ = 0° and^ = 90°. These radiation patterns match closely with the radiation
patterns in [5.1]. They resemble the radiation patterns of a dipole. There is little
degradation in the patterns up to
8
GHz providing a pattern bandwidth of 8:1. The
XFDTD computed gain for diPICA is shown in Figure 5.5. It ranges between 5 - 9 dBi
over the frequency range 1 - 1 0 GHz.
10
XFDTD
9
8
7
£4
C/2
>
6
5
4
3
2
1
1
2
3
4
5
6
7
8
9
Frequency (GHz)
Figure 5.3: XFDTD computed VSWR plot of the diPICA.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
10
54
EPhi. <|>= 0;
ETheta. 4> = 0:
EPlii. <(>= 90’
ETheta. 4> = 90(a) 1GHz
135.
135.
-140
a
1
-120
*100
-60
-60
225'
-20
j 15
-20
Angie
(b) 2 GHz
(c) 4 GHz
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
j 15
55
135.
135.
•140
19
•120
•120
1100
•20
225
(d)
6
'315
'315
GHz
(e) 8 GHz
Figure 5.4: XFDTD computed radiation patterns of the diPICA at various frequencies in
the range 1 - 8 GHz.
10
-
§
-10 -
■3
-15 -
-20
-25 -30 -35 M aximum Gain
-40
1
2
3
4
5
6
7
8
9
Frequency (GHz)
Figure 5.5: XFDTD computed maximum gain for the diPICA
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
10
56
5.3.1 diPICA with feed wire
The diPICA in [5.1] was fed at the two feed points. The distance between the two
feed points as shown in Figure 5.6 (a) is 2.286 mm. In order to feed the antenna at the
feed points, since in XFDTD the length of the feed is only one Yee cell size and it cannot
be connected directly between the feed points, a wire is connected from both ends of the
feed to the feed points as shown in 5.6 (b). The height of the wire is defined as the height
of the vertical portion o f the wire that connects the feed to the feed points. The Yee cell
size in the simulations was once again chosen to be the same as for the antenna described
in section 5.3.
— 2.286 mm
Feed
Points
Feed points
I I I r ~1
I* I l l l
kHeight o f the wire
Figure 5.6: (a) Geometry of diPICA.
with the feed points.
(b) Feeding of diPICA with height below the
surface of the substrate = 1 mm.
The impedance results computed using XFDTD when the height of the wire is
chosen equal to 1mm is shown in Figure 5.7. The real and imaginary parts agree fairly
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
57
well with the results in [5.1]. This shows the importance of proper feeding of the antenna
in order to obtain accurate results. The impedance of the antenna is very sensitive to the
method of feeding.
The XFDTD computed VSWR plot is shown in Figure 5.8. The VSWR is close
enough to 2 over the frequency band 1 - 1 0 GHz and hence the impedance bandwidth can
be taken to be 1 - 10 GHz. The radiation pattern results are shown in Figure 5.9. The
radiation patterns are similar to that of the dipole and there is little degradation in the
patterns up to
8
GHz. Thus the diPICA has a pattern bandwidth of 1 -
8
GHz. The
maximum gain computed for the diPICA with feed wire using XFDTD is shown in
Figure 5.10. The gain ranges between 5 - 9 dBi over the frequency range 1 - 1 0 GHz.
200
150 ■
100
-
Real - heightjl mm
Imaginary - heightjl mm
Real - [1]
Imaginary -[1]
-50 -
-100
1
2
3
4
5
6
7
8
9
10
Frequency (GHz)
Figure 5.7: XFDTD computed impedance of the diPICA with height of the feed wire
below the bottom surface of the substrate equal to 1 mm.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
10
VSW R -XFDTD
9
8
7
6
cn
5
4
3
2
1
2
3
4
6
5
7
8
9
10
Frequency (GHz)
Figure 5.8: XFDTD computed VSWR plot for the diPICA with height of the feed
below the bottom surface o f the substrate equal to 1 mm.
135.
11
-120
hoc
-50
■40
'315
EPhi, <t>= 0°
ETheta, <j>= 0°
EPhi. <|>= 90°
ETheta, <j>= 90°
A ngle
(a) 1GHz
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
59
135.
135.
)
■•110
11
•100
-100
•40
225
'315
225
'315
Angle
Angle
(b) 2GHz
(c) 4GHz
135.
135.
F110
r100
]
-120
y ilO
lioo
-«>•j 15
Angle
(d) 6 GHz
Angle
(e) 8 GHz
Figure 5.9: XFDTD computed radiation patterns for the diPICA with height o f the feed
wire below the bottom surface of the substrate equal to 1 mm.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
60
•
10
-
9-15
-
-20
-
-25 -30 -35 M aximum Gain
-40
1
2
3
4
5
6
7
8
9
10
Frequency (GHz)
Figure 5.10: XFDTD computed gain for the diPICA with height of the wire under the
substrate equal to 1 mm.
5.3.2 Comparison of results for various heights of the feed wire below the bottom
surface of the substrate
To observe the effect o f the height of the feed wire, impedance results for various
heights of feed wire below the bottom surface of the substrate are plotted in Figures 5.11
and 5.12. There is little variation in the real part of the impedance (Figure 5.11), for
different heights of the feed wire below the bottom surface of the substrate and the results
agree well with those in [5.1]. However the imaginary part (Figure 5.12) decreases in
amplitude as the height o f the feed wire below the bottom surface of the substrate
decreases and approaches the results presented in [5.1]. This may be due to the
inductance o f the wire o f the feed that increases as the length o f the wire increases.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
61
200
T3
-1 0 0
2
3
4
5
6
7
8
9
10
Frequency (GHz)
Figure 5.11: Real part of impedance as a function of frequency for different heights of
feed wire below the bottom surface of the substrate.
