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Design and analysis of microwave/millimeter-wave active arrays using a multilayered packaging architecture

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DESIGN AND ANALYSIS OF MICROWAVE/MILLIMETER WAVE
ACTIVE ARRAYS USING A MULTILAYERED PACKAGING
ARCHITECTURE
A Dissertation Presented
by
SEAN M. DUFFY
Submitted to the Graduate School of the
University of Massachusetts Amherst in partial fulfillment
o f the requirements for the degree of
DOCTOR OF PHILOSOPHY
May 1999
Department of Electrical and Computer Engineering
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U M X Number:
9932307
C o p y r ig h t 1999 b y
D u f f y , S e a n M a lc o lm
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©Copyright by Sean M. Duffy 1999
All Rights Reserved
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DESIGN AND ANALYSIS OF MICROWAVE/MILLIMETER WAVE
ACTIVE ARRAYS USING A MULTILAYERED PACKAGING
ARCHITECTURE
A Dissertation Presented
by
SEA N M. DUFFY
Approved as to style and content by:
David M. Pozar, Chair
Mark A. Gouker, M ember
Daniel H^'Schaubert, Member
K. STgfrid Yngvesson, Member
Seshu Desu, lltepkrtment Head
Electrical and Computer Engineering
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ACKNOWLEDGEMENTS
First and foremost, I wish to express m y deep appreciation to Dave Pozar. His
help and patience over the years have been greatly valued. Hopefully, I’ve been able to
pick up a little o f his belief and talent in applying the simple basics that often leads to
creative insight. My second round of thanks goes to my supervisors at MIT Lincoln
Laboratory, D avid Snider, Ronald Bauer and M ark Gouker, who provided the necessary
patience and financial support to make this possible. And thanks to my committee
members, Professors Knightly, Jackson, Schaubert and Yngvesson, for spending the time
and effort with me and my work.
Due to my unusual situation, I’ve had the opportunity to work with and have
discussions with a number of good people. M uch o f the fabrication of multilayer circuits
was performed by Christopher Donahue and Brian LaForge and some of the hybrid
assemblies done by Rick Magliocco, Stan Robertson and Lisa Hill. Their high quality
work, openness to experimentation and useful suggestions have been highly valued.
Finally, thanks must go to a group of people who have provided excellent discussions and
suggestions and have made a difference in my work and my life: Pamela Haddad, Chris
Cherry, Steve Targonski, John Delisle, Larry Kushner, and T. Chio.
iv
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ABSTRACT
DESIGN AND ANALYSIS OF MICROWAVE/MILLIMETER WAVE ACTIVE
ARRAYS USING A MULTILAYERED PACKAGING ARCHITECTURE
M AY 1999
SEAN M. DUFFY, B.S.E.E., UNIVERSITY OF MASSACHUSETTS AMHERST
M.S.E.E., UNIVERSITY OF MASSACHUSETTS AMHERST
Ph.D., UNIVERSITY OF MASSACHUSETTS AMHERST
Directed by: Professor David M. Pozar
The design of microwave/millimeter wave active arrays is investigated using a
multilayered packaging architecture. The goal or the packaging technique is to utilize
multichip module (MCM) technologies which offer the advantages of lower cost, higher
reliability and yield. The challenge o f using these technologies for constructing arrays is
achieving efficient and stable operation with substrate characteristics that are not ideal for
conventional microstrip antennas
Several novel circuit elements are studied that allow efficient and stable operation
of microwave/millimeter wave active arrays. Measurements demonstrate that high
radiation efficiency is possible with the cavity backed patch. Approximate and full-wave
models are developed for the cavity backed patch and several similar related antennas.
Novel use of the open end stub, found in many electromagnetic coupled antennas, is
found to lead to enhanced bandwidth and circular polarization perfoimance. The RF via
is presented with an equivalent circuit model and provides a compact, efficient and
isolated transition between layers. Finally, monolithic microwave integrated circuit
V
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(MMIC) amplifiers are placed in individual cavities that provide isolation from other
circuit elements and allow placement o f the device directly on the thermal carrier.
The application o f spatial power combining is used as a demonstration o f the
packaging approach, the modeling of the circuit elements and achieving desired array
characteristics. Design procedures for achieving high combining efficiency arrays and
calculating the radiated pow er are presented. Two single element active antennas and two
4 x 4 arrays will be presented, demonstrating the highest reported combining efficiency to
date, with accurate calculated predictions.
VI
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TABLE OF CONTENTS
ACKNOW LEDGEM ENTS ...........................................................................................
iv
ABSTRACT
v
.....................................................................................................................
LIST OF TABLES
..........................................................................................................
xii
LIST OF FIGURES
........................................................................................................
xiii
Chapter
1.
2.
INTRODUCTION...............................................................................................
1
1.1 Difficulties of Packaging.............................................................................
1.2 Proposed Multilayered Packaging Architecture.....................................
1.3 Area of Focus...............................................................................................
3
4
6
References.............................................................................................................
7
RADIATION EFFICIENCY MEASUREMENTS AND APPROXIMATE
MODELS FO R CAVITY BACKED PATCHES.........................................
9
2.1 Radiation Efficiency M easurements o f Conventional and Cavity
Backed Patches.............................................................................................
2.1.1
2.1.2
2.1.3
2.1.4
11
Far-Field M easurement Technique............................................ 11
W heeler Cap M ethod.................................................................. 15
Input Admittance M ethod........................................................... 18
Summary of Results..................................................................... 21
2.2 Transmission Line Model for Proximity Coupling and Cavity
Backing............................................................................................................ 22
2.2.1 Proximity Coupling....................................................................... 23
2.2.2 Cavity Backing.............................................................................. 25
2.2.3 Validation with M easured Results............................................. 29
2.3 Applications of Transmission Line M odel................................................ 35
2.3.1 An Enhanced Bandw idth Design Technique For
Electromagnetically Coupled Antennas.................................... 35
v ii
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2.3.1.1
2.3.1.2
2.3.1.3
2.3.1.4
Broadband M atching...................................................
Stub Designs................................................................
Proximity Coupled Patch Exam ple...........................
Aperture Coupled Patch Exam ple............................
2.3.2 Single Feed Circular Polarization Design using Proximity
Coupling........................................................................................
36
40
45
51
55
2.3.2.1 Design............................................................................ 55
2.3.2.2 Measured Results......................................................... 55
3.
References..............................................................................................................
59
FULL-W AVE MODEL FOR STRIPLINE-FED RECTANGULAR
APERTURES W ITH AND WITHOUT CAVITY BACKING...................
62
3.1 T heory.............................................................................................................
64
3.1.1 M ethod o f Analysis...................................................................... 64
3.1.2 M ode Layout................................................................................. 67
3.1.3 M atrix Elements............................................................................ 70
3.2 V alidation...................................................................................................... 73
3.2.1
3.2.2
3.2.3
3.2.4
Stripline Fed Slot...........................................................................
Cavity Backed Slot........................................................................
Stripline Fed Patch........................................................................
Cavity Backed Patch....................................................................
73
73
80
83
3.3 Discussion of Antenna Designs and M odel............................................. 86
3.3.1
3.3.2
3.3.3
3.3.4
Numerical Speed...........................................................................
Comparison of YfS, Ysi and Ycav................................................
Finite Sized Ground Plane of Stripline Fed Patch..................
Brief Discussion of the Opening in the Cavity Wall for
the Feed........................................................................................
3.3.4.1 Asymmetric Cavity Opening - Transmission
Line Analogy.............................................................
3.3.4.2 Symmetric Cavity Opening - Transmission
Line Analogy.............................................................
3.4 Convergence................................................................................................
3.5 Num ber o f V ias...........................................................................................
v iii
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86
88
90
92
93
96
98
100
3.6 Radiation Efficiency of Slots in Stripline................................................ 103
References.............................................................................................................. 105
4.
ARRAYS OF STRIPLINE-FED RECTANGULAR APERTURES
WITH AND WITHOUT CAVITY BACKING.............................................
107
4.1 Infinite Array M odel....................................................................................
108
4.1.1 M ethod of Analysis...................................................................... 108
4.1.2 Scanning - Stripline Fed and Cavity Backed Slots................ 109
4.1.3 Scanning - Stripline Fed and Cavity Backed Patches
112
4.2 Active Impedance for Broadside, Small Arrays......................................
115
4.2.1 Active Impedance of I x 4 Array of Cavity Backed Patch... 115
4.2.2 Comparison of Isolated and Infinite Cavity Backed Patch... 122
4.3 Gain M atching Technique for Reducing Active Impedance Effects...
124
4.3.1 Design Procedure.......................................................................
4.3.2 Conductance of Cavity Backed Slot........................................
124
126
4.3.2.1 Infinite Radiation Conductance...............................
4.3.2.2 Isolated Radiation Conductance..............................
4.3.2.3 Comparison of Isolated and Infinite Radiation
Conductance...............................................................
127
128
4.3.3 Relating Isolated Directivity to Cell Directivity.....................
4.3.4 Extension to Cavity Backed Patch............................................
130
133
134
References.............................................................................................................. 137
5.
MULTILAYERED RF INTERCONNECTS..................................................
