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A two-dimensional quasi-optical microwave power combining system based on a dielectric slab

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A Two Dim ensional Quasi-Optical
Microwave Power Combining System
Based On A D ielectric Slab
by
H U A N -S H E N G H W A N G
A dissertation su b m itted to the G rad u ate Faculty of
N orth C arolina State U niversity
in partial fulfillment of the
requirem ents for the Degree of
D octor of Philosophy
E L E C T R IC A L E N G I N E E R IN G
Raleigh
1997
APPRO VED BY:
V
C hair of Ad visorv C om m ittee
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UMI Number: 9819337
UMI Microform 9819337
Copyright 1998, by UMI Company. All rights reserved.
This microform edition is protected against unauthorized
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I5
A BSTR ACT
H w ang, H uan-Sheng
A T w o D im e n sio n a l Q u a si-O p tic a l M icro w a v e P ow er
C o m b in in g S y s te m B a s e d On A D ie le c tr ic S lab
U nder the d irection o f M ichael B. Steer
A quasi-optical (QO) power com bining system based on a two dim ensional hybrid
dielectric slab beam m ode waveguide (HDSBVV) with solid-state devices is demon­
strated. This 2D QO system can serve as a planar resonator or a planar amplifier
system , in which active E-plane taper-slot antennas are em bedded on the top sur!
face or underneath th e slab. The resonant frequencies and cavity m odes of the slab
[
resonator were investigated, and experim ental free-running and injection-locked op-
!
erations are shown and indicate th a t th e 2D resonator is an excellent single-mode
•
source. Im pedance m atching has been accomplished by studying the propagation
constants and wave im pedances in the HDSBVV and th e tapered horn. Theoretical
'
result of the T E m ode coupling betw een th e horn and th e HDSBVV system is accom-
;
plished and agrees w ith the m easured data. The active convex- and concave-lens
HDSBVV system s with the M E S F E T /M M IC amplifier units were also im plemented.
M easurem ents of the amplifier gain and system gain, scattering loss due the lenses
and antennas, and the surface fields of th e combined power are shown, and provide
the details of the designing m ethodology for the future planar QO power combiners.
The radiation p a tte rn s of the m etal-strip leaky-wave antenna located on the top
of the passive H DSBW has been characterized. This antenna has th e main beam
scanning at 10 degrees per 1 GHz shift and can be used as the radiating end for the
active HDSBVV am plifier system.
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Biographical Summary
Huan-sheng Hwang received th e B.S.E.E. and M .S.E.E degrees from T utung
In stitu te of Technology, Taipei, Taiwan in 1984 and 1986, and th e M .S.E.E. and
Ph.D . degree from N orth C arolina S tate University, Raleigh, in 1993 and 1997. From
1988 to 1991, he taught the Physics, Electrical Engineering and Electrom agnetics
in Chen-Shiu Junior College, K aohsiung, Taiwan. In 1996, he won th e Prestigious
Bronze Medallion for O u tstan d in g Scientific Achievem ent at the 20th Arm y Science
Conference. His research interests include quasi-optical and spatial power com bining
system s, antennas, electrom agnetics, microwave and millimeter-wave circuits, and
optics.
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Acknowledgm ent
I wish to express my sincere appreciation to those who provided support, en­
couragem ent and assistance th ro u g h o u t th e project and preparation of this thesis.
F irst, I would like to express my g ra titu d e to my advisor Dr. Michael B. Steer for
his support and guidance during m y grad u ate studies. I would also like to thank
m y past and present group m em bers and the people who sat in th e Daniels Hall
Room 336 and 343 for their suggestion and discussion of my research. I especially
ap p reciate the valuable help from Dr. Gregory M onahan, Dr. Todd Nuteson. Mr.
Steve Lipa, Mr. Chris Hicks, and M r. Dave VVinick.
I also thank Dr. Jam es W. M ink Dr. Jam es Harvey, Dr. Frank Kauffm an, and
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Dr. Hans Hallen for their interest in m y research and being my com m ittee members.
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Special appreciation of financial and m oral su p p o rt from the A rm y Research Office through grant DAAH04-95-1-0536 under the directio n of Dr. Jam es Harvey.
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Finally, I wish to thank my p aren ts and my wife for th eir patience and encouragem ent. W ithout their support, th is work cannot be done.
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Table o f Contents
L ist o f F ig u res
vii
L ist o f S y m b o ls
x iv
1
2
In tr o d u c tio n
1
1.1 M otivation For and O bjective of T his S t u d y ..............................................
1
1.2 Report O v e r v i e w ..................................................................................................
3
1.3 Original C o n tr ib u tio n s .......................................................................................
6
1.4 P u b lic a tio n s ............................................................................................................
S
L ite r a tu r e R e v ie w
10
2.1
B a c k g ro u n d ................................................................................................................ 10
2.2
C avity-Type Power C o m b in e r ..........................................................................
13
2.3
G rid-Type Power C o m b i n e r .............................................................................
IT
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2.3.1
G rid O s c illa to rs .......................................................................................
IT
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£
2.3.2
G rid A m p lifie rs ........................................................................................... 21
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2.4
Active P lan ar-A ntenna Power C o m b i n e r .........................................................23
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2.4.1
O scillator-Type Power C o m b i n e r .........................................................23
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2.4.2
A m plifier-Type Power C o m b in e r............................................................26
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2 -D P ow er C o m b in in g O scilla to r
28
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3.1
I n tro d u c tio n ................................................................................................................2S
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3.2
Passive C haracteristics of the 2-D Slab C a v i t y ................................................29
3.2.1
C avity Fields, Resonant C onditions and C utoff Frequencies . . 29
3.2.2
P ropagation C onstant, W avelength and R esonant Frequency
of C avity Modes
3.3
.......................................................................................35
Design and Perform ance of 2D Power Combining Resonator
3.3.1
.....................41
Free-Running O p e r a t i o n .........................................................................43
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3.3.2
3.4
4
Inject ion-Locked O peration
..................................................................47
Discussion and C o n c lu s io n ...................................................................................47
F ie ld s, W ave Im p e d a n c e and M o d e C ou p lin g in t h e H D S B W an d
R a d ia t io n /R e c e iv in g H orn
4.1
In tro d u c tio n .............................................................................................................. 50
4.2
fields in th e Slab S y s t e m ...................................................................................... 50
4.2.1
4.3
4.4
T E mode Field C o m p o n e n ts .................................................................. 52
Wave Im pedance M atching Between the Slab and T apered Horn . . . 55
4.3.1
W ave Im pedance in the S l a b ..................................................................56
4.3.2
W ave Im pedance in the Tapered Horn
..............................................57
Mode C oupling In th e Horn-Slab I n te r f a c e ................................................... 69
4.4.1
5
50
T E io to TEo, Mode C o u p l i n g ...............................................................72
D e sig n and M e a s u r e m e n t o f P o w er C o m b in in g in t h e 2 -D Slab S y s­
te m
77
5.1
In tro d u c tio n ..............................................................................................................77
5.2
Amplifier A rray on the Top Surface of the Convex-lens System . . . .
5.2.1
System D e s c rip tio n ....................................................................................77
5.2.2
M easurem ent of Amplifier Gains, System G ains and \Ey\ P a t­
tern s Across the Slab W aveguide
5.3
........................................................SO
Amplifier A rray under the Convex-Lens S y s t e m ......................................... 91
5.3.1
System D e s c rip tio n ....................................................................................93
5.3.2
M easurem ent of Amplifier Gains, System G ains and \Ey\ P a t­
tern s Across the Slab W aveguide
5.3.3
6
........................................................96
V ariation of Gains and O u tp u t Modes
............................................103
Im p ro v e m en t o f S y s te m C o m p o n e n ts for H igh er O u tp u t P ow er
6.1
77
105
Reduction of Scattering Loss of L e n s e s ........................................................105
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6.2 T he X-Band Vivaldi A ntenna W ith in A C a r r i e r .......................................... 109
6.2.1
Driving Point Reflection Coefficient (S u ) for the Vivaldi an tennal09
6.2.2
Transm ission Coefficient (S 2 1 ) between the Vivaldi A ntenna
and th e R adiating/R eceiving Horn
6.3
................................................... 112
The Concave-Lens System W ith a 4 x 1 , 2x2 and 5 x 4 Amplifier A rray
U n d e r n e a t h ..............................................................................................................115
6.3.1
Perform ance of The Am plifier Unit w ith Single and C ascaded
M M I C .......................................................................................................... 115
7
6.3.2
System w ith th e 4 x 1 and 2 x 2 Amplifier Array
6.3.3
System w ith th e 5 x 4 Am plifier A r ra y ................................................123
C o n c lu sio n s a n d F u tu r e R esea rch
........................... 116
130
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7.1
C o n c lu s io n s ...............................................................................................................130
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7.2
Future R e s e a rc h ........................................................................................................131
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R e fe r e n c e s
136
A L eak y-W ave A n te n n a in th e 2 -D S la b S y ste m
146
B S p a p a m e te r o f t h e M in iC ir c u its E R A -1
150
C M a p le P r o g ra m s
152
$
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List of Figures
1.1 A verage atm ospheric absorption of horizontally-propagating m illim eter
waves. A dapted from [ 1 ].....................................................................................
3
1.2 Pow er perform ance of different m illim eter-w ave sources. A dapted from
[2 ] ..................................................................................................................................................
4
1.3 (a) G rid type power com biner, (b) C avity ty p e power com biner...................
4
1.4 D ielectric slab w aveguide w ith convex/concave lenses.......................................
5
1.5 2D power com bining system with leaky-wave antennas in th e far end. . .
5
2.1
Pow er com bining hierarchy [2 4 ]................................................................................
12
2.2 T h e Fabry-Perot cavity for quasi-optical power combining. T he partially
tran sp aren t reflector can be replaced by a perfect reflector w ith a
waveguide hole in th e m iddle area ....................................................................
2.3
C av ity with resonant-tunneling-diode (R TD ) to operate a t 100 GHz re­
gion [30]....................................................................................................................
2.4
14
14
A G aussian-beam open resonator w ith highly reflective circular coupling
region [35] . T h e circular region has a gold-film strips w ith d = df =
6 3 /im ..........................................................................................................................
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2.5
16
Top view of a G aussian-beam oscillator [36] . The m etal strips serve as a
p artially tra n sp aren t region with d = d' =1 mm. The active devices
and slot antennas are built on th e p lan ar m irror su b stra te ............................IT
2.6 (a) G rid oscillators, (b) G rid am plifiers w ith polarizers....................................
2.7 (a)
IS
T w o-term inal device in an inductive unit cell, (b) T hree-term inal
device in an in ductive u n it cell. T he direct-feedback results in the gate
an d drain leads rad iatin g . The gate-feedback results in the source an d
d rain leads ra d ia tin g ..............................................................................................
IS
2.S T h e u n it cell of grid am plifier. A differential transistor pair is used w ith
th e source leads connected.......................................................................................22
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2.9
U nit cell of th e CPVV slot antenna oscillator with a F E T inside.......................24
3.1
G eom etry of th e P lanar quasi-optical slab cavity....................................................30
3.2
M inim um thickness d of dielectric su b strates required to support T E n and
TM„ modes. T h e thickness is norm alized to free space wavelength Xa. 34
3.3
Sn/ k 0 vs d/Xo for th e slab cavity w ith s T = 2.57..................................................... 34
3.4
C alculated 00mq for T E and TM m odes in the 2D cavity with d = 1.27 cm.
L = 30.48 cm , s r = 2.57...........................................................................................36
3.5
C alculated Xomq for T E and TM modes in the 2D cavity w ith d = 1.27 cm .
L = 30.48 cm , s r = 2.57...........................................................................................37
3.6
C alculated / 0ra, for T E mode in th e 2D cavity with d = 1.27 cm, L =
30.4S cm, s r = 2.57....................................................................................................3S
3.7
C alculated f 0mq for TM mode in th e 2D cavity w ith d = 1.27 cm .
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L = 30.48 cm , £r = 2.57. Unlike th e TE case,som e TM 0m, modes
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disappear in this cavity............................................................................................. 39
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3.8
P lan ar Q uasi-optical slab power com bining oscillator............................................ 41
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3.9
Single oscillator unit constructed on a Rogers R T /D uroid substrate w ith
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er = 2.33.........................................................................................................................41
3.10 M ax hold sp ectrum with oscillator u n it moved over slab. At any one
tim e there is at m ost only one oscillation frequency..........................................45
3.11 Spectrum of th e power combining oscillator with 1. 2. 3 and then 4 unit
oscillator biased...........................................................................................................45
3.12 Spectrum of th e power combining oscillator with 4 u n it oscillators, frequencies are offset from 7.444 G H z.......................................................................46
3.13 Single shot sp ectrum with 4 unit oscillators with injection locking. T he
resolution bandw idth is 1 kHz............................................................................... 4S
3.14 M axim um hold (10s) spectrum with 4 unit oscillators and injection lock­
ing. The resolution bandw idth is 1 kHz............................................................. 4S
3.15 Spectrum of the power combining oscillator with 50 kHz FM m odulation. 49
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3.16 S pectrum of the power com bining oscillator w ith 350 kHz FM m odulation. 49
4.1
C alculated propagation constant, /3, for TEo,m m ode in the dielectric slab. 57
4.2
C alculated wavelength, As, for T E 0,m mode in th e dielectric slab .................... 59
4.3
C alculated wave Im pedance, Z t e , for TEo,m m ode in the dielectric slab. . 59
4.4
The tap e re d horn connected w ith the dielectric slab system ............................. 61
4.5
The cascaded small-section waveguide...................................................................... 62
4.6
P artially loaded waveguide............................................................................................62
4.7
C alculated propagation constant at different position inside th e tran s­
m ittin g horn................................................................................................................ 64
4.8
C alculated propagation constant for T E 10, T E 2 0 and TE 3 0 in th e horn
a p e rtu re ........................................................................................................................ 65
4.9
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4.10 The m odel for a sm all-section w ith step change in the im pedance of the
si
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tap ered horn................................................................................................................. 68
4.11
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C alculated wave im pedance for T E i0, T E 2o an d T E 30 in the horn aperture. 65
C alculated reflection coefficient at the feeding neck of the tra n sm itti
horn. ( L = 12.5 cm, at = 2.85 cm,
bf
= 9 cm and d = 1.27 cm
. . . .
69
4.12 The calculated relative am plitudes for the G aussian-H erm ite TEo.o, T E 0 .2
[
f
[
and T E 0>., modes which are coupled from th e single T E 10 m ode of the
[
w id th ............................................................................................................................... 76
feeding waveguide. W 0 is th e beam spot size and equal to th e ap ertu re
r
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4.13 The calculated and m easured patterns of th e to tal coupled field in the
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slab...................................................................................................................................76
5.1
The Convex-lens slab waveguide system with amplifiers on top surface . . 79
5.2
Side term inations for th e HDSBW to reduce edge reflections............................79
5.3
M ESFET planar am plifier.............................................................................................80
5.4
Wave m odel of the amplified and through waves in the slab system with
a n ten n a array.............................................................................................................. S2
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5.5
M ESFET planar am plifier.........................................................................................
5.6
Received Power for th e slab system w ith/w ithout unbiased am plifier ar­
ray in location 1......................................................................................................
5.7
84
Received Power for th e slab system w ith/w ithout unbiased am plifier ar­
ray in location 3......................................................................................................
5.9
84
Received Power for th e slab system w ith/w ithout unbiased am plifier ar­
ray in location 2......................................................................................................
5.8
82
85
Insertion loss for am plifier array in location 1, 2 an d 3.................................... 85
5.10 Received Power for am plifier array w ith different biases in location 1. . . 86
5.11 Received Power for am plifier array w ith different biases in location 2. . . 86
5.12 Received Power for am plifier array w ith different biases in location 3. . . 87
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5.13 Amplifier gain for am plifier array in location 1...................................................
87
5.14 Power gain for am plifier arrav in location 1.........................................................
88
5.15 Amplifier gain for am plifier array in location 2...................................................
S8
5.16 Power gain for am plifier array in location 2.........................................................
S9
5.17 Amplifier gain for am plifier array in location 3...................................................
89
5.18 Power gain for am plifier array in location 3.........................................................
90
5.19 M easurem ent of power d istrib u tio n ........................................................................
92
5.20 Power d istributions on the slab................................................................................
92
5.21 Dielectric slab waveguide system w ith M ESFET am plifiers inside...............
93
5.22 Side view of system w ith m etallic to p ....................................................................
94
5.23 Amplifier array under dielectric slab waveguide.................................................
94
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5.24 M easurem ent of received powers w ithout and w ith amplifiers built on
different su b strates com pared to th e unperturbed HDSBVV system .
5.25 Amplifier gain for location 1.
T his location is 22 cm away from th e
second lens................................................................................................................
5.26 Amplifier gain for location 2.
95
97
T his location is 18 cm away from th e
second lens................................................................................................................
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5.27 Passive G ain ,|S 2 i|, of th e dielectric slab w ith /w ith o u t am plifiers. The
insertion loss of the u n it cells alone is th e difference betw een these
two |S2i| curves........................................................................................................... 99
5.2S M easured response of th e passive DSBYV am plifier system (no bias) with
and w ithout a m etallic top cover. W ith o u t th e cover, th e system loss
is 10 to 12.5 dB. W ith th e cover, th e system loss is 6.5 to 9 dB.
. . . 100
5.29 Transm ission gain for th e am plifiers w ith b ias...................................................... 101
5.30 Pout vs Pin for amplifiers w ith and w ithout bias.................................................101
5.31 M easured \Ey\ distribution across the top of th e HDSBW am plifier sys­
tem at 7.37GHz......................................................................................................... 102
5.32 Amplifier gain insertion loss of the array u n d ern eath the slab .........................104
5.33 M easured \Ey \ patterns a t 7.1S2 GHz.......................................................................104
6.1
The 2D HDSBW system w ith convex/concave lenses......................................... 106
6.2
Pass system gain for th e 2D QO system w ith convex/concave lenses.
Concave lenses cause less energy scatter th a n convex lenses, and the
average of th e loss reduces about 50%............................................................... 107
6.3
M easured \Ey \ patterns before and after a convex/concave lens. Guided
energy has less am p litu d e drop when it passes thought th e concave
lens.................................................................................................................................10S
6.4
P{n vs Pout for the con vex/concave-lens system with a 4 x 1 amplifier
array underneath, (a) th e system is w ithout metallic top, an d (b) the
system is w ith m etallic to p ....................................................................................10S
6.5
System gain for the system w ith /w ith o u t m etallic top. (a) represents the
convex-lens system , an d (b) represents th e concave-lens system .
6.6
. . . 109
An an ten n a elem ent sits inside a carrier u n d ern eath the slab system . The
m etallic carrier is also a heat sink for th e M M IC am plifiers...................... 110
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6.7
Vivaldi antenna: (a) The antenna w ith mesh stru ctu re used in MoM
analysis; and (b) M easured (dashed line) and sim ulated (solid line)
S n for th e antenna in a i r .....................................................................................I l l
6.8
S n for the tap er antenna in the carrier underneath the slab.......................... I l l
6.9
M easurem ent of |S n | and |i>2 i| for th e Vivaldi antenna underneath th e
half concave-lens system ........................................................................................113
6.10 |52i | between the Vivaldi antenna to horn in the half concave-lens system . 113
6.11
M easured
at 8.03 GHz........................................................................................114
6.12 M easured |£ y| at 10.01 G H z ...................................................................................... 114
6.13 A concave-lens system with a 5 x 4 am plifier array underneath the slab
system . d \ — 15.6 cm, d2 = 40 cm and d3 = 15.4 cm .................................. 116
6.14 A h alf concave-lens system with single amplifier unit, (a) system w ithout
;
a m etal window: (b)system with a m etal window........................................... 116
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6.15 T h e am plifier unit with single/cascaded MMIC................................................... 117
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dow. The amplifier has a single M M IC ............................................................. 117
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6.16 T h e single-amplifier gain for the system with and w ithout a m etal win-
6.17 T h e single-amplifier gain for the system with and w ithout a m etal window. The amplifier has two cascaded MMIC’s................................................. 118
6.18 A m plifier gain of the 4 x 1 amplifier a rray in the concave-lens system with
a w ith different Pt-n...................................................................................................120
6.19 S ystem loss of the concave-lens system with a 4x 1 array. This loss is
caused by the horn, lens and unbiased array................................................... 120
6.20 M easured \Ey | patterns for the system w ith a 4x 1 am plifier array working
at 8.667 G H z.............................................................................................................121
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6.21 A m plifier gain of the 2 x 2 amplifier array in the concave-lens system with
a w ith different Pm..................................................................................................121
6.22 S ystem loss of the concave-lens system with a 2 x 2 array. This loss is
caused by the horn, lens and unbiased a r r a y . ............................................... 122
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6.23 M easured \Ey\ patterns for th e system w ith a 2 x 2 amplifier array working
at S.667 GH z............................................................................................................. 122
6.24 5 x 4 -array gain for different P,n and the to tal loss. The to tal loss is due
to horn radiation to air, lens scattering and array scattering. This
system has metallic to p ..........................................................................................126
6.25 M easured |j£y| patterns for 5 x 4 array working a t S.87 G H z............................ 126
6.26 M easured \Ey \ patterns for 5 x 4 array working at 10.724 G H z........................ 127
6.27 Am plifier gain and to tal loss for the concave-lens system w ith 5 x 4 array.
T h e system is with a ad ju sted metallic to p ..................................................... 127
6.28 Pout vs frequency. The system is with a adjusted m etallic to p ........................ 128
6.29 Pin vs P0ut at S.828 G H z.............................................................................................. 128
6.30 System gain at 8.828 G H z........................................................................................... 129
6.31 M easured \Ey \ patterns for 5 x 4 array working at 8.828 G H z.......................... 129
7.1
The rectangular-aperture an ten n a unit under a closed slab sy stem ...............134
7.2
The HDSBW system w ith th e aperture antenna am p lifers............................. 135
•;
A .l The 2D HDSBW system w ith the leaky-wave antenna s tr u c tu r e s ................. 14S
[
A.2 Fields across the system w ith m etallic strips. T he space betw een strips
\
:)
is 3 cm ......................................................................................................................... 149
A.3 Beam scanning of the leaky-wave antenna. Scanning angle is 15degrees
!
for 1 G H z .................................................................................................................149
i
£
:
B .l D arlington circuit configuration of ERA-1 am plifier chip................................... 150
B.2 Typical biasing configuration of ERA-1 am plifier chip........................................ 151
xiii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
List of Symbols
A;
- Coefficient for num erical integration
Ate
- Coefficient for T E Gaussian mode.
At \ i
- Coefficient for TM Gaussian mode.
a
- Height of th e rectangular waveguide
a'
- Height of th e expended waveguide aperture
,
- Unit vector along th e x axis in C artesian coordinates.
ay
- Unit vector along th e y axis in C artesian coordinates.
ac
- Unit vector along th e c axis in C artesian coordinates.
R
- Radius of cu rv atu re for the lens.
B-mn
- Coefficient for m odal source field.
b
- W idth of th e rectangular waveguide
b'
- W idth of th e expended waveguide aperture
c
- Capacitance.
CAD
- Com puter A ided Design
CPW
- Coplanar W aveguide
c
- Speed of light.
d
- Dielectric su b stra te thickness and spacing above ground plane
di
- Distance betw een the radiating horn and lens.
di
- Distance betw een th e lenses.
dz
- Distance betw een the receiving horn and lens.
DR
- Direct R adiation
E
- Electric field.
Ein
- Input electric field of the amplifiers.
E 0u*
- O utput electric field of the amplifiers.
a
XIV
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Ea
- Amplified electric field.
E th
- Through electric field.
- Scalar electric field H erm ite-G aussian traveling vvave-beam w ith
propagation in th e ± a - direction.
E IP R
- Equivalent Isotropically R adiated Power.
EPR
- Effective R adiated Power.
F
- Focal length of th e lens.
/m.n,9
- Modal resonant frequency.
fo
- Cutoff frequency.
FET
- Field Effect T ransistor.
G n(x) - Function of field d istrib u tio n along x-axis w ith index n.
G aA s
- Gallium Arsenide.
H e m ( x )- H erm ite polynom ial of order m and argum ent x.
I
3
%
HBT
- H eterojunction B ipolar Transistor.
3
H E M T - High Electron M obility T ransistor.
I
{
H D SBW - Hybrid Dielectric Slab Beam Waveguide.
H F E T - H eterojunction Field Effect Transistor.
h
- height of the parallel plates .
Jm ( 2 :) - Bessel function of th e first kind and order m.
IM PA T T - Im pact Avalanche T ransit Tim e.
»
i
I
)
InP
- Indium Phosphide
k0
- Wave num ber in free space.
k3
- Wave num ber in dielectric substrate.
L
- Inductance.
LO
Local O scillator.
M E S F E T - M etal S em iconductor Field Effect Transistor.
XV
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
M C
-
M icrostrip Couple.
MMIC - Microwave M onolithic Integrated C ircuit
U nit outw ard norm al vector.
n
PAE
- Power Added Efficiency.
P in
Incident power to the amplifiers.
Pout
O u tp u t power form th e amplifiers.
Q
Q uality factor of antenna or resonator.
QR
- Q uasi-optical Resonator.
<7
Longitudinal m ode number.
R
Resistance.
RF
Radio Frequency.
RTD
- Resonant Tunneling Diode.
•S n
-
Driving point reflection coefficient.
S21
-
Transm ission coefficient.
TE
TEM
TM
Transverse Electric.
- Transverse Electrom agnetic.
Transverse M agnetic.
TVVT - Traveling Wave Tubes.
w0
Gaussian beam radius at waist.
W ;
Gaussian beam radius at z position.
Zo
Free space im pedance.
Zte
T E mode wave im pedance .
Z
TM mode wave impedance.
tm
,^slab
— Propagation constant inside the slab.
f t horn
Propagation constant inside the horn.
I'
Reflection coefficient.
XVI
0*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
<5,
- Skin depth.
^0
- P erm ittiv ity of free space.
Cr
- S ubstrate dielectric constant.
Ao
- Free space wavelength.
A,
- W avelength in th e slab.
Ho
- Perm eability of free space.
7T
- Circle circum ference divided by circle diam eter.
a
- C onductivity of a m etal.
&mn
- Phase coefficient of the traveling wave-beam m odes.
P
- Radius of th e phase curvature of th e beam m ode.
US
- Radian frequency'.
xvii
m
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Chapter 1
Introduction
1.1
M o tiv a tio n For a n d O b je c tiv e o f T h is S tu d y
A variety of scientific, com m ercial, law-enforcement and m ilitary com m unication and
radar system s at m illim eter-w ave frequencies rely on high power solid-state sources
with ten w atts to hundreds of w atts at 30 GHz or above.
A pplications include
high-resolution rad ar im age system , civilian wireless com m unication and satellite
cross links, sensitive detection of air pollutants, chemical warfare agents, and active
missile seekers. T h e particular frequencies are loosely based on th e propagation
"window,sr’ at 35, 94, 140 and 200 GHz or the “blockV ’ a t 21. 60, 119 and 183 GHz
shown in Fig.
1.1 [1].
A dequate power levels can be provided by tu b e devices
but not w ith the size and particularly the life tim e required. Only w ith solid-state
sources, th e required com bination of small size, light weight, high reliability and
I
m anufacturability can be achieved.
In th e past decade, high-speed device technology has advanced rapidly to the
point where 300 GHz transistors, and 1 THz diodes can be fabricated. As shown
in Fig.1.2 [2], GaAs P H E M T and InP-based H E M T are good for applications up
to 100 GHz, and IM PA TT diode, Schottky diode and RTD are potentially useful
from 100 GHz to 1 TH z. T h e im provement of th e fabrication techniques for the
sem iconductor devices significantly raises the application range of th e m onolithic
integrated circuits. However, the power level of those solid-state devices are still
not sufficient for th e m any millimeter-wave applications. In order to achieve higher
power levels, coherently com bining the power from many individual devices is a
promising way to investigate.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
M any power-combining m ethods have been investigated in the microwave and
m illim eter-wave frequency range since th e early 1970’s, and th ey are cataloged into
four types: chip level com biners, circuit level combiners, sp atial combiners, and the
com binations of these three [3]. In 19S6, Mink published a classic paper in which
the use of quasi-optical power-combining techniques is suggested [4] and provided a
detail analysis of com bining th e power from m ultiple solid-state devices. Nowadays,
the m ost m ature quasi-optical power com bining system s include grid type [5, 6. 7]
and cavity type [8, 9, 10] as shown in Fig.