200
Height - 1mm
Height - 0.5 mm
150
Height - 0.1m m
Height - 0.05 mm
100
cc
T5
4>
&
ce
-50
100
2
4
6
8
10
Frequency (GHz)
Figure 5.12: Imaginary part of impedance as a function of frequency for different heights
of feed wire below the bottom surface of the substrate.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
62
5.4 LPdiPICA
Since the dimensions of the diPICA (153.67 mm x 76.2 mm) described above are
too large to be practical for the antenna used in the E-field probe, the size of the antenna
has to be reduced. All dimensions of the antenna were first reduced to half including the
dimension o f the holes. However, by reducing the size of the antenna, the lower
impedance bandwidth frequency also increases, since the height of the antenna is A/4 at
the lowest frequency. This decreases the impedance bandwidth of the antenna. One of the
methods commonly suggested to increase the bandwidth is to back the antenna with a
dielectric substrate and ground plane. By using high relative dielectric constant and thick
substrates, the antenna length can be reduced by keeping the bandwidth intact, although
this reduces the antenna efficiency. In [5.1], an LPdiPICA was constructed that was a
diPICA backed with a dielectric substrate and ground plane (Figure 5.13 (a)). The
LPdiPICA was designed in [5.1] to create a unidirectional pattern instead of the omni
directional pattern o f the diPICA. The results of the LPdiPICA from [5.1] are duplicated
so as to compare them with results of the Half LPdiPICA (HLPD) whose dimensions are
half those of the LPdiPICA.
The substrate used to back the patch elements has a relative dielectric constant s r of
2.33 and thickness of 0.795 mm. This is the same substrate material used in [5.1]. The
substrate has a length of 157.7 mm and a width of 86.2 mm as shown in Figure 5.13 (a).
The patch elements have the same dimensions as the diPICA described in section 5.3.
The XFDTD mesh dimensions of the LPdiPICA are 0.265 m m x 0.5 mm x 1.27 mm.
The LPdiPICA mesh is shown in Figure 5.13 (b). An infinite ground plane was used for
this numerical simulation. The ground plane is placed at a height of 38mm below the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
63
patch, which is XL I 4 at the lowest frequency XL. Since the thickness of the substrate is
only 0.795mm a cell size o f 0.265 mm is chosen in the x-direction, which is l/3rd of
0.795 mm. This is recommended in the XFDTD software [5.3]. The antenna is fed at the
gap between the two patches.
The impedance results computed in XFDTD are shown in Figure 5.14 and agree
fairly well with the results from [5.1]. The discrepancy in the results is possibly again due
to the different types o f feeds used in [5.1] and by XFDTD. The XFDTD computed
VSWR plot is shown in Figure 5.15. The impedance bandwidth covers the whole range
o f frequencies from 1 - 1 0 GHZ. The radiation patterns could not be calculated as the
XFDTD software does not allow the calculation of radiation patterns, if an infinite
ground plane is used.
S u b s tr a te
umi hi ({iitifnl
III! H! i Hillm!
iliilliil!! I i
157.67
!!!!!!!!!!
i n
153.67
Patch
P a tc h
Substrate
76.2 •*
♦
86.2
Figure 5.13: (a) Geometry o f the LPdiPICA
(all dimensions are in mm).
(b) LPdiPICA mesh
generated in XFDTD.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
64
200
Impedance (Q)
150 -
100
Real - XFDTD
Imaginary - XFDTD
Real - [1 ]
Imaginary - [1 ]
-50
-100
1
3
2
4
5
6
7
8
9
10
Frequency (GHz)
Figure 5.14: XFDTD computed LPdiPICA antenna impedance.
10
VSW R - LPdiPICA
9
8
7
6
CO
>
5
4
3
2
1
1
2
3
4
5
6
7
8
9
Frequency (GHz)
Figure 5.15: XFDTD computed VSWR plot for the LPdiPICA.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
10
65
5.4.1 LPdiPICA without the ground plane
The ground plane o f the LPdiPICA is very large compared to the radiating part of
the antenna. So the ground plane of the antenna was removed and the antenna was
simulated to observe the effects of removing the ground plane. The antenna dimensions,
the meshing and, the feed used were identical to those used for the antenna in section 5.4.
The impedance computed using XFDTD is shown in Figure 5.16. The effect of removing
the ground plane can be observed. The amplitude of the real and imaginary parts of the
impedance are lower at the lower frequencies compared to those for the LPdiPICA with
the ground plane. In the frequency range from 2.5 to 7 GHz the results with and without
the ground plane are close. Beyond 7 GHz there are again differences. Thus since there
were no significant impedance differences we chose to use LPdiPICA without a ground
plane.
The VSWR plot computed using XFDTD is shown in Figure 5.17. The VSWR is
less than 2 from 1 - 1 0 GHz. Thus it has an impedance bandwidth of 1 - 10 GHz. The
radiation patterns calculated using XFDTD can be observed in Figure 5.18. The radiation
patterns of the LPdiPICA without a ground plane differ from that of the LPdiPICA with a
ground plane in that the latter has a unidirectional pattern due to the presence of the
ground plane and the former has an omni-directional pattern like that of a dipole antenna
in the absence of the ground plane. The patterns begin to degrade beyond
GHz. Thus
8
the LPdiPICA without the ground plane still has a pattern bandwidth of 1-
8
GHz. The
XFDTD computed maximum gain for the LPdiPICA is shown in Figure 5.19. The gain
ranges between 5 - 1 1 dBi over the frequency range 1 - 1 0 GHz.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
66
200
Real- LPdiPICA
Imaginary- LPdiPICA
Real-LPdiPICA-WG
Imaginary- LPdiPICA-WG
150 -
100
-
-50 -
-100
1
2
3
4
5
7
6
10
9
8
Frequency (GHz)
(W G -W ithout Ground)
Figure 5.16: Impedance as a function of frequency for the LPdiPICA antenna without a
ground plane
10
VSW R -XFDTD
9
8
7
6
5
4
3
2
1
2
3
4
5
6
7
8
9
10
Frequency (GHz)
Figure 5.17: XFDTD computed VSWR plot for the LPdiPICA without the ground plane.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
67
136.
a
•90
1
•40
------ EPhi. <|» = 0 °
------ ETheta. <f»= 0 °
------ EPhi. <j) = 90°
ETheta. <j>= 90°
30
-20
'315
•10
Angle
(a) 1GHz
135,
135.
-00
ia
-30
■20
•20
225*
-10
'315
-10
'315
A ngle
(b) 2GHz
(c) 4GHz
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Angle
Antfe
(d) 6 GHz
(e) 8 GHz
Figure 5.18: XFDTD calculated radiation patterns for the LPdiPICA without ground
plane.