139
5.1 RF V ia...........................................................................................................
139
5.1.1 Equivalent Circuit M odel...........................................................
139
5.1.1.1 Coaxial Line.................................................................
5.1.1.2 Capture Pads...............................................................
140
142
5.1.2 Validation with Measurements.................................................. 144
5.1.3 Results of Varying Via Diameter and Height......................... 149
5.1.4 W ideband Designs....................................................................... 156
ix
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5.1.5 High Frequency Resonance........................................................
5.1.6 Construction Technique..............................................................
158
161
5.2 Aperture Coupled Striplines with Cavity Backing.................................
162
5.2.1 Development o f Equivalent Circuit M odel............................... 163
5.2.2 Results............................................................................................. 166
References............................................................................................................... 171
6.
BURIED M MIC CAVITIES...............................................................................
173
6.1 Passive Cavity................................................................................................ 174
6.2 Active Cavity................................................................................................. 178
6.3 M M IC Characteristics.................................................................................. 181
References................................................................................................................ 184
7.
APPLICATION OF ARCHITECTURE AND MODELS TO SPATIAL
POW ER COMBINED ARRAYS......................................................................
186
7.1 Introduction....................................................................................................
186
7.1.1 Brief Discussion of Spatial Power Combining.....................
7.1.2 Shortcomings o f 45 GHz A rray..............................................
188
190
7.2 Single Element Active Antenna D esigns.................................................
193
7.2.1
7.2.2
7.2.3
7.2.4
7.2.5
Circuit Elem ents.........................................................................
MMIC M atching.........................................................................
Antenna Impedance....................................................................
M easured Results o f Single Element Active Antenna
Calculation o f Radiated Pow er.................................................
193
195
196
196
199
7.3 4 x 4 Array D esigns....................................................................................
200
7.3.1
7.3.2
7.3.3
7.3.4
Design of Arrays.........................................................................
Antenna Impedance....................................................................
M easured Results........................................................................
Tabulation of Losses...................................................................
202
203
207
215
7.4 Discussion of M easurements..................................................................... 218
7.5 Discussion of Results................................................................................ 219
References............................................................................................................... 220
x
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8.
CONCLUSION.....................................................................................................
222
APPENDICES
Av APPROXIM ATION.......................................................................................
TRANSM ISSION LINE M ODEL.....................................................................
BASIS FUNCTION EXPANSIONS................................................................
SPECTRAL DOM AIN GREEN’SFUNCTIONS...........................................
CAVITY REPRESENTATIONS......................................................................
224
226
228
230
233
BIBLIOGRAPHY.............................................................................................................
236
A.
B.
C.
D.
E.
xi
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LIST OF TABLES
3.1
CPU time for the full-wave model and Momentum for the four antenna
geometries............................................................................................................
87
5.1
Measured and calculated S n for RF via of Figure 5.5.................................
145
5.2
Measured and calculated S 2 1 for RF via of Figure 5.6.................................
146
7.1
Typical (average) MMIC characteristics..........................................................
217
7.2
Summary o f peak results for two array designs..............................................
218
7.3
Tabulation of losses for two array designs.......................................................
218
A.
1
Momentum calculations of resonant resistance (x 50 Q.) of patches as
feed height varies................................................................................................. 224
x ii
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LIST OF FIGURES
Figure
Page
1.1
Cross-section of multilayered packaging architecture...................................
5
1.2
Cutaway view of array architecture..................................................................
5
1.3
Organization and flow of work..............................................................
7
2 .1
Top and side view of cavity backed patch..........................................
10
2.2
Geometry and layout of conventional and cavity backed microstrip
antennas................................................................................................................
12
2.3
Side view of far-field gain measurement test setup.......................................
13
2.4
Measured E and H-plane patterns on £,=2.94 substrate, a) cavity backed
patch, b) conventional patch.................................................................
13
2.5
Measured E and H-plane patterns on £[=6.15 substrate, a) cavity backed
14
patch, b) conventional patch.................................................................
2.6
Measured E and H-plane patterns on £[=10.2 substrate, a) cavity backed
patch, b) conventional patch................................................................
14
2.7
W heeler cap measurement with reference plane outside cavity and quarter
wavelength from the patch...................................................................
16
2.8
W heeler cap measurements for £r=2.94.........................................................
16
2.9
W heeler cap measurements for £[=6.15.........................................................
17
2.10
W heeler cap measurements for £[=10.2..........................................................
17
2.11
Input impedance for £[=2.94 conventional and cavity backed patches....
19
2.12
Input impedance for £,=6.15 conventional and cavity backed patches
20
2.13
Input impedance for £[=10.2 conventional and cavity backed patches
20
2.14
Measured radiation efficiency results for the three methods for
conventional and cavity backed microstrip antennas.......................
x iii
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21
2.15
M easured VSWR<2 bandwidth of conventional and cavity backed
microstrip antennas.............................................................................................
22
2.16
Equivalent circuit model of proximity coupled patch....................................
24
2.17
Pictorial representation o f TMo surface wave impinging on
truncated dielectric.............................................................................................
27
2.18
Reflection coefficient o f surface wave diffraction.........................................
28
2.19
M odified transmission line model for proxim ity coupled and/or cavity
backed microstrip antennas................................................................................
29
2.20
M easured and calculated results of proximity coupled patch......................
30
2.21
Calculated results using TL model and M omentum [19] for proximity
coupled patch in [20]..........................................................................................
31
2.22
M easured and calculated results for small cavity on £1=10.2....................
32
2.23
M easured and calculated results for large cavity on e ^ l O .2 ......................
33
2.24
M easured and calculated results for 45 GHz cavity backed patch on
Alum ina.................................................................................................................
34
2.25
Broadband matching problem with equivalent circuit model for proximity
coupled and aperture coupled microstrip antennas.....................................
37
2.26
Bandwidth improvement using stub matching technique............................
39
2.27
Illustration o f matching problem, (a) original parallel RLC, Zpric,
( R n o r m = l - 3 , Q=20, S=2) (b) quarter-wavelength stub, Z*tU
b, (2^=200 Q),
and (c) total input impedance, Z,otai, (Ztotai=Zpric+Zstub)................................
40
Layout and geometry of proximity coupled microstrip antennas: a)
quarter-wavelength stub, b) three quarter-wavelength stub, c) dual stub,
and d) side view..................................................................................................
42
2.29
Detail o f symmetric dual stub design...............................................................
43
2.30
Smith chart plot of measured input impedance for three stub cases for
proximity coupled patch.....................................................................................
48
M easured S 11 for three stub cases for proximity coupled patch..................
49
2.28
2.31
x iv
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2.32 M easured gain for three stub cases for proximity coupled patch................
49
2.33 M easured patterns for quarter wavelength feed at 10.1 G H z........................
50
2.34 M easured patterns for three quarter wavelength feed at 10.1 G H z
50
2.35 M easured patterns for dual stub feed at 10.1 GHz..........................................
51
2.36 Smith chart of simulated results for original aperture coupled stacked
patch [27] and case with optimized dual stub design..................................
53
2.37 Calculated S u o f the original design [27] and dual stub design.................
54
2.38
Backlobe levels for Croq [27] and dual stub design....................................
54
2.39
a) Layout of single feed CP antenna,b) equivalent circuit m odel
56
2.40 M easured and calculated input impedance of single feed CP design
57
2.41
Axial ratio o f single feed CP antenna...............................................................
58
2.42
Spinning linear pattern at 10.0 GHz o f single feed CP antenna...................
58
3.1
Geometries of the four antennas, a) stripline fed slot (SLS), b) cavity
backed slot (CBS), c) stripline fed patch (SLP), and d) cavity backed
patch (CBP).........................................................................................................
63
3.2
Layout and parameters of antennas..................................................................
64
3.3
Reciprocity analysis [1] application at single region of the aperture for
SLP and C B P.....................................................................................................
66
3.4
Layout of modes for SLP and CBP.................................................................
68
3.5
Layout of modes for SLP and CBP.................................................................
69
3.6
Excitation o f slot from feed line......................................................................
69
3.7
Equivalent circuit model for proximity coupled aperture...........................
72
3.8
Calculated data for SLS.....................................................................................
74
3.9
Calculated full wave model and Momentum results and [10]....................
75
3.10
M easured and calculated results of proximity coupled CBS......................
77
XV
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3.11
Measured and calculated results o f proximity coupled CBS.......................
78
3.12 Calculated results of proximity coupled CBS using residue and without
residue o f SLS solution......................................................................................
79
3.13
Measured and calculated results o f proximity coupled SLP........................
81
3.14
Measured and calculated results of proximity coupled SLP........................
82
3.15 Calculated radiation patterns for SLP of Figure 3.14......................................
83
3.16
Measured and calculated results for proximity coupled CBP.......................
84
3.17
Measured and calculated results for proximity coupled CBP.......................
85
3.18
Measured and calculated radiation patterns for CBP in Figure 3.17...........
86
3.19
Conductance of SLS and C B S.............................................................................
88
3.20
Susceptance of SLS and CB S..............................................................................
89
3.21
Conductance of SLP and CB P............................................................................
89
3.22
Susceptance of SLP and CBP............................................................................
90
3.23
Measured results o f proximity coupled SLP without absorber at the
substrate edge.......................................................................................................