1.3. These stru ctu res are essentially
three dim ensional and have th e common property th at th e power from th e active
devices, which are oscillators in cavity ty p e and amplifiers in grid type, is com bined
in free space over a distance of m any wavelengths. An altern ativ e and potentially
more easily fabricated system is the planar quasi-optical power combining stru c tu re
i
i:
pursued here. This system is based on th e hybrid dielectric slab-beam waveguide
V
(HDSBVV) proposed by M ink and Schwering [11] and is shown in Fig. 1.4. This
:
waveguide bridges the gap between conventional dielectric waveguides em ployed in
1
the mm-wave region and slab type dielectric waveguides at optical frequencies.
I
In this dissertation, th e slab waveguide system with a M E SF E T /M M IC am plifier
r
|
array shown in Fig. 1.5 is investigated. T he theoretical an d experim ental studies
r
\
are based on the assum ption th a t only T E Gaussian waves propagate inside the
t_______________________________
i
slab. T h e convex- and concave-lens HDSBVV systems w ith am plifiers located above
j
and u nderneath the slab were investigated, the combining power levels, system gains
■
and losses were m easured. T he planar notch-antenna am plifier was designed for this
]
slab system to amplify the guided power level. The experim ental results provide
1
positive inform ation about th e availability of this slab system for the future M M IC
fabrication of the quasi-optical power com biners.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
W avelength (mm)
30
15
100
40
10
8
20
S e a Level
10
4000 M Altitude-----
6
5 4.5 4
3
2
1.5
1
0.4
0.2
0.1
0.04
H „0
0.02
0.01
0.004
0.002
H _0
0.001
10
15
20 25 30
40
50 60 70 80 100
150
200 250 300
F req u e n cy (GHz)
|
i
Figure 1.1: Average atm ospheric absorption of horizontally-propagating millimeter
waves. A dapted from [1].
1.2
R e p o r t O v e r v ie w
C h ap ter 2 presents a review of the previous studies on the quasi-optical power
combiners. Various power combining techniques and methodologies are described.
In C hapter 3 theoretical analysis and im plem entation of the 2D slab resonator
f
w ith active ta p e r antennas inside are presented. Expressions for th e cavity fields.
|
resonant conditions and cutoff frequencies of the cavity modes are derived.
>
free-running an d injection-locked operations of power combining oscillators are mea-
1
sured and discussed.
Also.
C hapter 4 presents the theory behind th e behaviors of T E Gaussian beam m odes
as well as m ode coupling between the H DSBW and th e radiating/receiving horns.
T he TE-m ode field com ponents, wave im pedances and propagation con stants inside
the HDSBW an d the tapered horns are presented. Im pedance m atching and energy
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
o
V v N IMPATT ■
PHEMT
-I
r'
10
10 0.1
V
\
\ v
1
:
\\V ^ -G u n n -
10
\
100
1000
FREQUENCY (GHz)
Figure 1.2: Power perform ance of different m illim eter-wave sources. A dapted from
[2 ]-
ACTIVE GRID SURFACE
OUTPUT POLARIZER
i
I;
\ E
N PU T
SEAM
PARTIALLY
TRANSPARENT
SP H E R IC A L
REFLECTOR
OUTPUT
IN PU T POLARIZER
(a)
(b)
Figure 1.3: (a) G rid type power combiner, (b) C avity type power combiner.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
5
^ le n s > ^ sla b
x
A
W
f A
ground plane
dielectric slab
8 slab
phase transformers
I
£ |ens
.
x
ground plane
^ le n s < ^ sla b
Figure 1.4: D ielectric slab waveguide w ith convex/concave lenses.
BOTTOM GROUND PLANE
COVERING DIELECTRIC
2D
QUASIOPTICAL
SOURCE
LENS
AMPLIFIER ARRAY
LEAKY-WAVE ANTENNA
Figure 1.5: 2D power com bining system w ith leaky-wave antennas in th e far end.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
6
reflection at the H D SB W -horn interface is also studied.
C hapter 5 describes th e im plem entation of a 2D quasi-optical slab-waveguide
power combiner in w hich a taper a n te n n a array with M E SF E T is used. T h e active
array is located on th e top surface or u n d ern eath the dielectric slab for com parison of
th e ir perturbation to the o u tp u t beam m odes. M easured d a ta includes th e am plifier
gain and system gain, system loss due to passive com ponents and active antennas,
an d o u tp u t power level and com bining field patterns.
C h ap ter 6 describes th e im provem ent of the HDSBW system for higher o u tput
pow er by reducing system loss and using m ore amplifier elem ents. System perfor­
m ances are com pared for th e system w ith convex and concave lenses. T h e o u tp u t
responses of the concave-lens system w ith a 4 x 1. 2x2 and 5 x 4 amplifier array which
uses cascaded M M ICs are also shown.
£
f
I
\
C h ap ter 7 provides a sum m ary of the dissertation and suggests th e possible
directions for the fu tu re work related to this topic.
it
j.
|
1 .3
O rig in a l C o n tr ib u tio n s
v
c
|
i
T h e original contributions related to th is dissertation are:
|
• A two-dim ensional quasi-optical power combining system based on th e dielec-
|
trie slab is d em o n strated for th e first tim e. This 2D QO system can serve as
j
a planar resonator or a planar am plifier system, in which active E-plane Vi­
s'
valdi antennas are em bedded on th e top surface or underneath th e slab. This
t
|
;
2D system also provides a good p ro to ty p e for the fu tu re MMIC fabrication of
the quasi-optical power com biner in the m illimeter- and subm illim eter-w ave
region.
• Theoretical an d experim ental studies of the 2D power combining resonator is
presented in C h a p te r 3. The characteristics of th e passive resonator provide
the details of resonant frequencies and cavity m odes for designing th e active
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
I
resonator on the dielectric slab or sem iconductor substrate.
Experim ental
results, including free-running and injection-locked operations, show th a t this
2D resonator is an excellent single-mode source for th e future planar quasioptical power combining system s.
• The im pedance m atching and T E m ode coupling between th e tapered horn and
the HDSBYV system has been investigated. The propagation constants in the
HDSB W and tapered horn are studied and applied to achieve good im pedance
m atching. The theoretical and experim ental results on m ode coupling indicate
th a t m ultiple modes will appear inside th e slab system even when only single
rectangular waveguide m ode is injected to the HDSBYV system .
• T he 2D QO power com bining system experim entally described in C h ap ter 5
i
k
s
£
f
L
and C h ap ter 6 provides th e details of th e designing m ethodology for th e future
MMIC fabrication of th e planar QO power combiners. Different optical lenses
are applied to the 2D QO system to test the system perform ance, and the
^
^
■
m easured results strongly suggest th a t the concave-lens is more appropriate
I
for th e 2D QO system th a n the convex-lens. The surface wave p attern s of
the active HDSBYV system s with the M E SF E T /M M IC am plifier units on top
or underneath the slab were also m easured and show the inform ations of the
field p erturbation, beam forming, and beam scanning.
M easurem ents of S
p aram eters and radiation patterns for th e amplifier unit underneath the system
also give the message for im pedance m atching between MMIC am plifier and
E-plane radiator, and th e energy coupling between the horn and the am plifier
unit.
• The radiation patterns of the m etal-strip leaky-wave an ten n a located on the
top of the passive HDSBYV has been accomplished and are described in Ap­
pendix A to show the behaviors of beam scanning at different frequencies. T he
radiation patterns from the m etal strips scan 10 degrees per 1 GHz shift, and
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
s
show th a t this leaky-wave a n te n n a cab be used as an radiating en d for the
HDSBVV system .
1 .4
P u b lic a tio n s
T he work associated w ith this dissertation resulted in th e following publications:
• J. W. M ink, H. Hwang, T. W. N uteson, M. B. Steer, J . Harvey. "Spatial Power
Com bining for Two-Dimensional S tructures,” presented in 1997 Top. Symp.
on Mill. Waves.
• T. VV. N uteson, H. Hwang, M. B. Steer, K. N asishadham , J. Harvey and J. W.
Mink, "A nalysis of finite grid stru ctu res with lenses in quasi-optical system ."
IE E E Tran. Microwave Theory Tech. vol. 45, pp 666-672, May 1997.
r
|
• M. B. Steer, J. VV. M ink and H. Hwang, "Dielectric Slab Com biner.” C hapter
|
7 in Active and Quasi-Optical Arrays, John Wiley &: Son Inc.. New York, 1997.
J. Harvey, M. B. Steer, H. Hwang, T. W. Nuteson, C .W . Hicks, and J.VV. Mink
"D istributed power combining an d signal processing in a 2D quasi-optical sys­
te m ,” Proc. W R I International Sym p. on Directions fo r the Next Generation
j
o f M M IC Devices and Systems, S eptem ber 1996.
• H. Hwang, T . VV. Nuteson, M. B. Steer, J.W . M ink, J . Harvey, and A. Paollela.
"A 2-dim ensional slab quasi-optical power com bining system ,” U R S I Symp.
Dig., p.354, Ju ly 1996 .
• J. Harvey, M. B. Steer, J. VV. M ink, A. Paollela, H. Hwang and T. VV. N ute­
son, “Advances in quasi-optical power combiners provide path to ra d a r and
com m unications enhancem ents,” Proc.
20th A r m y Science Conference, pp.
121-124. Ju n e 1996.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
9
• H. Hwang, T . VV. N uteson, M. B. Steer, J.VV. Mink, J. Harvey, and A. Paol­
lela, “Tw o-dim ensional quasi-optical power com bining system perform ance
an d com ponent design,” IE E E M T T - S Int. Microwave Symp. Dig., pp. 927930, Ju n e 1996.
• H. Hwang, T. VV. N uteson, M. B. Steer, J. VV. Mink, J. Harvey, and A. Paollela.
“A quasi-optical dielectric slab power com biner,” I E E E Microwave Guided
Wave Lett., vol. 6, pp. 73-75, February 1996.
• H. Hwang, T . VV. N uteson, M. B. Steer, J. VV. Mink, J. Harvey, and A. Paollela.
"A slab-based quasi-optical power com bining system .” Twentieth International
Conference on Infrared and Millimeter Waves Dig., pp. 157-15S. Decem ber
1995.
• H. Hwang, T . VV. N uteson, M. B. Steer, J. VV. Mink. J. Harvey, and A. Paollela.
'I
is
I*•
I
•
i
"Q uasi-optical power com bining techniques for dielectric su b strate s.” Proc.
International Semiconductor Device Research Sym posium, pp. 243-246. Decem ber 1995.
i
• H. Hwang, T . VV. N uteson, M. B. Steer, J. VV. Mink, J. Harvey, and A. Paollela.
1
"Q uasi-optical power com bining in a dielectric substrate, ” Proc. International
1
m Symposium on Signals, Systems and Electronics, pp. 89-92, O ctober 1995.
s
[
|
• H. Hwang, T . VV. N uteson, M. B. Steer, J. VV. Mink. J. Harvey. A. Paollela
I
and F. K. Schwering, “A dielectric slab waveguide w ith four planar am p lifiers.'
)
IE E E M T T - S Int. Microwave Symp. Dig., pp. 921-924, M ay 1995.
i
• F. Poegel, S. Irrang, S. Zeisberg, A. Schuenem ann, G. P. M onahan, H. Hwang.
M. B. Steer, J. VV. M ink, F. K. Schwering, A. Paollela and J . Harvey, "D em on­
stratio n of an oscillating quasi-optical slab power com biner,” IE E E M T T - S
Int. Microwave Symp. Dig., pp. 917-920, May 1995
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
I
10
Chapter 2
Literature Review
2.1
B a ck g ro u n d
In cooperating active devices d irectly into the antenna stru ctu re has been pursued
at least since th e mid-1940s. In th e early 1960s, active dipole an d slot antennas em ­
ploying param etric devices and tu n n el diodes were developed by Frost and PendinofF
[15, 16]. Later, th eir approaches were applied to spatial am plifier arrays [17, IS, 19].
t.
and to reflective arravs
** with diode switches in the large pillbox array ap ertu re for
beam scanning [20]. In 1980s. th e development of m icrostrip antennas and high
£•
I
perform ance m onolithic microwave integrated circuit (MMIC) resulted in a high de-
|
m anding for active arrays for m ilitary warfare electronics. Based on this trend, Rut-
I
ledge et al [21] published an im p o rtan t report about the planar antennas and arrays
|
integrated with sem iconductor devices, which were used for the sub-m illim eter-w ave
I
focal-plane receiver. Later, in 1983 and 1986, papers published by W andinger et
|
al [22] and M ink [4] suggested a com bination of active antennas and arrays with
f
quasi-optical (QO) components for millimeter-wave power com bining. M ink’s paper
gave an im p o rtan t im petus for th e later research activity on quasi-optical power
f
com bining techniques.
C om pared to conventional waveguide power combining system s, quasi-optical
power com bining has several advantages. Quasi-optical power com bining systems
depend on m etallic structures less th an conventional power com bining system s in
which large conductor loss appears with the high operating frequencies.
Quasi-
optical system s also have large transverse dimensions to accom m odate a large num ­
ber of active devices than the waveguide structure. Additionally, quasi-optical sys-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
11
terns have less over-m oding problem than the waveguide power com biner such as
the Kurokawa type waveguide com biner [23].
Q uasi-optical power com bining system s use three dim ensional an d two dim en­
sional active array to generate a certain output power level. Each u n it of the array
occupies a sm all area whose w idth and length are usually selected as one wavelength,
and em ploys a lot of power devices, circuits and circuit-level power com biners. These
power devices, circuits and com biners are suggested to be built on th e wafer active
circuitry so th a t each array unit can accom m odate m ore devices and com pact cir­
cuits inside a tiny area. A good exam ple of power com bining hierarchy is shown
in Fig. 2.1 (after [24]). Power generated from each array unit is com bined in free
space or in dielectric m aterial over a distance of one or more wavelengths. Basi­
cally, rad iated power from each device should be controlled to be coherent and then
constructive power combining can be achieved,
f.
t
i
Several review articles have been w ritten about th e quasi-optical system s and
m illim eter-w ave power com bining techniques by C hang et al [3], W iltse et al [26] and
I
G oldsm ith [25]. Chang et al sum m arized different m illimeter-wave power-combining
I
techniques an d th eir perform ance, and also reviewed their advantage and disad-
\
vantage.
j.
subm illim eter-w ave regions using G aussian beam m odes and quasi-optical compo-
G oldsm ith described quasi-optical techniques for m illim eter-w ave and
r
;
nents. In 1993 and 1996, York provided the global reviews of the latest quasi-optical
[
power com bining techniques and system s [24, 27].
>
1
)
This C h a p ter will m ainly describe the experim ental work which has been done
for the quasi-optical power com bining components and systems including cavity-
j.
!
type resonators, grid oscillators, grid amplifiers, as well as active planar-antenna
power com biners.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
P ow er D evice
Large area/gate periphery
Power Circuits
Multiple-device integrated circuits
- Multistage am ps
- Push-pull power satge
- 3dB Hybrid combiner
- Wilkinson combiner
- Distributed Power am ps
Circuit C om biners
Transmission-line/waveguide-based
- Corporate combiners
- N-way/radial line combiners
- Chain-coupled combiners
- R esonant cavity combiners
O)
Q uasi-optical or Spatial Com bining
2D or 3D arrays of power devices,
pow er circuits, or power moules
- Circuit-fed or spatially fed
- Active array or grids
- C losed waveguide, dielectric waveguide,
b eam (lens) waveguide b ased
Figure 2.1: Power com bining hierarchy [24].
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
13
2 .2
C a v ity -T y p e P o w e r C o m b in er
A cav ity -tv p e power com biner is constructed by placing the active antenna array
in th e quasi-optical cavity and has been extensively studied [28]-[40].
Basically,
this cavity is a Fabry-Perot cavity which can be formed by two or more planar
reflectors, two or m ore curved reflectors, or a com bination of curved and planar
reflectors.
For exam ple, in Fig. 2.2 the cavity has one planar reflector and one
curved reflector which may be partially transparent or has a waveguide ap ertu re in
th e m iddle of the reflector. Pow er generated from each antenna oscillator is combined
into th e G aussian cavity m ode and is coupled out through the partially transparent
reflector or th e waveguide hole. T he curved reflector also provides feedback which
su p p o rts oscillators synchronization. Cogan et al [28] first designed a cavity-type
quasi-optical power com biner w ith a large num ber of IMPATT diodes based on the
previous theoretical work from M ink [4]. The planar reflector has 21 IM PATT diodes
em bedded. Phase coupling a t 35 GHz has been done and R F power exceeded the
sum of th e individual diode o u tp u ts. T he loaded cavity Q was m easured to be 5,000
and th e oscillation bandw idth is less than 50 kHz. T heir m easurem ent stated th a t
th e com bining power from two diodes is 4 tim es th a n th at from a single diode, and
this agrees w ith the theoretical prediction in [4]. A fter Cogen, Young et al [29] used
p lan ar microwave circuits in th e open cavity instead of using IM PA TT diodes. They
successfully dem onstrated th e oscillator at X-band w ith a m axim um o u tp u t power of
13.3 mVV at 10 GHz. They also incorporated a 31 GHz G unn-diode oscillator with
a m onolithic GaAs m icrostrip resonator, and th eir experim ental results indicated
th a t th e ir technique will be useful above 30 GHz.
Brow n et al [30] designed a semiconfocal open-cavity resonator with resonanttu n n elin g diodes (RTD) as show n in Fig. 2.3. T he RTDs were m ounted in a VVR-6
rectan g u lar waveguide which has a round 0.075-in-diam eter coupling hole in the
m iddle of th e flat reflector. T his resonator worked near 103 GHz, and the Q was
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14
PLANAR
REFLECTOR
SOURCE
ARRAY
PARTIALLY
TRANSPARENT
SPHERICAL
REFLECTOR
Figure 2.2: T h e Fabry-Perot cavity for quasi-optical power com bining. T he partially
transparent reflector can be replaced by a perfect reflector w ith a waveguide hole in
th e middle area.
Movable curved
reflector
Rate reflector
To bias circuit
4
^
Stablizing absorber
Circular
aperture
Waveguide
hole
1/e locus of
TEM oonmocje
Figure 2.3: C avity with resonant-tunneling-diode (RTD) to o p erate a t 100 GHz
region [30].
■•r
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15
routinely over 106 in th e infrared region of the spectrum . The stabilized oscilla­
tor linew idth was about 10 kHz. This linevvidth was 100 tim es narrow er th an the
linew idth of the unstabilized waveguide oscillator. Later, Brown im proved th e op­
eration frequency up to 210 GHz [31], and also connected a horn rad iato r to the
waveguide inside which the RTDs were m ounted. T he m axim um o u tp u t and the
linew idth were approxim ately 50 /zVV and 20 kHz, respectively, at 200 GHz. T he res­
onant frequency was adjusted over a 0.4 GHz range by changing th e cavity length.
This RTD oscillator is suitable for a local oscillator for a low-power radiom etric
mixer.
Unlike the cavities in the works ju st described previously. Mizuno et al. con­
stru cted a Fabry-Perot cavity with a grooved m irror instead of the plan ar reflector
[32, 33, 34]. The active devices were m ounted in the grooves, and th e d ep th of the
grooves were adjustable. The size of the grooved m irror was 5.0A x 5.0A. They suc­
cessfully operated IS G unn diodes and 6 GaAs M ESFETs at X-band an d generated
the fundam ental mode (TEMoo)- A frequency tuning range of 6% was obtained by
adjusting the depth of th e grooves. They also tested this cavity at U -band and YVband. At U-band. 3 diodes were used and th e combining power at 50 GHz was about
50% larger than the power from a single diode. At YV-band, they used InP Gunn
diodes (A crotec NT-YV50) and generated a m axim um o u tp u t power of 5.7 dBm .
T he tuning range of resonant frequency was 1.8 GHz for U-band and YV-band. In
order to enlarge the frequency tuning range, they applied a resonant tunneling diode
(RTD) array to the grooved cavity [34]. Com bining th e power from two RTDs has
been observed at 74.6 GHz, and the frequency tuning range was im proved up to S%.
A nother new quasi-optical cavity-type power com biner was developed by Kiyokawa
et al. [35, 36]. At first, Kiyokawa designed a cavity w ithout active elem ents inside,
and the cavity had a partially transparent circular gold-grid region inside as shown
in Fig. 2.4. The signal was coupled in and out as a Gaussian beam , and the Q
of this cavity reached 2 x 10° and had high signal-to-noise ratio at 105.9 GHz. By
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16
ro ta tin g th e o u tp u t mirror, th e Q factor was able to be adjusted. Later, Kiyokawa
designed an o th er cavity-type com biner w ith slot antennas and H EM T devices inside
as shown in Fig. 2.5. The slot was 4.3 m m x l.2 m m and the open stu b was 4.4 mm
long. T h e Q for this new cavity was about 10,900 at 10.2 G H z. and th e operating
frequency range was able to be tu n ed over 1 GHz by changing th e length of m irror
[35]. C ontinuous work at 40 GHz has been successfully com pleted w ith the Q of
5,600 [36].
O th e r studies of the cavity-type com biner w ith higher-order m ode has been done
by M cC leary et al [37, 38]. Basically, they used th e Fabry-Perot cavity as a low-pass
filter. For close reflector spacings, the waveguide couples energy efficiently through
a slot into th e cavity, and
TE M 400
as well as
T E M 300
modes were generated. The
unloaded Q varied from 1,000 to 7,000 with a insertion loss less th en 1 dB a t X-band.
and varied from 1.500 to 3,000 a t K a-band. T h e tunable frequency range was over
a 25% b an d w id th at X-band and Ka-band.
Curved reflectors
Glass substrate
Gold film
Resonant
mode
Figure 2.4: A G aussian-beam open resonator w ith highly reflective circular coupling
region [35]. T h e circular region has a gold-film strips with d = d! = 63/zm
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17
Partially transpareit*
circular region
Plane
reflector
Slot
j Gold film
strips
Slot
G
'f !
Curved
reflector
Active circuit
D
L!
-
c d
Vg
Vd
Figure 2.5: Top view of a Gaussian-beam oscillator [36]. T h e m etal strips serve
as a p artia lly tran sp arent region with d = d' =1 mm. T he active devices and slot
antennas are built on the p lan ar m irror substrate.
2.3
G r id -T y p e P o w e r C om b in er
G rid-type power com biner is th e most m ature an d popular stru c tu re for the quasi1
t
i:
jt
[
f
I
i
t;
array worked at 66 GHz w ith watt-level o u tp u t powers. They also dem onstrated a
£
G unn device grid oscillator an d a 25-element M ESFET grid oscillator at 10 GHz.
I
tr
;
Basically, their work was a set of proof-of-principle experim ent, and provided the
f
their followers [46]-[T4]. In th e following sections, th e recent work on grid-type power
|
y
com biners is reviewed according to their functions as oscillators or amplifiers.
optical power com bining nowadays. The grid array is built on a dielectric su b strate
and can be used as oscillators or amplifiers as shown in Fig. 2.6. The early work
4-
on grid -ty p e power com biner was pursued by Rutledge's group [41]-[45]. Thev first
dem o n strated a m onolithic grid array with 2,000 Schottky diodes, and the grid
prototypes for the later grid oscillators and amplifiers developed by themselves and
2 .3 .1
G rid O sc illa to r s
The grid oscillator stru ctu re shown in Fig. 2.6(a) has a m etal grating loaded w ith
two- or th ree-term in al solid-state devices. T he grid structure is built on a dielectric
su b strate and the period of th e grids is much sm aller than a free-space wavelength.
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18
ACTIVE GRID SURFACE
OUTPUT POLARIZER
ACTIVE GRID SURFACE
-J
\E
INPUT
BEAM
W
^
O UTPUT
BEAM
r*
MIRROR
TUNING S L A B
\
\>
OUTI
1
BE/
INPUT POLARIZER
(a)
(b)
Figure 2.6: (a) G rid oscillators, (b) G rid amplifiers with polarizers.
The vertical leads of th e grating serve as antennas and th e horizontal leads are used
for D.C. bias lines. T h e purpose of the m irror is to provide feedback for oscillation.
The two- or three-term inal active device in each grid is shown in Fig. 2.7. Directfeedback or gate-feedback is used for the three-term inal active devices to oscillate.
two-terminal
device
(a)
three-terminal
device
(b)
Figure 2.7: (a) Tw o-term inal device in an inductive unit cell, (b) Three-term inal
device in an inductive u n it cell. The direct-feedback results in the gate and drain
leads radiating. The gate-feedback results in the source an d drain leads radiating.
The first works on grid oscillators was presented in [43, 44] and it was for a
25-transistor grid stru ctu re. This structure was a direct-feedback grid. The period
of the grids was 0.4Ao a t 9.7 GHz. This grid oscillator provided an effective radiated
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
{
i
19
power (E PR ) of 20.7 W atts at 9.7 GHz, ^nd the power from the grid was 474 mW
which is about 25 tim es th e power typically m easured from a single-device m icrostrip
oscillator. Later, they extended this grid structure to be a 2500-diode grid oscillator
to work at 66 GHz [45]. Since the thin-m etalized su b strate of th e grid oscillator
m ay provide a m icrostrip mode which couples the devices through th e source leads.
Popovic et al. [46] presented a bar-grid oscillator which elim inated th e dielectric
su bstrate. This bar-grid oscillator had 36 M ESFET transistors and generated an
ER P of 3 W atts at 3 GHz. The directivity of radiation pattern was 11 dB and
th e DC-to-RF efficiency was 22%. T he adjustable tu n in g frequency was over a 10%
bandw idth.
An im portant work after [43]-[46] was a 100-M ESFET planar grid oscillator [47].
T he design of this oscillator was sim ilar to th a t of bar-grid structure; all three
I
leads of the M ESFET transistors were on one side of th e substrate, and the whole
v
stru ctu re can be fabricated m onolithically w ithout backside processing. This 100-
|
elem ent oscillator had an ERP of 22 W at 5 GHz w ith a D C-to-RF rate of 20%.
!1
j
T he directivity of th e radiation p attern was 16 dB. This oscillator is one of the
.
direct-feedback grid oscillators.
jj
f
I
f
'
oscillator using gate-feedback [48]. This gate-feedback grid oscillator can work at
j
m uch higher frequency th an the direct-feedback grid oscillator. E xperim ental re-
[
suits were observed a t X-band and Ku-band and showed th a t a 16-M ESFET 2 x 2
|
grid oscillator generated 335 mW at 11.6 GHz w ith a DC-to-RF ratio of 20%, and
5
T he grid oscillators previously described use tw o-term inal or direct-feedback
three-term inal devices. Weikle et al. first d em onstrated a planar M E SFE T grid
a 36-M ESFET grid oscillator generated the o u tp u t power of 235 m W a t 17 GHz.
T heir results showed a significant im provement in th e perform ance of th e previous
grid oscillators in [47] whose oscillating frequency was lim ited to 5 GHz with o ut­
put power of 6 m W , when using the identical M E S FE T transistor was used. In
[49], another gate-feedback grid oscillator using heterojunction bipolar transistor
4*
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20
(H BT) was n rst presented. T his H B T grid oscillator had 100 elem ents and worked
at 35 GHz. In [50], this grid even generated o u tp u t power of 10.3 W at 9.8 GHz w ith
a D C-to-RF ratio of 23%. This o u tp u t power is th e highest o u tp u t power generated
by th e planar transistor-grid oscillator to date. Since the E -plane radiation p attern
of this grid had two big side-lobes ju st 2 dB less than th e m ain beam , a 43-GHz
A lIn A s/G aln A s/In P HEMT grid oscillator was reported in [51] for th e im provem ent
of th e radiation p attern . This 43-GHz H EM T grid oscillator h ad 36 element and
generated an E R P of 200 mW w ith th e side-lobes 10 dB below th e m aim beam.