15
10
5
0
^ -5
^ -1 0
•1-15
o
-20
-25
-30
-35
Maximum Gain
-40
1
2
3
4
5
6
7
8
9
10
Frequency (GHz)
Figure 5.19: XFDTD computed maximum gain for the LPdiPICA without ground plane.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
69
5.5 LPdiPICA with dimensions reduced by half
Since the goal of this thesis is to design a broadband antenna of small dimensions
for use as an E-field probe, the length and width of the diPICA as well as the dimension
of the holes were reduced by half to create the Half LPdiPICA (HLPD). No ground plane
was used. The dimensions of the HLPD are shown in Figure 5.20. The length of the
antenna is 76 mm and the width is 38 mm. The distance between the patch elements is
0.635 mm, which is half that of the LPdiPICA (1.27 mm). The dimension (diameter) of
the circular holes is chosen to be 5.08 mm which is one half of the diameter of the
circular holes o f the LPdiPICA (10.16 mm). The substrate used to back the patch
elements has s r o f 2.33 and thickness of 0.795 mm. The substrate has a length of 80.635
mm and a width o f 43 mm. The XFDTD mesh dimensions of the HLPD are chosen to be
0.265 mmx 0.5 mm x 0.635 mm as shown in Figure 5.20 (b). The cell size in z-direction
is chosen to be 0.635 mm, since this is the gap between the two patches. The cell size is
chosen to be as 0.265 mm in the x-direction as explained in section 5.4. It is fed at the
gap between the two patches.
The XFDTD computed impedance for the HLPD is presented in Figure 5.21. The
LPdiPICA impedance from [5.1] is also plotted for comparison purposes. The result of
reducing the dimensions by half is observed in Figure 5.21. The lower impedance
bandwidth frequency of the antenna increases as the antenna length is reduced. As
explained before, the reason for this behavior is that the length of the antenna is X J 4 at
the lowest frequency.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
70
S u b stra te
80.635
76.635
.0.635
1
Patch
liiilMii
5.08
Substrate
P a tc h
(b) HLPD mesh
generated in XFDTD.
Figure 5.20: (a) Geometry o f the HLPD
(all dimensions are in mm).
150
Real-HLPD
Imaginary- HLPD
Real - LPdiPICA-WG
Imaginary- LPdiPICA-WG
100
S'
-50
-100
2
3
4
5
6
7
8
9
10
Frequency (GHz)
(WG - W ithout Ground)
Figure 5.21: Impedance as a function of frequency for the HLPD ( e r = 2.33) calculated
using XFDTD.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
71
The formula for the lower frequency of the band can be written as,
c
/, =
L
=
Ax4
3x10n
38x4
= 1.974 GHz
(5.1)
From Figure 5.21, it is observed that, the impedance bandwidth of the HLPD is decreased
by 1 GHz and now is from 2 GHz to 10 GHz. Also, the amplitude of the real part of the
HLPD impedance is lower compared to the impedance of the antenna in section 5.3.1.
This may be due to the reduction in the size of the radiating part of the antenna. The
VSWR and radiation patterns are shown in Figures 5.22 and 5.23 respectively. The
VSWR plot also confirms the fact that the impedance bandwidth starts from 2 GHz.
10
V S W R -X F D T D
9
8
7
6
5
4
3
2
1
2
3
4
5
6
7
8
9
Frequency (GHz)
Figure 5.22: XFDTD computed VSWR plot for the HLPD ( s r = 2.33).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
10
72
The radiation pattern plots show degradation of the patterns at
8
GHz. Thus the HLPD
has a pattern bandwidth of 8 GHz. The XFDTD computed maximum gain for the HLPD
( e r = 2.33) is shown in Figure 5.24. The gain ranges from 4 . 8 - 1 0 dBi over the
frequency range 1 to 10 GHz.
135.
K
120
*
1
hoo
-5tJ
•40
-20
------ EPhi, <}>= 0 °
------ ETheta. <J>= 0 °
------ EPhi, <|) = 90°
ETheta, <j>= 90°
*315
(a) 1GHz
135,
18(
135.
•140
)
18
[120
-40
-20
j15
'315
A ngle
(b) 2GHz
(c) 4GHz
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
73
135,
135.
-90
19(
191
-10
(d) 6 GHz
(e) 8 GHz
Figure 5.23: XFDTD computed radiation patterns for the HLPD ( s r = 2.33).
10
-20
-
-
-25 -30 -35 Maximum Gain
-40
2
3
4
5
6
7
8
9
Frequency (GHz)
Figure 5.24: XFDTD computed gain for the HLPD ( s r = 2.33).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
10
74
5.5.1 HLPD ( s r = 10.2, thickness = 1.59 mm)
The dielectric constant and the thickness of the substrateof the HLPD are varied to
observe the effect o f thesubstrate on the impedance bandwidth. Particularly, the focus
was on lowering the frequency o f the impedance bandwidth. A relative dielectric constant
of
1 0 .2
was chosen as follows:
The length of a dielectric patch antenna with a substrate of dielectric constant s r is given
by [1, chapter 5]:
i= -4 =
(5-2)
Then if L]= 2 x L2 (since the LPdiPICA is twice the length of the HLPD), and keeping the
free space wavelength the same, equation (5.2) becomes:
V ^7 = 2 xyfe^ ,
(5.3)
The detailed derivation o f the equation is provided in Appendix A
Substituting^, =2.33, we get e r2 =9.32 which is close to the relative dielectric
constant o f 10.2 available commercially (Rogers Corporation, Chandler, Arizona [5.3]).
The XFDTD computed impedance results are shown in Figure 5.25. The real part o f
the impedance o f the HLPD ( s r = 10.2) shifts towards the left to lower frequencies
compared to the HLPD ( s r =2.33) in section 5.5 (comparison shown in section 5.9).
This shift may due to the increase in the thickness of the substrate. While the shift is very
small, the amplitude decreases noticeably. This may be attributed to the increase in the
dielectric constant o f the substrate which decreases the efficiency of the antenna. Due to
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
75
the increase in dielectric constant and the thickness of the substrate, the electromagnetic
fields tend to couple tightly inside the substrate and hence the decrease in the efficiency
of the antenna.