91
3.24
Layout of asymmetric and symmetric opening in cavity................................
93
3.25
Equivalent circuit model for asymmetric cavity.............................................
94
3.26
MDS calculation of equivalent circuit model for f r e s = 1 0 GHz, L=1 nH
and (31=90 degrees (at 10 GHz), step freq: 0.5 G H z.....................................
95
3.27
Equivalent circuit model for symmetric cavity openings..............................
97
3.28
Momentum and reciprocity calculation of opening in via wall....................
97
3.29
Pictorial representation of M om entum calculations of y directed
magnetic current strength along slot width using edge modes and two
modes...................................................................................................................
98
Convergence test for CBP with 3, 5, 7, 9 and 11 modes along the slot
length...................................................................................................................
99
3.30
xvi
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3.31
Measured results o f antennas with 0, 2 ,4 , 6 and 14 vias along a side
3.32
Momentum simulations of full CBP, SLP and with 2 shorting vias a side.
3.33
Radiation efficiency o f SLS................................................................................
104
3.34
Radiation efficiency o f 1 x 2 E-plane array of SLS........................................
104
3.35
Radiation efficiency o f SLP and conventional microstrip antenna..............
105
4.1
Calculated power transmission factor results for infinite array of SLS....
Ill
4.2
Calculated power transmission factor for infinite array of CBS.................
Ill
4.3
Scanning behavior o f CBS and SLS.................................................................
112
4.4
Scanning behavior o f CBP and SLP.................................................................
113
4.5
Smith chart plot o f m easured and calculated input impedance of
waveguide simulator for a CBP antenna........................................................
114
Measured active antenna impedance o f isolated and array elements,
1 x 4 E plane array..............................................................................................
117
4.7
Load-pull measurement of typical M M IC amplifier at 10 GHz.................
118
4.8
Measured active antenna impedance of isolated and array elements,
1 x 4 E-plane array with 0.59 XQspacing........................................................
120
Calculated input impedance using full-wave model for isolated and
infinite CBP antenna...........................................................................................
121
Calculated input impedance using full-wave model for isolated and
infinite CBP antenna.............................................................................................
121
4.11
Variation of infinite array impedance with array spacing for CBP.............
122
4.12
Variation of infinite array impedance with array spacing for CBP.............
123
4.13
Variation of infinite array impedance with array spacing for CBP.............
123
4.14
Comparison of Fp approximations for isolated slot with full wave results.
131
4.15
Comparison of closed form expressions with full wave calculated results.
131
4.6
4.9
4.10
x v ii
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101
102
4.16
Comparison o f closed form expressions with full wave calculated results.
132
4.17
Comparison o f closed form expressions with full wave calculated results.
132
4.18
Comparison o f closed form expressions with full wave calculated results.
133
4.19
Measured active antenna impedance of isolated and array elements, 1 x 6
E plane array with 0.59 Xo spacing....................................................................
135
4.20
Calculated active antenna impedance using M omentum of isolated and
array elements, 1 x 4 E plane array with 0.54 X^ spacing............................... 136
4.21
Calculated active antenna impedance using M omentum of isolated and
array elements, 1 x 4 E plane array with 0.8 Xo spacing................................
136
Calculated active antenna impedance using M omentum of isolated and
array elem ents, 1 x 4 H-plane array with 0.8
spacing...............................
137
5.1
Side and top view of RF via geom etry..............................................................
140
5.2
Section of coaxial line...........................................................................................
142
5.3
Equivalent circuit model for RF via...................................................................
142
5.4
Circuit components of cross section.................................................................
143
5.5
Measured and calculated S u data for RF via................................................
145
5.6
Measured and calculated Sot data for RF via of Figure 5.5.........................
146
5.7
Measured and calculated S u data for RF via..................................................
147
5.8
Measured and calculated S u data for RF via.................................................
148
5.9
Input impedance o f HFSS and circuit model calculations for RF via
150
5.10
Input impedance o f HFSS and circuit model calculations for RF via
150
5.11
Input impedance o f HFSS and circuit model calculations for RF via
151
5.12
Input impedance o f HFSS and circuit model calculations for RF via
151
5.13
Comparison o f HFSS and circuit model inductance calculation.................
152
4.22
x v iii
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5.14
Comparison o f HFSS and circuit model capacitance calculation.................
152
5.15
Comparison o f HFSS and circuit model inductance calculation.................
153
5.16
Comparison o f HFSS and circuit model capacitance calculation.................
153
5.17
Comparison o f inductance of RF via versus via height..................................
154
5.18
Comparison o f capacitance of RF via versus via height.................................
154
5.19
Comparison of inductance of RF via versus via height...................................
155
5.20
Comparison of inductance of RF via versus via height.................................... 155
5.21
M aximum frequency for VSW R < 1.5 for 0 GHz to Fmax.............................
157
5.22
M aximum frequency for VSWR < 1.5 for 0 GHz to Fmax.............................
157
5.23
Input impedance of pi network for L = 1 nH and C = 1 pF ............................
159
5.24
M atched transitions at 10 GHz and 38 GHz using proper Dgap/Dvt-a ratio... 160
5.25
Layout and geometry of aperture coupled stripline with cavity backing...
5.26
Equivalent circuit model for aperture coupled stripline..................................
164
5.27
M easured and calculated results for aperture coupled cavity backed
stripline for port 1.................................................................................................
167
Measured and calculated results for aperture coupled cavity backed
stripline for port 2 .................................................................................................
168
M easured results for aperture coupled cavity backed stripline using
symmetric cavity opening...................................................................................
169
Measured and calculated results for aperture coupled cavity backed
stripline for port 1.................................................................................................
170
Measured and calculated results for aperture coupled cavity backed
stripline for port 2 .................................................................................................
170
5.28
5.29
5.30
5.31
163
6.1
Photograph of open cavity with MMIC carrier................................................. 174
6.2
Layout of the passive cavity circuits, a) through line and b) open ended
stubs........................................................................................................................
x ix
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175
6.3
Measured and calculated data for through line and open ended stubs for
large cavity...........................................................................................................
176
6.4
Measured data for open ended stubs for small cavity...................................
176
6.5
Side view of MMIC in cavity................................................................................ 177
6.6
Measured S 2 1 of passive cavity with MMIC carrier.......................................
178
6.7
Generalized feedback amplifier.........................................................................
179
6.8
Measured results o f small signal MMIC amplifier gain, closed cavity
unbiased MMIC, small signal closed cavity MMIC amplifier, and
Barkhausen criteria equation (6.1)....................................................................
180
6.9
Output power characteristics o f MMIC am plifier..........................................
182
6.10
Large signal conditions with cavity open and closed.....................................
182
6.11
Load-pull measurement of MMIC attached to carrier...................................
184
7.1
Cutaway view o f architecture of 45 GHz array design...................................
191
7.2
Antenna layer layout for 45 GHz array design.................................................
192
7.3
Side view for multilayered packaging architecture..........................................
194
7.4
Layout of single element active antennas, a) antenna layer without
quarter wave transformer, b) antenna layer with quarter wave
transformer, c) MMIC layer...............................................................................
194
Measured input impedance for antenna with and without quarter wave
transformer.........................................................................................................
197
7.6
EIRP of single element active antenna designs...............................................
198
7.7
Radiated power of single element active antenna designs.............................
198
7.8
DC-RF efficiency of single element active antenna designs..........................
199
7.9
Calculated radiated power for single element active antenna designs
7.10
Layout of feed and antenna layers for arrays...................................................
201
7 .11 Input layer showing corporate divider and open MMIC cavities.................
201
7.5
XX
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200
7.12
Output layer showing cavity backed patches....................................................
7.13
Smith chart plot o f measured and calculated edge elem ent active
impedance at load-pull reference plane for Array # 1 .........................................205
7.14
Smith chart plot o f measured and calculated inner element active
impedance at load-pull reference plane for Array # 1 .....................................
206
Smith chart plot o f measured and calculated edge elem ent active
impedance at load-pull reference plane for Array # 2 .....................................
206
Smith chart plot o f measured and calculated inner elem ent active
impedance at load-pull reference plane for Array # 2 .....................................
207
7.17
EIRP results o f arrays..........................................................................................
208
7.18
DC-RF efficiency of arrays.................................................................................
208
7.19
Available power, measured and calculated radiated power for Array # 1 .... 209
7.20
Available power, measured and calculated radiated power for Array # 2 .... 209
7.21
Combining efficiency of arrays........................................................................... 210
7.22
E-plane radiation patterns at 10.2..GHz for Array # 1 ....................................... 210
7.23
H-plane radiation patterns at 10.2 GHz for Array # 1 ......................................... 211
7.24
E-plane radiation patterns at 10.1 GHz for Array # 2 ....................................... 211
7.25
H-plane radiation patterns at 10.1 GHz for Array # 2 .........................................212
7.26
Amplitude excitation at10.2 GHz for Array #1 from nearfield scan
7.27
Phase excitation at 10.2
7.28
Amplitude excitation at10.1 GHz for Array #2 from nearfield scan
7.29
Phase excitation at 10.1
A. 1
Comparison o f equation (2.5) and Momentum simulations of input
resistance for varying feed heights....................................................................