T he previous grid oscillators used m irror ad ju stm en t or variation of D.C. bias
to tune the oscillation frequency. A nother way to tune th e oscillation frequency
is to cascade a transistor-grid oscillator with a tuning-diode grid. These two grids
are separated by a dielectric slab, and have th e sam e dim ensions and m etalization
;
p attern s so th a t each unit-cell waveguide only has one tra n sisto r and one tuning-
l
ST
f
diode. By varying th e voltage across the diodes, th e oscillation can be tuned. T his
i:
by Popovic’s group [53, 54], T hey constructed a 7 x 7 dipole V O C w ith a 7% tuning
|
bandw idth at 2.8 GHz, and th e variation of o u tp u t power was 25 dB. They also
f
constructed two bow-tie grids which were a 7 x 7 and a 6 x 4 arrays.
|
bow-tie VOC had a 10% tuning frequency range a t 6 GHz w ith a 12 dB variation
I
of o u tp u t power, and the 6 x 4 bow-tie VOC perform ed a 10% tuning range at
oscillator is called a voltage-controlled oscillator (VOC) and was first dem onstrated
The 7 x 7
5 GHz with less th an 2 dB variation of o u tp u t power. Later, O ak and Weikle [52]
{
showed a gate-feedback VOC a t X -band, and th ey em bedded varactor diodes and
[
th e transistors on the same side of th e dielectric substrate. A 2% tunable frequency
bandw idth was obtained through varactor tuning, and this bandw idth was m ore
th an twice to th e bandw idth obtained through th e m irror tuning.
Based on th e grid oscillators described in previous paragraphs, a 100-transistor
quadruple grid oscillator was rep o rted in [55] an d produced an ER P of 8 VV at
5 GHz and o u tp u t power of 265 m W . Later in [60], a cascaded active and passive
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
21
quasi-optical grid was presented as a dual-frequency grid oscillator. T his cascaded
system oscillated at 6.2 GHz with an ER P of 0.25 VV and a t 3.9 GHz w ith an ERP
of 0.26 VV.
For subm illim eter-wave region, a quasi-optical Josephson Junction array working
a t 190 GHz was reported [57]. This grid oscillator was built with an 11 x 58 array of
niobium Josephson Ju n ctio n s and generated an o u tp u t power of 0.36 //VV. This work
is only th e th ird tim e th a t near-//VV power levels of th e Josephson Ju n ctio n array
rad iatin g in free space have been observed. T he previous work about Josephson
Ju n ctio n array was reported in [5S, 59].
2 .3 .2
G rid A m p lifie r s
T h e grid amplifier stru ctu re is the same as the grid oscillator except th a t th e m irror
|
l.
I
and tuning slab are not used (see Fig. 2.6 (b)). T he active device for th e grid ampli-
|
as input port (receiver) an d the vertical leads are used for output port (radiator).
;
*
I
T he input and output ports have cross polarization and result in two advantages.
|
t|
due to feedback from o u tp u t port is largely reduced. Secondly, the circuits in input
(
1
[
fier is a differential tra n sisto r pair as shown in Fig. 2.8. T h e horizontal leads serve
F irst, good isolation betw een input and o u tp u t ports is achieved and th e oscillation
and o u tp u t ports are independently tuned by using th e m etal polarizers which also
confines the output beam to the forward direction (see Fig. 2.6 (b)).
T he first grid am plifier was developed by Kim et al in 1991 [61] and was a
25-elem ent grid structure. This grid amplifier was a hybrid structure w ith packed
i
M E S F E T attached to th e Duroid substrate.
A peak gain of 11 dB at 3.5 GHz
was obtained from this 25-element amplifier. Later, K im et al also developed a 100elem ent hybrid HBT grid amplifier [62, 63]. This 100-HBT amplifier had a peak gain
of 10 dB at 10 GHz, w ith a 3 dB bandw idth of 10%. W hen the bias was not applied,
th e am plifier gain was below -8 dB. The saturation power was 450 m W . This grid
am plifier also generated steering beams, and three radiation patterns incident at 0.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
II
i
00
Differential
T ransistor
Pair
Receiver
Radiator
Receiver
Radiator
Grid Unit Cell
Figure 2.8: T he unit cell of grid amplifier. A differential tran sisto r pair is used with
th e source leads connected.
4-20. -20 degrees were achieved. The beam patterns in th ese three angles had sim ilar
w idth of m ain beam, side-lobe level and null locations. T hey also indicated th a t
this 100-element grid can amplify beam s with the incident angle up to 30 degrees
w ith less th an -3 dB gain reduction. T he modeling of this 100-HBT grid amplifier
was reported in a later paper [64]. Furtherm ore, th e gain and power combining
was sequentially dem onstrated at the millim eter-wave region w ith monolithic grid
am plifiers [65, 66, 67].
Kim also operated a grid amplifier w ith a twist reflector a t th e range of 6.5 GHz
to 11.5 GHz, and this amplifier generated an ERP of 6.3 W a t 9.9 GHz [68]. In [66].
a m onolithic 40 GHz H BT grid am plifier was presented. T his am plifier had a gain
of 5 dB at 40 GHz with a peak power added efficiency (PA E) of 4%. This is the
first power m easurem ent for a m onolithic quasi-optical am plifier.
To produce high gain, high output power, high efficiency and low noise at fre­
quency above 100 GHz. th e pHEM T is an excellent device for th e grid amplifiers.
*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
and studies for pHEM ET have been reported in [69]-[72]. In [67], a 44-60 GHz
m onolithic pH EM T grid amplifier was reported. This grid was fabricated using the
pH EM T developed by Tu et al. [72]. Each grid cell had two 0.1-/*m pH E M T s whose
sources were tied together to becom e a differential pair. The grid s tru c tu re was a
6 x 6 array and was built on a 15-mil GaAs substrate. This am plifier had a peak
gain of 6 dB at 48 GHz with a 3 dB bandw idth of 1.7 GHz. Later, th e m odel of a
100-pHEMT grid amplifier was developed in [73].
T he latest report for grid am plifier is a terahertz grid frequency doubler devel­
oped by R utledge’s group [74]. This frequency doubler is a 12 x 12 grid structure
with 144 Schottky diodes inside, and th e size of each grid is 70 fim. T his frequency
doubler had a o u tp u t power of 5.5 m W at 1 THz for 3.1-^s, 500-GHz input pulses.
The input pulses had peak power of 36 VV. T he o u tput power is th e largest recorded
I
o u tp u t power for a frequency m ultiplier working at terah ertz frequency.
$
2 .4
t
j
A c t iv e P la n a r -A n te n n a P o w er C o m b in er
In th e past two decay, many planar antennas have been successfully developed and
I
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1
described in books [75, 76, 77].
•
coplanar-waveguide-fed slot antennas [78] and taper-slot antennas [79], and a recent
j
t
f
review of power combiners using planar antennas is also provided by Lin and Itoh
[80]. In this section, the recent works about planar-antenna power com biners will
|
be described according to their functions for oscillators or for am plifiers.
are very suitable for the active planar power-combining arrays. M ost of them were
Some active planar power com biners w ith two-
or three-term inal devices have been developed based on the patch an ten n as [75].
2 .4 .1
O sc illa to r -T y p e P o w e r C o m b in e r
An early work for the planar power com biner was reported by Chang et al [81], and
they experim entally dem onstrated two types of active antenna elem ents for power
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
com bining. O ne ty p e used a patch an ten n a on which a G unn diode was directly
m ounted, and th e o th er used an active device coupled to a patch an ten n a through
an ap ertu re. For th e single active p atch antenna, th ey obtained a m axim um o u t­
p u t power of 15 m W a t 10.1 GHz w ith a tuning frequency range of 9%. For the
two-elem ent active array, they obtained a m axim um o u tp u t power of 30 m W at
10.42 GHz. L ater C hang’s group developed a w ideband integrated varactor-tunable
active notch an ten n as for power com bining [82].
T hey used a slotline-coplanar
waveguide (C P W ) as an endfire notch antenna which can provide a broadband
im pedance m atch , and a G unn diode and a varactor were installed in th e antenna.
T h e varactor provided an o u tp u t power of 14.5±0.8 dB m a t 9.6 GHz w ith a tunable
frequency range of 14%.
In [81, 82], the active devices were tw o-term inal. For three-term inal radiating
oscillator, C h an g ’s group again used th e C PW notch an ten n a with a F E T inside as
i
\
shown in Fig. 2.9. T he slot line betw een drain and gate provided the feedback for
(
oscillation. By varying th e length and w idth of this slot line, th e operating frequency
|
varied from 5 to 8 GHz. This three-term inal active an ten n a generated an output
|
JI
t
\
t
!
power of 8.9 m W at 6.98 GHz w ith an efficiency of 7.4%.
Figure 2.9: Unit cell of the C P W slot antenna oscillator with a F E T inside.
C om pton’s group also developed high-efhciency F E T radiating oscillators for
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
quasi-optical power combining [84, 85, 86].
T hey used a rectangular m icrostrip
a n ten n a as the rad iato r and the load for class B and C operation.
At first, a
single feedback pickup was applied, and 83-mYV co-polarized radiated power and
25-mW cross-polarized radiation power were obtained at 9.84 GHz with a DC-toR F efficiency of 59%.
Later, two sym m etrical feedback pickups were used, and
th e cross-polarization R F power was 20-30 dB below the co-polarization RF power
which was 57 m W w ith an efficiency of 44%.
Based on th eir previous work on a CPVV-fed active slot antenna [87], Kormanvos
et al reported two quasi-optical slot oscillators for the subm illim eter wave region.
T hey employed a m onolithic InP-based 10 /im -gate-w idth HFET w ith a C PW line
which was connected to the slot antenna. T hese two oscillators were individually
built on the wafers: one oscillated at 155 GHz, and th e other oscillated at 215 GHz.
T he o u tp u t power was estim ated to be l^YV. and th e DC-to-RF efficiency was about
0.014%.
As well as th e oscillators described previously, two kinds of coupled oscillator
arrays were developed by York’s, Itoh’s and M ortazaw i’s groups [S9]-[94]. One is
a direct radiation (DR) coupled oscillator arrays in which each oscillator directly
couples the radiation signal from all of other oscillators. The oth er is a m icrostrip
circuit (MC) coupled oscillator array in which each oscillator couples signal directly
from its nearest neighbors through m icrostrip lines. T he coupling in a DR oscillator
array is weak; in th e MC oscillator array, the coupling is stronger. In [89], a 4 x 4 DR
oscillator with G unn devices and M ESFETs was presented. The G unn device array
generated an E IR P of 22 W at 9.6 GHz with an efficiency of 1%, an d the M ESFET
array generated an E IR P of 10 W at 8.2 GHz w ith an efficiency of 26%. In [90]. a
push-pull 8-FET oscillator array was reported w ith an ER P of 31.7 dB m at 6 GHz.
In [91] a 16-element F E T oscillator array was dem o n strated using external injection
locking to generate an ER P of 28.2 W at 6 GHz. A periodic second harm onic spatial
power com bining oscillator with 4 Gunn devices was reported in [92] with an ERP of
m
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
26
25.7 dBm at 9.36 GHz w ith an efficiency of 15%. In [93], a M ESFET oscillator array
was reported w ith a total radiation power of 7.92 VV with an efficiency of 15%. [94]
reported slot antennas cooperated with 9 M E S FE T s producing an E IR P of 2.4 VV
at 10.11 GHz.
2 .4 .2
A m p lifie r -T y p e P o w er C o m b in e r
Several studies of single or m ultilayer planar am plifiers have been repo rted by Mortazaw i’s group [95]-[98]. In [95], they presented several two-stage sp atial amplifiers.
T he amplifiers were constructed on double layers of back-to-back m icrostrip circuits
w ith a shared ground plane. T he ground plane provided isolation betw een the input
port (receivers) an d the o u tp u t port (radiators), and also served a good heat sink
for the active devices. Couplings between I/P port and O /P port were accomplished
'
i.
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t
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|
through the m icrostrip line to slot transition. T h e m axim um gain for an unit cell of
two-stage double layers of spatial amplifier was 18.5 dB a t 9.8 GHz. T h e maximum
gains for a 1 x 3 and a 3 x 3 tw o-stage spatial am plifiers were 18 dB a t 9.8 GHz and
18 dB at 9.95 GHz, respectively. Later, they reported th a t a net gain of 8 dB and
I
f
f
an o utput of 37.4 m W w ith an efficiency of 45% were obtained by placing the 3 x 3
|
they improved th e o u tp ut power of the 3 x 3 up to 90 mW at 2-dB compression
£
point, and the sm all signal gain was 16.2 dB a t 9.98 GHz. Recently, they demon-
J
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i
t
strate d a 3 x 3 transm it-receive amplifier array in which orthogonal ports of the
am plifier array in th e near field of th e tran sm ittin g and receiving horns [96]. In [98],
1
m icrostrip patch antennas were used to provide isolation between tra n sm itte r and
receiver parts [99]. This am plifier array had m axim um gains of 8.2 dB and 6.9 dB
at 10 GHz for tran sm it and receive modes, respectively.
O ther work on active planar amplifier has been reported in [100]-[106]. In [100].
a two-level power combining pH E M T patch an ten n a lens amplifier was reported
w ith 8 dB of absolute power gain at 9.7 GHz. T his antenna lens am plifier had the
functions of beam form ing and beam-switching. In [100], they also reported that a
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
24-M E SFE T patch array worked as a satu rated class A am plifier w ith an o u tput
power of 0.7 VV at 10 GHz and a PAE of 21%. Later a bi-directional quasi-optical lens
am plifier based on th e work in [100] was dem onstrated in [106]. T he bi-directional
lens am plifier worked at X-band and h ad an O N /O F F ration of 25 dB for both
tra n sm ittin g and receiving modes w ith associated am plifier gains of 5 and 10 dB.
In [101], a high-power hybrid quasi-optical Ka-band am plifier was first reported.
This am plifier had a 6 x 6 slot-antenna array, and each a n te n n a elem ent consisted of
a MMIC driving am plifier followed by a two-stage high-power am plifier chip. This
am plifier array produced a gain of 6 dB at 29 GHz. Tasi et al. also applied the
slot antennas to the planar amplifier [102, 103]. They presented a 4 x 4 array with
10 dB gain at 11 GHz w ith a 4% b an d w id th [102]. In [103], they d em o n strated a
C P W m ultiple slot an ten n a array using an HBT gain block MMIC chip, and the
gain was 8 dB. They also used V ivaldi-type slots and a hybrid m icrostrip M ESFET
|
i
i
traveling wave am plifier (TW A) for th e quasi-optical TW A am plifier, an d this TWA
am plifier had a 50% of fractional b an d w id th at 3.5 GHz.
i
i
I
t
I
r
i
s
i
i
i
\
\
\
\
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
28
Chapter 3
2-D Power Combining Oscillator
3 .1
I n tr o d u c tio n
As described in [11], the hybrid dielectric slab b eam waveguide system (HDSBW )
com bines the wave-guiding principles of a dielectric surface wave and a confined
beam corresponding to G auss-H erm ite beam m odes. For this 2-D H DSBW system ,
launching the G aussian modes into th e dielectric waveguide is an im p o rt issue for
co n stru ctin g the whole system. T here are m ultiple R F sources th at can be selected
for generating th e G aussian m ode for the HDSBW system . For exam ples, one can
inject th e energy into the slab waveguide using a horn antenna which is connected
|
\
to an external R F sources such as a sweeper or T W T . Alternatively, one can build
5
an internal resonator within the HDSBW system including solid-state devices which
f
1
serve as oscillators. For the whole 2-D quasi-optical power combining system , an
[
r
i
t
;
e
a ttra c tiv e internal power source is a planar cavity w ith solid-state oscillators which
work a t some certain resonant frequencies. Energy generated from each solid-state
device is com bined into a G auss-H erm ite cavity m ode, and part of th e cavity en-
r
1
[
1
ergy th en penetrates through the partially tra n sp aren t interface between cavity and
[
In this C hapter, th e design and perform ance of a 2-D slab cavity w ith solid-state
!
oscillators are presented. The passive characteristics of the slab cavity, including
waveguide into the slab waveguide system .
resonant frequency, wavelength and propagation inside the slab, and cavity modes,
are described to explain the m easured d ata in [13]. M ultiple M ESFET oscillators
were inserted into th e cavity, and th e energy from each oscillator is eventually com­
bined w ithin the slab cavity. T he oscillator elem ent consists of an E-plane tapered
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
antenna which serves as receiver and rad iato r, and a M ESFET was inserted into the
middle position of the tapered antenna. T h e 2-D slab cavity consists of a curved
and a p lan ar reflector. Energy propagates in a quasi-optical mode in a direction
perpendicular to the planar reflector which is at the waist of th e resonant modes.
The curved reflector is parabolic approxim ating the phase-front of the modes. In
this way energy radiating from one oscillator is coupled into a quasi-optical mode,
which is reflected by the curved reflector, and then illum inates all of the other os­
cillators — th u s one-to-m any coupling is achieved. Therefore, the energy from each
active device is eventually combined into th e G aussian-H erm ite cavity mode.
3.2
3.2.1
P a s s iv e C h a r a c te r istic s o f th e 2-D S la b C a v ity
C a v ity F ie ld s, R e so n a n t C o n d itio n s a n d C u to ff F re­
q u e n c ie s
In the hybrid slab beam m ode waveguide system , the convex or concave phase tra n s­
former provides the phase correction for guided waves so th a t the beammodes can
travel along th e dielectric slab without energy diverging outside the waveguide sys­
tem. In th e construction of a 2-D slab cavity the phase transform er in the HDSBW
system is replaced with a curved reflector, and at the sam e tim e, a planar reflector
is inserted a t the waist of the slab waveguide. Therefore, the original propagating
waveguide beam m odes are confined w ithin a volume, and th e incident and reflected
energy m erge together to form the cavity m odes. The geom etry of the passive 2-D
planar slab cavity with a ground plane and two reflectors is shown in Fig. 3.1. where
L and W respectively represent the length and width of the cavity, R and F are the
radius of curvature and focal length, d is th e thickness of slab, and cr is the relative
dielectric co n stan t of th e substrate.
For th e cavity modes, the field distributions are approxim ated as Gaussian-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
30
planar metal reflector
dielectric slab
curved metal refltctor
ground plane
Figure 3.1: G eom etry of the Planar quasi-optical slab cavity.
Herm ite functions, and so the field expressions for the HDSBW system can be
directly used to express the cavity modes. The incident fields of the T E nm mode in
the slab waveguide is [11] :
'y ,n m
=
A t e ■exp
—
—
(vn y ) 2
(3.1)
— ( m + 1 ) tan - l
exp
Hx . n m
11
l
9
a2
“ l + ( ^ ) 2
n
F y.nm
&V-0 '
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
( a2
A
(3 .2 )
t
31
w ith
A
A'ee —
\/2 v Ti y
Vr
'j 2 r k 0B nmG n (x) f3n
1 /4
a2
1
+
( M
11
a2
l +
2
(3.3)
1/2
( £ ^ ) 2
-
where A-pE is the am plitude w ith G aussian-H erm ite function H e m, n is the surA
face m ode number and m is th e th e G aussian-H erm ite mode num ber, and f3n is the
propagation constant. G n {x) is a function related to the field d istrib u tio n in the
x-direction, and is defined in En. (4.10). For th e T M nm m ode th e fields are £ r ,„m
and //y,nm = ( ^ t 0£r//?n )£ ’x,nm, and have th e sam e phase term as in En. (3.1) with
different propagation constant 3n and am p litu d e A t m • Details of th e En. (3.1) will
be discussed in C hapter 4. T he reflected field has am plitude w ith ISO-degree phase
w ith —z in th e En.
change, and can be expressed by replacing
(3.1). Thus
one can express the cavity modes in term s of th e incident and backw ard waveguide
beam m odes. Therefore, th e cavity field E y>nm for T E nm mode is :
=
Jy , m n
1
(WnJf)3
A^E e x p ^ - -
(3.4)
l+ ( ^ ) 2
PtX
sin
—
Pn z +
l +
/ a2
^ tan 1 Yr
A -S
^
\
0n
>
where A ^ E = —‘- / A t e - F °r TM modes, th e E-field is E x and has th e sam e expresA
sion as in En. (3.5) except th a t A ^ e an<^ &n are replaced by A£p\i and /?„. Referring
to Fig. 3.1 the distance L is selected as th e focal length F of th e confocal reflector
A
and F = u2/ 0 n [11], In this confocal case th e phase term in En. (3.5) should be
equal to qir. where q is an integer. Along th e optical axis y = 0 th e phase term
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
becomes
A
PnF
-(m+i) tan
(1) = qir
(3.5)
or
^
7T
n- f
(3.6)
T he above two equations show th e relation betw een the propagation constant and
cavity length for both TE and TM modes. T h e propagation constants of T E and
TM modes in term of the thickness of the dielectric slab are th en :
\ j —kl t an \ j k d2- ,3nd
\ l $ l ~ k l cot
=
= - \ J k j - f3n
for T E m ode
(3-7)
kd — 0 ^
for TM m ode
(3.S)
where kd = '2-f nyJ n 0£0z r = koy/£ ^. By su b stitu tin g En. (3.6) into (3.7) and (3.S).
all the possible resonant frequencies, / n, of th e T E and TM cavity modes can be
A
predicted. In the following sections, for convenience,
and f n will be respectively
A
replaced by (3nmq and f nmq for cavity modes w ith index (n . m , q ).
Before solving for the resonant frequency f nmq, the cutoff frequencies for the
groups of T E n and TM n m ode should be considered. The group cutoff frequency
is independent of th e mode index (m . q ), and only depends on th e thickness of the
slab. Therefore one needs to pick the right thickness for supporting the desired
cavity modes w ithin a certain frequency range. Since the group cutoff frequency
can be obtained from the cutoff wavenum ber, we will discuss th e cutoff wavenumber
instead of cutoff frequency. T he cutoff wavenum ber. kQ = 2 ~ //c . for T E n and TM „
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
groups are related to the index n
kQd =
(n +
■
k0d =
. Ui
v /iT ^ T
2
) T—
for T E mode
(3.9)
for T M mode
(3.10)
v
'
where n = 0, 1, 2, 3, • • -. For convenience, the thickness of th e slab can be expressed
in term s of th e wavelength in free space as in th e following:
d
(n + 5 )
— = ----- ,------- =
— \J C. r
1
A0
for T E mode
(3.11)
for T M mode
(3-12)
From th e above equations, the normalized m inim um su b stra te thickness, d f \ 0.
for TE and TM modes are shown in Fig. 3.2. From this figure, one can choose th e
right su b strate thickness for different m aterials to support th e desired cavity modes.
For exam ple, th e slab with s r = 2.57 only supports groups of TEom? and TMom?
modes if 0 < d/X 0 < 0.39. As d /X 0 increases, higher-order m odes will occur inside
A
the cavity. A nother im portant curve for designing the 2D cavity is 8n f k 0 vs d /X 0.
A
and the relation for ,8n / k 0 vs d jX 0 can be easily obtained by rearranging Equations
(3.7) and (3.8). S ubstituting er = 2.57 into E quations (3.7) and (3.8) yields th e
A
values of (3n j k Q for the TEom? and TMom9 m odes for the cavity with different
A
substrate thickness. Figure 3.3 shows curves for j3n f k 0 vs d /X Q with eT = 2.57.
A
From the values of [3n / k a, one can determ ine th e operating frequency ranges for
A
different T E and TM modes w ith a selected su b stra te thickness. However. 8n / k a
A
has a lim it value th a t is
and no cavity m ode will exist if 3 n / k 0 > y/s^.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
I
34
TM(n=0)
TE(n=0)
TM(n=1)
TE(n=1)
TM(n=2)
TE(n=2)
TM(n=3)
TE(n=3)
1.5
d/Xo
0.5
-
0.5
2
4
6
8
10
12
Relative Dielectric Constant
, er
Figure 3.2: M inim um thickness d of dielectric substrates required to support T E n
and T M n modes. The thickness is normalized to free space wavelength A„.
1.7
I
I
'I
I
I 11 11 ■ T
ye7
1.6
TM(n=0)
. TE(n=0), ' ' "
TM(n=1).- ‘
1.5
. TE(n5r>'
1.4
Pn
—
/ TM(n=2Xf
/
✓
. ' TE(n=2)
1.3
.
*
/
1.2
•
/
'
TM(n=3)^
/
/
/
/ TE(n=3)
1.1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
d/A0
Figure 3.3: 3 n/ k 0 vs d f A0 for the slab cavity with cr = 2.57.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
3 .2 .2
P r o p a g a tio n C o n sta n t, W a v e le n g th a n d R e so n a n t F re­
q u e n c y o f C a v ity M o d e s
The construction of a 2-D cavity is based on th e cutoff frequencies and the ch ar­
acteristics of th e cavity m odes. At first, the thickness of th e su b strate needs to
be determ ined from th e cutoff frequency so th a t only T E 0mg or TMom, m ode ex­
ists for th e given dielectric constant er and operating frequency range. A fter th e
right dim ensions for th e cavity have been selected, the resonant frequency of each
T E and TM cavity m ode can be solved from En. (3.7) and (3.8). For X -band op­
eration, th e cavity dim ensions for supporting m odes with n = 0 were selected as
d = 1.27 cm and F = L = 30.48 cm w ith er = 2.57. T he propagation constant
and wavelength for (0. m ,q ) mode in which m = 0 ,1 ,2
and q = 14. 15, • • ■. 31, 32
are shown in Figures 3.4 an d 3.5. The propagation constant, /3omi7, and wavelength
j
A0m, are th e same for b o th T E and TM modes, and only have sm all variations for
|
the adjacent m —th m ode w ith fixed values for n and q. T h e resonant frequencies
|
of the TEomg and T M 0m, m odes are shown in Fig. 3.6 and Fig. 3.7 respectively.
|
t
>
and their calculated values are shown in Table 3.1.
a frequency increm ent a b o u t 70 MHz for T E m odes and 72 MHz for TM modes.
»
These small increm ents reveal th at the sensitivity of the frequency shift due to th e
\
f
?
small perturbation to the dim ensions of the cavity. For exam ples, the T E 0 .i .2 6 has
A djacent m -th modes have
resonant frequency at 9.78199 GHz w ithout any p ertu rb atio n . However, if p e rtu r­
bation makes d = 1.23 cm or L — 30.19 cm, th en the resonant frequency shifts
;
and becomes 9.85227 GHz or 9.85324 GHz. T hese two frequencies are close to th e
original frequency of TEo,2 ,2 6 mode. T h a t is to say, only 3% p ertu rb atio n to th e
substrate thickness or 1% p ertu rb atio n to the length of the cavity will easily cause
cavitv modes shift.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
300 B
co
to
c
o
o
♦*
m=0 mode
m=1 mode
m=2 mode
i
325 ■
♦♦
350
♦43
■
■
i
a
a
a
a
•
:36
%
1
1
275 ■
i
I
250 I
%
1
CO
o>
CO
Q.
O
I
225
%
I
200 ■
a
I
1
175 I
150 ■
I
a
I
1
a
1 4 1 5 1 6 1 7 1 8 1 9 2 0 21 22 23 2 4 2 5 26 2 7 2 8 2 9 30 31 32
mode index q
Figure 3.4: C alculated l30mq for T E and TM m odes in the 2D cavity w ith d =
1.27 cm , L = 30.48 cm , s r = 2.57.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4.5 i - ■■ ■
♦
m=0 mode ♦
m=1 mode ♦
m=2 mode a
♦
♦
♦
£
^
O)
c
o
O
3
3.5
♦
o
I
!
5
I
S
i
a
a
1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 22 23 2 4 2 5 26 2 7 2 8 29 30 31 32
m o d e in d ex q
Figure 3.5: Calculated A0m? for T E and TM m odes in th e 2D cavity with d 1.27 cm, L = 30.4S cm, s r = 2.57.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
38
12
11.5
N
X
o
>»
o
c
CD
3
O’
m =0 m ode
m=1 m ode
m=2 m ode
11
10.5
I
I
9.5
S
9
CO
c
o
CO
0)
GC
I
10
<D
C
!
♦
♦
°
8.5
S
8
7.5
I
7
6.5
I
I
6
1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 22 2 3 2 4 2 5 2 6 2 7 2 8 2 9 3 0 3 1 32
TE-m ode index q
Figure 3.6: C alculated f 0mq for TE m ode in th e 2D cavity w ith d = 1.27 cm.
L — 30.48 cm , s r = 2.57.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
39
10
9.5
■
■
I
N
I
o
>*
o
c
0)
3
or
0)
9 ■ m =0 m od e
m=1 m od e
m =2 m od e
8.5
8
!
*
a
!
1
J
B
!
7.5
1
CO
7
I
<D
oc
6.5
c
o0)
♦
I
1
♦
!
I
!
!
6
a
!
a
5.5 ■ I
5
1 4 1 5 1 6 1 7 1 8 1 9 2 0 21 22 23 2 4 2 5 2 6 2 7 2 8 29 30 31 32
TM-mode in d e x q
Figure 3.7: C alculated fomq for TM m ode in th e 2D cavity w ith d = 1.27 cm.