The VSWR plot computed using XFDTD is shown in Figure 5.26. The effect of
using the higher dielectric constant can be seen in the plot. The VSWR is greater than
two over most o f the frequency band and hence this antenna is not desirable as a
broadband antenna. This is due to the decrease in the efficiency o f the antenna because o f
the high relative dielectric constant substrate. Due to this low efficiency, a large
mismatch occurs between the antenna and free space. As explained in chapter 2, an
antenna is the guiding structure between the feed and free space. So due to this mismatch
less of radiation is transferred to free space and hence the higher VSWR (Figure in 5.26).
The XFDTD computed radiation pattern results are shown in Figure 5.27. It can be
observed that the radiation patterns degrade as the frequency increases. The pattern
bandwidth is still greater than
6
GHz. The XFDTD computed maximum gain for the
HLPD with£r = 10.2 is shown in Figure 5.28. The gain ranges between 5 - 1 4 dBi over
the frequency range 1 - 1 0 GHz.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
76
200
R e a l-X F D T D
Imaginary- XFDTD
150
100
-50
-100
2
3
4
5
7
6
9
8
10
Frequency (GHz)
Figure 5.25: Impedance as a function of frequency for HLPD ( s r = 10.2).
10
VSWR - XFDTD
9
8
7
6
5
4
3
2
2
3
4
5
6
7
8
9
Frequency (GHz)
Figure 5.26: XFDTD computed VSWR plot for the HLPD with s r = 10.2.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
10
77
135.
•100
ia
30
-20
•10
------ EPhL<t> = 0 °
------ ETheta. <|>= 0 °
------ EPhi <|>= 90°
ETheta. <j>= 90°
Angle
(a) 1 GHz
135,
135.
ia
•100
*90
40
•30
•20
•20
•10
-10
Angle
(b) 2 GHz
(c) 4 GHz
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
*315
78
135.
-50-
-20
j 15
Angle
(d)
GHz
6
(e)
8
GHz
Figure 5.27: XFDTD computed radiation patterns for HLPD w ith fr =10.2.
1-10
-20
-25
-30
-35
Maximum Gain
-40
1
2
3
4
5
6
7
8
9
Frequency (GHz)
Figure 5.28: XFDTD computed gain for the HLPD w ith^r = 10.2.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
10
79
5.6 Q uarter LPdiPICA (QLPD)
The dimensions of the HLPD are still too large for use in the E-field probe. Hence,
the dimensions are further reduced by half, which makes it 1/4*11 the size of the
LPdiPICA. The dimensions of the QLPD are shown in Figure 5.29 (a). The length of the
antenna is 38.317 mm. The width is 19 mm. The diameter of the circular holes is 2.54
mm. The gap between the two patch elements is 0.317 mm. The antenna size is small
enough to be used as a receiving element in the E-field probe. It is backed by a substrate
o f length 40.317 mm and width 24 mm. The dielectric constant and thickness of the
substrate are varied to extract optimum performance from the antenna structure.
substrate
38.317
!>!!>
40.317
Patch
2 .54
patch
Substrate
Figure 5.29: (a) Geometry o f the QLPD
(all dimensions are in mm)
(b) QLPD mesh
generated in XFDTD.
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80
5.6.1 QLPD ( s r = 2.33, thickness = 0.795 mm)
The QLPD is first backed with a substrate of dielectric constant 2.33 and thickness
0.795 mm. This is the same substrate as was used for the LPdiPICA in section 5.3. This
substrate is used to observe the effect of shortening the length of the antenna. The
XFDTD generated mesh for the QLPD is shown in Figure 5.29 (b). The Yee-cell
dimensions are chosen to be 0.265 mm x 0.5 mm * 0.635 mm. The Yee-cell size in the xdirection is 0.265 mm, l/3rd of the 0.795 mm thickness of the substrate, and is chosen
according to the recommendation in the XFDTD manual [5.3]. Also, the cell size in the zdirection is chosen as 0.635 mm since this is the size of the gap between the two patches.
The XFDTD computed impedance results are shown in Figure 5.30.
From the
graph, it can be observed that the lower impedance bandwidth frequency further increases
to 4 GHz. This can be explained from the equation (5.4):
c
3x10"
^ = Al x 4 = W
19x4 = 3 *9 4 7 GHz
(5
4)
where ‘A’ is the free space wavelength.
The amplitudes of the real and imaginary parts are also reduced. As explained in section
5.5.1, this is due to the reduction in the size of the antenna. The real part is close to 50 Q
and the impedance bandwidth is 4 - 10 GHz. The XFDTD computed VSWR plot is
shown in Figure 5.31. The impedance bandwidth can be observed more accurately in the
VSWR plot. From Figure 5.31, it can be seen that the VSWR becomes less than two from
a little above 3 GHz and thus the bandwidth is from 3.2 GHz to 10 GHz. The goal of this
work is to have a broadband antenna which has acceptable performance over the
frequency range 1 - 6 GHz. Although the frequency range specification at the upper limit
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
is met, the lower impedance bandwidth frequency of 2.2 GHz is higher than the desired 1
GHz. The various attempts that were made to reduce this lower frequency limit will be
explained in the following sections.
200
Real - Q LPD
Im aginary - QLPD
Real - L P d P IC A W G
150
Im agin ary- - LPdiPIC A -W G
100
a
-50
-100
1
2
3
4
5
7
6
8
9
10
Frequency (GHz)
Figure 5.30: Impedance as a function of frequency for the QLPD ( s r = 2.33) computed
using XFDTD.
The radiation patterns computed for the HLPD using XFDTD are shown in Figure
5.32. The radiation patterns degrade very little up to
bandwidth o f
8
8
GHz giving a radiation pattern
GHz. The maximum gain computed using XFDTD is shown in Figure
5.33. It ranges between -1 to 9 dBi. The negative gain at 1 GHz may be due to the fact
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82
that antenna becomes very much smaller than A/4 at that frequency. This leads to very
low efficiency of the antenna.
10
V S W R -X FD T D
9
8
7
6
CO
>
5
4
3
2
1
2
3
4
5
6
7
8
9
Frequency (GHz)
Figure 5.31: XFDTD computed VSWR plot for the QLPD ( s r = 2.33).
135.