7.15
7.16
B .l
GHz for Array #1 from nearfield scan.............
202
212
213
213
GHz for Array #2 from nearfield scan..................214
225
Transmission line model for microstrip antenna.............................................. 226
xxi
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CHAPTER 1
INTRODUCTION
M odem and future communication and radar systems for commercial and military
applications demand increased functionality and performance with reduced cost and size.
Some examples o f current systems with these characteristics are high speed wireless
LANs, cellular base stations, multipoint distribution networks, automotive radar, air
traffic control radar and satellite communications. The antenna systems for some of these
high performance applications utilize digital beamformed arrays, phased arrays and
spatial power combined arrays. Data rate requirements and the availability o f spectrum
drive the frequency and transmitter power of the RF front end into the microwave/
millimeter wave bands. The relative bulkiness o f waveguide and high loss o f planar
circuitry make the need for com bining the active devices into the antenna package
important. Therefore, the separation o f the antenna from the electronics is yielding to a
more integrated approach.
A tight integration of the transm itter/receiver electronics with the antenna is
required to achieve the degree of functionality necessary for high performance antenna
systems. In a digital beamformed array, phased array or spatial power combined array,
active devices are typically used at each array elem ent or at a subarray level, and results in
many active devices. Therefore, methods of properly packaging the active devices and all
required bias and control circuitry into the array or subarray module must be investigated.
There are two basic approaches to combining active devices and antennas into a
single package: a monolithic or hybrid approach. The monolithic approach o f fabricating
1
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all o f the active circuitry, matching networks and antennas onto a single wafer has been
intensely researched over the past decade for phased arrays [1], [2]. However, it is clear,
given the high cost and low reliability o f dealing with semiconductors appropriate for
millimeter wave frequencies such as GaAs, that this is not an attractive approach.
Another effort at producing monolithic packages has been underway under the context of
developing “quasi-optical” power combiners such as grid oscillators and amplifiers [3][5]. A significant difficulty with this approach (among many) is providing an adequate
thermal path for removing heat from the active devices. Therefore, many of the grid
designs have been operated for pulse power.
The capabilities o f semiconductor foundries to manufacture high performance
single functional elements, such as low noise or power amplifiers, with adequate yield is
well established. Therefore, the hybrid approach to constructing complex active arrays is
attractive. The hybrid or multichip module (MCM) approach used here utilizes
unpackaged, bare die IC devices placed on a common carrier substrate [6]. In particular,
the use of monolithic microwave integrated circuits (MMICs) is necessary for
microwave/millimeter wave systems. Advantages of the approach include high yielding
modules that can be attained by using known good devices with similar performance and
characteristics, lower cost modules since the substrate supporting the antenna, matching
networks and bias lines can be constructed on relatively inexpensive material and higher
performing circuit elements since specific substrate characteristics may be used to
optimize behavior. For example, microstrip antennas will usually benefit from substrates
that are thicker and possess lower dielectric constants than the semiconductor wafers [7].
?
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Examples of hybrid or MCM approaches for constructing active arrays include a
Ka band subarray phased array module [8] and more recent work [9]. These multilayered
arrays use a ground plane to separate the M M ICs from the radiating antenna. Several
designs discussed in [10], [11] utilize a circuit-fed, tile approach to spatial power
combining. The experience from that work led directly to the proposed multilayered
architecture outlined in this chapter.
1.1 Difficulties of Packaging
Several fundamental problems can be identified that make the packaging of active
devices and antennas particularly difficult at millimeter wave frequencies. A significant
but sometimes overlooked problem is that circuit space is limited. This results from the
typically electrically large dimensions of MMICs at higher frequencies and the need to
include all the bias, control, stabilization, antenna and matching circuitry. This problem
was alleviated in monolithic approaches by constructing antennas and circuitry on a high
dielectric constant material which results in small transmission lines and antennas, but
also low efficiency and stability. The circuit space problem was alleviated in [8]-[l 1] by
using multiple layers.
Another difficulty of packaging MMICs, particularly power amplifiers, is the
increased heat flux. Since device spacing is determined by the array constraints, higher
frequencies lead to closer spacings. Also, active devices suffer from reduced efficiency at
higher frequencies [3]. This reduced efficiency leads to more heat generation. Adequate
thermal management m ust be undertaken to ensure efficient, reliable performance.
3
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The stability o f the active array must be assured for amplifying designs.
Controlling the isolation from the antenna to the input o f an amplifying device is
important since most MMIC designs do not incorporate this feedback. The desire to use
com m ercial-off-the-shelf M MICs results from the low cost possible with high volume
manufacturing. Finally, predictable high performance designs should be attained with an
active array to justify the added complexity over a sim pler modular approach to antenna
and transm itter/receiver architectures.
1.2 Proposed Multilayered Packaging Architecture
The proposed multilayered architecture is shown in Figures 1.1 and 1.2. The
circuit space problem for the RF components is alleviated by stacking stripline layers.
Bias and control circuitry can use any of the three metal layers associated with the
stripline layers. Vias can be used for packing circuit elements closely, transitioning
signals between layers, improving antenna performance and increasing the isolation
between circuit and antenna elements. The thermal performance is controlled by
reserving one side o f the board stack for a thermal heat path. The MMIC devices are then
directly mounted to the metal base.
One of the keys to this work is the realization that, with the use of modem MCM
technologies [6], stacked layers with interconnecting vias can be a fundamental part of the
proposed architecture. For digital applications, multiple layers provide a way in which
many interconnecting lines can be routed in minimal area. In addition, the quantity of
vias or number of layers (within reason) need not be a consideration. M ultilayered
4
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Cavity backed
patch
RF via
MMIC Cavity
Figure 1.1. Cross-section of multilayered packaging architecture
Cavity backed
patch
MMIC Cavity
Figure 1.2. Cutaway view of array architecture
5
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antenna designs without vias have been investigated in some previous work [12], [13],
however, the use of vias represents a degree of freedom not available in those studies.
1.3 Area of Focus
This dissertation presents efforts for packaging active devices in a microwave/
millimeter wave active array architecture. Principally, the design and analysis of the key
circuit elements is undertaken.
Several novel and efficient circuit/antenna elements are studied in this work. The
cavity backed patch will be shown to provide high efficiency operation on thick and high
dielectric constant materials. These substrate characteristics are often found in MCM
technologies. A buried via connection (RF via) will be shown to be compact, efficient
and broadband. In fact, the same design can be used for the microwave/millimeter wave
signal and for the DC bias/control circuitry. The MMIC amplifier is buried in a cavity for
isolation from other circuit elements and a low thermal resistance path to the heat sink.
In addition to these basic elements, several other antennas and another efficient
multilayered transition will be studied.
There are three basic tasks accomplished in this work. A multilayered packaging
architecture is presented that addresses most of the packaging problems already
discussed. The second task is developing models and tools for the important circuit
elements that enable the design to meet desired specifications. Finally, several
operational arrays are described that demonstrate the packaging and modeling approaches
developed here. The success of this work is demonstrated by the high efficiency
measured in the spatial power combined arrays.
6
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Chapters 2-4
Antenna Design and
M odeling
Chapter 5
M ultilayered
RF Interconnects
Chapter 6
MMIC Amplifiers
in a Cavity
Chapter 7
^
Spatial Power Combining
Array Examples
Figure 1.3. Organization and flow of work
The organization of the dissertation is illustrated in Figure 1.3. The three
principal circuit elements (antennas, interconnects, amplifiers) are studied separately.
The dissertation concludes with the description of several array examples. Chapters 2-4
deal with antenna investigations, Chapter 5 deals with two methods of multilayered signal
transfer, Chapter 6 investigates the effect o f a cavity around an amplifier, and Chapter 7
investigates spatial power combined arrays.
References
[1]
M ailloux, R.J., “Phased array architecture for millimeter wave active arrays,”
IEE E Antennas Propag. Soc. New sletter, vol. 28, pp. 5-7, February 1986.
7
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[2]
M cllvenna, J.F., “Monolithic Phased Arrays for EHF Communication Terminals,”
M icrowave Journal, pp. 113-125, March 1988.
[3]
York, R.A., “Quasi-optic power combining,” in Active and Quasi-Optic Arrays
fo r Power Solid-State Power Combining, R.A. York and Z.B. Popovic, ed., New
York: John Wiley & Sons, Inc., pp. 1-48, 1997.
[4]
Popovic, Z.B., Shiroma, W.A. and Weikle II, R.M., “Grid oscillators,” in Active
and Quasi-Optical Arrays fo r Solid-State Pow er Combining, R.A. York and Z.B.
Popovic, eds., New York: John Wiley & Sons, Inc., pp. 293-330, 1997.
[5]
De Lisio, M.P. and Cheh-Ming Liu, “Grid amplifiers,” in Active and
Quasi-Optical Arrays fo r Solid-State Pow er Combining, R.A. York and Z.B.
Popovic, eds., New York: John Wiley & Sons, Inc., pp. 331-376, 1997.
[6]
Tummala, R.R., Rymaszewski, E J. and Klopfenstein, A.G., ed., M icroelectronics
Packaging Handbook., New York: Chapman & Hall, 1997.
[7]
Pozar, D.M., “Considerations for millimeter wave printed antennas,” IEEE Trans.