L = 30.48 cm, er = 2.57. Unlike th e T E case, some TM om, modes disappear in this
cavity.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
<7
14
15
16
17
IS
19
20
21
22
23
24
25
26
27
28
29
30
31
32
[
[
m=0
6.30345
6.59987
6.89078
7.17796
7.46259
7.74551
8.02729
8.30836
8.58903
8.86955
9.15009
9.43077
9.71171
9.99297
10.27461
10.55668
10.83920
11.12220
11.40568
T E 0mq (GHz)
m=l
m=2
6.37820
6.45249
6.67303
6.74588
6.96287
7.03475
7.24932
7.32053
7.53345
7.60422
7.81604
7.88651
8.16789
S.09761
8.37855
8.44873
8.65917
S. 72930
8.93968
9.00981
9.22024
9.29040
9.50098
9.57120
9.78199
9.85229
10.06334 10.13374
10.34509 10.41559
10.62726 10.69788
10.90990 10.98064
11.19302 11.26388
11.47663 11.54761
m=0
5.17822
5.46490
5.75107
6.03717
6.32347
6.61018
6.89741
not exist
not exist
7.76292
S.05277
8.34329
8.63448
8.92631
9.21876
9.51180
9.80541
10.09957
10.39425
TM 0m, (GHz)
m=1
m=2
5.24996
5.32165
5.53647
5.60802
5.S2259
5.89411
6.10S72
6.18028
6.39511
6.46677
6.68193
6.75372
not exist not exist
not exist not exist
not exist not exist
7.83531
7.90776
S. 19795
8.12533
8.41603
8.48880
8.70738
S. 78031
S.99936
9.07246
9.36521
9.29196
not exist not exist
not exist not exist
not exist not exist
not exist not exist
Table 3.1: Calculated resonant frequency, fomq, for TE and TM mode in the
cavity with d = 1.27 cm , L = 30.48 cm , z r = 2.57.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
41
3.3
D e s ig n a n d P e r fo r m a n c e o f 2 D P ow er C o m b in in g R e s ­
o n a to r
^ SMA CABLE
(DETECTOR)
C Y U N D R IC A L -SE C T IO N
C O PPE R REFLECTO R
DIELECTRIC SLAB
CO PPER
G R O U N D PLANE
MESFET OSCILLATORS
PLA N A R C O P P E R R EFL EC TO R
Figure 3.S: P lanar Q uasi-optical slab power com bining oscillator.
G ‘A cD
B
S
20 mm
4 5 mm
Figure 3.9: Single oscillator unit constructed on a Rogers R T /D uroid substrate w ith
er = 2.33.
The design and perform ance of the 2D slab cavity with active devices is described
here. The power com bining slab resonator w ith four E-plane oscillators located on
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
th e top surface is shown in Fig. 3.8. By one-to-m any coupling, the energy from each
active device is com bined into G aussian-H erm ite cavity modes. For the purpose of
supporting TEo or TMo modes only, some practical considerations are applied to
for constructing th e cavity as follows:
(\ ta /)TEo.TMo - v/i73T
L ^
w
l^^a/a6
> 3A max
R = 2F
w here A max is th e 1/e-beam w idth of the fundam ental G aussian beam at the position
of the curved reflectors. From th e above considerations, th e distance between the
planar reflector an d the center of the curved reflector (L) was selected as 30.48 cm.
an d th e radius of th e curved reflector ( R ) was selected as 60.96 cm. Since th e E-plane
r
i
oscillators are applied to this cavity system , only T E m odes are expected. In order
j
to support dom inant TEom? m odes only, th e thickness was chosen from 1.27 cm by
1
Equation (3.11) for X-band operation. T he w idth of th e dielectric slab was selected
t
j
|
as 38.10 cm so th a t side reflection of th e cavity modes would be insignificant and
[
could be ignored. T h e dielectric is Rexolite (er = 2.57, tan£ = 0.0006 at X-band).
(
•
Furtherm ore, these dimensions of the cavity facilitate th e capture of second and
|
f
I
th ird harmonics (T E 0m, modes w ith m = 2,3) in th e spectrum of the oscillator
|
To generate th e expected TEomq family, th e Vivaldi E -plane antenna tap er serves
|
as the rad iato r/receiv er for the oscillator unit. A 4.5 cm x 2 cm oscillator unit built
signal.
on R T /D uroid 5870 substrate (er = 2.33, thickness=30 mil) is shown in Fig. 3.9.
an d uses a H ew lett Packard ATF-10235 M ESFET. T his Vivaldi antenna is an endfire antenna ta p e r derived from [83. 109] which provides excellent decoupling of
forward and backw ard traveling waves. T he antenna su b stra te has er = 2.33 so that
th e discontinuitv betw een the an ten n a su b strate and th e cavitv substrate will be
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
I
43
reduced a lot. In order for th e circuit to oscillate, there m ust be feedback between
the drain and gate of th e M ESFET , and this drain-gate feedback is controlled by
changing th e length and w idth of th e slit between gate and drain. The slit feedback
basically dom inates th e oscillating frequency, and the frequency can be tu n ed in a
certain range by changing th e slit an d moving the oscillator unit inside th e cavity.
The design of the oscillating elem ents was optim ized so th a t oscillation in free space
did not occur. F urtherm ore, this oscillator design was not susceptible to surface-ofslab to ground-plane resonance. This was a common problem w ith earlier antenna
designs since the thickness of the slab is close to a half wavelength. M ode signals
were sensed by a sm all Vivaldi an ten n a located on the periphery of the cavity where
the beam m ode p e rtu rb a tio n due to th is sensor is expected to be small.
To o b tain the quasi-optical modes using the one-to-m any coupling concept, one
oscillator was slowly m oved around th e top surface of th e slab to pick up one of
i
the resonant TEomq m odes. W hen th e first oscillator u n it was moved to a certain
r
i
peak-value point of th e cavity m odes, th e drain taper receives m axim um energy
i
^
reflected by curved and p lan ar reflectors so th a t feedback is strong enough to trigger
r
|
M ESFET to oscillate. T h e n , the rest of the oscillators were sequentially located onto
|
the cavity and staggered individually on th e top surface to generate the cooperative
>
&
[
cavity beam m odes.
\
coupling.
Basically, the oscillators were m utually locked by th e waves
reflected from th e p lan ar and curved m etal walls, not by direct nearest neighbor
3 .3 .1
F r e e -R u n n in g O p e r a tio n
The procedure for establishing the o p eratin g frequency of th e whole cavity with
oscillators is:
1. Establish th e frequency range which allows a set of possible T E oscillation
modes in th e cavity.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
44
2. A pply bias to th e on-axis oscillator to ensures T E nm<? modes.
3. Tune the length of th e drain-gate feedback slit.
4. Sequentially stagger oscillator units to generate desired cavity T E nm?
modes.
T E nm, m odes have an electric field parallel to the ground plane and transverse to
th e cavity axis. The n index refers to field variations through th e slab and the m
index to variations across th e slab. T he q index is often dropped but refers to the
num ber of standing wave p a tte rn s along the optical axis of the cavity. Oscillation
through T E 00, mode resonances is preferred because these m odes have the lowest
loss, and the energy is m ostly inside the dielectric and is localized along the axis of
the resonator.
All possible oscillation m odes were found by m ounting a single oscillator cell on
;
top of the slab and m oving it over the entire surface of the slab and flexing the
-
R T /D uroid 5870 substrate. T he resultant spectrum with the HPS566A spectrum
;
analyzer set to m axim um hold is shown in Fig. 3.10, and the resonant frequency
i
|
!
I
varies from 5.5 GHz to 8.5 GHz. C om paring th e oscillation frequencies to the un-
[
i
•
mode. From Table 3.1 and Fig. 3.10, one can see th a t below 7 GHz the oscillator
loaded resonator cavity m easurem ents [13], locking is achieved via a TEom? HDSBYV
couples into TEomgi m =
1
, 2, 3 modes, and above 7 GHz only TEoog modes are
excited. M easured oscillation frequencies in th e range from 7 to
8
GHz are 7.15.
7.44. 7.70 and 7.95 GHz and correspond to th e calculated TEoo? modes with <7 = 17.
i
18, 19 and 20 for the unloaded cavity. W hen only one oscillator unit was in the cav-
‘
ity, oscillation above
8
GHz was not observed presum ably because of the frequency
lim itations of the transistor. F urtherm ore only T E 0 oq modes were excited when the
oscillator was located near th e cavity axis. As such it was a sim ple m atter to select
th e desired TEqo9 modes.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
45
-30
-40
m
2.
-50
ID
Q
=J
-60
Q.
<
-70
s
-80
-90
5
5.5
6
6.5
7
7.5
8
8.5
9
FREQUENCY (GHz)
F igure 3.10: Max hold spectrum w ith oscillator unit moved over slab. At any one
tim e there is at m ost only one oscillation frequency.
-20
-30
-40
m
LU
Q
=»
-50
Q.
s
<
-60
-70
-80
-90
8
8.005
8.01
8.015
8.02
8.025
8.03
FREQUENCY (GHz)
F igure 3 .Li: S pectrum of the power com bining oscillator with 1. 2. 3 and then 4
u n it oscillator biased.
!*'
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
I
46
-10
-20
m
TJ
ui
a
3
—I
a.
S
<
-30
-40
-50
-60
-70
-80
-90
-100
60
r
.
80
100 120 140 160 1 8 0 20 0 220 240
FREQUENCY (kHz)
Figure 3.12: Spectrum of th e power combining o scillator with 4 unit oscillators,
frequencies are offset from 7.444 GHz.
r-
|
In Fig. 3.11. the oscillation behavior with 1, 2, 3 and then 4 oscillators biased
I
were investigated. This figure shows the spectrum a b o u t the TEo,o.2 0 mode. The
|
oscillators were arranged on th e slab as shown in F igure 3.8. Note th a t with just
{
one oscillator (th e on-axis one) biased, the oscillation frequency is shifted relative
|
to th at shown in Fig. 3.10 d u e to the presence of th e o th er oscillation units on the
j
I
I
slab. Subsequently the second, then third and fourth oscillators were biased. W ith
four oscillator units biased, th e linewidth is < 6 kH z a t 30 dB down which was
j
!'
determ ined by T E 0,o,i7 as shown in Fig. 3.12. Over an extended interval (10 s and
i
i
l
longer) the cen ter frequency w anders by up to 7 kHz w ith negligible change in output
power level. A t all tim es th e narrow linewidth was m ain tain ed . The m easured DC'to-R F efficiency was 1 %. T h is is low and is a ttrib u te d to the low coupling of the
sense antenna which is on th e edge of the cavity. M ore realistic on-axis efficiency
m easurem ent aw aits the developm ent of a fully engineered system with a partially
tran sm ittin g curved reflector and lenses to propagate and then collect th e radiated
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
47
power.
3 .3 .2
In je c tio n -L o c k e d O p e r a tio n
For free running oscillation, the frequency linewidth is less 6 kHz at 30 dB down,
and this linewidth can be improved by injecting a small signal into the 2D cavity to
lead oscillator working in b etter perform ance. Injection locking the power com bining
oscillators with a signal from a H ew lett Packard HP8340B synthesized source 35 dB
below th e oscillator level reduces th e linew idth to < 3 kHz a t 30 dB down. Here the
resolution bandw idth of th e spectrum analyzer was set to th e minimum resolution
of 1 Hz. Single shot a n d m axim um hold spectra are shown in Figures 3.13 and 3.14.
T h e lock-in bandw idth is 350 kHz and th e locking bandw idth is 470 kHz. Increasing
th e power of the in jected signal by 3 dB increases the bandw idth to 590 kHz and
700 kHz respectively. Injection locking by an FM m odulated signal at 50 kHz and
th en 350 kHz is shown in Figures 3.15 and 3.16.
3 .4
D is c u s s io n a n d C o n c lu s io n
In this chapter, the 2D slab cavity using an oscillator array has been dem onstrated
for quasi-optical pow er combining. T his is the design of a planar cavity w ith active
devices located inside. T h e 2D slab cavity provides an excellent single-mode source
for th e HDSBW and o th e r quasi-optical power com bining system s, and also has the
attra c tiv e advantages which are light weight, low cost and suitable to m onolithic m i­
crowave integrated circuits. Therefore, it will be an im p o rtan t m icrow ave/m illim eter
wave source for fu tu re applications.
However, in its present form, the 2D cavity
power com biner is lim ited to only a few oscillator elem ents as the presence of the
oscillators disturb th e quasi-optical cavity fields. To im prove th e field p ertu rb atio n ,
th e next phase of w ork will move the oscillator elem ents u n d er the slab so th a t the
p ertu rb atio n will be m inim ized.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-IS
CD
3
111
Q
Q.
s
<
-110
8.01124
8.01126
8.01128
8.0113
8.01132
8.01134
FREQUENCY (GHz)
Figure 3.13: Single shot spectrum with 4 unit oscillators with injection locking. The
resolution bandw idth is 1 kHz.
-30
-40
-50
GQ
2,
-60
UJ
Q
3
-70
_i
0.
2
<
-80
-90
-100
-110
8.01124
1------------1------------ 1------------1-----------8.01126 8.01128
8.0113
8.01132
8.01134
FREQUENCY (GHz)
Figure 3.14: M axim um hold (10s) spectrum with 4 unit oscillators and injection
locking. The resolution bandw idth is 1 kHz.
#r
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
49
-20
-30
-40
m
2,
ui
Q
3
H
_l
Q.
s
<
-50
-60
-70
-80
-90
.100 U------------ 1------------1------------ 1----------- 1---8.0088
8.009
8.0092 8.0094 8.0096
FREQUENCY (GHz)
Figure 3.15: Spectrum of th e power combining oscillator with 50 kHz FM m odula­
tion.
-20
-30
-40
00
2
UJ
Q
3
H
—I
OL
-50
-60
s
<
-70
•80
-90 L-L
8.0088
8.0092
8.0096
8.01
8.0104
FREQUENCY (GHz)
Figure 3.16: Spectrum of th e power combining oscillator with 350 kHz FM m odu­
lation.
5*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
50
Chapter 4
Fields, Wave Im pedance and M ode Coupling in
th e H D SB W and R adiation/R eceiving Horn
4.1
I n tr o d u c tio n
In this C hapter, theoretical investigation of a HDSBW system with a pair of tapered
E-plane horns which servers as radiator and receiver is discussed.
At first, the
fields inside the slab are cataloged as T E and TM mode which are expressed in
term s of G aussian-H erm ite functions, and th e phase curvatures and beam spot sizes
are also described. T h e wave im pedances in the HDSBW and the tap ered horn
are calculated, and th en reflection between th e HDSBW system and th e horn is
obtained from the wave im pedances so th a t well m atching can be done between the
HDSBW and the horns. Thirdly, the m ode coupling between the horn and the slab
system is investigated for b e tte r understanding about th e modes propagating into
the slab system . Mode coupling is an im p o rtan t issue for launching energy from the
waveguide system into th e HDSBW system . Finally, the theoretical coupling modes
will be shown and com pared with the m easured data.
4.2
fie ld s in t h e S lab S y s te m
The slab waveguide w ith phase transform ers is shown in Fig.
1.4. T h e relative
dielectric constant of th e slab is es, and su b strate thickness d. Generally, the field
form ulations are analyzed by the superposition of an E-field with Hx = 0 and an
H-field w ith Ex = 0. T he E-field and H-field are respectively derived from th e xdirected electric and m agnetic vector potentials ax ('£) and aT (<£). T he governing
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
51
equations for th e E-field are:
V 2^ + it2^
E -
^
(I)
(4.1)
= 0
(4.2)
v x (v * a ,* )
H = j k Q( v
X
(4.3)
ax
w here ^ and (kQ/ k ) • { d ^ / d x ) are continuous a t i = </, and { 3 ^ / d x ) = 0 at x = 0.
For th e H-field, th e governing equations are:
V 2$ + ifc2<& = 0
(4.4)
£ = j i o ( v x a r $)
(4.5)
x ax
(4.6)
(y
I
\I
|
?
|
w here $ and (3<f>/3x) are continuous at x = d , and $ = 0 a t r = 0. The value of
k is the wave num ber in th e slab, k = u!y/y0£0cs = koy/F^.
I
In the conventional analysis of the fields in a dielectric waveguide, all field compo-
:
nents are assum ed to be independent of the (/—coordinate; th e guided modes are well
*
known and the expressions can be found in the books [107, 108]. However, according
t
|
to th e Huygensrs principle, waves will propagate both in the y and r directions in
\
th e slab waveguide, and generalization of fields into the three-dim ensional expres-
f
sions is necessary. For the three-dim ensional expression, there is an assum ption th a t
th e fields are strongly collim ated along the s —axis; i.e., the “wavebeam condition"
exists in the dielectric slab waveguide [11]. T he wavebeam condition is th at waves
propagating along th e s —axis diverge slowly in th e
y-axis.U nder this assum ption,
th e fieldcom ponents (E y, H ~ ) of th e E-field and ( H y, E : )
of th e H-field are sm all
when com pared w ith oth er com ponents, and they can be neglected. Therefore, the
H-field and E-field are viewed as the TM and T E waves, respectively. Since this
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
system has a ground plane, E-plane circuit is more preferable than H-plane circuit.
Hence, for this reason, only the T E waves will be discussed in the following sections
while TM waves is not.
4 .2 .1
T E m o d e F ie ld C o m p o n e n ts
U nder the assum ption of wavebeam collimation, the T E mode field com ponents
(Hx , E y, Hz ) can be expressed by th e orthogonal G aussian-H erm ite functions, and
are given as the followings equations [11]:
E„
=
3„ C „(x) Q nm (y ,x )< r"-=
E
(4.7)
n=0 m =0
=
E
(4.S)
3 l G„(x) Q m (y, : ) t - i
E
n= 0 m =0
,V
j E
00
A
% dGn{x) a
e.
dx
E
n=0 m =0
*
(4.9)
with
for 0 < x < d
in ( \ J k s - Pnx J
(4.10)
Gn(x) = <
in y \ / k ] — /ind^ e -^J$n-kl(x- d) f or d <
iV < ^
v
7T
(4.11)
^ T - 1 / 2
where B nm is th e am p litude of the m -th mode, k0 = u:^/pL0s 0, and dnis th e propaA
gation constant for T E m ode in the waveguide. The value of j3n is determ ined by
th e well known characteristic equation of a conventional dielectric slab waveguide
in which fields do not vary in the y-direction. This characteristic equation is
a2
V d n - k 02 tan
\j1
a2
- V k l - ,3n
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(4.12)
The function Qnm (y . z ) is com posed of th e Gauss-Herm ite function. H e m(x) =
( —l ) me:c2^2(drn/ d x m)(e~x2^2). Q nm {y,z) im plicitly includes th e inform ation about
the beam size and phase cu rv atu re of the guided waves in the slab, and is given as:
A
Q nm
(y -z)
=
V 2 tn y
v/2 tp
1 /4
m
A -
a
I+(^-)2
0n
.
.
exp <
i
9
K y
4 ) ~y
2
)2
a2
“ l + (>r)2
1 /2
2
l+ ( ^ ) 2
On
.
tan - l
1+
a2 \
V„
A
(4.13)
)
Hr.
A2
A
,--------------------------------------------
where vn = 3 n / J { s / 2 ) { 2 f — s /2 ) . f oc is th e focal length of the convex or concave
lenses, and s is the separation betw een lenses. If 0n is real, then th e guided waves can
keep propagating in the r-d irectio n for long distance without loosing the Gaussian
beam shape. On the contrary, if un is imaginary, then the guided waves have increas­
ing am p litu d e in the y-direction, and this physically means th a t th e guided waves
significantly radiate out of th e slab in y-direction and Gaussian beam m odes decay
a lot. To avoid this energy leakage, focal length should be selected as f oc > (s/4).
In other words, if focal length is chosen first, then the space betw een lenses should
be set as s < (4f oc) so th a t reform of the guided waves in the H D SBW system is
guaranteed.
To get b e tte r expressions for the Gaussian beam m odes in the slab, one can rearA
range Q nm (y, •=) so that ( i / x, E y, H.) are expressed in term s of th e beam w idth and
A
phase curvature. To rearrange Q nm (y,-=), th e first step is to define r 0,„, IT7^ - ) and
R n(=) to be the confocal p aram eter, beam w idth and phase cu rv atu re of th e n-th
beam m ode, respectively. T hey are expressed in the following form s
*»'
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
~ o,n
Rn(z) =
—
9
= confocal param eter
(4-14)
vl
---------
= phase cu rv atu re
(-4.1-5)
■L l A *-
dn
W n{z) =
= beam w idth
(4.16)
T h e beam w idth is defined by th e distance between the optical-axis to th e point at
which the am plitude of fields decreases to 1/e of its value on the axis. T he whole
beam spot size is usually defined as 2VVrn(z). A fter som e tedious derivations, the
phase curvature and beam w idth can be expressed in sim pler forms in which the
physical meanings can be easily understood as followings :
_2 •
R n(z) = z
1+
~ o ,n
_2
W n{z) = Wo,n
9-
W 0,n = Wn(z = 0) =
A
1+
(4.17)
1/2
-2
= beam w idth a t z = 0
(4.18)
(4.19)
(*n
Therefore, substituting (4.17)-(4.19) into (4.7)-(4.9) yields Hx , E y, H z which have
th e following equations which are sim ilar to the conventional expressions for the
G aussian beam m odes in a 3-dim ensional structure:
i* r
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Ey,nTn(%i !/1 ■*) — C nm(jn (^ )
fln / ^o,n
Wn { z )
i r*
2 ^
• Her
Wn(5)
^o.n
IV'o.r,
exp i (m
exp
• exp
\
(4.20)
+i) t a n -
w ith
Hx(x, y . ~)
C mn =
A _ ^ £ _
^o/yo
(4.21)
1 dGn(x)
k0y/^ fJ T 0 ^ ’n(*^) d x
(4.22)
-n/2trfc0
(4.23)
B„
Equation (4.20) explicitly shows inform ation of th e beam w idth and phase curvature
^
A
of the fields at any position (x , y , z ) in the system . As f3n, vn and W on have been
determ ined, the am plitude of th e field, phase curvature and beam spot size can be
predicted from the above expressions.
4 .3
W a v e Im p e d a n c e M a tc h in g B e tw e e n t h e S lab and T a­
p e r e d H orn
To excite T E Gaussian beam m odes into the slab, an E-plane expansion horn antenna
w ith a dielectric tap er inside is an appropriate interface. T h e length of the dielectric
tap er is usually several wavelengths so th a t the horn can sm oothly convey the energy
from the feeding waveguide to th e horn aperture with m inim um energy reflection.
However, th e discontinuity betw een the horn a p ertu re and slab affect the energy
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
56
launched, and im pedance m atching problem s occur. For perfect m atching between
horn a p ertu re and slab, the wave im pedance in both sides should be the same. T hat
is, th e propagation constants in both sides should be the same. In the real system ,
these two constants will not be perfectly equal. Therefore, th e dimensions of the
ta p er and horn should be well selected so th a t these two propagation constants can
be as close as possible, and the im pedance m ism atch will be reduced significantly.
In th e following, the wave im pedances of a partially dielectric-loaded rectangular
waveguide and th e dielectric slab are discussed so th at the appropriate sizes for
ta p er and horn will be theoretically determ ined for the input and output ports of
the experim ental system .
4 .3 .1
f
£
I
W a v e Im p e d a n c e in th e S lab
T he TE-wave im pedance of the n-th Gaussian beam m ode is obtained from the
A
propagation constant, f3n.
A
The value of /3n is determ ined from the n-th root of
i
ii
I
I
t
the ch aracteristic equation in (4.12), and th e wave im pedance of the n-th m ode in
the slab is calculated by
Z te =
EV
ko $
^
Tj~ = ---- 1— — Pn = ~
1
v
V-o
i3n
/| on
(4.24)
In order to only allow dom inant m ode (n = 0) in the slab, operating frequency or the
thickness of the slab should be appropriately selected. For th e substrate thickness
1.27 cm which is the same thickness for th e experim ental system in C hapter 5.
the o p erating frequency for the dom inant m ode can be determ ined from Equation
(4.11), which ranges from 4.74 GHz to 14.23 GHz.
In this frequency range, the
wavelength (As ), propagation (flo) and wave im pedance (Z te ) for the dom inant
m ode TEo,m are calculated and shown in the Table 4.1 as well as in Figures 4.1. 4.2
and 4.3. Fig. 4.1 shows th at the propagation constant linearly increases with the
frequency, and one can find the unknown propagation constants for some specific
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
57
frequencies by linearly interpolating the d a ta in Table 4.1. T he wavelength and
the wave im pedance decrease as the frequency increases. This implies th at m ore
input energy can propagate through th e ta p e r into th e dielectric slab at higher
frequencies. This can be explained by th e concept of P oynting vector (propagating
energy density) |5 | = |£ ’t e /*-^ t e |- At higher frequencies, the Z te becomes sm aller
and then the propagating energy density |S'| going through th e tap er is higher.
450
400
Slab T hickness=1.27cm
350
E
300
a
u
ffl 250
200
150
100
|
?
I
(
6
7
8
9
10
11
12
13
14
F requency (GHz)
Figure 4.1: Calculated propagation constant,
slab.
4 .3 .2
l3. for TEo.m m ode in the dielectric
W ave I m p e d a n c e in t h e T a p ered H o r n
!
the tap ered horn connected to the dielectric slab waveguide system is shown in Fig.
■
4.4. This radiating horn can be viewed as a system w ith cascaded small-section
dielectric-loaded rectangular waveguides as in Fig.
4.5.
To calculate the fields
and wave im pedance inside th e horn, one can start by analyzing th e small-section
waveguide. T he sm all-section waveguide is a partially loaded rectangular waveguide
as shown in Fig.4.6, the fields of the TE m ode inside th e waveguide can be derived
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
I
(GHz)
6
6.25
6.5
6.75
7
7.25
7.5
7.75
8
8.25
8.5
8.75
9
9.25
9.5
9.75
10
10.25
10.5
10.75
11
11.25
11.5
11.75
12
12.25
12.5
12.75
13
13.25
13.5
13.75
14
fia (1 /m )
134.799
143.157
151.729
160.461
169.317
178.262
187.274
196.335
205.431
214.549
223.683
232.824
241.968
251.110
260.248
269.379
27S.501
287.612
296.712
306.000
314.874
323.935
332.983
342.016
351.036
360.043
369.035
378.015
386.981
395.933
404.874
413.802
424.717
A (cm)
4.66
4.39
4.14
3.92
3.71
3.52
3.36
3.20
3.06
2.93
2.81
2.70
2.60
2.50
2.41
2.33
2.26
2. IS
2.12
2.05
2.00
1.94
1.89
1.84
1.79
1.75
1.70
1.66
1.62
1.59
1.55
1.52
1.49
Z t e (ft)
351.44
344.713
338.248
332.140
326.429
321.12
316.208
311.667
307.478
303.610
300.038
296.736
293.680
290.848
288.221
285.779
283.506
281.388
279.411
277.562
275.835
274.211
272.689
271.257
269.910
26S.641
267.443
266.312
265.243
264.231
263.271
262.362
261.498
Table 4.1: C alculated propagation constant /?0, w avelength As, and wave im pedance
Z t e f°r the d o m inant TEomq m ode in the HDSBYV w ith d = 1.27 cm , s r = 2.57.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
•59
4.5
S lab T hickness=1.27cm
£o
r
%
c
©
©
s
5
3.5
3
2.5
1.5
6
7
8
9
10
11
12
13
14
F requency (GHz)
Figure 4.2: C alculated wavelength, As, for T E 0,m mode in the dielectric slab.
i
[
I
360
350
340
S lab T hickness=1.27cm
E
sz
3 , 330
01
c 320
■<oo
g. 310
E
»
300
5
290
(B
280
270
260
6
7
8
9
10
11
12
13
14
F requency (GHz)
Figure 4.3: C alculated wave Im pedance. Z t e • fc>r TEo.m mode in th e dielectric slab.