161
[103
[93.5
EPhi <t>= 0°
ETheta, <J>= 0°
EPhi, <j>= 90°
ETheta, <j>= 90°
(a) 1 GHz
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10
83
136,
-110
-100
-40
'315
(b) 2 GHz
(c) 4 GHz
135,
I8d
Artfe
(d)
6
GHz
(e)
8
GHz
Figure 5.32: XFDTD computed radiation patterns for the QLPD { s r = 2.33)
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84
-25
-30
-35
Maximum Gain
-40
2
3
4
5
6
7
8
9
10
Frequency (GHz)
Figure 5.33: XFDTD computed gain for the QLPD ( s r = 2.33)
5.6.2 QLPD ( s r = 37.28, thickness = 0.795 mm)
One of the methods suggested for increasing the impedance bandwidth as explained
in 5.5.1 is to increase the relative dielectric constant and the thickness of the substrate.
Therefore, to observe the effect of dielectric constant on the impedance bandwidth of the
QLPD, the antenna is backed with a substrate having s r =37.28. This value is obtained
by using the equation (5.3). Substituting e rl = 2.33 and 4 = 4x ^ (since the LPdiPICA
is 4 times the size of the QLPD) in equation (5.3), we get s n =37.28. The Yee-cell
dimensions are chosen to be 0.265 mm x 0.5 mm x 0.635 mm. The dimensions are the
same as that o f the QLPD described in section 5.6.1.
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85
The impedance results are shown in Figure 5.34. As observed in section 5.3, the
acceptable value o f the real part of the impedance moves towards lower frequencies.
However, the amplitude of the impedance decreases drastically due to the high dielectric
constant of the substrate. As the dielectric constant increases, the efficiency of the
radiating structure decreases due to the tight coupling of the fields inside the substrate.
The higher the relative dielectric constant, the lower is the radiation efficiency of the
antenna. Resonant peaks can also be observed at higher frequencies. This is because the
antenna becomes resonant at those frequencies. The XFDTD computed VSWR plot is
shown in Figure 5.35. As observed in section 5.5.1, the VSWR is greater than two over
the most o f the frequency band. This is again due to the decrease in the efficiency of the
antenna because o f the high relative dielectric constant, thus causing a mismatch between
the antenna and free space.
- — R eal - QTDH
Imaginary- QTDH
R eal-L P d iP IC A
Imaginary- LPdiPICA
200
150 -
100
-
G
oL)
s
U
a
M
-50 -
-100
1
2
3
4
5
6
7
e
9
10
Frequency (GHz)
Figure 5.34: Impedance as a function o f frequency for the QLPD ( e r = 37.28)
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86
The radiation patterns computed using XFDTD are shown in Figure 5.36. The patterns
begin to degrade at 8 GHz, and thus the QLPD has a pattern bandwidth of 8 GHz. The
XFDTD computed maximum gain is shown in Figure 5.37.
10
V S W R -X FD T D
9
8
7
6
4
3
2
1
1
2
4
3
5
6
7
8
9
10
Frequency (GHz)
Figure 5.35: XFDTD computed VSWR plot for the QLPD ( e r = 37.28 )
135.
181
(a) 1 GHz
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87
136.
135.
-70
•40
•30
-20
-20
r315
-10
10
(b) 2 GHz
135.
(c) 4 GHz
135.
18
-35
•15
A ngle
(d) 6 GHz
(e) 8 GHz
Figure 5.36: XFDTD computed radiation patterns for the QLPD ( s r = 37.28).
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88
-15
-20
-25
-30
-35
Maximum Gain
-40
1
2
3
4
5
6
7
8
9
10
Frequency (GHz)
Figure 5.37: XFDTD computed gain for the QLPD ( s r = 37.28).
5.7 Investigation of various methods for the extension of the impedance bandwidth
for the QLPD
The goal of this work is to design a broadband antenna whose bandwidth ranges
from 1 -
6
GHz. However the impedance bandwidth for the QLPD (section 5.6) starts
from a little above 3 GHz. Therefore to increase the bandwidth o f the QLPD various
techniques were investigated. These include increasing the width of the patch, wire
loading the patch, and loading the antenna. This section presents the results of applying
these techniques and they are compared with the QLPD results to compare the amount of
increase in the bandwidth.
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89
5.7.1 Increasing the width of the QLPD patch
Increase in the width of the QLPD patch increases the area of the patch and, the
region that radiates. Also, as explained in section 2.2 of chapter 2, a thicker dipole has a
larger bandwidth than a thin wire dipole. The width of the patch is made equal to that of
the total length of the antenna. The antenna is then simulated in XFDTD and the results
are presented.
The dimensions o f this wider antenna are shown in Figure 5.38. All the dimensions
are chosen to be the same as that of the QLPD, except for the widths of the patch and the
substrate. The width of the patch and substrate are increased to 38 mm and 43 mm
respectively. The wider QLPD mesh generated in XFDTD is shown in Figure 5.39. The
Yee-cell dimensions are chosen to be the same as that of the QLPD (0.265 mm x 0.5 mm
x 0.635 mm).
substrate
40.317
38.317
0.317
2.54
patch
Figure 5.38: Geometry of the wider QLPD (all the dimensions are in mm)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Patch
F eed
Substrate
Figure 5.39: Wider QLPD mesh generated in XFDTD.
The impedance o f the wider QLPD computed using XFDTD and compared with the
impedance o f the QLPD is shown in Figure 5.40. There is little difference between the
impedance bandwidths o f the wider QLPD and QLPD. The XFDTD computed VSWR
plot for the wider QLPD is shown in Figure 5.41. The difference between the impedance
bandwidths can be observed clearly in the VSWR plot. The impedance bandwidth is
increased by 100 MHz, but it still does not meet our initial specifications for the antenna.
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91
200
Real-W ider QLPD
Imaginary - Wider QLPD
Real - QLPD
Imaginary - QLPD
150 -
100
-
-50 -
-100
1
2
4
3
6
5
7
8
9
10
Frequency (GHz)
Figure 5.40: XFDTD computed impedance for the wider QLPD and compared with
impedance for the QLPD.
10
VSWR - Wider QLPD
VSWR-QLPD
9
8
7
6
5
4
3
2
1
1
2
3
4
5
6
7
8
9
10
Frequency (GHz)
Figure 5.41: XFDTD computed VSWR for the wider QLPD and compared with the
VSWR for the QLPD.