Antennas Propag., vol. 31, no. 5, pp. 740-747, September 1983.
[8]
Sanzgiri, S., Bostrom, D., Pottenger, W. and Lee, R.Q., “A hybrid tile approach
for Ka band subarray modules,” IEEE Trans. Antennas Propag., vol. 43, pp. 953959, September 1995.
[9]
Ommodt, EC., Sanzgiri, S., German, F. and Jones, T., “Vertical interconnects for
phased array packaging,” 1996 IEEE Antennas Propag. Int. Svmp. Dig., pp. 13341337, 1996.
[10]
Gouker, M.A., Delisle, J.T. and Duffy, S.M., “A 16-element subarray for hybridcircuit tile-approach spatial power combining,” IEEE Trans. Microwave Theory
Tech., vol. 44, pp. 2093-2098, November 1996.
[11]
Delisle, J.T., Gouker, M.A. and Duffy, S.M., “45-GHz MMIC pow er combining
using a circuit-fed, spatially combined array,” IEEE Microwave Guided Wave
Lett., vol. 7, pp. 15-17, January 1997.
[12]
Das, N.K. and Pozar, D.M., “Multiport scattering analysis of general multilayered
printed antennas fed by multiple feed points: Part II - Applications,” IEEE Trans.
Antennas Propag., vol. 40, pp. 482-491, M ay 1992.
[13]
Herscovici, N.I. and Pozar, D.M., “CAD of multilayer feeding networks,”
M icrowave Journal, pp. 84-96, June 1994.
8
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CHAPTER 2
RADIATION EFFICIENCY MEASUREMENTS AND
APPROXIMATE MODELS FOR CAVITY BACKED PATCHES
The choice of substrate material for an M CM package is often determined by the
type of packaging technology [1]. Many M CM technologies use “hard” substrates such
as ceramics, glass-ceramics and silicon [1]. These materials have relatively high
dielectric constants, typically greater than 4 or 5. Some o f the advantages of using these
materials are enhanced line resolution and definition due to processing techniques
utilizing integrated circuit techniques, consistent coefficient of thermal expansion (CTE)
with the active devices and good thermal conductivity [1]. These characteristics enable
construction o f accurate millimeter wave circuitry containing active devices.
Traditionally, due to the favorable characteristics of wide bandwidth and high
radiation efficiency [2], microstrip antennas have been constructed on low dielectric
constant (1-3) substrate materials. “Soft” substrates such as polytetrafluoroethylene
(PTFE such as RT/duroid) and foam possess CTE orders of magnitude different from the
semiconductor devices, less reliable chip attachments and low thermal conductivity [1].
Therefore, the use of hard substrates for constructing MCM packages has the
electrically undesirable quality of poor radiation efficiency for the microstrip antenna [2].
However, M CM technologies, due to the requirement of interconnects, have vias.
Surrounding a microstrip antenna by a wall o f shorting vias can be used to suppress the
excitation o f surface waves. The use of shorting vias around a microstrip antenna forms a
cavity backed patch. The geometry of this element is shown in Figure 2.1.
9
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S trip lin e .
Feed
M icrostrip
A n te n n a
^
P lated T hru H oles
T op G round P la n e
w
r m
i T
■*
F e e d L ayer
\
B ottom G round P la n e
Figure 2.1. Top and side view of cavity backed patch.
This chapter describes an investigation into cavity backed microstrip antennas. In
particular, the motivation for using this antenna element is provided by measuring the
radiation efficiency o f conventional and cavity backed microstrip antennas on thick
substrates with relative dielectric constants ranging from 3 to 10 [3]. Following this,
modifications to a transmission line model [4] are developed that incorporate a proximity
coupled feed and cavity backing [5]. This model is intuitively satisfying because it shows
how the open ended stub can be viewed as an integral circuit element that enables designs
for enhanced bandwidth or providing circular polarization.
10
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2.1 Radiation Efficiency Measurements o f Conventional and Cavity Backed Patches
A series o f radiation efficiency measurements are perform ed to compare
conventional and cavity backed microstrip antennas on thick, high dielectric constant
substrate materials. The microstrip antennas use the proximity coupled feed method
which has two distinct advantages: the geometry is consistent with the use of stripline,
and it allows the use o f thick substrates. The antennas were constructed at 10 G Hz on
several sized boards o f 7.6, 10.2 and 17.8 cm width. The total substrate thickness for all
cases was 0.196 cm or 0.065 X0. Substrates with dielectric constants of 2.94, 6.15 and
10.2 were used. The number of shorting vias around each cavity backed microstrip
antenna is large, from 19 to 9 along each edge.
Three techniques for measuring radiation efficiency are used: a far-field gain
measurement, W heeler cap method and an input admittance method. A summary o f the
results is given in section 2.1.4.
2.1.1 Far-Field Measurement Technique
A straightforward measure of radiation efficiency is the ratio of the gain to
directivity [11]. The directivity can be calculated to a good degree of accuracy and the
gain can be measured with a simple gain measurement. The difficulty is achieving highly
accurate gain measurements, which is particularly challenging for low efficiency, low
gain antennas because diffraction and reflections from finite sized ground planes and
substrates can be significant [6]-[10]. For the strongly excited surface wave in the
conventional microstrip antenna, properly terminating the surface wave power at the
substrate edges is problematic.
ll
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'inset
‘inset
P la n e
’ ;w
T
n
in
T
Figure 2.2.Geometry and layout of conventional and cavity backed microstrip
antennas.
Diffraction is seen in the radiation pattern and reflections affect the input
impedance. To minimize these effects as best as possible, the setup in Figure 2.3 was
used. The substrate was thinned over a guide wavelength and a lossy dielectric material
(Emerson & Cuming, Eccosorb CR124) was coated on the substrate in this region. Also,
an absorber is placed around the substrate to help absorb the diffracted power.
Patterns of the six antennas are shown in Figures 2.4 - 2.6. A demonstration of
the utility o f using the cavity is seen by comparison of the patterns in Figure 2.6. The
cavity offers a means of achieving good patterns even on thick, high dielectric constant
substrates. The gain was measured and the radiation efficiency is shown in the composite
chart of the three methods in Figure 2.14. Due to the substrate diffraction/reflection, the
12
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results are expected to deviate somewhat from the ideal. The corresponding uncertainty
in gain +/- 0.5 dB for these cases, is sim ilar to other work [11].
Microstrip
Antenna
Absorber
Figure 2.3. Side view of far-field gain measurement test setup.
135
135
45
45
-20
-20
-30
-30
.-40 .-30
r10
,-2j
180
180
E-Plane
H-Plane
E -Plane
H -Plane
225
315
225
315
270
270
a)
b)
Figure 2.4. Measured E and H-pIane patterns on £,-=2.94 substrate, a) cavity backed patch,
b) conventional patch. Dimensions: CBP: Lcx=Lcy= 1.499 cm, t= 0.198 cm, £r=2.94,
Ls= 1.397 cm, Ws=0.333 cm, hf=0-0635 cm, Wf=0.0254 cm, Lstub=0.366 cm, Linset=0.0508
cm. CONVP: Lp=Wp=0.732 cm, t=0.198 cm, £r=2.94, hf=0.0635 cm, Wf=0.0254 cm,
Lstub=0-366 cm, Linset=0.0508 cm. Freq: 10 GHz.
13
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90
90
•10
1 35
45
135
45
•20
-30
-30
.-40 .-30
.-40 .-30
*10
180
180
E-PIane '
H -Plane
E-PIane
H -Plane
315
2 25
225
315
2 70
a)
b)
Figure 2.5. M easured E and H-pIane patterns on £,-=6.15 substrate, a) cavity backed patch,
b) conventional patch. Dimensions: CBP: L c^L cj^l.2 6 cm, t=0.198 cm, £,=6.15,
Ls=1.158 cm, Ws=0.338 cm, hf=0.0635 cm, Wf=0.0191 cm, Lstub=0-241 cm, Ljnser=0.0508
cm. CONVP: Lp=Wp=0.483 cm, t=0.198 cm, £,=6.15, hf=0.0635 cm , Wf=0.0191 cm,
Lstub=0.241 cm, Ljnset=0-0508 cm. Freq: 10 GHz.
45
13 5
45
135
-20
•20
-30
-30
.-40 .-30
.-2J
180
180
E-PIane
H -Plane
E-PIane
H -Plane
31 5
225
315
225
270
270
a)
b)
Figure 2.6. M easured E and H-plane patterns on £,=10.2 substrate, a) cavity backed patch,
b) conventional patch. Dimensions: CBP: Lcx=Lcy=l.041 cm, t= 0 .198 cm, £,= 10.2,
Ls=0.940 cm, Ws=0.295 cm, hf=0.0635 cm, Wf=0.0127 cm, Lstub=0-175 cm, Linset=0.0635
cm. CONVP: Lp=Wp=0.351 cm, t=0.198 cm, £,= 10.2, hf=0.0635 cm, W^O.0127 cm,
Lstub=0-175 cm, LjnSet=0-0635 cm. Freq: 10 GHz.