*#»'
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
60
form th e following equations:
/ d2
32
+ TT-T +
#x2 dy2
H~
*
I h z( x . y ) = 0
(-1.25)
= h~(x,y)e 1
-
T
-
(4.26)
t
H■ - i f ^
Er
„
(l-28»
—
dH~
- ~
k 2 dy
ju yd H z
~
/.2
=
4.29)
/|on^
(4.30)
w ith A:c = ka = uj^/y0e0 in the air and kc = ^ = ujy/f.i0e3 in the dielectric region.
h z( x , y ) in a small-section partially loaded waveguide can be assum ed as
h z( x . y ) = [>i cos k j x -f B sin Ar^x] cos
^f/ —
^
for 0 < x < dz
h z( x , y ) = [C cos ka (az — x) + D sin ka (az — x)] cos
^
(4.31)
(4.3i2)
for d- < x < a~
where q = 0, 1,2,3 - *-; a z and bz are the waveguide dimensions; d z are the dielec­
tric thickness. S ubstitute equation (4.31) and (4.32) into Equation (4.25). then the
propagation constant j3z inside horn at position x is given as:
ft =
( |^ ) 2 =
(4.33)
For solving A:*, ka and 3~, one has to solve the characteristic equation for the field
5*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
61
x
Slab
a
V
Ground Plane
Taper
t
t
Slab
Horn
k
T
Phase Front
Figure 4.4: T he tapered horn connected with the dielectric slab system .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
62
*4
b'
slab
small section waveguide
tapers
slab
z
Figure 4.5: T he cascaded sm all-section waveguide
Figure 4.6: P artially loaded waveguide.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
63
com ponents using the boundary conditions th a t th e tangential fields are continuous.
S ubstituting Equations (4.31) and (4.32) into (4.30) will yield E y as follows:
Ey =
[—A sin
E„ =
ka
+ B cos k^x] cos
f
jj
for
[C sinka (az — x) + D cos ka (az — a:)] cos
0<
x < dz (4.34)
^y +
(4.35)
for d- < x < aT he boundary
condition E y(x = 0) = E y(x = a , ) = 0 yields B = D = 0. Also. E y
and H z are continuous at x = dz, and we have the follows
(C sin ka (az — dz)) = —
(A sin kddz)
C cos ka (az — dz ) = A cos kjd z
Using these two equations above, the characteristic equation is obtained as
-j- tan k a {az - dz ) = —y - ta n kj.dz
Kd
Kd
(4.36)
or alternatively, substituting (4.33) into (4.36), then the characteristic equation be­
comes
31 - ( j P )
=
— \J w 2fi0s 0 - 3 1 -
tan
(j^ )
\Juj2fi0£0 - (32 -
tan
(az - d z ]
~ 31 -
d
(4.37)
This characteristic equation shows th a t /3Z is determ ined by the aperture size
(a : ,b: ) and th e thickness dz of the taper. For a linear taper. a z = (a' —a ) z / L + a'.
bz = (b' — b ) z / L + 6' and dz = z / L . T here are infinite solutions for propagation
constant j3z corresponding to th e T E n(? tapered-w aveguide m ode b ut only the solu­
tions of n = 1 . 2 and 3 with q = 0 will be considered here. T he reason for setting
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
64
q = 0 is th at only TEio mode is excited in the rectangular waveguide. For a tapered
waveguide with a = 2.29 cm, a' = 2.85 cm, b = 1.02 cm , b' = 9 cm, L = 12.5 cm and
d = 1.27 cm, (3Z at different c positions for the dom inant waveguide m ode (n = I)
was calculated with different frequencies and is shown in Fig. 4.7. T he values of a.
a 6, 6', L and d are related to the experim ental system in C hapter 5. T he calculated
d a ta shows th at propagating constant j3z increases as : is close to horn aperture.
T he value of j3z at horn aperture which is at z = 12.5 cm will affect th e impedance
m atching between horn and slab system , and this will be discussed next.
300
6GHz —
7 G H z---8GHz °
9GHz ■
10GHz
250
-§
200
<0
ffi
150
100
50
0
2
4
6
8
10
12
Z (cm)
I
Figure 4.7: Calculated propagation constant at different position inside the trans­
m ittin g horn.
i
■
For the tapered horn, there are two considerations which result in good energy
transm ission from the feeding waveguide to the slab system .
At first, the wave
im pedances of the horn and slab system should be well m atched. Secondly, the
reflection coefficient in the feeding neck (i.e. a t th e position z — 0 cm) should be as
sm all as possible. In order to get good im pedance m atching, selecting appropriate
height of taper as well as width and height of the horn aperture is im portant. Af-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
65
450
400 •T E 10 m o d e ——
TE20 mode - —
TE30 mode
350
300
«
m 250
200
150
100
6
7
8
9
10
11
13
12
14
Frequency (GHz)
Figure 4.8: C alculated propagation constant for TEio, T E 2o and T E 3 0 in the horn
aperture.
3500
3000 ■TE10 m o d e ——
TE20 mode
TE30 mode
2500
ou>
T3
2000
<
U
a.
E 1500
<
u
>
a
5 1000
500
0
6
7
8
9
10
11
12
13
14
Frequency (GHz)
Figure 4.9: C alculated wave im pedance for TE io, T E 2o and T E 30 in the horn ap er­
ture.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
66
te r th a t the height an d w idth have been selected, the wave im pedance Z te a t any
position z can be calculated by
Ey
^TE = - J T
T he value of
Ujy.Q
= ---- 7r=~r = - F
\/S *
(4-3S)
*
can be obtained by E quation (4.37), then Z je is then obtained by
E quation (4.38). By this way the propagation constants and wave im pedances of
TE io, T E 2o and T E 3 0 modes at th e horn aperture are calculated as shown in Fig.
4.8 an d Fig. 4.9. Here, the sizes of ta p e r and horn are a' = 2.85 cm . b' = 9 cm
and d = 1.27 cm.
and
1 2 .8
In Fig.4.S, T E 2o and T E 3 0 modes appear at ab o u t 9.5 GHz
GHz a t th e horn ap erture region even though only the dom inant T E 10
m odes are excited by the feeding waveguide at : = 0 cm. This m eans th a t for
i
this tapered horn, higher-order modes cannot be avoided inside the tap ered horn if
i
o p eratin g frequency is greater than 9.5 GHz. In the frequency range from
\
14 G H z, the slab system only allows th e T E 10 waveguide m ode propagating into the
6
GHz to
*
!|
dielectric and becom ing th e dom inant TEom G aussian-H erm ite modes, and therefore
jj
th e higher-order tapered-w aveguide m odes can not en ter the slab system and are
I
t
t
reflected back to th e horn from th e horn-slab interface. T he reflection is because
th a t T E 2q and T E 3 0 waveguide m odes have much higher wave im pedances than
th eir corresponding TEom modes in th e slab (See Figs. 4.3 and 4.9). Even th e field
distributions for TEjo, T E 20 and TE30 waveguide modes at horn are sim ilar to those
for T E 0m, T E tm and T E 2m modes in th e slab system , T E im and T E 2m Gaussian
m odes do not exit in th e frequency range from
6
GHz to 14 GHz, and this stop T E 20
and TE30 waveguide m odes into slab, too.
Since only th e dom inant mode is preferred, the wave im pedances for T E 10 mode
at horn aperture and for TEom G aussian mode in the slab system are th e ones
necessary to be m atched. Form th e Equation (4.38), one can see th a t if 3Z in the
horn aperture is close to th at in th e slab, the wave impedances on b o th side of
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
67
th e horn-slab interface are almost m atched. The propagation constants in Fig. 4.1
(th e T E 0m modes in the slab system ) and in Fig. 4.S (th e TEio m ode in the horn
ap ertu re) are very close to one another, and hence th e wave im pedance is m atched.
T h a t is, the appropriate sizes for tap ered horn have been well selected for m atching
problem in the whole slab system.
For minimizing energy reflection a t th e feeding neck, a taper with sufficient length
can achieve this goal. The total reflection a t the feeding waveguide can be estim ated
if th e reflection coefficient between each two sm all-section tapered waveguide is cal­
culated. Assume th e increm ental section of length dz w ith an im pedance change
(/Z te for the tapered waveguide as in Fig. 4.10, and th e increm ental reflection coef­
ficient can be defined as the following, by using d(ln f ( z ) ) / d z =
—
a t
TE
(-Z te +
< /Z T e ) -
T
1
/ f(z)-d(f(z))/dz :
.,Q .
i e
( z TE + d z TE) + r TE
dZj E
~
2Z
~
-
i ( -L\ (
2
( "
}
te
{ ^ )
\
m )
ddz
dj3:
20; dz
1
*
\
;
“
In order to m inim ize the reflection, we can set dFxE as small as possible. This
|
im plies th at d0~/dz —>• 0 is a good choice, and selecting th e long tap er will achieve
|
i
[
this. The total reflection looking from the feed position at z = 0, into the horn
section is then obtained by integrating equation (4.40) as:
f
T te ( - = 0) = -
exp(-jl3-:)dTTz =
exp(-jff.z)
{ ^
) d : ('U 0 )
T he term exp( —j 0 zz) represents th e phase delay from a point ~ to the feeding
waveguide at : = 0. Since the characteristic equation (4.37) is com plicated, it is
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
6S
(dielectric slab)
(horn section)
—z
small section
waveguide
Z
ZD dZTE
Z+dZ
- Z
z+dz
Figure 4.10: The model for a small-section w ith step change in the im pedance of
the tapered horn.
impossible to find the closed-form solution for /?-, and hence T te I - =
0
) can only
be obtained by the approxim ation of the partitioned sum:
Tte
iV
1
= Iim ^ e x p O ' d ^ n ) •V—0 0 n = 0
\ ZPz.n ,
N
,
\ ( 3 z,n
^
jV- ° ° n = 0
V
where zn = n l / N , 6z = zn — z n^ i, and
the reflection coefficients a t z =
0
S 3 z,n
^
=
'S3,
Sz
Sz
3 z . n —l
(4.41;
n
3 z,n — 3 z , n - i -
From Equation (4.41)
for different frequencies are num erically calculated
with different partition num bers N =20, 40, 80, 160, and are shown in Fig. 4.11.
The purpose for using different partition num ber here is to check the convergence of
the calculated d ata. Theses curves show th a t th e reflection coefficient at th e feeding
neck becomes lower as th e operation frequency goes higher. In other words, at a
higher frequency, energy can be easily tra n sm itted through th e dielectric tap er to
horn aperture and into th e HDSBVV system .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
69
0.04
N=20 N=40
N=80
N=160
r 0.035
2> 0.03
■o
0.025
0.02
o 0.015
cc 0.01
0.005
6
6.5
7
7.5
8
8 .5
9
9 .5
10
F requ en cy (GHz)
Figure 4.11: C alculated reflection coefficient at th e feeding neck of th e tra n sm ittin g
horn. (L = 12.5 cm. a/ = 2.85 cm. b/ = 9 cm and d = 1.27 cm
4 .4
M o d e C o u p lin g In th e H o r n -S la b I n te r fa c e
W hen a single mode is excited in the feeding waveguide, m u ltip le modes will be
transform ed from this waveguide m ode due to th e discontinuity of th e field d istrib u ­
tion in th e horn-slab interface. As the input wave travels from th e feeding waveguide
to the horn aperture (see Fig. 4.4), th e wave can be viewed as a plane wave in the
ap ertu re if th e flare angle (f> for th e horn is sm all. T h a t is, if th e phase difference.
S \ is less th an A/8 , the phase front in the horn ap ertu re is assum ed to be plane.
If <j> is large, then th e phase front is a spherical curve near th e ap ertu re, and the
phase change between center y =
0
and side wall y = b'/2 needs to be considered:
this phase difference is approxim ately ex p (—j(3 (R i — R-2 ))- In this section, the horn
is designed w ith a sm all flare angle so th a t the com plicated derivation of the phase
term can be avoided, and the waves arriving at th e apertu re are still viewed as plane
waves. T he electric fields in the horn ap ertu re can be expressed by equations sim ilar
to Equations (4.34)-(4.35) with a- = a', bz =
6
', d z = d:
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
!
^
[—A sin k dx ] cos
(y
E„ = < 'jf-[C sin ka (o' - x)] cos
+
7
fo r
))
(y 4 -
7
0
< x < d , \y\<~
(4.42)
))
f o r d! < x < a' , |y| <
where q =
0
7
, 1 , 2 ,3 . - • •.
For the mode coupling from the horn ap erture to slab system , wave reflection
between horn ap ertu re an d the slab should be taken into account. T he reflection
coefficient Tte can be obtained by viewing horn and slab as two transm ission lines
which are cascaded and have different characteristic wave im pedances. T h e wave
impedances of both sides can be obtained from the equation (4.24), and th e reflec­
tion coefficient at th e horn-slab interface is calculated by
I"te =
'T E .s l a b
E
t
E 'T E yh o rn
E , slab 4 ” Z ' Y E . h . o r n
fih o rn
f is la b
(4.43)
f i h o r n 4 ” f ts la b
As the reflection coefficient r scriptsize T E *s calculated, one can app roxim ate the
field relation between horn and slab by th e equation of E y,siab = (1 4- T te )^.apertureUsually any field distribution can be represented by a group of orthogonal bases
and hence the waveguide mode in th e horn aperture can be represented by the
orthogonal modes in th e slab. Therefore, by the m ethod of modal expansion, the
fields in the horn a p e rtu re can be representable using G aussian-H erm ite functions
as orthogonal bases.
Since the fields along y —axis inside the tapered horn are
represented by cosine function as well as th e rectangular function n ( y f b ' ) which
represents the boundary lim it |?/| < b'/2 , a group of G aussian-H erm ite m odes should
exist in the horn a p ertu re a t the same tim e. T h a t is, the term
c o s ( ( < 77r / 6 ' ) ( y
+ 6 ' / 2 ))n
{y/b') can be composed of many G aussian-H erm ite functions, and this also implies
that even with a single m ode excited in th e waveguide, m ultiple slab beam m odes
will be coupled into th e slab.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
To find the G aussian-H erm ite modes in th e horn-slab interface, th e cosine term
in Equation (4.42) is expended into the sum of th e slab beam m odes sim ilar to those
of Equation (4.20) w ith z = 0:
cos {
(»+ 1 ) ) n
v
where H(y/b') =
1
(v)
=
(444)
as |y| < 6'/2. and is zero as |?/| > 6'/2. W0-n is the beam spot size
of th e n th G aussian-H erm ite mode at th e horn aperture. The am plitude am of each
T E nm G aussian-H erm ite m ode can be obtained using th e orthogonality of the Herm ite functions. M ultiplying another H erm ite function into both sides of Equation
(4.44). rearranging th e exponential term , an d integrating both sides of Equation
(4.44) yield
r
J
-
f ; amH e m (Y ) H e n ( V) e ' Y^ 2d Y
— C O
m = 0r\
{Y +
£
) n C w Y ) H e ° ( n e~r V i d Y
{iM)
where Y = 2y /W 0,n. By the orthogonality of th e H erm ite functions given as follows.
0
I " H e m ( Y ) H e n ( Y ) e - Y2' 2d Y =
J— OO
\p2/Km\
as m
n
(4.46)
as m — n
the am is expressed as
am =
f o m .n
( q ~ W 0.n ( ^ t
, / ,
cos
\ +
v 2 ~m! J - b l\v0.n
\
2b'
\
1
-n r -
b' W LI
_v-2/, ;v.
) ) H e m (V )e
' d\
W 'o .n ) J
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(4 .4 1 )
or alternatively with H e m( Y ) = 2 m/ 2 H m{Y)
2
-
-m / 2 f b'/^2W0,n
( QirWnn (
b'
\\
V + ^ r j ) H^ Y)*' , d Y (4-4S)
=
The above equations, (4.47) or (4.48) give th e am plitudes of all the TE nm slab beammodes coupled from an T E n<7 waveguide m ode in the horn aperture. Considering
the relation EapertureU + T te ) = £siab a t th e horn-slab interface and the Equations
(4.7) and(4.42), the field am plitude B nm of each T E nm G aussian-H erm ite m ode in
the slab system is then shown as:
(1 + r TE.nm) ( - ^ f ) ^4 sin (kdd) amH e m ( ^ T ~ )
= —B nmkQSn
Sin
N k * - 0 n2d \ ^
Hem
or
„
w 0,n (1 + r TE.nm) ( j u n \
sin {kdd)
= ^'ly/ir
&
{C ~ k T )
( I ---------( 4 4 9 )
71
sin I V ^2— ,8n d J
where am is expressed in equations(4.47) or (4.48), A is th e excited am plitude of
waveguide mode, and B nm is the coupled am p litu d e of th e slab mode. B nm strongly
depends on the beam spot size, reflection coefficient in th e horn-slab interface and
propagation constant in th e dielectric slab.
In practical application, beam spot
size is selected as th e sam e as the ap ertu re w idth, and th e energy reflection is also
designed as small as discussed in the previous section.
4 .4.1
TEio to T E o9 M o d e C o u p lin g
From Equations (4.44)-(4.49), we know th a t any single T E n(? waveguide m ode will
become m ultiple T E nm slab beam m odes. Since the dom inant m ode is the preferred
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
73
one in th e horn or in th e slab system , only the do m in an t mode coupling will be
derived here. By selecting ap p ro p riate operating frequency, only TEio waveguide
mode is excited and can be converted into TEo, modes in th e slab. Generally, the
beam spot size may n ot equal to th e ap ertu re size, and th e n a m may also vary with
this size. If we consider different beam spot sizes and let I\ = b'/\V on, then am for
T E 10 m ode in the horn a p e rtu re is calculated by setting q = 0 in Equation(4.4S):
9 -m /2
Qrn
(4.50)
------
For K = b 'j\V on varying from 1 to 3. th e calculated a m are shown in the following:
I<
ao
ax
a2
a3
a4
as
ae
a-
1
.736
0
- .2 5 3
0
.0402
0
- 3 .6 4 • 10" 3
0
1.25
.SSI
0
-.2 3 4 1
0
.0223
0
3.09 • lO" 4
0
1
1.50
1.006
0
-.1 7 8 8
0
- .0 0 2 1
0
4.26 • 10" 3
0
-6 .9 4 • 10"
0
1.75
1.109
0
-.0 9 4 7
0
-.0 2 7 0
0
6.76 • 10~ 3
0
-7 .1 4 • 10“
0
2
1.192
0
.0090
0
-.0 4 6 7
0
6.90 • 10" 3
0
-3 .9 0 • 10-
0
2.25
1.257
0
.1 2 2 1
0
—.0564
0
4.64 - 10" 3
0
1.26 • 1 0 " 4
0
2.5
1.305
0
.2349
0
—.0544
0
7.05 • 10~ 4
0
6.07 • 10"
4
0
2.75
1.314
0
.3392
0
-.0 4 1 0
0
- 3 .6 8 • lO" 3
0
8.45 • lO” 4
0
3
1.366
0
.4309
0
-.0 1 8 3
0
0
3.41 • 10"
0
as
«9
1.67 • lO"
4
0
i
o
o
>o
0
o
u1
to
1
-]
[a m ] —
4
From th e above d a ta m atrix , one can see th a t the am plitudes of the slab beam ­
mode w ith m > 5 are very sm all com pared with the 0th, 2nd and 4th modes as the
value of K varying from 1 to 3. T he flare angle d for th e horn is usually assum ed
to be sm all, and the beam spot size of the slab beam m odes near the aperture is as­
permission of the copyright owner. Further reproduction prohibited without permission.
74
sum ed close to the ap ertu re w idth if th e excited waveguide mode is the T E i 0 mode.
T h a t is b' = VVon an d K =
1
. T h e am plitude of each slab beam m ode for K =
1
is calculated as [am]= [a0, a x, a 2, a3. a4, a 5, a6, a7, aSl ct9]=[0.736,0, —0.253. 0,4.026 •
10- 2 .0 , —3.641 • 10- 3 , 0 , 1.6091 • 10- 4 ,0]. Note th a t TEio waveguide m ode only gen­
erates the even slab beam m odes as A' =
1
, and th e odd slab beam m odes do not
appear. This is due to the sym m etrical field distribution that of th e TEio waveg­
uide mode. For higher-order waveguide modes, th e odd slab beam m odes may exist
during mode coupling.
Since all th e W 0tTl are assum ed th e same in th e horn aperture, then we can use
W 0to to represent every W 0,n in E quations (4.44) and (4.49). U nder the condition
K =
1
, g 6 and a8 are very small when compared with a0, a2, a4. th e TEio m ode
in the horn ap ertu re can be approxim ated by the n = 0 , 2. 4 G aussian-H erm ite modes
■^aperture =
A y ,a p e rtu r e
=
^ [—A sin
e y !w°-a
kd
2y
a0H e 0
-(- a2H e 2
W ^.
[C s in
a0H e 0
(a - ~
2y
Wo*.
X )} e
(4.51)
-?y
w o,0t
T
a4H e4
2y
WOJ0j
for
0
< x < d
(4.52)
^
2y
iy
Wo*.
WoJO,
where C = A cos (Ar^eA) / cos [A:a (cu —<A)] and VV0fi =
6
for d < x < a
'. In the slab region, the
field distributions along the y —axis have the sam e G aussian-H erm ite p atterns as
in (4.52),and along th e x —axis th e field distributions are expressed by the function
Gn(x) in (4.10). T h e am plitudes of th e coupled slab beam m odes can be obtained
by equation (4.49), and the coupling am plitude B 0m of th e TEom group as:
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
S ubstitute Z?o,m and n — 0 int ° equations (4.20) and (4.23) and only consider the
even m odes, then the to tal coupled E y^iab can be expressed as
E y .sla b
(X, V, o) =
E y '0 0
(x ,y ,0 ) +
= —\Z2rk0 /30 Go (x )
E
y,02 ( x ,y ,0 ) +
E
y,04 (x, y,0 )
(-1-54)
o_e-y2/w l0
Z o,0
~
/
o
o
\
VS
\
\
6 o ,
k
_
where y/2 fto / Z Q<o =
/
\
a
0
+ Bq2 H e 2
A
V\
\
/
\
^ o ,
/
\
+
B o ^ H e ^
0
\
\
*
0- y3n
o
67o , 0 y
/
_
(see En.(4.19)). T he calculated relative am plitudes for the
coupled TEoo: T E 0 2 and T E 0 4 m odes in the slab are shown in Fig. 4.12 with only a
TEio waveguide mode excited in th e feeding rectangular waveguide. The to tal field
profile com bining these th ree individual modes is compared to the m easured field
profile in Fig. 4.13. The curve shows th at the theoretical d a ta m atches the m easured
result. Only a small p attern offset along the y-direction was found, and this is due to
the sensor position offset and the m isalignm ent of the lens. T he measured d a ta was
obtained by moving a sm all L-shape sensor along the y-axis above the slab system .
In Fig. 4.12, the m ode curves provide useful inform ation of the input am plitudes
and phases for amplifiers which will be located on top or underneath the slab system
in C hapter 5. If the amplifiers are located in th e proper places, then the com bined
o utput waves will be constructive rath er than destructive.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
i
i
76
Oth M o d e-----2nd Mode ----4th Mode ......
0.8
3
g.
0.6
<
at
3
o
0.4
■M
O
<a> 0.2
>
a
0
CC
-
0.2
-0.4
-4
3
2
1
0
1
2
3
4
y/Wo
Figure 4.12: T he calculated relative am plitudes for the G aussian-H erm ite TE 0 ,oTEq .2 an d TEo ,4 m odes which are coupled from the single TEio m ode of the feeding
waveguide. W 0 is the beam spot size and equal to the aperture w idth.
1.1
Theoretic Data ----Measured Data •
0.9
CL
E
<
o
a
ocn
0.8
0.7
0 .6
0.5
0.4
£
0.3
0 .2
0 .1
-4
■3
2
1
0
1
2
3
4
y/Wo
Figure 4.13: The calculated and m easured patterns of the total coupled field in the
slab.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Chapter 5
D esign and M easurement o f Power Combining in
th e 2-D Slab System
5.1
I n tr o d u c tio n
In C h ap ter 4, fields inside th e slab waveguide system and th e tapered horn, reflec­
tion coefficient in the horn-to-slab interface, and coupling betw een horn ap e rtu re and
slab system were discussed. In this C hapter, th e previous theoretical considerations
are applied to the design of the dielectric-slab power-combining system and the in­
p u t/o u tp u t horns. This quasi-optical power combining system includes convex lenses
(phase transform ers) and the taper-slot-antenna amplifier array. Power-com bining
levels and surface field p a tte rn s are m easured and com pared w ith the am plifier array
located on th e top surface and located underneath the dielectric slab. T he system
losses due to the Vivaldi an ten n a array and th e lenses are also discussed.
5.2
A m p lifie r A r r a y on th e T op Surface o f t h e C o n v e x -le n s
S y s te m
5 .2.1
S y s te m D e s c r ip tio n
In this section, a HDSBVV system with two convex lenses inside is designed for
the first tim e, with four M ESFET power amplifiers located on the top surface of
the slab waveguide. T his HDSBW system is shown in Fig.5.1, and the M E S FE T
amplifiers were random ly placed on the top surface. Basically, th e dielectric slab is
composed of Rexolite (er = 2.57. tan<5 = 0.0006 at X-band ). and its dim ensions are
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
78
selected to be 27.94 cm wide and 1.27 cm thick. The value of su b strate thickness is
determ ined from Equation (3.9) so th at o p eratin g frequency for the dom inant slab
beam m odes (TEom modes) is
6
GHz ~ 14 G H z. For this frequency range, X -band
waveguide is appropriate for launching energy into the HDSBW system . The w idth
of the slab is selected about three tim es th e m axim um beam size so th a t the effect of
edge on th e beam m odes can be be ignored. To reduce the reflection from the edge,
either absorbing m aterial or tapered edge shown in Fig. 5.2 were used to reduce
the side reflection significantly. T here was no apparent difference between absorbing
m aterial a t th e edge or with an edge taper.
T he lenses are fabricated of Macor ( tr = 5.9, tan<5 = 0.0025 a t 100 kHz), and
their radius and th e focal length are 30.48 cm and 28.54 cm , respectively. N ote
th at the focal length, / oc,is calculated by th e equation f oc = R f{ 2(1 — n)). where
n = \J Qens/^siabi and R is the radius of th e curvature of lens. T he convex lenses
I
are inserted into th e waveguide w ith a spacing of d2 cm. T his system is built as
a confocal system so th at the guided waves are focused and reiterated periodically
1
along th e waveguide, and the beam spot sizes near the horns and m iddle area of the
|
system are th e same, i.e. W x = W2 = Wz- For this confocal system . d x, d2j 2 an d d 3
f
f
l
are equal to th e focal length, 28.54 cm. A djusting dx, d2 and d 3 will lead to different
j
The inp u t and o utput horns are the E-plane extended horns w ith dielectric tap ers
;
inside to sm ooth th e transition. T he tapered horn has a sm all energy reflection (see
I
Fig.4.11) and ensures most of the input energy is conveyed to the slab system . T he
\
width an d height of the horn are 9 cm and 2.85 cm. respectively. Basically, the
;
input waves have a spot size the same as th e aperture size and propagate as the
W x, \V2, Wz if necessarv.
Gaussian beam m odes along th e system . W hen the input waves pass the lenses, they
are focused to th e middle region between lenses. In that region, the focused beam
has the strongest field strength to efficiently drive the am plifier array.
5.3 and it is built on a
t
T he M E SFE T amplifier unit cell is shown in Fig.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
79
RECEIVING
HORN ANTENNA
TRANSMITTING
HORN ANTENNA
d3
w2
LENSES
AMPLIFIERS
SIGNAL GENERATOR
DETECTOR
Figure 5.1: T h e Convex-lens slab waveguide system with am plifiers on top surface
w
(a)
I 111 11111 111 II
G
R O
U
N
D
^slab
IJ I I
111 11 111
P L A N E
(b)
iim n n 1 m rn g jwi
ABSORBER
(C)
TAPER ( e r = e sl ab)
Figure 5.2: Side term inations for the HDSBW to reduce edge reflections.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
so
R T /D u ro id 5S70 su b strate . The su b strate has dielectric constant er = 2.33 close to
£s[ab = 2.55 so the discontinuity between these two su b stra te s is as sm all as possible.
T h e dim ension of this am plifier unit is 7 cm x 1.5 cm . T h is design is derived from
th e fin-line oscillator described by M einel [109] and activ e slotline notch an ten n a
by Leverichef al. [83]. T he essential stru c tu re of th e am plifier includes two end-fire
Vivaldi an ten n a tap ers which consisted of gate-receiver an d drain-radiator. T h e E
plane amplifiers were designed to specifically elim inate surface-of-slab to groundplane resonance, th u s oscillation does not occur when th ere is no energy radiated
from th e feeding horn. By moving th e amplifiers aro u n d th e m iddle of th e top sur­
face, different am plifier characteristics were obtained.
Gate-receiver
copper
Drain-radiator
:
MESFET
i
I
I
I
MESFET ampilifier on
FT/Duriod substrate
Figure 5.3: M E SFE T planar am plifier.