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92
5.7.2 Wire loading of the QLPD patch
Another method used to increase the impedance bandwidth is wire loading the
antenna. In [5.5], an antenna is wire loaded on the top to increase the impedance
bandwidth at the lower frequencies. Wire loading entails adding a length of wire on top
o f the antenna. This effectively increases the height of the antenna without adding much
volume to the antenna.
Taking cue from the above method, the QLPD was modified by adding a wire on top
o f the antenna. The length of the wire, after experimenting with several lengths, was
chosen as 10 mm. Even though, for lengths greater than 10mm the impedance bandwidth
increased slightly, the VSWR was not below two uniformly over the whole frequency
band making it undesirable for use in the 1 - 6 GHz frequency band.
The geometry o f the wire loaded QLPD is shown in Figure 5.42 (a). The
dimensions o f the wire loaded QLPD are the same as those of the QLPD in section 5.5.1
except for the addition o f the wire at the top. The length of the wire is 10 mm. The wire
loaded QLPD antenna mesh generated in XFDTD is shown in Figure 5.42 (b). The Yeecell dimensions are also same as those used for the QLPD.
The XFDTD computed impedance results for the wire loaded QLPD are shown in
Figure 5.43. The results are compared with the QLPD results. It can be observed clearly
from Figure 5.43, that the impedance bandwidth has shifted to lower frequencies, thus
increasing the lower impedance bandwidth. However the shift is only a couple of hundred
MHz. This still doesn’t meet the initial frequency range specification. The shift can also
be observed in the VSWR plot calculated using XFDTD (Figure 5.44). The lower
impedance bandwidth shifted from 3.2 GHz to 3 GHz. Thus the impedance bandwidth is
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93
improved by 200 MHz. However this shift is not sufficient to meet the initial bandwidth
specification.
Various other methods o f loading the antenna were tried, like loading the antenna on
both sides o f the antenna. However, there was no significant impact on the lower
impedance bandwidth and hence the results are not presented.
substrate
38.317
40.317
Patch
0.31
2.54
patch
Substrate
Figure 5.42: (a) Geometry o f the wire loaded
QLPD (all dimensions are in mm).
(b) Wire loaded QLPD mesh
generated in XFDTD.
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94
200
Real-WiderQLPD
Imaginary - Wider QLPD
Real-QLPD
Imaginary - QLPD
150 -
100
-
-5 0 -
-100
1
2
4
3
6
5
7
9
8
10
Frequency (GHz)
Figure 5.43: XFDTD computed impedance for the wire loaded QLPD. The results for
the QLPD are also plotted for comparison.
10
VSWR - Wirebaded QLPD
VSW R-QLPD
9
8
7
6
5
4
3
2
2
3
4
5
6
7
8
9
10
Frequency (GHz)
Figure 5.44: XFDTD computed VSWR for the wire loaded QLPD. The results for the
QLPD are also plotted for comparison.
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95
5.7.3 Loading the patches of the QLPD
As shown in Figure 5.37, the QLPD is loaded by creating slots in the two patches at
the feed points. This method was employed in [5.6] to increase the lower impedance
bandwidth. This increase in lower bandwidth is due to the fact that the current takes a
longer path around the slot to reach the tip of the antenna. This helps in increasing the
lower bandwidth. The dimensions of the loaded QLPD shown in Figure 5.45 (b) are the
same as those o f the QLPD described in section 5.5.1. Two new elliptical slots were
created near the feed ends. The antenna was then simulated in XFDTD and the mesh
generated is shown in Figure 5.45 (b).
s u b s tr a te
38.317
QQ
OQ
40.317
Figure 5.45: (a) Geometry o f the loaded
QLPD (all dimensions are in mm)
(b) Loaded QLPD mesh
generated in XFDTD.
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96
The XFDTD calculated impedance and VSWR results are shown in Figures 5.46
and 5.47 respectively. The results are compared with those obtained for the QLPD. The
impedance bandwidth is almost the same for both the antennas. The loading did not have
much effect on the impedance bandwidth. This may be due to the very small size o f the
antenna.
200
Real -Loaded QLPD
Imag inary - Loade d QLPD
Real - QLPD
Imaginary - QLPD
150
100
-100
2
3
4
5
6
7
8
9
10
Frequency (GHz)
Figure 5.46: XFDTD computed impedance for the loaded QLPD. The results for the
QLPD are also plotted for comparison.
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97
10
VSWR - Loaded QLPD
VSWR - QLPD
9
8
7
6
> 5
4
3
2
1
1
2
3
4
5
6
7
8
9
10
Frequency (GHz)
Figure 5.47: XFDTD computed VSWR for the loaded QLPD. The results for the QLPD
are also plotted for comparison.
5.8 Comparisons
In this section, comparison plots for impedance and VSWR of the various antennas
are presented. The parameters that are used for comparison purpose include the length of
the antenna, and the relative dielectric constant and thickness of the various substrates.
These comparisons are helpful in observing clearly the parameters that affect the
impedance bandwidth.
5.8.1 Effect of decreasing the length of the antenna
A comparison is made between the LPdiPICA without a ground plane, the HLPD
which has dimensions that are half those of the LPdiPICA, and the QLPD which has
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98
dimensions that are quarter those of the LPdiPICA. This helps illustrate the effect of
decreasing the length o f the antenna. The comparison plot of impedance bandwidth is
shown in Figure 5.48. The plot contains only the real part of the impedance to clearly
show the shift in impedance bandwidth. It can be observed that as the length of the
antenna is decreased the lower impedance bandwidth shifts towards higher frequencies,
thus effectively decreasing the impedance bandwidth.
d iP IC A -X F D T D
HLPD
QLPD
140
120
100
80
a
60
40
20
0
1
2
3
4
5
6
7
8
9
10
Frequency (GHz)
Figure 5.48: Real part of impedance as a function o f frequency for the different antennas
(full (LPdiPICA), half (HLPD), and quarter (QLPD)).