14
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2.1.2 Wheeler Cap Method
The W heeler cap method [11], [12] for measuring radiation efficiency was
perform ed on the cavity backed patches. In the method, a metal “cap” is placed over the
antenna, such that radiation is blocked and reflected back through the input. By
com paring the input resistance with the cap on and with the cap off, the radiation
efficiency can be calculated.
The input impedance of a m icrostrip antenna can be modeled by a parallel RLC
when the input port is defined at its edge [13]. However, a parallel RLC can be
transformed to a series RLC using a quarter wave section of line. Thus, the input port for
these measurements was defined a quarter wavelength from the patch edge. Figure 2.7
shows the measurement setup for the cavity backed patches.
The radiation efficiency of a series RLC circuit with radiation resistance, Rrad, and
loss represented by a series resistance, Rioss, can be separated by “shorting” the radiation
resistance written as
r>
D
K>rad
D
c a p .o ff
c ap.on
77™/=-^— —T— = ------ p-------------•
t'r a d “
^ lo s s
t x
(2.1)
^ c o p .o ff
The radiation efficiency from a conventional microstrip antenna is composed of
conductor, dielectric, and surface loss [2]. The W heeler cap measurement method is not
appropriate for the conventional patch since it is not possible to block the radiation by
covering the antenna and still allowing the surface wave to exit the cap. For example, a
guided wave on a dielectric slab contains some of the power in the substrate and some in
the air [14]. Therefore, placing a cap around a conventional microstrip antenna does not
allow the surface wave power to escape the measurement apparatus. This is important
15
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because the surface wave from a microstrip antenna carries real power. The results in
Figure 2.8 - 2.10 show the input impedance plots for the cap on and cap off
measurements for the three cavity backed patch cases.
^rad
loss
Reference
Plane
A/4
Figure 2.7. Wheeler cap measurement with reference plane outside cavity and quarter
wavelength from the patch.
9 GHz
10 GHz
■*— Isolated
* — Cap
11 GHz
Figure 2.8. Wheeler cap measurements for £t=2.94. Start freq: 9 GHz, stop freq: 11
GHz, step freq: 0.2 GHz.
16
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9 GHz
1 0 GHz
— Isolated
■■— Cap
11 GHz
Figure 2.9. W heeler cap measurements for £r=6.15. Start freq: 9 GHz, stop freq: 11 GHz,
step freq: 0.2 GHz.
■— Isolated
■—Cap
9 GHz
10 G H z
GHz
Figure 2.10. W heeler cap measurements for 8 ^ 1 0 .2 . Start freq: 9 GHz, stop freq: 11
GHz, step freq: 0.2 GHz.
17
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2.1.3 Input Admittance Method
This method was developed as a comparison of the radiation efficiency of two
antennas using only an input impedance measurement. A parallel RLC is assumed to
possess a radiating conductance,
G ra d ,
and parallel loss conductance,
G i oss.
At resonance,
the radiation efficiency is
Prod
_
2 ° rad^
_
^ G rJ V \2 + ^ G ,J V \2
P r a d + P 'o s s
Grad
G r ° « + G 'oss
Comparison o f the conventional and cavity backed microstrip antennas is made by
assuming that the cavity does not affect the radiation conductance but instead affects the
loss conductance. This approximation is used again in the transmission line model
developed in the next section. Therefore, a ratio o f the conventional to cavity backed
patch is
^Ico n v
n
Icav
ST
radxonv
/*♦
, /*»
rad .conv
loss x o n v
V—
T
rad x a v
loss x a v
rad x a v
/-r
ra d x a v
.
ra d xo n v
v—»
loss x a v
/-t
lo s sx o n v
(2.3)
which can be written simply as
T)Icav
C*res x a v
Rr e s x o n v
C resxonv
Rr e s x a v
(2-4)
Therefore, for similar antennas (ie, radiation conductance equivalent), a simple
comparison of the input resistance at resonance provides a relative measure of the
radiation efficiency of two antennas. The true utility of the approach is that
R re s .c a v
and
Rres,conv are read directly from an impedance measurement on a network analyzer.
The input impedance without the quarter wave matching network used is shown
for the six antennas in Figures 2.11 - 2.13. The £[=10.2 case demonstrates clearly the
18
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effect o f losses on the input admittance. Finally, if the radiation efficiency of the cavity
backed patches are assumed to be approximately 100 %, then the ratio (2.4) gives an
absolute number for the conventional patch. However, since the conductor and dielectric
loss is the same for both antennas, it should be noted that the method only determines the
radiation efficiency based on surface wave loss.
— Conventional
-*— Cavity Backed
Figure 2.11. Input impedance for £,=2.94 conventional and cavity backed patches. Start
freq: 9 GHz, stop freq: 11 GHz, step freq: 0.2 GHz.
19
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v .W
'\ » -- tv
^ ~~
A Il
Conventional
Cavity Backed
Figure 2.12. Input impedance for 8r=6.15 conventional and cavity backed patches. Start
freq: 9 GHz, stop freq: 11 GHz, step freq: 0.2 GHz.
Conventional
Cavity Backed
Figure 2.13. Input impedance for 8r=10.2 conventional and cavity backed patches. Start
freq: 9 GHz, stop freq: 11 GHz, step freq: 0.2 GHz.
20
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2.1.4 Summary of Results
A summary o f the radiation efficiency results are presented in Figure 2.14. It is
well known that the radiation efficiency of conventional microstrip antennas decreases
with increasing substrate permittivity [2]. However, the radiation efficiency o f the cavity
backed patches remains fairly constant with substrate permittivity. Thus it can be
concluded that the cavity backing provides an effective means of improving a microstrip
antenna on high dielectric constant materials.
The bandwidth is also measured for these antennas and shown in Figure 2.15. As
another measure o f efficiency, it is well known that reduced efficiency leads to greater
bandwidths [14]. For reduced loss to surface waves, cavity backing is expected to
provide less bandwidth for a given microstrip antenna element.
1
0.9
0.8
c
0 .7
£•*LU
0.6
a>
C
’A-
0.5
o
ra 0 .4
’T■co35
oc
-•—
-a -■ —
-♦ -
0.3
0.2
C avity - Far-fieid
C o n v en tio n a l - F ar-field
C avity - W h eeler c a p
C o n v en tio n a l - In pu t a d m itta n c e
0.1
0
*****
i. I I » » t » I • «-
5
6
7
8
10
11
Dielectric Constant
Figure 2.14. Measured radiation efficiency results for the three methods for conventional
and cavity backed microstrip antennas.
21
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14
12
—• — C avity b a ck ed
- -■ - C o n v en tio n a l
5
T3
C
(0
CQ
2
3
4
5
6
7
8
9
10
11
Dielectric Constant
Figure 2.15. M easured VSWR<2 bandwidth o f conventional and cavity backed
microstrip antennas.
2.2 Transmission Line Model for Proximity Coupling and Cavity Backing
Com puter aided design invoking full wave analysis is increasingly more common
place in the design of microstrip antennas [13]. A theme that propagates through this
work is that m odem EM simulators provide accurate and fast calculations of many
generic micro wave/millimeter antenna and circuit geometries. However, the tools offer
no insight on how the physical layout impacts the performance of the antenna. The goal
of almost all models developed in this dissertation is to provide the physical, intuitive
insight that enables the designer to quickly change the appropriate parameters to achieve
the desired performance.
In this work the classic transmission line (TL) model for rectangular microstrip
antennas o f Pues and Van de Capelle [4] is extended to account for proximity coupled
feeds and cavity backing. The proximity coupled feed model provides a means of
22
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separating the antenna from the feed. The cavity backing separates the antenna from the
cavity. In each case, the model provides a powerful tool for understanding the
mechanisms of the antenna behavior.
2.2.1 Proximity Coupling
The method of proximity coupling has been shown to have wide band
characteristics due to the ability to locate the feed on a thin substrate while the patch is on
a thicker substrate [13]. Several approximate models have been developed [15]-[17] for
this antenna element. However, a model that incorporated the TL model [4] for the patch
was desired to utilize the accuracy of its predictions. The TL model provides useful
predictions o f the resonant frequency and input impedance. A microstrip antenna is
viewed as a half wave resonant microstrip line that possesses admittances at each end that
account for radiation and fringing. The radiation mechanism is a slot.
In the proximity coupled model, the concept of the radiating slot at each end of
the microstrip antenna is important. On the edge where the feed line passes beneath the
patch, the slot is viewed as both a radiating element and a coupling element from the feed
to the patch. In the reciprocity analysis [18], a line that feeds a slot results in a series
loading to the line. This will also be shown in Chapter 3. A discontinuity voltage is
established at the feed point. The stub under the patch has now been decoupled from the
patch with the input impedance found from a transmission line analysis. Therefore, the
equivalent circuit model shown in Figure 2.16 results.
The patch impedance is found with the transmission line model [4] as an edge
feed. The coupling transformer used is similar to that of [15]. For homogeneous
23
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substrates, a constant electric field at the edge of the patch is assumed and the feed line
couples into it. Therefore the coupling ratio is simply the ratio of the feed to patch heights
Ypatch
Av
in
Zstub
Figure 2.16. Equivalent circuit model of proximity coupled patch.