5 .2 .2
M e a s u r e m e n t o f A m p lifie r G a in s , S y s te m G a in s a n d
\Ey\ P a tte r n s A cro ss t h e Slab W a v e g u id e
As shown in Fig.5.4, p art of the guided energy is am plified by each unit am plifier,
an d th e rest of the energy travels through the dielectric waveguide. T h e through
waves include the original beam m odes as well as th e sc atte red waves due to the
existence of th e Vivaldi antenna array.
In different positions, each am plifier has
different input am p litude and phase, so th e am plifier a rra y m ay generate different
power com bining levels. To obtain a high level of energy com bining, all am plifier
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
SI
units were moved around to different locations and with different biases to achieve
th e best o u tp u t level. Here, three configurations were selected to p ut the M ESFET
am plifiers on the top surface of the dielectric slab as shown in Fig. 5.5. These
th ree positions are around th e m iddle area between lens, w here th e beammodes are
focused to have the strongest field strength.
The am plifiers were biased with two groups of drain voltage Vos and gate voltage
Vgs to observe their am plifier gain and power gain. For each configuration, th e
separation distances among th e amplifiers were carefully ad ju sted to avoid m utualcoupling oscillation and to o b tain the largest gain. To set up th e array, an amplifier
was first moved around th e m iddle area on th e slab to get its highest gain. Then,
th e second am plifier was carefully moved close to the first one as possible to get th eir
highest gain. At this m om ent, unwanted oscillations due to stro n g m utual coupling
between th em should be avoided. Sequentially, th e third and fourth amplifiers were
iJ
added to the slab system by th e same m ethod.
i
If
jj
am plifiers are shown in Fig. 5.6—5.S for these three configurations. The loss due
|
to the array inserted in to th e system was calculated by su b tractin g Pout (w ith
j
amplifiers in system ) from Pout (without th e amplifiers in sy stem ). This insertion
\
loss is m ainly due to scattering of the guided beam m odes p ertu rb e d by the Vivaldi
|
antenna, and it varies with frequency and location. The loss in location 1 is higher
I
th an for th e o th er two, and this is assumed to be because all of th e antennas are
i
T he m easured outp ut power Pout for th e slab system w ith and w ithout unbiased
i
?
}
:
located at the peak of the guided field distribution and so scatte rin g th e guided waves
peaks. In location 3, the antennas were arranged carefully to reduce perturbation to
t
th e beam m odes and the m inim um loss is obtained with an average of about 2 dB.
Hence, th e insertion loss can be improved by moving the am plifiers to appropriate
positions, and th e power gain of the system can be increased. T h e causes of insertion
loss are fu rth er exam ined by plotting the field profile using th e technique shown in
Fig. 5.19.
**■
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
82
GROUND PLANE
Ea/fra = t E a . n / ^ n
1
Ein
a»l
AMPLIFIED
WAVES
Eout = Eth/4>, + Ea/^a
THROUGH
WAVES
E t h / i > ,
£
f
5
Figure 5.4: Wave model of the am plified and through waves in th e slab system with
an ten n a array.
Figure 5.5: M E SFE T planar amplifier.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The insertion loss, amplifier gain and power gain are calculated by the following
definitions:
Insertion Loss
= Pout (w ith unbiased am plifier in system )
(5.1)
— ^out (w ithout am plifier in system )
Am plifier G ain
System G ain
= Pout (w ith bias) — Pout (w ithout bias)
(5.2)
= Am plifier Gain — Insertion Loss
(5.3)
By adjusting th e bias Vos an d Vos in each location, various gains can be ob­
served. For approaching the best gain in each location, two different bias levels for
(L gsit Vgs 2 , Lgs 3 .
Vdsa) were applied. In location 1 th e biases were (-0.S V.
-1.2 V, -1.3 V, -0.9 V, 2 V) and (-0.8 V, -l.S V, -1.6 V, -0.S V, 2 V): in location 2 the
biases were (-0.7 V, -1.3 V, -1.4 V, -0.8 V. 2.5 V) and (-0.7 V. -1.3 V. -1.4 V. -0.8
;
V, 1.5 V); in location 3 the biases were (-0.8 V, -1.2 V, -1.3 V, -0.8 V,
r
(-0.8 V, -1.2 V, -1.4 V, -0.8 V, 1.1 V ). T he total drain current in each location, ( / d i -
1 .6
V) and
j;
!
f
I
t
/D 2 ). for these two bias levels were (34.43 mA. 15.2 m A ), (43.1 mA. 37.75 m A).
(37.76 mA, 23.2 mA) for location 1, 2 and 3, respectively.
!
5.10—5.12. T h e am plifier gain and power gain for each location are calculated and
i
shown in Fig. 5.13—5.18. The highest am plifier gains obtained in location 1. 2. and
•
3 were
(
5 dB, respectively. This d ata shows th a t the am plifier array generates positive gains
»
for the slab system in th e frequency range from 7 GHz to 8.5 GHz, and also shows
The o u tp u t powers for different biases in each configuration are shown in Fig.
11
dB, 13.8 dB, and S dB, and the largest power gains were 7 dB, 11 dB and
th a t the higher Vos, th e higher th e gain is in each location. Note th a t gains vary for
different locations, and this is due to the antenna array in each configuration having
different am plitudes,
and phase Lcj>in of the in p u t signal (see Fig.5.4). As a
consequence th e am plified wave
E a
and through wave
E th
also change for different
locations.
Ideally the T E beam m ode across the dielectric slab is supposed to be a Gaussian-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
S4
-30
with amplifiers; bias o f f ----without amplifier
-32
-34
-36
-gm
-o
3O
-38
_
~4 0
Q-
-42
-44
-46
-48
-50
7.6
7.7
7.8
7.9
8
8.1
8 .2
8.3
8.4
8.5
FREQUENCY (GHz)
Figure 5.6: Received Power for th e slab system w ith /w ith o u t unbiased am plifier
array in location 1 .
- i
- —■
■i -
■■
w ith amplifier; bias off —
w i t h o u t amplifier ♦
U
3O
a.
-32
7.2
7.4
F RE Q U E N C Y
7.6
(GHz)
7.8
Figure 5.7: Received Power for th e slab system w ith /w ith o u t unbiased am plifier
arrav in location 2 .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
So
-16
with amplifier: bias o f f ----without amplifier
-18
-2 0
-22
E
m
■a
-24
o
a.
-26
-28
-30
-32
7.2
7
7.8
7.4
7.6
FREQUENCY (GHz)
8
Figure 5.8: Received Power for the slab system w ith /w ith o u t unbiased amplifier
array in location 3.
8
location 1
location 2
location 3
7
m
tj,
co
co
O
6
5
4
DC
LU
co
3
2
1
0
7.6
7.8
8
8 .2
8.4
FREQUENCY (GHz)
Figure 5.9: Insertion loss for am plifier array in location 1, 2 and 3.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
86
-30
with bias 1 —
with bias 2 without bias —
-32
-34
-36
■g
-38
CD
5-
-40
CL
-42
ao
-44
'
v
*
s t
V *
-46
-48
-50
7.6
7.7
7.8
7.9
8
8.1
8.3
8 .2
8.4
8.5
FREQUENCY (GHz)
Figure 5.10: Received Power for amplifier array with different biases in location
1
.
-18
with bias 1
with bias 2
without bias
-2 0
-22
=>
o
CL
-26
-28
-30
-32
7
7.2
7.4
7.6
7.8
8
FREQUENCY (GHz)
Figure 5.11: Received Power for amplifier array with different biases in location 2.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-14
with bias 1 —
withbias 2 without bias —
-16
-18
-20
I
-22
I
-24
2.
a.
-26
-28
-30
-32
7
7.6
7.4
7.2
7.8
8
FREQUENCY (GHz)
Figure 5.12: Received Power for am plifier array with different biases in location 3.
Ia
?
r
12
with bias 1 —
with bias 2
10
co
2.
z
<
CD
0.
5
<
7.6
7.7
7.8
7.9
8
8.1
8.2
8.3
8.4
8.5
FREQUENCY (GHz)
Figure 5.13: Am plifier gain for am plifier array in location
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1
.
ss
12
with bias 1
with bias 2
10
8
m
~o
6
2
<
O
4
CO
o
2
0.
0
•2
-4
7.6
7.7
7.8
7.9
8
8.1
8.2
8.3
8.4
8.5
FREQUENCY (GHz)
Figure 5.14: Power gain for am plifier a rray in location 1.
12
with bias 1
with bias 2
10
m
•o
8
2
<
O
6
Q.
4
2
0
7
7.2
7.6
7.8
FREQUENCY (GHz)
Figure 5.15: Amplifier gain for am plifier array in location 2.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
8
S9
12
with bias 1 —
with bias 2
10
z
<
o
cc
III
5
o
Q.
-2
•
7
7.2
7.4
7.6
7.8
8
FREQUENCY (GHz)
Figure 5.16: Power gain for am plifier array in location 2.
£
8
16
with bias 1 —
with bias 2 -
14
12
10
z
<
o
Q.
5
<
7
7.2
7.4
7.6
7.8
FREQUENCY (GHz)
Figure 5.17: Amplifier gain for am plifier array in location 3.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
8
90
16
with bias 1
with bias 2
14
12
CQ
"O
<
a
oc
HI
oCL
S
10
8
6
4
2
0
■2
-4
7
7.2
7.4
7.6
7.8
8
FREQUENCY (GHz)
Figure 5 .IS: Power gain for amplifier array in location 3.
H erm ite distribution as the slab system is with or w ithout the am plifier array. How­
ever, when the am plifier array is placed on the top surface of th e system , it perturbs
the field distribution and suppresses the field strength. To exam ine the E y field dis­
tributions across th e HDSBW system with or w ithout th e am plifier array, a sensor
was moved along th e y-axis from 11.5 cm to -11.5 cm . This sm all sensor is built on
R T /D uroid 58S0 su b strate and is shown in Fig. 5.19. Its size is 1 c m x ‘2 cm and is
located 18.2 cm away form the second lens and close to the receiving horn. Measured
d a ta shows that this sensor causes only 0.2 dB power loss when it was located on
the top surface. Hence its perturbation of the slab beam m ode is negligible, and the
m easured \Ey\ p attern s is believable. The m easured \Ey\ distributions across the
slab with the amplifiers a t location 3 are shown in Fig. 5.20 for th e amplifiers with
and without biases, and with no amplifiers located in th e system . T he operating
frequency is selected to be 7.372 GHz because the amplifiers have th e highest gains
at this frequency.
W ith no amplifiers in the system , the |
| distribution is m ainly a TEoi Gaussian
beam . The beam w idth is about 9 cm which is the horn ap ertu re size. T he ripples
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
91
in |y| > 5 cm are due to th e reflections from the edge of waveguide and from the
lenses. Most of the slab beam m ode energy still propagates inside the beam -w idth
region and is not much affected by the side reflection. C om paring the field curves
of the "am plifiers O F F ” and “no amplifiers on the slab” conditions, one can find
the power decreases by about 4 or 5 dB in th e |t/| < 5 cm region, and the ripples
in the |y| > 5 cm region rise a little. T his shows th at am plifiers placed on the
top scatter p art of the guided energy from th e beam spot region toward th e side
wall. T he am plitude drop betw een the “am plifier O F F ” and “no amplifier on slab”
curves represents the am ount of this scatterin g loss. Even th e insertion loss exists
in the |y| < 5 cm region, th e m easured d a ta shows th at the am plified power level is
high, and th e insertion loss is th e n com pensated. The power density increase is a
m inim um of 10 dB, at y = 0 cm , and is a m axim um of 32 dB, at y = 5 cm. O ne can
see th a t th e amplified field p a tte rn s jum ps up a lot but is not sym m etrical, an d the
power gain between “am plifier O N ” and “am plifier O FF ” is higher in |y| > 5 cm
th an in |y| < 5 cm . The reasons for this unsym m etrical shape is th a t every am plifier
has different input power and am plifier gain, and the locations for each am plifiers
are not sym m etrical to the c-axis, either. Therefore the power increase is not equal
in the y >
5.3
0
and y <
0
region.
A m p lifie r A rra y u n d e r t h e C o n v ex -L en s S y s te m
T he power-combining study in th e previous section is based on the amplifiers placed
on the top surface of the dielectric slab system . However, locating th e amplifier array
on the top surface of the slab suppress th e beam m ode w ith consequent increased
scattering (see Fig. 5.20). Locating th e amplifiers underneath th e dielectric slab
and on th e ground plane m ay reduce beam m ode perturbation, scattering loss, and
the reflection of the input energy due to th e am plifier structure. These are problem s
w ith the conventional grid system which has amplifiers m ounted on the surface of
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
92
Radiator
Receiver
d
s
*
f
(+Y)
Figure 5.19: M easurem ent of power distribution.
t
-20
amplifier ON
amplifier OFF
no amplifier on slpb
-25
„
-30
«»«
. *35
cr
ju - 4 0
5
2
-45
UJ
-50
Q
oc
3
co
<
Ui
5
♦ * -
-55
/ ♦ •
-60
-65
-70
-10
5
0
5
Y (cm)
Figure 5.20: Power distrib u tio n s on the slab.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
10
the dielectric su b strate. In this section, th e amplifier array was located underneath
the slab, and m easurem ents of am plifier gain and system gain, o u tp u t power vs
input power and transverse electric field \Ey\ are presented.
5 .3 .1
S y s te m D e s c r ip tio n
Basically, the slab waveguide system w ith amplifiers underneath itself is sim ilar to
the system with amplifiers on top, and is shown in Fig. 5.21. This slab waveguide
system was adjusted (dl = 12 cm , d‘2 = 44 cm and d3 = 16 cm) to let th e through
waves and amplified waves be w ithin th e ap erture of th e receiving horn so th a t more
power can be received, and to enlarge th e beam spot size in the m iddle area where
m ore amplifiers can be put. Since th e ab ru p t discontinuities between the lenses
and slab always scatter some of th e guided energy which generally radiates into free
I
space, a metallic top was applied to th e system as shown in Fig. 5.22 (M = 1.6 cm.
f
h'2 = 1.27 cm). This plate was chosen to be 12 cm wide and 64 cm long so that
I
I
scattered energy can be reflected back to the system as much as possible.
Coax To Radiator
DIELECTRIC SLAB
AM PLIFIER S
IN SID E SLAB
v
1
Figure 5.21: Dielectric slab waveguide system with M E S FE T amplifiers inside.
T he amplifier array located on the ground is shown in Fig. 5.23, and its location
is in the middle of the slab system . Each amplifier unit cell is the sam e size as
described in Section 5.2 and also em ploys the same M E SFE T transistor. Excessive
insertion loss was initially experienced w ith this configuration. As an alternative the
i!**
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-METAL TOP
hi
z s z z y fi
SLAB
Figure 5.22: Side view of system with m etallic top.
dielectric slab
ground plane
gate-receiver drain-radiator
Ein
FET
source
FET ampilifier
Figure 5.23: Amplifier array under dielectric slab waveguide.
fttcReproduced with permission of the copyright owner. Further reproduction prohibited without permission.
su b strate of th e an ten n a was changed to R T /D uroid 6010 su b strate with er = 10.6 .
In Fig. 5.24, th e received power for three conditions: (a) w ithout amplifiers; (b) w ith
amplifiers b u ilt on R T /D uroid/5870 s u b stra te (er = 2.57); and (c) with am plifiers
b uilt on R T /D u ro id 6010 su b strate (er = 10.5). It is obvious th a t the insertion loss
due to the array is significantly higher (approxim ately 6—10 dB ) when the am plifier
unit cell is built on the su b strate with a low dielectric constant. This is because the
lower p erm ittiv ity m aterial allows more guided waves to leak through the su b strate
into free space below the amplifiers than does th e higher p erm ittiv ity m aterial. For
this reason, all of th e slab power com bining system s considered from here use unit
amplifiers built on R T /D uroid 6010 su b strate.
-15
-20
No Amplifiers Underneath —
With Amplifiers (5870 Subatrate) —
With Amplifiers (6010 Subatrate)
E
m
■o
W -25
O
5
o
a.
■a -30
23
0)
/ \
CO
a>
2
-35
-40
7.5e+09
9e+09
Frequency (Hz)
Figure 5.24: M easurem ent of received powers without and w ith amplifiers built on
different su b strates com pared to the u n p ertu rb ed HDSBW system .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
96
5 .3 .2
M e a su r e m e n t o f A m p lifie r G a in s, S y s te m G ain s a n d
\Ey\ P a tte r n s A c r o ss th e S la b W a v eg u id e
As was done in Section 5.2.2 w ith th e surface m ounted unit cells, th e amplifier gains,
system gains a re m easured. Here, th e amplifier arrays were located at two locations:
location
1
an d 2 are 22 cm an d IS cm, respectively, before the second lens.
In Figs. 5.25 and 5.26, th e am plifier gains w ith system input powers o f -16 dB m .
-13 dBm an d -10 dBm are shown.
The am plifier gains are obtained by taking
th e ratio of th e m easured large signal transm ission param eter |.?2 i| with the u nit
amplifiers biased and unbiased.
T h a t is, A m plifier Gain = IS2 1 I (with bias) —
IS2 1 I (w ithout bias). The highest amplifier gain is 19 dB in location
1
with a system
in put power -16 dBm . T he d a ta shows that am plifier gain becomes lower as th e
input power increases. T he reason for this phenom ena is th a t th e transistors are
I
nearing the sa tu ratio n region when input power rises (see Fig. 5.30). The bias levels
s
I
|
for the am plifiers was ( V'd
-1.3 V), and th e drain current level was (Ip 1; I p 2, / d 3 , I da) =
|
S.5 mA,
6
s
,
F c s i,
Lgs3 ? F g s - i ) = (2-0 V. -1.3 V, -1.3 V, -0.9 V.
(6
mA, 3.5 m A .
m A ). These biases were chosen to let am plifiers reach th e maximum gain.
|
r
E
f
l
I
I
C
•
f
f
In Fig. 5.27. th e passive svstem gain and insertion loss are included. The gain
th e total loss including beam m ode scattering by th e lenses, the horn radiation loss
5
and insertion loss of the array. Lens scattering and th e insertion loss are the m ajo r
indicates th a t th e passive system loss is 7.5—11.5 dB when the system is w ithout
amplifiers, an d is 10—12.5 dB when the system is w ith amplifiers. T h e upper curve
(dash line) indicates the to tal loss of the system including beam m ode scattering by
th e lenses and th e horn radiation loss into the air. T h e lower curve (solid line) shows
losses for this system . Insertion loss can be calculated from the IS2 1 I curves in this
figure; i.e. Insertion Loss = |S 2i |(No Amp) — l^ iK A m p O FF). From Fig. 5.27. one
can see th a t th is loss varies from 0.5 dB to 4.5 dB over the 7 to S GHz range and
reaches the highest value at 7.7 GHz. Com paring th e gains in Figs. 5.25—5.26 w ith
mReproduced with permission of the copyright owner. Further reproduction prohibited without permission.
97
20
Pin=-10dBm ----Pin=-13dBm ----Pin=-16dBm .......
14
m
T»
Z
<
o
7.25
7.3
7.35
7.4
FREQUENCY (GHz)
Figure 5.25: Am plifier gain for location
second lens.
7.45
7.5
f
f
r
\
i
F
I
the insertion loss in Fig. 5.27, we find that the am plifier gain can com pensate th e
|
insertion loss. W ith th e unbiased amplifiers in th e system , and with the metallic
1
i
f
top, the loss of th e passive HDSBW system is shown in Fig. 5.28. W ith the m etallic
\
50% of the system energy loss can be guided back to the system , not scattered into
f
space.
1
. This location is 22 cm away from th e
top cover, th e system loss is about 3 dB less th a n w ithout th e cover. This m eans
i
I
;
The active system gain (defined as Pout/ P in ) w ith the amplifiers turned on is
shown in Fig. 5.29 with P,-n= -10 dBm . The solid line is th e reverse transm ission
gain, |S l2|, and the dotted line is the forward transm ission gain, |S’2 1 1- The solid
line shows th a t th e back radiation into the input port is m inim al with the amplifiers
on and a positive power gain is achieved through th e com plete system . W hen th e
amplifier gain is m axim um and overcomes all th e loss in the system , th e system has
a positive gain of 3.5 dB at 7.372 GHz.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
9S
Pin=-10dBm ---Pin=-13dBm —
14
12
00
3
z
<
0
7.25
j-'
*
7.3
7.4
7.35
FREQUENCY (GHz)
7.45
7.5
Figure 5.26: Amplifier gain for location 2. T his location is IS cm away from th e
second lens.
[
|
Fig. 5.30 shows th e system o u tput power Pout vs input power P ln when th e
\
amplifiers were with an d w ithout bias. The o perating frequency is a t 7.372 GHz,
!
and th e m etallic top was also applied. From Fig. 5.30, the am plifier gain is th e
|
difference between Pou((A m p ON) and Pou*(Amp O F F ) and the system power gain
l
(
•
is obtained by su btracting Pin from POU((Amp O N ). W hen Pout = -16 dB m . system
power gain and am plifier gain are 9.5 dB and 19 dB , respectively. N ote th a t the slope
1
of th e P out(Am p ON) is less th a n 1, and this reveals th a t the M E S F E T transistor is
;
operating in the satu ration region. If P,-n decrease, then am plifiers will work in th e
linear region and the gain will be higher. However, th e o u tput power will be lower.
T he transverse E-field distributions for the system with and w ith o u t amplifiers
were m easured at d = 13 cm and is shown in Fig.
5.31.
C om paring the field
distributions for amplifiers w ithout bias and for no amplifiers inside the slab, one
can find th a t \Ey\ decreases about 2 to 3 dB due to the existence of th e amplifiers
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
99
Amps Off —
No Amps —
m
•a
-10
CM
CO
-11
-12
-13
7
7 .4
7 .2
7 .6
7 .8
8
FREQUENCY (GHz)
Figure 5.27: Passive G ain ,|S 2i|, of the dielectric slab w ith /w ith o u t am plifiers. The
insertion loss of th e u n it cells alone is th e difference betw een these two I-S21 [ curves.
in the -5 cm < y
< 0
cm region. This drop shows th a t locating th e am plifier array
underneath disturbs th e guided TE G aussian mode less th a n locating the am plifier
array on th e top surface of th e slab. Locating th e am plifier array on the top causes
about 6—8 dB loss in th e -5 cm < y < 5 cm region (see Fig. 5.20). T he curve of
amplified field also shows th a t the beam w idth of of th e am plified waves is wider
than the receiving horn, and this m eans th a t only p a rt of th e amplified energy is
caught by th e receiving horn. To estim ate the received po rtio n of amplified energy,
one can integrate th e area under the m easured E-field curve as follows,
/
15cm
I G n{x) |2| E m easured I2 ^ x d y
(5.4)
| G n(x) |2| E m easured I2 dxdy
(5.5)
•15cm
/
5cm
-5 cm
where cl is th e su b strate thickness and G n(x) is the field d istrib u tio n function along
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
II
100
w/oTop —
w/Top —
•a
v^a
.A
w -10
-11
-12
-13
7
7.2
7.4
7.6
7.8
8
FREQUENCY (GHz)
Figure 5.28: Measured response of the passive DSBW am plifier system (no bias)
with and w ithout a m etallic top cover. W ithout the cover, th e system loss is 10 to
12.5 dB. W ith the cover, th e system loss is 6.5 to 9 dB.
B*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
IS
T3
Z
0
w
tn
1
CO
z
<
tr
i-
Reverse —
Forward —
-10
-12
-14
7.2
7.25
7.3
7.35
7 .4
7.4 5
7.5
7.55
7.6
FREQUENCY (GHz)
Figure 5.29: Transmission gain for the amplifiers with bias.
-K A—'
-0
|TJ
0'
‘10
>C
X
3
O -15
Q.
.x'
-20
. . -Gf
-
nr
Amps ON w/o top -©—
Amps ON w /T op -+—
Amps OFF.w/ q topi.
Amps ;OFF w /T op x
-25
-30
-15
-10
5
0
5
Pin (dBm)
Figure 5.30: Pout vs Pin for am plifiers w ith and w ithout bias.
S*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
102
-20
Amps w /Bias —
fm psw/o Bias —
No Amps —
-25
-30
jCDj "35
-o
5 -40
UJ
a
-45
UJ
AC
=> -50
<0
<
jg -55
-60
-65
-70
-15
;
-5
5
0
Y POSITION (cm)
-10
10
15
Figure 5.31: M easured \Ey\ d istrib u tio n across th e top of the HDSBYV amplifier
system at 7.37GHz.
C
v
r
I
i
i
the x-direction as in Equation (4.10). The power added efficiency (PA E) of this
system is defined by Pou!(Amp O N ) / P d
c
- P
d c
is th e D.C. power from th e supplier
;
i
]
and is calculated by I d Vq - In order to obtain th e m axim um am plifier gain, the
I
-1.3 V, 2 V). and the drain cu rren ts were ( Id i, I d 2 •
;
8.5 m A, 6 m A ). W hen P,n = 5 dB m at 7.37 GHz, th e received P ouf(A m p ON) is 2
i
dB m , and then th e highest PAE is ab o u t 3.35%. However, if the scatterin g loss from
i
th e second lens is considered, which is about 3.5 dB (see the passive gain curve in
amplifiers were biased w ith
( V g s i, Vg
s
2-. P g s 3 - K j s - j , P g s ) =
(-1.3 V. -1.3 V. -0.9 Y\
Ida) = (6 m.A. 3.5 mA.
Fig.5.27), the PAE is adjusted to be 7.5%. Furtherm ore, the calculated Shorn/Ssiab
for Fig. 5.31 indicates th at only 63% of the amplified energy is cap tu red by the
receiving horn. If th e 37% of am plified energy which is outside the horn aperture is
also considered, the corrected PAE is 11.2%.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
103
5 .3 .3
V a r ia tio n o f G a in s a n d O u tp u t M o d e s
In th e previous section, th e am plifier gains in Fig. 5.25 and 5.26 always show positive
values in th e operating frequency range, and the o u tp u t field pattern in Fig. 5.31
also keeps th e shape of th e first-order G aussian beam m ode. However, according to
th e wave m odel in Fig. 5.4, th e am plifier gain and o u tp u t beam form should vary
due to th e changes of th e in p u t am plitudes and phases of th e amplifiers. In order to
observe th e variations of th e gain and beam forms, th e am plifier array was moved a
little tow ard th e second lens. W ith the sam e bias levels used in the previous section,
th e am plifier gain and insertion loss of amplifiers are shown in Fig. 5.32. and the
o u tp u t |E y \ p attern is shown in Fig. 5.33.
In Fig. 5.32, the insertion loss is ab o u t 2.5 dB to 4 dB and is a little less than
th a t in Fig. 5.27. This m eans th a t the insertion loss can be reduced by a d ju stin g the
position of th e am plifier array. Since th e input am p litu d e and phase were changed
by th e position shift of th e array, the am plifier gain was also changed. T h e highest
gain is ab o u t 19.5 dB, and this gain is higher than those in Fig. 5.25 and 5.26.
F u rtherm ore, the frequency for the highest gain is also shifted to 7.215 GHz. The
am plifier gain reaches 0 dB a t 7.182 GHz and becomes negative value a t frequency
lower th a n 7.12 GHz. In Fig. 5.33, the area under th e uA m p with bias*’ curve is
bigger th a n th a t under “A m p without bias” curve, and hence the am plified energy
in still higher th an th e unam plified energy a t 7.1S2 GHz. Since the o u tp u t beam
m ode is m ost likely the second-order G aussian m ode w ith a null in the m iddle, the
receiving horn can only catch a small p art of the o u tp u t energy, and therefore the
m easured am plifier gain drops down to zero. More troublesom e is th at th e two main
lobes of th e the beam are 180 degrees out of phase and so cancel each o th e r inside
th e horn.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
104
20
Amplifier gain
Insertion Loss
15
10
7.1 7.15 7 .2 7.25 7.3 7.35 7.4 7.45 7 .5 7.55 7.6
Frequency (GHz)
Figure 5.32: Amplifier gain insertion loss of the array u n d ern eath the slab.