The comparison o f VSWR (Figure 5.49) shows the actual amount of shift. The
lower impedance bandwidth is 1 GHz for the LPdiPICA, 1.8 GHz for the HLPD and
above 3 GHz for the QLPD. This reduction in impedance bandwidth is due to the fact
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99
that as the length of the antenna decreases, the volume that radiates also decreases. Also
an antenna radiates efficiently when its length is a quarter wavelength or higher. If the
antenna length is decreased below a quarter wavelength, the efficiency of the antenna
decreases. Hence, as the antenna length decreases, the lower frequency for which the
antenna length is a quarter wavelength also increases. Thus the lower impedance
bandwidth shifts towards higher frequencies as the antenna length decreases.
10
V S W R - LPdiPICA
V S W R -H L P D
V S W R -Q L P D
9
8
7
6
>
5
4
3
2
1
2
3
4
5
6
7
8
9
10
Frequency (GHz)
Figure 5.49: Comparison of VSWR as a function of frequency for the different antennas
(full (LPdiPICA), half (HLPD), and quarter (QLPD)).
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100
5.8.2 Effect of varying the relative dielectric constants of the substrate (thickness =
0.795 mm)
As stated, the goal o f this work is to have a broadband antenna with a bandwidth of
1 - 6 GHz. However, the lower impedance bandwidth of the QLPD is 3.2 GHz. To
decrease this lower impedance bandwidth, the dielectric constant of the QLPD substrate
is increased and its effect is observed. The dielectric constants used were 2.33, 4, 10.2,
and 37.28. The first three are commercially available (Rogers Corporation, Chandler,
Arizona). The last dielectric constant was obtained by using equation 5.1 as explained in
section 5.5.1. The substrates for all the dielectric constants have a thickness of 0.795 mm.
The comparison plots for impedance and VSWR are presented in Figures 5.50 and 5.51
respectively. In Figure 5.50, only the real part of the impedance is shown to clearly show
the shift in the impedance bandwidth. As the relative dielectric constant is increased the
impedance bandwidth shifts towards lower frequencies but only slightly. Also, at higher
frequencies resonant peaks begin to appear. As explained in section 5.5.1, this is due to
the fact that the efficiency o f the antenna decreases as the dielectric constant increases.
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101
a-2.33
200
a - -4
& -
10.2
150 -
100
-
50 ce
-50 -
-100
1
2
3
4
5
6
7
8
9
10
Frequency (GHz)
Figure 5.50: Comparison of the real part of impedance as a function of frequency for
different relative dielectric constants of the substrate used in the QLPD (thickness of
substrate = 0.795 mm)
The shift can be more accurately observed from the VSWR plot (Figure 5.51). The
shift in impedance bandwidth is in fact very low. It can be observed that, for a relative
dielectric constant greater than 4, the VSWR is greater than two over most of the
frequency band. This is because the antenna efficiency decreases and the antenna
mismatch increases.
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102
10
VSWR- £ r -2 3 3
9
VSW R- £ r - 4
VSW R - £ r - 1 0 2
8
V S W R - £ r - 3728
7
6
> 5
4
3
2
1
1
2
3
4
5
6
7
8
9
10
Frequency (GHz)
Figure 5.51: Comparison of VSWR as a function of frequency for different relative
dielectric constants o f the substrate used in the QLPD (substrate thickness = 0.795 mm).
5.8.3 Effect of varying the thickness of the substrate ( e = 2.33)
Another method to decrease the lower impedance bandwidth of the antenna is to
increase the thickness o f the substrate. The different thicknesses used were 0.795mm,
1.59 mm, 3.18 mm and 10 mm. The first three are commercially available (Rogers
Corporation, Chandler, Arizona). The last one is not available commercially, but it was
used in the simulation to observe the effect of a thicker substrate. The relative dielectric
constant o f all these substrates is 2.33. The comparison plots for impedance and VSWR
are presented in Figures 5.52 and 5.53 respectively. As observed from Figure 5.52, even
though the lower impedance bandwidth shifts towards lower frequencies, the shift is very
small. Even for the thickness of 10 mm the shift is very small.
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103
200
R e a l - 0 .7 9 5 m m
I m a g in a iy - 0 .7 9 5 m m
R e a l - 1 .5 9 m m
I m a g m a iy - 1 .5 9 m m
R e a l - 3 .1 8 m m
I m a g in a r y - 3 .1 8 m m
R eal - 10 m m
I m a g in a r y - 1 0 m m
150
100
-50
///
-100
1
2
3
4
5
6
7
8
9
10
Frequency (GHz)
Figure 5.52: Comparison o f impedance as a function o f frequency for different
thicknesses for the QLPD (full, half, quarter).
The decrease in lower impedance bandwidth can be clearly observed in Figure 5.53,
which is the VSWR plot as a function of frequency. The lower impedance bandwidth is
3.25 GHz for the 0.795 mm thickness and 3 GHz for the 10 mm thickness, a shift of 250
MHz. But this amount of shift is not enough to meet our initial specifications.
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104
10
VSWR -Thickness - 0.795 mm
VSWR -Thickness -1.59 mm
VSWR -Thickness- 3.18 mm
VSWR -Thickness -1 0 mm
9
8
7
6
4
3
2
1
2
3
4
5
6
7
8
9
10
Frequency (GHz)
Figure 5.53: Comparison of VSWR as a function of frequency for different thicknesses
o f the QLPD (full, half, quarter)
5.9 References:
[5.1] S-Y. Suh, “A comprehensive investigation o f a new planar wide band antenna,”
Ph.D. Dissertation, Virginia Polytech. Inst. State Univ., Blacksburg, VA, July 2003.
[5.2] “SolidWorks 2005,” SolidWorks Corporation, Concord, Massachusetts
[5.3] “XFDTD 6.8.3.8,”Remcom Corporation, State College, Pennsylvania
[5.4] A.K. Bhattacharyya, R. Garg, “Effect o f substrate on the efficiency o f arbitrarily
shaped microstrip patch antenna,” IEEE Trans. Antennas and Propagation, Vol. 34, No.
10 , October 1986, pp. 1181-1188.
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105
[5.5]. S-Y. Suh; W.L. Stutzman.; W.A. Davis, “Multi-broadband monopole disc
antennas,” IEEE Trans. Antennas and Propagation, Vol. 52, No. 5, May 2004, pp. 13611365.