" fe e d
Av =
PE - d l
h'feed
(2.5)
^hctal
E-dl
total
From this, the model approaches the limiting cases. As the feed line height approaches
the patch height, the coupling increases until the proximity coupled input impedance
becomes close to the edge fed input impedance. As the feed line height approaches the
ground plane, the coupling decreases until the proximity coupled input impedance
reduces to the input impedance of the stub. An example using HP Momentum [19] is
shown in Appendix A that demonstrates the accuracy o f equation (2.5). Momentum is a
commercial “2.5 d” moment method solver which provides good agreement to the planar
antennas/circuitry considered in this dissertation.
24
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The input impedance of the model is
(2.6)
where
(2.7)
Z** = ~JZ o cot(Pl)
for a sim ple open end stub. In this equation, the characteristic impedance of the stub is
that o f stripline. The transmission line model equations for
Y p a tc h
are listed clearly and in
more detail in A ppendix B.
O f interest for the proximity coupled patch is the simple circuit model of a parallel
RLC with a series C [20]. Results shown in Figure 2.21 demonstrate that the model
developed here naturally accounts for the capacitive shift o f a proximity coupled patch
with a stub terminated directly under the center of the patch. Due to fringing at the edge,
a resonant patch is less than a half guide wavelength long resulting in an open ended stub
of less than a quarter wavelength, which is capacitive.
This model provides a very useful, physical interpretation of the proximity
coupled patch that the patch and stub (except for the feed point at the edge of the patch)
are decoupled. Therefore, the stub can be used as an integral part of the design for
broadband matching or creating circular polarization (CP). These applications are
discussed in Section 2.3.
2.2.2 Cavity Backing
A previous version of a cavity backed patch TL model [5] used custom
transmission line model parameters to account for surface waves. Upon investigation of
25
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the antennas used in the previous section for the radiation efficiency and numerous
others, it was found that the TL model [4], although not explicitly treating surface waves
in the analysis, results in input impedances that agree well with measured and simulated
data for thick, high dielectric constant substrates. It should be also noted that a frequency
shift arises [4] that was accounted for by a length scaling [5], and is included here.
Therefore, if the slot conductance were to account for radiation and surface waves,
then the cavity can be included by interaction o f the surface wave conductance.
Therefore, breaking the slot conductance into two components, radiation and surface
wave loss, results in
G s =
G ra d +
G su rf -
( 2 -8 )
Since the radiation efficiency is related to the radiation and surface wave losses as shown
in equation (2.2), the surface wave conductance can be written as
c„„ =
(2.9)
I rad
with Gs found in [4] and Tirad found using a closed form solution [21]. Now the two
terms, Grad and Gsurf can be found from these two equations.
The cavity is included in the model through the surface wave term. Other
investigators have treated surface waves from microstrip antennas [9] with reflections
from the end of the substrate, and a similar concept is applied here. The diagram in
Figure 2.17 demonstrates the idea. The microstrip antenna excites radiation and surface
waves. The surface waves impinge on a cavity wall where some is reflected and some
diffracted.
26
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Diffraction
Reflection
TM
/
Figure 2.17. Pictorial representation of TM0 surface wave impinging on truncated
dielectric.
A solution for a TMo surface wave mode impinging an electric wall has been
solved in [22]. An approximate expression has been derived for the cases of 2 < £r < 10
and 0.03 < t/Xo < 0-15
( 2 . 10)
►
Curves of the reflection versus substrate height for two dielectric constants are
shown in Figure 2.18. In the curves, thin substrates correspond to low reflections since
very little power is contained in the substrate [14] and as more power is contained in the
substrate, more o f it is reflected.
Assuming a section of dielectric guide with a load given by the above reflection
coefficient, the transmission line equation
(2 . 11)
" l + \R\e~liPl
27
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results. For small cavities, the length of line (pi) is small and (2.11) reduces to
1-1*1
l + \R\Gnaf'
( 2 . 12)
Therefore, the effect of the cavity on a microstrip antenna is primarily to alter the
input resistance without changing the resonant frequency. The six cases above in Figures
2.11 - 2.13 and many more cases included in this dissertation confirm this conclusion. It
also should be noted that the bandwidth of a patch in a cavity is reduced since the overall
loss o f the antenna is reduced.
The full modified transmission line model for proximity coupled microstrip
antennas with or without cavity backing is shown in Figure 2.19. More details of the
parameters are given in Appendix B.
0.8
0.7
DC
■g* 0.6
0
10) °-5
<5 0.4
!o ,
o
M—
d) 0.2
■
DC
0.1
•
Exact-er=2.49
R-er=2.49
Exact-er=10
R-er=10
^ 1- 0.02
0.04
0.06
0.08
0.1
0.12
0.14
tA,
Figure 2.18. Reflection coefficient of surface wave diffraction.
28
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0.16
-£=>
-C=>
G ccav
a v or
C j,surf
'
Y.s.ncw
O-
YmV!
P ,Y =
YraV 2
■e-
Y s.n e w
-d >
G cav O r G su rf
A v:l
Z stu b
Figure 2.19. Modified transmission line model for proxim ity coupled and/or cavity
backed microstrip antennas.
2.2.3 Validation with Measured Results
The first two examples compare conventional proxim ity coupled patches on thin
substrates with other results shown in Figures 2.20 and 2.21. These antennas give
confidence in the model since the original TL model [4] provides good impedance results
with these parameters. The next two antennas are cavity backed patches on a thick, high
dielectric constant substrate with two different sized cavities (one very large) with results
shown in Figures 2.22 and 2.23. The predictions in Figure 2.23 for the large cavity use
(2.11). Even with these two designs, very usable input impedance data are obtained.
Finally, the results o f a cavity backed patch with a three quarter wavelength stub
constructed on Alum ina for 45 GHz operation is shown in Figure 2.24. This example
shows the extension o f the model for millimeter wave antennas.
29
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10 GHz
/ "/ *0 s
«— Measured
■- - TL Model
Figure 2.20. M easured and calculated results o f proximity coupled patch. Dimensions:
Lp=Wp=0.800 cm, t=0.1067 cm, Er=2.94, hf=0.0508 cm, Wf=0.066 cm, Lstllb=0.400 cm,
Linse^O.038 cm. Start freq: 9 GHz, stop freq: 11 GHz, step freq: 0.2 GHz.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
■CM
// ©
• — TL Model
*- - Momentum
3 GH
4 GHz
Figure 2.21. Calculated results using TL model and Momentum [19] for proximity
coupled patch in [20], Dimensions: Lp=2.5 cm, W p=4.0 cm, t=0.316 cm, £,=2.2, hf=0.158
cm, Wf=0.5 cm, Lstub= 1.25 cm. Start freq: 3 GHz, stop freq: 4 GHz, step freq: 0.1 GHz.
31
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^ 1 0 . 4 GHz
CM
^ 1 0 GHZ
/ / ©.
-•— Measured
* • • TL Model
Figure 2.22. M easured and calculated results for small cavity on £1=10.2. Dimensions:
Lcx=Lcy= 1.041 cm, t=0.198 cm, £^10.2, Ls=0.940 cm, W s=0.295 cm, hf=0.0635 cm,
Wf=0.0127 cm, Lstub=0-239 cm. Start freq: 9 GHz, stop freq: 11 GHz, step freq: 0.2 GHz.
32
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/■/ O
«— Measured
■ TL Model
Figure 2.23. Measured and calculated results for large cavity on 8r=10.2. Dimensions:
Lcx=Lcy= 1.694 cm, t= 0 .198 cm, e^ lO .2 , Ls=1.598 cm, Ws=0.617 cm, hf=0.0635 cm,
Wf=0.0127 cm, Lstub=0.178 cm, Linset=0.0635 cm. Start freq: 9 GHz, stop freq: 11 GHz,
step freq: 0.2 GHz.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
42 GHz
47 GHz
CM
/ / P.
* — Measured
■ TL Model
Figure 2.24. Measured and calculated results for 45 GHz cavity backed patch on
Alumina. Dimensions: Lp=Wp=0.80 mm, t=0.508 mm, £r=9.8, hf=0.254 mm, Wf=0.0305
mm, L s tu b ^ l^ mm, Linset=0.387 mm. Step freq: 0.5 GHz.
34
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2.3 Applications of Transmission Line Model
The following two applications o f the transmission line model are elucidated by
the equivalent circuit model given in Figure 2.16. Since the stub is separate from the
antenna radiation mechanism, it becomes a circuit element that can be used to the
designers’ advantage. In the first example, an enhanced bandwidth design technique uses
the stub as an integral reactive tuning element. In the second example, a single feed CP
design uses the stub to feed both polarizations of a patch.
2.3.1 An Enhanced Bandwidth Design Technique for Electromagnetically Coupled
Antennas
Extensive and successful effort to improving the bandwidth of microstrip
antennas has been made over the last two decades [13]. While certain limitations will
always exist, it is often the feeding mechanism that limits the achievable bandwidth. The
electromagnetically (EM) coupled feed methods, namely proximity coupling and aperture
coupling, offer an appropriate method for achieving wider bandwidth performance since
the antenna and feed substrates can be individually optimized [13]. However, in EM
coupled feed methods, the stub can often be separated from the antenna radiation
mechanism [5], [18], allowing the stub to be used as an integral reactive tuning network.