-35
-40
_rt0 _7/J
-45
>»
UJ
TJ
O
w
3
CO
CO
0)
2
-50
-55
-60
-65
Amp with bias
l A m p w it h o u t b i a s
-70
No Amp underneath
-75
-15
-10
5
0
5
10
1
Y (cm)
Figure 5.33: M easured |E y\ p attern s at 7.182 GHz.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
15
Chapter 6
Improvement o f System Components for Higher
Output Power
In C h ap ter 5, a 4 x1 am plifier array successively located on the top surface of the
convex lens system or underneath th e slab has a m axim um o u tp u t power, Pout, of
5 dB m . T he m axim um amplifier gain and system gain are 19 dB and 9.5 dB. Even
though th e gain is high, its low o u tp u t power level lim its the applications of this
system . Im proving th e o u tp u t power level for th e 2D slab system is the aim of this
chapter. O u tp u t power can be increased several ways: (1) reduce th e losses from the
passive com ponents of th e system , such as horns and lenses; (2) reduce guided waves
]
scattered by the am plifier antenna array; (3) use higher power M MIC chips; and
|
(4) increase th e num ber of amplifier elem ents. T he developm ents described in this
chapter includes th a t replacing the convex lenses by th e concave lenses which cause
\
bI1
I
~
less scattering loss; optim izing the tap er antenna of th e unit amplifiers to reduce
;
am plifier has cascaded MMIC chips (M ini-C ircuits ERA-1): placing a m etallic top
i'.
the driving point reflection coefficient ( 5 u ); m axim izing the transm ission coefficient
(P 2 1 ) at the horn-slab interface; using a 5 x 4 am plifier array in which each unit
on the slab system to stop scattered radiation from array and lenses.
r
6.1
R e d u c tio n o f S c a tte r in g L oss o f L en ses
T he 2D slab system w ith convex lenses or concave lenses is shown in Fig. 6.1, and
has different system perform ance due to the shapes of the lens. W hen no amplifier
array is located inside th e slab system, th e passive system gains for these two systems
is shown in Fig. 6.2. and the curves show the concave-lens system has 2—3 dB less
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
L06
scattering loss th an the convex-lens system . T h e scattering loss results from the
discontinuity betw een the propagation constants /?s/a&and duns- and the am ount of
this loss is basically determ ined by th e m iddle area of lens where m ost of the guided
energy passes [11]. For a concave lens, this m iddle area is less th a n th a t of a convex
lens, and hence th e scattering loss from the concave lens is ex pected to be small. A
good estim ate of th e scattering loss from convex or concave lens can be obtained byexam ining th e [£7y| patterns before and after th e lens. The m easured \Ey\ curves in
Fig. 6.3 show th a t field am plitude has a bigger drop when the guide energy passes the
convex lens, and th e area of this am plitude drop represents th e scattering loss from
the lens. The scattering loss from a convex lens and a concave lens are obtained
by integrating the area under th e l-Eyl curves in th e Fig. 6.3 using the equation
5 = / _ [ | G n{x) |2| E y \2 dxdy, where G n(x) is given in E quation (4.10). After
obtaining 5i(before a lens), 52(after a convex lens) and S ^ a fte r a concave lens), the
scattering loss ( S 2 — S 1 )= -3.66 dB for a convex lens and (53 — 5 i ) = -1.IS dB for a
concave lens, respectively.
Dielectric Slab
d1=12cm
d2=28cm
Coax To Radiator
Pin
d3=16cm
. ------
Receiver To Coax
Port 2
Port 1
Convex/Concave Lens
or
p° ut
Amplifiers Under Slab
Gate
Source
Drain
MESFET
Figure 6.1: The 2D H DSBW system w ith convex/concave lenses.
A fter discussing the passive perform ance of th e system w ithout amplifiers inside,
the active system perform ance will be exam ined as follows. For th e convex/concaveIens system with a 4 x 1 M E S FE T amplifier array, the Pout vs Pin and the system
I
•irReproduced with permission of the copyright owner. Further reproduction prohibited without permission.
107
gain are shown in Fig. 6.4 and 6.5 for the system with an d w ithout a m etal top.
From these two figures, one finds th a t the concave-lens system has higher o u tp u t
power and system gain than th e convex-lens system if th e system is without a m etal
top. W ith a m etal top. most of the scattered energy is sto p p ed and the system
o u tp u t powers an d gains for both system s becomes closer to each other. From the
m easured d ata in Fig. 6.2—6.5, we see th a t th e convex-lens usually cause m ore loss
an d m ay not be an appropriate passive com ponent for th e fu tu re 2D power com bing
system . Furtherm ore, the system w ith top has b etter o u tp u t power and system
gain, and this im plies that th e parallel-plate slab waveguide system may be m ore
su itab le for the fu tu re applications in which less scattering radiation is preferred.
m
T3
z
<
a
2
uj
£
-12
CONVEX-LENS SYSTEM
CONCAVE-LENS SYSTEM
-13
-14
[
t
!
7
7.2
7.4
7.6
7.8
8
FREQUENCY (GHz)
Figure 6.2: Pass system gain for th e 2D QO system w ith convex/concave lenses.
Concave lenses cause less energy sc atte r than convex lenses, and th e average of the
loss reduces about 50%.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
10S
B efore len s After C onvex L ens —After C on cave Lens~
|
-40
■o
>>
ui
■o
-45
0>
3<0
aai
S
-60
— -V-
-65
0
5
5
15
10
Y (cm)
Figure 6.3: M easured \Ey\ p attern s before and after a convex/concave lens. Guided
energy has less am plitude drop w hen it passes thought the concave lens.
10
10
(1) AMP ON —(2) AMP ON —
3) AMP OFF
4) AMP OFF —-
(1) AMP ON —(2) AMP ON — ■
[3TAMP OFF~i=
4) AMP OFF —-10
-10
E
m
=5
E
GO
•a 20
3O
O.
-20
a
o
a.
-30
-40
•40
(1)4(3); CONVEX-LENS SYSTEM
(2)A(4):C0NCAVE-LENS SYSTEM
-50
-60
-50
-40
•30
-20
-10
0
10
-(f)&(3)r CONVEX-LENS SYSTEM
(2)&(4):CONCAVE-LENS SYSTEM
-50
-60
-50
-40
-30
-20
Pin (dBm)
Pin (dBm)
(a)
(b)
-10
0
Figure 6.4: P,„ vs Pout for the convex/concave-lens system w ith a 4x1 amplifier
array underneath, (a) the system is w ithout m etallic top, and (b) the system is
w ith m etallic top.
•A*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
10
10
0■o
i
--------1--------1-------- -------- 1--------1
..........
AMP OFF!-Ot-t .
AMP ON; W/D TOP: -t—
AMP ON; W/TOP: -EJ-• a - s - e " ‘3~ Q"1 D--G-E
AMP OFF.-*—
AMP; W/OTOP :-t—
AMP ON;
-EJ--
10
11- 13.
0*o
z
<
0
20
0>
<n
! 'la i
.........%....... Q..........
:% :»
'i — -—►
—
! \
! X
X•% E
*\
V
:
>*• 1 *
<
o
sIU
0K
0
-10
-10
_____ ■
-60
-50
«
-40
_____ i_____ i_____ i_____
10
-30
-20
-10
-60
-50
-40
-30
-20
Pin (dBm)
Pin (dBm)
(a)
(b)
*10
Figure 6.5: System gain for the system w ith /w ith o u t m etallic top. (a) represents
the convex-lens system , and (b) represents th e concave-lens system .
6.2
6 .2 .1
T h e X -B a n d V iv a ld i A n te n n a W ith in A C arrier
D r iv in g P o in t R e fle c tio n C o e ffic ie n t
( S n )
for th e V i­
v a ld i a n te n n a
For the slab system w ith amplifiers underneath the slab, there is an unavoidable
radiation loss which is due to 50% of th e energy radiated by the taper antenna
leaking through the an ten n a substrate into air (see the stru ctu re in Fig. 5.23). In
order to reduce this radiation loss, a carrier shown in Fig. 6.6 is used to force the
leaky radiation back to th e dielectric slab waveguide. T he size for this m etallic
carrier is 24 mm wide and 7.5 mm long.
W ith the new system (unit amplifiers
with in a carrier and placed underneath th e slab), S u of th e tapered antenna differs
from th a t of the old ta p e r antennas which were used in the system described in Fig.
5.3. T h e old tapered an ten n a doesn’t have a carrier. Hence the variation of S u of
the an ten n a should be carefully considered again to ensure m atching between the
antenna and MMIC chip.
Su m ainly depends on the size of th e antenna, the dielectric around the antenna
and the stru ctu re of th e carrier. Since th e stru ctu re of the dielectric slab and the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0
10
110
carrier are unchanged in the system , optim izing th e size of the tap ered antenna
is th e only option. By iteratively using the MoM m ethod sim ulator developed by
Nuteson [110], th e tapered an ten n a is selected as 11 m m wide and 23 m m long, and
the gap between tap ers is selected about 50 /zm to have an input im pedance close to
50 fi at the driving point. For a tap ered antenna w ith this size, th e sim ulated and
m easured S h is shown in Fig. 6.7 for the antenna sittin g in air. W hen th e antenna is
sittin g in carrier an d located u n d ern eath the slab, its m easured S u is shown in Fig.
6.8. T he m easured value of |S n | is less than 0.33 (about -10 dB) a t 6.9—7.8 GHz
and 9.9—10.8 GHz in Fig. 6.7(b), and at 6.8—8.0 GHz and 9.4—10.5 GHz in Fig.
6.8.
The S u in these two figures positively suggests th a t this size of the tap er
an ten n a is ap p ro p riate for X -band operation. In th e following sections, all of the
ta p er antennas have th e size discussed here.
Radiaing
Antenna
MMIC
Amplifiers
Carrier/Heat Sink
Receiving .
Antenna &
Figure 6.6: An an te n n a elem ent sits inside a carrier underneath th e slab system.
T he m etallic carrier is also a heat sink for the M M IC amplifiers.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Ill
10 -
0 .9
0.8
5
E
E
-•
■
!
i
I
*
i
•
■
i
1
!
0
-5
X
-: ■
i
i
I
:
!__1
r
-
1
:
i
i
,
!
r
>
I I
0 .7
A
^
■
“*’*
1
1
;
-t—
;
'
!
!
:
i
|
1
!
i
'
!
1
1
j
!
I
i" r
-
-
55
ui
o
0.6
^
0 .5
O
0 .4
2
r v i
0 .3
0.2
-1 0
0.1
-
10
15
20
0
25
X (m m )
2
4
6
8
10
12
F R E Q U E N C Y (G H z )
(b)
(a)
Figure 6.7: Vivaldi antenna: (a) The an ten n a w ith mesh structure used in MoM
analysis; and (b) M easured (dashed line) and sim ulated (solid line) 5 n for the
an ten n a in air
A ntenna underneath (w / carrier)
0.8
0.6
co
0.4
0.2
2
4
6
8
10
12
14
FREQUENCY (GHz)
Figure 6.8: 5 u for the tap er an ten n a in the carrier underneath the slab.
t
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
14
112
6 .2 .2
T ra n sm issio n C o efficien t (£ 2 1 ) b e tw e e n th e V iv a ld i
A n te n n a a n d th e R a d ia tin g /R e c e iv in g H orn
Just as S u of the tapered antenna in th e carrier need to be optim ized, so does
the transm ission coefficient, S 2 1 , between th e antenna and radiating/receiving horn.
The purpose of measuring
^21
is to understand how much th e energy radiated from
antenna can be received by th e horn or how much th e energy radiated from horn can
be received by the antenna. T he m easurem ent of S 21 between port 1 (antenna) and
port 2 (horn) is described in Fig. 6.9. For th e concave-lens system , the |S2i| of th e
horn-to-antenna path for th e system with and w ithout a m etal cover is shown in Fig.
6.10. In X-band, |S2i| is -9 to -12 dB w ith a m etallic top and about -11 to -14 dB
without a m etallic top. T hese curves indicate th a t the energy coupled between th e
horn and antenna is low b ut th e metal top does provide a 2 —3 dB increase for th e
1
energy transfer. The low energy transfer rate is due to th a t th e radiation p attern
from a single antenna spreads very fast as shown in Fig. 6.11 and 6.12. One can see
I
th at the am plitude of radiation pattern drops about 7 dB at 8.03 GHz and 13 dB at
10.01 GHz even though th e waves just travel a short distance from antenna ap ertu re
j
?
at z = 0.5 cm to the position at z = 3.0 cm . This fast spreading pattern causes th e
!
receiving horn to only catch small part of th e radiated energy from a single antenna.
;
Since the S 21 between th e horn and th e antenna is not high, improving th e
i
energy transfer rate for this 2D system is necessary. To raise |i>2 i|, the radiation
|
beam should be narrower so th a t the horn m ay receive most of the radiated energy.
I
Since the radiated beam of an array w ith proper phasing should be narrower th an
i
f
th at of a single antenna, locating more tap ered antennas along the y-direction of
the system should be an appropriate way to m ake a narrower beam . Based on this
consideration, the 4 x 1 , 2 x 2 and 5x 4 array were built and are described in th e
following sections.
i .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 6.9: M easurem ent of |S’n | and IS2 1 I f°r th e Vivaldi an te n n a underneath the
half concave-lens system.
w/ metallic top
w/o metallic top
-10
m
■o
m
(0
-12
-14
-16
Concave-lens system
-18
-20
7
8
9
10
11
12
13
FREQUENCY (GHz)
Figure 6.10: |52i| between th e Vivaldi an ten n a to horn in th e half concave-lens
system.
B*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
114
8.03GHz —
-20
Measured lEyl (dBm)
Measured lEyl (dBm)
-25
-30
-35
-40
-45
-50
-55
- 5 - 4 - 3 - 2 - 1 0 1 2 3 4
Y p o sitio n (cm )
(a)
(b)
Figure 6.11: M easured \Ey\ at S.03 GHz.
-20
A tZ =-0.5cm
A t Z= 1.0cm
At Z=3.0cm
A t Z=5.0cm
, A t Z=7.0cm
Measured lEyl (dBm)
-25
1 0 .0 1 G H z —
—
—«
-
Measured
lE yl
(dBm]
-30
-35
-40
-45
-50
-55
- 5 - 4 - 3 - 2 - 1 0
1
2
3
4
Y p o sitio n (cm )
(a)
Figure 6.12: M easured \Ey\ at 10.01 G H z .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
115
6 .3
T h e C o n c a v e -L e n s S y s te m W ith a 4 x 1 , 2 x 2 a n d 5 x 4
A m p lifie r A rray U n d e r n e a th
A convex-lens system with a large array underneath th e slab is shown in Fig. 6.13
w ith d 1 = 15.6 cm , d2 = 40 cm an d d3 = 15.4 cm. Before building an d testing this
new system , it is necessary to exam ine the perform ance of a single am plifier unit
first. After testing the single am plifier unit, the 4 x 1 , 2 x 2 and 5 x 4 am plifier array
will be in turn p u t into the slab system to examine th e system perform ance.
6 .3 .1
P er fo rm a n ce o f T h e A m p lifier U n it w ith S in g le an d
C a sca d ed M M IC
T h e amplifier unit located in a half system is shown in Fig. 6.14 and has either
f.
?;
a single MMIC or two cascaded M M ICs as shown in Fig. 6.15.
T h e MMIC is
i
a M iniCircuits ERA-1 amplifier chip.
Its S param eter and other characteristics
|
IJ
are described in Appendix B. In Fig.
6.14 (a), th ere is no "window", and the
^
E th, propagating in th e slab, i.e. 2s,n <C E th- In this case the amplified wave is also
i
i
|
m uch smaller th an th e through wave E th- Therefore, th e output wave ( E amp + E th)
is close to E th and th e perform ance of the amplifier unit is masked.
I
6.14 (b) if the a p ertu re is applied to block most of th e through waves outside the
|
am plifier unit so th a t
I
wave is close to E amp and the m easured amplifier gain will be close to th e inherent
;
gain of the unit amplifier. The am plifier gain of a single amplifier in th e half system
energy incident to the unit am plifier, E {n, is much less than the through energy.
is alm ost equal to Ethi th en E amp
As in Fig.
E th• T he output
w ith and w ithout a window is shown in Fig. 6.16 and 6.17, respectively, for the
am plifier unit w ith single MMIC or w ith two cascaded MMICs. T hese two figures
show that the am plifier gains for th e system w ithout a metal window are always
11'J*.
m uch lower than those of the system with window. Also, the am plifier unit with
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
116
cascaded MMICs has higher gain over 7—11 GHz w ith a m axim um gain of 28 dB at
8.3 GHz. Basically, the gain of th e unit amplifier w ith cascaded M M IC is at least
10 dB over 7—10.2 GHz.
dl
d2
<33
Pout
Pin
Figure 6.13: A concave-lens system w ith a 5 x 4 am plifier array underneath the slab
system . d\ = 15.6 cm, d‘2 — 40 cm an d d3 = 15.4 cm.
- —
Ss
—
- 1
J
r
E ln —
— 1
5.5 a n
S S an
E m rE in
Eta*
i
iCONCAVE
LENS
(a)
(b)
Figure 6.14: A half concave-lens system with single amplifier u n it,
w ithout a m etal window; (b)system w ith a m etal window.
6 .3 .2
(a) system
S y s te m w ith th e 4 x 1 and 2 x 2 A m p lifie r A rray
A single am plifier unit with cascaded MMICs in a half concave system has been
exam ined in th e previous subsection, and the m easured d ata shows th a t it has an
amplifier gain of up to 28 dB. Therefore, this am plifier unit will be used again for
th e 4x1 and 2 x 2 amplifier array in this subsection. The array was put into th e
m iddle area of the whole concave lens system which has the sam e size as shown in
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
L IT
FERRITE BEAD
_
✓Vd
MMICAMPLIFEFft%
3
I/P
FERRITE BEADJfd1
MMICAMPLIFERSA ^
^~0/P
4L
ITP
amp
am p
GND
GND
(a)
(b)
Figure 6.15: T he amplifier u n it w ith single/cascaded M M IC.
8
w/ metal window ----w/o metal window -----
6
m
■o
4
<
CJ
cc
2
UJ
Q.
2
<
0
2
-4
-6
7
7.5
8
8.5
9
9.5
10
10.5
11
FREQUENCY (GHz)
Figure 6.16: The single-amplifier gain for th e system w ith and w ithout a m etal
window. The am plifier has a single M M IC.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
118
30
w/ metal window ----w/o metal window-------
25
oo
20
15
<
a
cc
iii
a.
S
<t
5
r*i
0
/v/ " V
\ /
5
-10
-15
-20
7
7.5
8
8.5
9
9.5
10
10.5
11
FREQUENCY (GHz)
Figure 6.17: T h e single-am plifier gain for the system w ith and w ithout a metal
window. The am plifier has two cascaded MMICs.
Fig. 6.13. Different in p u t power levels were injected to th e system to m easure the
am plifier gain an d th e satu ratio n power level for the array. T he am plifier gains are
shown in Fig. 6.18 for th e 4 x 1 array and in Fig. 6.21 for the 2 x 2 array. From
th e figures, one c an see th a t the 4 x 1 array has b etter am plifier gain, and th e gain
reaches 17.5 dB a t 7.4 G Hz and 8.7 GHz. For the 2 x 2 array, the am plifier gain
only reaches 15 dB a t 8.7 GHz. T he factor causing th e 2 x 2 array to have sm aller
am plifier gain is th a t th e input power received by the 2 x 2 array is less th a n th at
received by the 4 x 1 array. Moreover for th e 2 x 2 array, th e second-colum n units
m ay have less in p u t power com pared to th e first-colum n u n its, and this also results
th a t less o utput pow er can be generated from the 2 x 2 array.
W hen the in p u t power is too high, th e amplifiers in th e 4 x 1 or 2 x 2 array tend to
work in the sa tu ra tio n region and the am plifier gain becom es small (see th e curves
for P,n=20 dBm in Fig. 6.18 and Fig. 6.21). In the m ean tim e, since th e m axim um
in p u t power for a M iniC ircuits ERA-1 MMIC to reach its 1 dB compression gain
5*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
119
is -0.25 to -1.4 dBm and the |5 2i | in th e Fig. 6.10 is -9 to -12 dB, the m axim um
in p u t power for amplifiers to work in the linear region can be estim ated about 9.2512.4 dB m . Hence, using input power of 20 dB m excesses the m axim um lim it for the
array to work in the linear region.
T he system gain is calculated by (amplifier gain - total system loss), w here to tal
system loss is (loss fro m the horn and lens + insertion loss fr o m the array). At
S.66 GHz, th e amplifier gain for the 4x1 an d 2 x 2 array is about IS dB in Fig. 6 .IS
and about 15 dB in Fig. 6.21; the total system loss is about -18.5 dB in Fig. 6.19 and
ab o u t -17.5 dB in Fig. 6.22. Hence, for th e system with the 4 x 1 and 2 x 2 array,
th eir system gains are about -0.5 dB and -2.5 dB, respectively. Obviously, these
two system gains are not good enough. However, if we exam ine th e |
| p a tte rn s
generated by the array, th e system gain should be higher th an th e m easured results.
T he m easured \Ey\ p attern s for the system with the 4x1 and 2 x 2 array working
a t S.667 GHz are shown in Fig. 6.20 and Fig. 6.23. For the 4x 1 array, we can see
th a t \Ey\ for th e “No A m p” case in Fig. 6.20 is more seriously perturbed by the
array, and this explains why the 4x1 array causes more system loss than th e 2 x 2
array. Also, the am plitude of \Ey \ for "A m p ON” is 5—10 dB greater than th a t for
th e “No A m p” case over 0 < y < 10 cm range, and this guarantees th at th e system
gain is positive. However, the pattern of th e amplified wave is 5 cm offset from the
center of th e receiving horn, and this is why th e system gain for th e system w ith the
4 x 1 array is only -0.5 dB as discussed in th e previous paragraph. For th e system
w ith the 2 x 2 array, the \Ey\ for “Amp O N ” is less than th a t for “No A m p” , but
th e p a tte rn also has higher am plitude outside |y| >5 cm region and causes th a t the
receiving horn only catches sm all part of th e amplified energy. This also tells the
! *»VV.
reason th a t the system gain is about -2.5 dB for the system w ith th e 2 x 2 array.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
120
20
Pin=10dBm
Pin=20dBm
15
in
■o
z
<
o
cc
Ul
10
-I
a.
£
<
-10
-15
7
7.5
8.5
8
9
9.5
10
10.5
11
FREQUENCY (GHz)
Figure 6.18: Am plifier gain of the 4 x 1 am plifier array in the concave-lens system
w ith a w ith different P m.
T"
T
L oss from horn and lens
Insertion loss from array
ID
2.
(0
<n
-5
M
A
o
-10
a/*
A Vf
-20
7
7.5
8
v '
f
-i,/--
K " \t X
N\
■.
r
X
8.5
f
i
9
9.5
10
10.5
11
FREQUENCY (GHz)
Figure 6.19: System loss of the concave-lens system w ith a 4x1 array. T his loss is
caused by the horn, lens and unbiased array.
1
N*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-45
Amp ON Amp OFF NoAmp
-50
|
-55
m
TJ
s
m
a01
2
-60
2,
-65
A.
W \
-70
-75
»' • A !
^
V/.
.
--V -
Freq=8.667GHz
-80
-15
0
■5
-10
5
10
15
Y Position (cm)
Figure 6.20: M easured \Ey\ patterns for the system with a 4 x 1 amplifier array
working at S.667 GHz.
20
Pin=10dBm Pin=20dBm •
15
m
T3
10
z
<
o
oc
LU
u.
-J
Q.
s
<
-10
-15
-20
7
7.5
8
8.5
9
9.5
10
10.5
11
FREQUENCY (GHz)
Figure 6.21: A m plifier gain of th e 2x 2 am plifier array in th e concave-lens system
w ith a with different P{n.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
5
Loss from horn and lens
Insertion lo ss from array
CO
01
O
AA -
-10
-15
-20
7
7.5
8
8.5
9
9.5
10
10.5
11
FREQUENCY (GHz)
Figure 6.22: System loss of th e concave-lens system w ith a 2 x 2 array. This loss is
caused by th e horn, lens and unbiased array.
-45
-50
|
Amp ON
Amp OFF
No Amp
-55
■o
>.
UJ
-60
■o
2
m -65
a*
a
S
-70
-75
-15
-10
-5
0
5
10
15
Y Position (cm)
Figure 6.23: M easured \Ey\ p attern s for the system w ith a 2 x 2 amplifier array
working at 8.667 GHz.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
6 .3 .3
S y s te m w ith th e 5 x 4 A m p lifie r A rray
For the purpose of raising the o u tp u t power level, more am plifier units are added
into the slab system and they are arranged to be a 5 x 4 array. T h e area of this array
is 12 cm wide and 30 cm long. T he whole concave lens system is also covered by a
m etal plate with a w idth of 12 inches so th a t m ost of the scatte red waves can be
stopped by this plate and are guided back to the slab system. T he amplifier gain,
system gain and in p u t power vs o u tp u t power and the field p a tte rn s are measured
under this circum stance.
The amplifier gain and to tal system loss are shown in Fig. 6.24 for the system
w ith a metallic top. The gains for P,n = -4 dB m and 9 dBm are close to each other,
but the gain for P,n = 25 dBm drops about 5 dB or more over some frequency
ranges.
This m eans th at the 5 x 4 array works in the saturation region for this
high input power. T he good array gains appear over the range of S.6—9 GHz and
10.55—10.S5 GHz, and the m axim um value is ab o u t 38—44 dB. T he to tal loss due
to horn radiation to air, lens scattering and array scattering to the guided waves
is about 20 to 40 dB over the whole frequency range. Note th a t the loss has the
m inim um values when the am plifier gains are high, and therefore the system gains
can not reach a high value. For exam ple at 8.87 GHz and 10.724 GHz th e amplifier
gains are 23 dB an d 38 dB and th e total losses are 26 dB and 40 dB. Thus the
system gains are only -3 dB and -2 dB at these two frequencies. To explain these
low gains, further exam ination of th e field p a tte rn is necessary. T he |£7^| patterns
at these two frequencies are shown in Fig. 6.25 and Fig. 6.26. Even th e amplified
p attern is much higher than th a t of the “Am p O F F ” system and also keeps the
first-order Gaussian-beam shape. Its am plitude still can not surpass the am plitude
for “No Amp” . T his tells us why th e system gain is negative. O ne also can see that
the field patterns become narrow er a t higher frequencies and results in the horn
receiving more power at higher frequencies. T his explains why th e system gain is
higher at 10.724 GHz rather at S.87 GHz.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
124
Since the flatness of the m etal plate located above th e system largely affected
the Ein of each am plifier unit and th e output beam E out of the array, a heavy block
was placed on this plate. This block was slowly moved around this top to adjust
the flatness so th a t the proper am plitudes and phases for E{n could be obtained. In
the m eantim e, m oving the block on this top also adjusts the E amp to have coherent
am plitudes and phases th at constructive o u tp u t waves can be achieved. In Fig.
6.27, the amplifier gain and loss for the system w ith a “adjusted” m etallic top is
shown and has the m axim um am plifier gain of 30 dB at S.S2S GHz as P,„ = -3 dBm .
T he o utput power vs frequency is shown in Fig. 6.28 and the d ata shows th at the
system gain is ab o u t 7.5 dB as P,n = -3 dBm . T his system gain is higher th an th a t
for th e system w ith a nonflat top, and em phasizes th a t th e system perform ance not
only depends on th e ability of th e amplifier array b ut is also highly sensitive to the
flatness of the plate. Furtherm ore, note th a t th e bandw idth of the positive system
c.
t
t
•
gain is 70 MHz, and this reveals th a t the difficulty of adjusting th e E{n to let the
f.
o u tp u t power are yet to be investigated.
an ten n a generate high output power. Efforts to broaden the bandw idth for higher
T he Pout vs Pin and system gain vs P{n at S.82S GHz are shown in Fig. 6.29 and
|
Fig. 6.30. From Fig. 6.29, we can find th at th e “ad ju sted ” metallic top saves about
I
I
•
20 dB for Pout w ith the fact th a t th e 5 x 4 array highly scatters the guided waves.
T he m axim um o u tp u t power is about 9 dBm as P tn = -6 dBm and P,„ = 10 dBm .
;
T he system gain has a m axim um value of 14 dB w ith P,„ = -6 dB m and the gain
?
t
decreases with P(n > -6 dBm. VVe see that -6 dB m is the maxim um input power for
the 5 x 4 array to work in the linear region. M oreover, note th a t the m axim um input
power for the 5 x 4 array to work in the linear region is less th at for th e 4 x 1 array
which was discusses in Section 6.3.2. This is due to the third- and forth-colum n
am plifier units in th e 5x 4 array being satu rated by the amplified power from the
first and second colum n amplifier units.