[5.6] J. Powell, “Antenna Design for Ultra Wideband Radio” M.S. Thesis, Massachusetts
Institute of Technology, Massachusetts, May 2001.
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106
CHAPTER 6
CONCLUSIONS AND FUTURE WORK
6.1 Conclusions
In this thesis, the design and characterization of several broadband antennas based
on the basic tear drop antenna, that could potentially be used in a broadband E-field probe
operating in the frequency range 1 - 6 GHz is presented. In addition, a microwave
amplifier has been designed that can be used in conjunction with the antenna to form the
basis o f an E-field probe that can be used in an anechoic chamber to map broadband
fields.
Starting from the basic diPICA, it was possible to design a LPdiPICA whose size
was reduced to l/4th its original size, thus obtaining an antenna that is small enough to be
used in the E-field probe. However, since this resulted in the reduction of the impedance
bandwidth of the antenna, several methods were implemented to increase the impedance
bandwidth. These included increasing the relative dielectric constant and thickness of the
substrate, increasing the width of the antenna while maintaining the length constant, wire
loading the antenna, and loading the antenna with slots near the feed points.
By increasing the dielectric constant of the substrate, the lower impedance
bandwidth o f the antennas was observed to increase slightly, by about 200 MHz. This
increase in bandwidth did not meet the initial specifications set forth in this thesis. Also,
as the dielectric constant o f the substrate was increased, the efficiency and hence gain of
the antenna decreased. This is due to the tight coupling of the fields inside the high
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107
dielectric constant substrate. Thus increasing the dielectric constant did not provide
sufficient improvement in the impedance bandwidth of the antenna.
The thickness of the substrate was also increased to improve the impedance
bandwidth of the antenna. In this case also, the bandwidth increased only slightly, while
the efficiency o f the antenna decreased. The decrease in efficiency is due to the fact that
more fields will be present in the substrate due to increase in thickness of the substrate.
Thus this method also did not improve the bandwidth. Similarly, increasing the width o f
the antenna while keeping the length constant resulted in only a small increase of the
impedance bandwidth.
Another method implemented to increase the bandwidth was to wire load the
antenna. Wire loading entailed adding a short length of wire on top of the antenna. The
ideal length of wire after several simulations was found to be 10 mm. This also only
improved the impedance bandwidth by 200 MHz and hence did not meet the initial
specifications. The last method implemented to increase the bandwidth of the antenna
was to load the antenna by creating slots near the feed points. This would increase the
path o f the current as it has to go around the slots to reach the edge of the antenna and
thus increase the lower impedance bandwidth of the antenna. However, this method also
did not help much in improving the bandwidth.
Although the impedance bandwidth met specifications only from 3 - 8 GHz, the
pattern bandwidths for all the antennas were 1 - 8 GHz. This may be because the antenna
dimensions were small compared to the wavelength at 1 GHz, being less than 1/16* of
the free space wavelength. The efficiency of the antenna decreases when its dimensions
are below a quarter wavelength which may explain why attempts to improve its
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108
bandwidth may have been unsuccessful. However, the designed antenna is definitely a
good candidate for use in an E-field probe in the frequency range 3 - 1 0 GHz.
The microwave amplifier designed for the purpose of amplifying the E-field
probe received signal showed acceptable gain up to 5 GHz but a rapidly decreasing gain
at higher frequencies.
6.2 Future Work
Future work would involve improvements to the antenna design that would
attempt to increase the impedance bandwidth to meet the original specifications of
1
-
6
GHz. These would include 1. designing broadband lossless matching networks that
would be implemented on the antenna substrate, stacking the QLPD’s one above the
other to form an array, using probe compensation methods including proximity
techniques for feeding the antenna, etc. Other types of commonly used broadband
antennas such as the circular disc antenna and spiral antenna should be investigated for
use as the receiving element. In addition, the current amplifier design should be improved
to meet the initial gain specification of 10 dB, and a separate microwave amplifier should
be designed for the higher frequency range and a switch implemented between the two
frequency ranges or alternatively a broadband amplifier with acceptable performance
over the entire frequency range can be designed.
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APPENDIX A
1 Stability Calculations
S-parameters at the center frequency (3.375 GHz) are
Sn = 0.652 Z 1410
Si2 = 0.109 Z 47.25°
521= 2.13 Z 34.25°
522 = 0.278 Z -99.5 °
The stability factor K can be found using
\-\su\2- \s22\2+\a\2
K = — 1 111 , 1 22'— LL
(1)
A = SnS 22 —Sn S2l
(2)
where,
Therefore A from the above S-parameters is
A =0.149
and K from the above S-parameters and A is
K = 1.119 > 1
2 Formulae for finding Stability Circles
Have to talk to you about it.
3 Simultaneous Match Coefficients
Simultaneous conjugate match coefficients from section 3.5, [3, chapter 3]
s ,± V s M c if
2C,
<3)
and
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110
B2 ± ^ B l - 4 |c , | 2
MS
2C 2
where
= l + |Sll| 2 - | s 2 2 |2 -|A | 2
*2= h ^ i2-
m
2- h 2
(5)
(6)
C ,= S u -A S i
(7)
C j= S jj-A S '
(8 )
Bi and B2 calculated using (5) and (6 ) are given by:
Bi = 1.326
B2 = 0.63
Ci and C2 are calculated using (7) and ( 8 ) and the values obtained are
Q = 0.653
C2 = 0.292
Tms andTMi can then be calculated using (3) and (4) and the values obtained are
1 ^ = 0.841 L-144
0
=0.674 L 80.036°
These values closely match those obtained from ADS.
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Ill
APPENDIX B
The length of a dielectric patch antenna with a substrate of dielectric constant s r is given
by [ 1 ]:
* =- t
(l)
4 Sr
Then if we take two different lengths of microstrip patch Li and L2 , then from equation 1
£, = - p =
(2 )
L2 = - ^ =
\sr
(3)
S.
and from equations 2 and 3, Lj= 2 x L2 . Keeping the free space wavelength same
= A2 - A ) gives:
A
A
= 2 —t=
S rl
(4)
\ S r2
Rearranging the above equation we get
(5)
Squaring both sides gives:
^
2
= 2 x (s r l ) 2
if e rl = 2.33
then from equation (6 ), e r2 = 9.32
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(6 )
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