T he m easured \Ey\ patterns are plotted in Fig. 6.31. The profile of \Ey\ (Amp
1#*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
125
ON) is a b o u t 10 to IS dB above th a t of \Ey\ (No A m p) for the
— 1
> y > 9 cm
region, an d this indicates th at th e positive system gain appears at 8.828 GHz. The
am plified \Ey \ has a dip in the m iddle of the field p a tte rn an d looks like the secondorder G aussian beam m ode. Since the horn ap ertu re is from -4.5 cm to 4.5 cm . then
only som e p art of th e amplified energy is received. If th e Equations (5.4) and (5.5)
are again used here, then an additional gain of 5.68 dB needs to be added into
the o u tp u t power level. T hat is to say, the m axim um Pout in Fig. 6.29 should be
14.68 d B m instead of th e 9 dBm cap tu red by the horn.
In C h a p te r 5, the m axim um o u tp u t power for th e convex-lens system w ith a 4 x
1
M ESFE T array is about 5 dBm (see Fig. 5.30), and th e system with a 5 x 4 MMIC
array in this chapter has output power up to 14.68 d B m . Obviously, an im provem ent
of 9.68 dB for the o u tp u t power level has been successfully achieved. T his means
t
th at a 5 x 4 MMIC array generates alm ost 10 tim es th e power th a t a 4 x 1 M ESFET
i
array does. However, 14.68 dBm is ab o u t 30 m W an d is still not high enough for
s’
practical applications. Therefore, using high-power M M ICs (up to several w atts)
f.
will be necessary for th e future im provem ent of th e 2D power combining system .
»:
|
t
|
1**
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
126
50
Amp Gain (Pin=-4dBm) -
«<n
o
—I
E
v
«
>»
(O
■o
c
c
40 - A m p Gaiiv(Pin=9dBm>30 .
Amp Gain (Pin=25dBm) Total Loss -
20
10
a
®
-10
a.
-20
E
<
-30
-40
-50
8
8.5
9
9.5
10
10.5
11
11.5
12
FREQUENCY (GHz)
Figure 6.24: o x 4-array gain for different Pin and the to ta l loss. T he total loss is
due to horn radiation to air, lens scattering and array scattering. T his system has
m etallic top.
-30
Amp ON
Amp OFF
No Amp
-35
_
-40
E
jo
-45
^
-50
<n
3
(0
o
•55
S
-60
■o
£
— ■! —
-65
-70
-75
-15
-10
5
0
5
10
15
Y Position (cm)
Figure 6.25: M easured \Ey\ p attern s for 5 x 4 array working at S.S7 GHz.
m?
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
127
Amp ON
-Amp OFFNo Amp
_
-40
S.
-45
E
m
■a
£3
M
aa>
S
-60
-65
Freq=10.724GHz
5
0
5
10
15
Y Position (cm)
Figure 6.26: M easured \Ey\ patterns for 5 x 4 array working at 10.724 GHz.
40
A m plifier G ain ------
- Total Loss -----
30
20
10
m
■D
-10
-20
V 1
-30
-40
-50
8
8.5
9
9.5
10
10.5
11
11.5
12
FREQUENCY (GHz)
Figure 6.27: Amplifier gain and to tal loss for the concave-lens system with 5 x 4
array. The system is with a adjusted m etallic top.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
10
Pin
P out (AMP OFF)
Pout (AMP ON)
E
m
T
3
>
2o
CL
0
10
3
a.
1
-15
20
-25
30
8.5
8.6
8.7
8.8
9
8.9
9.1
9.2
9.3
FREQUENCY (GHz)
0
X
......:.........a
■■
E
m
■o
3
o
0
.
-10
X"
... i r Q...
-20 .................... ........i .........j#:.....
i
X''"
j . ' ' r........ jq:....
; -B
*■#....1
-30
•
-50
........
Y "
..X "
-40
--------
....
10
AMP OFF (w//o top) -e—j
A M P O N liki/n ton) —
1—•
AMP OFF w/ top) E>• I
AMP ONj
L
^ X.
£ ___ I \ y I
20 ------- 1--------1--------1--------1-------- ....... -| -
..........
Figure 6.2S: Pout vs frequency. T he system is w ith a adjusted m etallic top.
J3” :
^
\
BT
-60
-70 _______ 1_______ L
-30 -25 -20
_ i ----------- i----------- i _____
-15
-10
-5
0
Pin (dBm)
Figure 6.29: P,„ vs Pout at S.S2S GHz.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
_____
10
129
20
System with m e ta llic top @ 8.828G H z
15
10
5
0
•5
-30
-25
-20
-15
-10
-5
5
0
10
Input Power (dBm)
Figure 6.30: System gain a t 8.S2S GHz.
-10
; No AM P
-15
AM POFF-4-—
iAMP ON -EJ--
-20
E
m
2,
-25
UJ
-30
Q
111
cc
3
tn
<
-35
-40
UJ
-45
-50
-55
-60
-15
-10
5
0
5
10
15
Y P osition (cm)
Figure 6.31: M easured \Ey\ patterns for 5 x 4 array working at 8.828 GHz.
1**
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Chapter 7
Conclusions and Future Research
7.1
C o n c lu s io n s
A two-dim ensional quasi-optical power combining system based on a dielectric slab
was d em o n strated for the first tim e. This system can be used as an active planar
resonator or a planar am plifier system in which active E-plane Vivaldi antennas are
laid on th e top surface or underneath the slab. This 2D QO system also provides an
excellent p ro to ty p e for th e future quasi-optical power com biner in the millimeterand subm illim eter-w ave region using m ature MMIC m anufacturing techniques.
►
'
i
»
1
The theoretical and experim ental studies of a 2D power combining resonator
was presented in C h apter 3 w ith respect to the TE and T M modes. The passive
characteristics of the resonator provide the details of m ode resonant frequencies.
mode cutoff frequencies, and cavity modes for designing th e active resonator on
;
the dielectric slab or sem iconductor substrate. Experim ental results for the active
resonator, including free-running and injection-lock operations, show th at this 2D
resonator is an excellent single-m ode source for the future p lan ar quasi-optical power
combining system s.
;
In C h a p ter 4, the im pedance m atching and TE-m ode coupling between the ta-
i
pered horn and th e HDSBVV system has been investigated. T h e propagation con­
stants in th e HDSBW and th e tap ered horn are also studied and applied to achieve
im pedance m atching. T he reflection coefficient between th e feeding horn and the
slab system is then reduced significantly to 0.005. The propagation constants also
provide clues on the right dim ensions for the dielectric slab and th e tapered horns
to have good im pedance m atch. T he theoretical studies for m ode coupling give im­
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
131
portant inform ation th a t m ultiple modes will appear inside the slab even when only
a single rectangular waveguide m ode is injected to th e HDSBW system . Measured
field patterns m atch the theoretical d a ta for mode coupling.
In C hapter 5 an d 6 a design m ethodology for the 2D QO power combining
system is presented. Locating the active Vivaldi antenna array underneath the slab
system successfully reduced beam m ode pertu rb atio n from the array. T h e surface
wave patterns of th e active HDSBW system s with the M E S FE T /M M IC amplifier
units on top or underneath slab were also m easured, and provide inform ation on
field p erturbation, beam forming, and beam scanning. Different optical lenses are
also applied to the 2D QO system , and the m easured results strongly suggest th at
th e concave-lens is more ap p ro p riate for the 2D QO system than th e convex-lens.
In C h ap ter 6 im proving th e o u tp u t power level of th e slab am plifier system
has been achieved by replacing th e M ESFET transistor with MMIC chips, and by
placing the am plifier units in th e m etallic carrier to stop energy leakage through
j
th e antenna su b stra te to air. M easurem ents of S param eters and radiation patterns
f
from a single am plifier unit underneath the system were also presented. From these
;
S-param eter m easurem ents, th e real combining power generated from th e amplifier
■
array can be estim ated .
1
The radiation p attern s of th e m etal-strip leaky-wave antenna placed on the top
;
f
j
of the passive HDSBW have been characterized and are described in Appendix A.
This quantifies beam scanning behaviors at different frequencies.
|
patterns from th e m etal strips scan 10 degrees per 1 GHz shift, and show th at this
I
leaky-wave an te n n a is ap propriate as a radiating end for the HDSBW system .
7.2
T h e radiation
F u tu re R e se a r c h
In order to fu rth er th e tw o-dim ensional quasi-optical power com biner for future
applications, m ore experim ental and theoretical work needs to be explored to provide
I
i
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
d etailed inform ation for future com puter added engineering.
T his would provide m odifying the 2D slab resonator by building a partially
tra n sp a ren t curved reflector, a m etal top ground to the slab 2D cavity, and ap ertu re
an ten n as to generate TM cavity modes. T h e 2D slab resonator described in C hapter
3 is an open T E ty p e cavity w ith one ground plane and a curved m etal reflector.
In order to employ th e slab resonator as th e signal source for the H DSBW system
shown in Fig. 1.5, a partially tran sp aren t curved reflector is necessary. Presum ably
this would be sim ilar to th e curved reflector b ut a gold-film grid in the m iddle area
as shown in Fig. 2.4. T he w idth of the strips. </, and th e gap between th e strips.
d' . would be determ ined by th e spot size of th e TE or TM beam m ode. Since the
curved reflector in th e open T E type slab resonator is a big discontinuity which
g reatly decreases th e Q value of th e cavity, a m etal top would be added to the
slab resonator so th a t no leaky radiation from the curved boundary occurs.
For
generating TM cavity m odes, T he Vivaldi antenna unit m ay be inappropriate. An
altern ativ e choice m ay be th e rectangular ap erture antenna unit shown in Fig. 7.1.
w hich has a m icrostrip line and active devices on the back side.
In C hapter 6 a m o derate o u tp u t power was achieved by improving th e lens and
a n te n n a stru ctu re and by using the M iniC ircuits am plifier chips. Since a power
com biner with high o u tp u t power up to 10 w att or 100 w att level is necessary for
p ractical use, em ploying higher power chips (up to several w atts per chip) to th e unit
am plifier or adding parallel p late to the HDSBW system is one of th e likely ways
to reach this goal. In th e open HDSBW amplifier system , the scattering loss due
to th e convex and concave lenses and th e amplifier array is unavoidable. Usually,
th e am plifier array is m ajor cause of large scattering loss which can not be easily
com pensated by th e am plifier gain. T here are two options to improve the scattering
loss and the system perform ance. One is to install the high power chips in the
u n it amplifiers to have higher am plifier gain: at the same tim e, fewer array elem ents
would be required so th a t th e scattering loss can be significantly reduced. T he other
ft*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
133
m eth o d is to add a top ground plane to th e HDSBW system to stop th e scatte rin g
loss from the lens an d th e amplifier array.
In the second option, th e HDSBW
system can accom m odate a large array which may em ploy high power chips; but th e
conductor loss from th e parallel plates along the whole system should be considered,
too. Moreover, for th e HDSBW system to am plify the TM slab beam m odes instead
of th e T E modes, th e ap ertu re antennas shown in Fig.7.2 will be applied w hether
th e HDSBW system is an open or closed waveguide. T h e ap ertu re an ten n a for th e
H D SBW am plifier system is sim ilar to th e ap ertu re an ten n as in the T M -ty p e slab
resonator, it m ay also provide less scatterin g to the guided beam m ode th a n th e
Vivaldi antenna because of its small a p ertu re area.
O th er work includes im proving the D C -to-R F efficiency and total rad iated power,
verifying the th eo retical d a ta of the reflection coefficient in th e feeding waveguide
(see C hapter 4) , an d developing a m odeling tool to m atu re the 2D slab power
!
I/.
com biner for th e fu tu re applications w ith MMIC m anufacturing techniques.
ir
IE
It
t
c
i
i
5
c
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<
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1
i
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
134
GROUND PLANE
DIELECTRIC SLAB
( dielectric constant=2.55)
, , CROSSSECTIONAL
VIEW
(a)
SLOTS
H
SUBSTRATE
FLip _ c h ip
MICROSTRIP
dielectric c o n s ta n ts 0.5)
POWER AMPLIFIER
GROUND PLANE
RECEIVING PART
RADIATING PART
S2
( b )
TOP VIEW
FLIP-C H IP
POWER AMPLIFIER
( d )
MICROSTRIP
SLOT
BOTTOM VIEW
SUBSTRATE
FIGURE 2
Figure 7.1: T he rectangular-aperture antenna unit under a closed slab system.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
AMPLIFIERS UNDER SLAB
DIELECTRIC
SLAB
Pin
Pout
TRANSMITTING.
HORN
GROUND PLANE
LENSES
(a)
2D PHOTONIC
BAND-GAP REGION
TOP VIEW
DIELECTRIC
SLAB
2D PHOTONIC
BAND-GAP
REGION
c io t s
b L U ,b
(c)
T58W
CROSSSECTIONAL
VIEW
MICROSTRIP
SLOT
FLIP-CHIP
POWER AMPLIFIER
MICROSTRIP
BOTTOM VIEW
FLIP-CHIP
POWER AMPLIFIER
mm
(b)
2D PHOTONIC
BAND-GAP
REGION
(d)
FIGURE 1
Figure 7.2: T he HDSBW system with the ap ertu re an ten n a am p lifers.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
136
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IE E E A P -S Int. Sump. Dig., pp. 1292-1295, 1995.
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[72] D. VV. Tu, S. VV. Duncan, A. Esakandarian, B. Golija, B. C. Kane. S. P.
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[78] G. M. Rebeiz, “M illimeter-wave and terahertz integrated circuit antenna."
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[SO] J. Lin and T. Itoh, “Active integrated antennas,” IE E E Trans. Microwave
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[82] J. A. Navarro, Y.-H. Shu and K. Chang, “W ideband integrated varactortunable active notch antennas and power com biners,” IE E E M T T -S Interna­
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[84] W .P. Shillue, S.-C. VVong, and K.D. Stephan, “M onolithic IMPATT
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2
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[89] R. A. York and R. C. C om pton, “Q uasi-optical power com bining using mutually synchronized oscillator arrays,” IE E E Trans. Microwave Theory Tech..
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1
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•
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[91] J. Birkeland and T. Itoh, “A 16 element quasi-optical FET oscillator power
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[92] A. Mortazawi, H. D. Foltz, and T. Itoh, ~A periodic second harm onic spatial
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[93] P. Liao and R. A. York, “A high power two-dim ensional coupled-oscillator
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144
[96] T. Ivanov and A. M ortazaw i, “One- and tw o-stage spatial am plifiers," IE E E
Trans. Microwave Theory Tech., vol. 43, no. 9, pp. 2138-2143, S ept. 1995.
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increased active device density,” 25th Eur. Microwave Conf. Proc., pp. 320322, Sept. 1995.
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[101] J. Hubert, J. Schoenberg, an d Z. B. Popovic, "High-power hybrid quasi-optical
Ka-band am plifier design,” I E E E M T T - S Int. Microwave Sym p. Dig., pp. 585588, May 1995.
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ls
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[102] H. S. Tsai and R. A. York, "Q uasi-optical am plifier array using direct integra­
tion of MMICs and 50 fi m ulti-slot a n te n n a s,” I E E E M T T - S Int. Microwave
Symp. Dig., pp. 593-596. M ay 1995.
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circuits,” I E E E Microwave Guided Wave Lett., vol. 5, pp. 180-182. June 1995.
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[
[104] A. Alexanian, H. Tsai, and R. A. York. "Q uasi-optical traveling wave amplifiers,” IE E E M T T - S Int. Microwave Sym p. Dig., pp. 1115-1118. M ay 1995.
|
r
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[105] J. T. Delisle, M. A. Gouker, and S. M. Duffy, "45-GHz MMIC power com bining
using circuit-fed spatially com bined array ,” I E E E Microwave Guided Wave
Lett., vol. 7, pp. 15-17, Ja n . 1997.
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I
[106] S. Hollung, J. Viam and Z. B. Popovic, "A bi-directional quasi-optical lens
amplifier” , I E E E M T T - S Int. Microwave S ym p . Dig., pp. 675-678. June 1997.
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Academic Press, 1974.
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1991.
[109] H. Meinel, “A 30-GHz FE T -oscillator using fin line circuitry,” Proc. 11th E u­
ropean Microwave Conference Digest, pp. 297-300. 1981.
[110] T. VV. Nuteson, Electromagnetic Modeling o f Quasi-Optical Power Combining.
Ph.D. D issertation. N orth C arolina S tate U niversity. 1996.
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145
[111] Y. T. Low, Antenna Handbook .New York: Van Nostrand Reinhold C om pany
Inc., 19S8.
[112] D. Nghiem, J. T. W illiams, D. R. Jackson, and A. A. O liner."E xistence of a
leaky dom inant mode on a m icrostrip line w ith an istropic su b strate : theory
and m easurem ent.” IEEE M TT-S Dig., pp. 1291-1294. 1993.
i-ir.
tt
?
I
i
r
t
iL
f>
\
i
c
f;
i
i
5^
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
146
Appendix A
Leaky-Wave Antenna in the 2-D Slab System
A common feature of leaky-wave antennas is th a t their radiation patterns depend
on frequency.
Thus th ese antennas can be used to generate frequency-scanning
radiation beam s. M any kinds of leaky-wave antennas have been investigated in past
years [111]: for exam ple edge-slot array antenna, tap ered dielectric-rod antenna,
periodical dielectric an ten n a, and dielectric-grating an ten n a. The leaky dom inant
mode on a m icrostrip line with isotropic su b strate was first found by Nghiem et
al. [112]. They indicated th a t even when only one m etal perturbation is placed on
the substrate, there is leaky radiation from this m etal a t some frequency. To get
stronger leaky radiation, building m ore m etal strips on th e substrate is necessary.
One way to build the leaky-wave an ten n a on the su b strate is selecting a periodic
1
metal grating. D iffraction from the m etal grating switches the guided waves into
|
leaky waves.
j.
a
The HDSBW system with the leaky-wave antenna on its top is shown in Fig.
'i
1.5, and the antenna can be built uniform strips, tap ered strips and nonuniform
]
strips as shown in Fig. A .I. The advantage of building a planar m etal-strip leaky-
i
wave antenna is th a t it is conformal and m onolithic. T h e T E Gaussian beam m ode
;
propagating along th e slab can be easily transfered to free space by the induced
x
current on the strips. W ith different separation (d), w idth (W ), and length (L) of the
[
m icrostrip lines, different leaky-wave propagation constant and radiation patterns
e
;
for the stru ctu re can be calculated using G alerkin’s m ethod in the Fourier-transform
domain.
T he G alerkin’s m ethod approach also allow us to obtain the radiation
pattern from near field in the Fourier dom ain.
Before startin g any theoretical prediction of the leaky-wave radiation patterns,
the experim ental work for understanding th e behavior of th e radiation has been
accomplished by placing a uniform nine-strip antenna on th e passive slab waveguide
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
L47
w ith T E Gaussian modes inside. T he space of th e m etal strips is 3 cm. and the w idth
of the m etal strips is eith er 1/S inch or 1/16 inch. T he TE G aussian beam m ode is
launched by the tap ered E-plane horn described in C hapter 4. T he m easured E y
p a tte rn across th e passive slab waveguide is shown in Fig. A.2 when the slab is
with and w ithout the leaky-wave antenna. W ith th e antenna, th e am plitude of th e
surface E y p a tte rn drops 2.5 dB and 4.5 dB for 1/16-inch-wide and 1/8-inch-wide
strip a t 9 GHz. This reveals th a t p art of the guided TE-m ode energy is radiated
into free space. Also, one can see th a t wide-strip an te n n a radiates m ore energy th an
narrow -strip an ten n a does.
In order to observe th e frequency-scanning behavior of the leaky-wave antenna,
th e l/S-inch-w ide m etal-strip an ten n a was used again, and T E G aussian beam m ode
was established. The frequency-scanning radiation patterns for this leaky-wave an ­
ten n a from 9 GHz to 11 GHz is shown in Fig.
A.3. The beam scanning angle
of the leaky-wave an tenna is 15 degrees per GHz. We can see th a t the shape of
th e radiation p attern s is alm ost constant during frequency shifts. This is a good
}
characteristic of th e leaky an ten n a built in the H DSBW system.
i
tt
i
ii
i
i
*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
14S
i x
^ jr
/
leaky-wave radiation
/
4
/
4
4
—Z
dielectreic
ground plane
/■ Y
Uniform strip-loaded dielectric slab
Ajr
/
leaky-wave radiation
/
4
/
4
/
—z
sunace
waves
dielectreic
ground plane
Tapered strip-loaded dielectric slab
A*
leaky-w ave radiation
Ai r
4
4
4
4
Z
waves
dielectreic
ground plane
?y
Nonuniform strip-loaded dielectric slab
Figure A .l: The 2D H D SB W system with th e leaky-wave an ten n a structures
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
149
-
S
m
dN)
a
’A
A
--
-10
v
-15
E
o
z
-20
-25
No^leaky-wave antenna Antenna w/ nine 1/16"-strips Antenna w/ nine 1/8"-strips
-30
-35
-10
-8
-6
-4
-2
0
2
4
6
8
10
Y position (cm)
i
\
t
r
Figure A .2: Fields across the system w ith m etallic strips. T he space betw een strips
is 3 cm .
r:
9GHz —
10GHz —
11 GHz °
o
■o
c
o
CQ
■<o0
cr
§j
-10
(0
5I
>*
J£
-15
ca
v
-20
-25
•40
-30
-20
-10
0
10
20
30
40
PHI (degree)
Figure A .3: Beam scanning of the leaky-wave antenna. Scanning angle is 15 degrees
for 1 GHz
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
150
Appendix B
S papam eter of the MiniCircuits ERA-1
ERA-1 am plifier is a Darlington circuit including two heterojunction bipolars tran­
sistors (H BT) and is shown in Fig. B .l. The H BT in ERA-1 is a n-p-n transistor,
and its e m itte r an d base are m ade of Alo.3 Gao.7 As and GaAs, respectively. The
impedace of th e ERA-1 is designed to m atch a 50-ohm system , and can be applied
to the m icostrip-line and slot-line circuits. T he m icostrip lines an d slot lines should
be fabricated close to 50 ohms as posssible to realize full specifications of the ERA-1
chip. The typical biasing circuit for ERA-1 is shown in Fig. B.2. Usually, it requires
DC blocking capacitors at the input and o u tput ports, with a com m on o u tp u t port
and bias term ial. An RF choke in series with a biasing resistor is necessary to block
RF signal to th e bias suppliers. T he RF choke should offer an im pedance of at
least 500 ohm s a t th e lowest operating frequency, and be free of resonance at the
highest operating frequency. T he S parem eters and th e perform ance of the EAR - 1
are shown in Table B l and B2.
R1
Output/Bias
A /W
Input
Figure B .l: D arlington circuit configuration of ERA-1 am plifier chip.
TABLE Bl. S Paremeter of the ERA-1 Amplifier Chip
ERA-1
Icc=40 mA
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
^ bias
Vc c
w v
RFC
OUT
block
block
Figure B.2: Typical biasing configuration of ERA-1 am plifier chip.
FREQ.
GHz
Mag
.100
.550
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
0.23
0.23
0.23
0.23
0.26
0.30
0.31
0.28
0.23
0.26
Ang
177.06
165.79
154.34
125.98
99.10
82.07
70.12
64.88
61.70
66.57
Mag
4.01
4.02
3.95
3.97
3.83
3.53
3.40
3.17
3.43
3.07
S22
S12
S21
Sll
Ang
176.01
159.02
141.86
105.21
64.56
31.00
-5.44
-37.92
-75.62
-113.35
Mag
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.14
0.13
Ang
Mag
-2.74
-11.4
-20.87
-41.71
-66.81
-84.38
-110.94
-134.20
-163.71
-191.95
0.16
0.17
0.18
0 .21
0.24
0.27
0.29
0.32
0.35
0.38
K
Ang
178.86
163.26
151.35
131.70
116.94
102.47
80.32
60.17
37.57
22.12
Performance At Various Device Currents
TABLE B 2 . ERA-1 i
Device
Current
(mA)
Gain
Gain
(dB)
40
45
50
12.2
12.35
12.4
Flatness
to 2 GHz
+-(dB)
0.27
0.27
0.28
VSWR
IN
<31GHz
1.48
1.51
1.52
VSWR
OUT
(31GHz
IP3
(31GHz
(dBm)
1.38
1.39
1.40
25.5
27
29
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Noise
Figure
(dBm)
5.3
-----
7
Pout QldB
Comp.
(dBm)
10.8
12.1
13.2
1.03
1.02
1.03
1.00
1.00
0.99
0.98
1.03
1.03
1. 12
A ppendix C
M aple Programs
Progarm 1:
* * * * * * * * * * * * I*** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
This program is designated to integrate results for Hermite polynomial
Filename: Hm_Hem_transfer.ms
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
> Digits :=4 ;
> with(orthopoly) ;
> for j from 0 by 1 to 10
> do
>
H(j,x);
>
od;
1
2 x
2
4 x
- 2
3
8 x
- 12 x
4
16 x
5
5
32 x
2
- 48 x
3
3
- 160 x
+ 120 x
4
2
6
64 x
- 480 x
7
128 x
9
512 x
+ 720 x
5
- 1344 x
8
256 x
+12
6
- 3584 x
- 120
3
+ 3360 x
- 1680 x
4
2
+ 13440 x - 13440 x + 1680
7
5
3
- 9216 x + 48384 x - 80640 x
+ 30240 x
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
10
1024 x
8
- 23040 x
6
+ 161280 x
4
2
- 403200 x + 302400 x - 30240
> for j from 0 by 1 to 10
> do
>
He(j,x):= simplify(2**(~j/2)
> od;
>
He(j,x):= simplify(2**(-j/2)
> od;
He(0,
x) := 1
He(l,
x) := x
*
H ( j ,x/sqrt(2)));
*
H ( j ,x/sqrt(2)));
2
H e (2, x) :- x
He(3,
x)
:= x
- 1
2
(x - 3)
4
2
H e (4, x) := x - 6 x + 3
4
2
He(5, x) := x (x - 10 x + 15)
6
He(6, x) := x
He(7, x)
H e (7, x)
- 15
105)
:= x (x - 21 x
8
6
105)
2
8
He(10, x) := x
2
+ 45 x
6
4
2
:= x (x - 21 x + 105 x 6
4
2
H e (8, x) := x
He(9, x) := x
10
4
- 15 x
+ 105 x
4
-
- 28 x + 210 x - 420 x
6
4
(x - 36 x
8
- 45 x
+ 378 x
6
+ 630 x
- 1260
4
- 3150 x
+
2
x
105
+ 945)
2
+ 4725 x
- 945
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
P rogarm 2:
*************************************************************************
This program is used to calculate radius, R, for concave lens which
has focal length, 28.54cm. The slab is Rexolite.
•mr
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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F = focal length
Er_slab = dielectric constant of slab
Er_lens = dielectric constant of lens
>
>
>
>
>
>
f := 28.54;
Er_slab :=2.55 ;
for Er_lens from 1 by 0.2 to 2.0
do
print ( Er_lens, 2*f *( sqrt( Er.lens / Er_slab) -1 ) );
od ;
f *
3(53(5
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newpage P rogarm 3:
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This program is to calculate beamwidth in lense and in slab by using
the equations in Mink's paper.
The values of W_min and W_max are the same as obtained in programs
of convex_S_So_W_Wo .ms and horn_size_beam_iterationl.ms
filename:W_max_min_paper.ms
W_min = minimum beam spot size
W_max = maximum beam spot size
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> W_max_cm:=sqrt(2)* sqrt(Zt/beta) * (Zt/2/f * (l-Zt/2/f) )“(-0.25) ;
1/2 / Zt \l/2
2
I------ I
\b eta /
W_max_cm := 1.189207115 ---------------------/
/
Zt W . 2 5
IZt 1 1 - 1 / 2
I
\
1--\
f
1I
/I
------------ 1
f
/
cm:=sqrt(2)* sqrt(Zt / beta) * (2*f/Zt -1)~.25
1/2 / Zt \l/2 /
W_min_cm := 2
\ •25
f
1/2 / Zt \l/2 /
f
1 2 --1--- 1
\beta/
\
Zt
\ •25
- 11
/
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
155
> Zt := 28.54;
> beta := 2.0543;
# beat =2.0543 is for 8 GHz. For other frequency, you need put a new
value for beta.
> f := 28.54;
> print ( simplify(W_max_cm) , simplify(W_min_cm) );
7.454612047, 5.271206729
•4^
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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