In this section, a tuning stub is used to increase the bandwidth of EM coupled
antennas. Treating the tuning stub as a reactive element for broadband matching results
in some attractive features. The thickness of the substrate is not altered, so increased
bandwidth can be achieved while not degrading the radiation efficiency and scanning
35
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capabilities. The tuning stub is placed directly under the patch so that little substrate
space is used and good cross-polarization characteristics are displayed.
2.3.1.1 Broadband Matching
In general, impedance bandwidth of a load network can be increased through the
use o f a reactive matching network. However, fundamental limits exist on the degree of
m atching and bandwidth that can be obtained [23]. A design procedure was presented in
[24] that utilized broadband matching concepts to optimize the bandwidth characteristics
o f microstrip antennas. Sim ilar broadband matching problems exist for EM coupled
antennas, such as the aperture coupled microstrip patch antenna [18] and proximity
coupled microstrip patch antenna [5], At the proper reference plane, both of these
antennas exhibit a parallel RLC antenna response. The equivalent circuit model of an
EM coupled antenna has been shown in Figure 2.16 (note that the model is valid for both
proximity and aperture coupling).
A simple design procedure is outlined:
1) design a proximity coupled or aperture coupled microstrip antenna using
existing techniques and tools [13],
2) design the tuning stub using simple expressions presented below,
3)
iterate for an optimized design using simulations or measurements.
In [24], an expression relating the bandwidth, B, and the resonator quality factor,
Q, o f a simple RLC circuit was derived. This relationship is dependent on the degree of
m atching desired, as given by Rnorm=Rmax/Zo, where Rmax is the maximum (resonant)
36
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prlc
•stub
Radiating
Element
Reactive
Matching
Network
Figure 2.25. Broadband matching problem with equivalent circuit model for proximity
coupled and aperture coupled microstrip antennas.
resistance for a parallel RLC with a system impedance of Z q and the acceptable mismatch
as given by the maximum standing wave ratio. S, and is written as
n _ J _ l(SRnorm- l X S - R norm)
B\
S
(2.13)
The bandwidth, B, is defined as ( / 2 —/ , ) / f r where ft and f2 are the frequencies
where VSWR(f!)=VSWR(f 2 )=S, and fr is the resonant frequency.
An expression for the impedance of a parallel RLC resonance about a narrow
band of frequencies can be approximated as [14]
R n0 m
Z p r lc
) ~
R p r lc
~ V R nom Q
(2.14)
J X prlc —
r /±f_v ~
l +
4 < 2 :
\frj
where A/ = / —f r , or the frequency away from resonance.
In (2.13) and in the following expressions, it is assumed that the antenna is
inherently matched to the system impedance, either through proper choice of substrate
37
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thickness and feed height or patch and slot size. This requirement is not overly restricting
when considering EM coupled antennas [13]. An antenna matched at resonance results in
1/S <
R n0r m <
S and the frequency for which Re(Zpric)= l/S gives the maximum possible
band edge Afmax. which is found from (2.13) to be
4 /m a x
_
f r
~
^ S R n° rm
2 Q
1
^
'
At this band edge, if a reactive matching network were to present the conjugate reactance
of (2.14) so that
Z - t A /'.J =
( 2 .1 6 )
then the total input impedance of the parallel RLC network and a reactive load would be
Z total
(Afmax )
= Z p rlc
+ Z s,ub
= I/ 5
(2.17)
.
In (2.16) and (2.17), it is assumed that Xpric of (2.14) is approximately an even
function of Af, such that a solution for one band edge is adequate. Therefore, (2.15)
represents half the achievable bandwidth and the total new bandwidth is
(2.18)
J r
With this expression it is noticed that using the reactive tuning of (2.16) will
always provide more bandwidth than the original RLC circuit. This improvement in
bandwidth can be found using equations (2.13), (2.15) and (2.18). An example of the
amount of improvement as a function of R
n 0 rm
is shown in Figure 2.26.
38
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m
0c)
CQ
0.4
0.6
1.4
0.8
1.6
1.8
Rnorm
Figure 2.26. Bandwidth improvement using stub matching technique.
As a visual example demonstrating the technique, a calculation o f the effect of
combining the parallel RLC and series LC given by Figure 2.25 is made. A VSWR<2
bandwidth is assumed for convenience in this section. The system impedance is 50 £2;
however, the feed line under the patch or slot can be a different characteristic impedance,
Zc. Therefore, a parallel RLC with Rnorm= i.3 , Q=20, and S=2 is placed in series with a
series LC network. The result is an overall tighter input impedance locus as shown in
Figure 2.27. The original RLC network has a bandwidth of 3.8 %, however using the
stub characteristics given by (2.16) results in a bandwidth of 6.3 %. It was noted above
that this bandwidth enhancement technique does not require a change to the original
antenna impedance. This results in the feature that the antenna and stub can be
individually optimized. However, it does not account for the Bode-Fano [23] criteria. By
sacrificing the match at resonance, or changing the antenna radiating resistance, greater
bandwidth can be achieved. For example, using Rn0nn=S=2 and using the new stub
39
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impedance determined by (2.16) results in a bandwidth of 8.7 %. Fano’s theory [23], [24]
results in an ideal maximum bandwidth o f 14 %.
2.3.1.2 Stub Designs
In this section a novel “dual stub” design is presented which is shown to possess
advantages over the traditional quarter wavelength stub. In addition, simple equations are
developed to achieve the potential bandwidth enhancements detailed above.
M ost EM coupled microstrip antenna designs use a quarter-wavelength openended stub, illustrated in Figure 2.28a, perhaps due to its simplicity in design and
fabrication. However as seen above, this results in a sub-optimal design. The input
— Zprlc
-♦— Zstub
* — Ztotal
(b)
Figure 2.27. Illustration of matching problem, (a) original parallel RLC, Zpr|C, (Rnorm= l.3 ,
Q=20, S=2) (b) quarter-wavelength stub, Zstub, (Zc=200 Q ), and (c) total input impedance,
ZtotaU (Ztotal==Zpric+Zstub)-
40
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impedance of an open-ended quarter-wavelength stub is
Z smb —
where Lstub
jZ c
c ° t ( p L stub)
( 2 .1 9 )
/ 4 . M aximum power transfer to the radiating resistance would require
the stub input impedance to be close to zero, which occurs when an open-ended stub is a
quarter-wavelength long or odd multiples thereof.
It is possible to rearrange (2.19) as a function o f Af and fr, facilitating comparison
with (2.14). Taking a Taylor series expansion of the cotangent function for the stub at a
quarter-wavelength and retaining the first term results in
( 2 .20 )
This expression approximates (2.19) well over the bandwidths typically associated with
microstrip antennas (< 30 %).
Methods of increasing the achievable reactances in (2.20) for a given Af include
increasing the characteristic impedance of the stub and increasing the length of the stub.
Altering the line impedance generally results in minor changes to the overall
performance. For example, an antenna consisting of R norm=l -3, Q=20 and S=2 has a
bandwidth of 3.8 %, which is a typical microstrip antenna result. However, to satisfy the
input impedance characteristics of (2.16), the stub requires a characteristic impedance of
660 Q.. Obviously, a stub design with a more realizable characteristic impedance is
desired. The other param eter of interest is the length o f the stub. In [25], a three quarterwavelength stub, shown in Figure 2.28b, was used to achieve greater bandwidths than a
traditional quarter-wavelength stub. However, this design was not optimized for
maximum bandwidth capabilities.
41
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Considering these factors, a design better suited to achieving the requirements
given by (2.16) than a quarter or three quarter-wavelength stub seems desirable. This
new design, the dual stub design, shown in Figures 2.28c, incorporates a section of
quarter-wavelength line and dual symmetric half-wavelength open-ended stubs that use
impedance transformations to achieve greater frequency variation. In the design, shown
in detail in Figure 2.29, Li is a quarter-wavelength long with characteristic impedance of
Zqi and L t is a half-wavelength long with characteristic impedance of Z0i- The input
t
t
a)
b)
c)
d)
Figure 2.28. Layout and geometry of proximity coupled microstrip antennas: a) quarterwavelength stub, b) three quarter-wavelength stub, c) dual stub, and d) side view.
42
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t
"02
U-A./2
Lr y 4
\
"stub
t
Zol
Zo2
U -V 2
Uj
D isc o n tin u ity
R e f e r e n c e P la n e
Figure 2.29. Detail of symmetric dual stub design.
impedance of such a stub configuration is
stub
= j Z ol
(2 .21 )
tan(/3L2 ) —cot(/?L; ) | .
Unknowns Z0i and Z 0 2 can be easily adjusted to obtain the ZstUb value of (2.16). An
approximate expression is derived below to solve for these unknowns; this expression is
then further reduced to account for narrow bandwidth cases.
As above, a simpler expression of (2.21) is found by taking a Taylor series
expansion about the appropriate argument for the tangent and cotangent expressions, and
then retaining only the first terms. Using Li and L 2 as quarter and half-wavelengths,
respectively, results in
A/
—
jr iZ -o x
2 Z ol { 1
( 2 .22 )
\frj
43
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For Zstub o f (2.16) at Afmax, equation (2.22) can be solved for Z o2 to obtain
(2.23)
ft
VA/*max Jy
Since Z0i is the feed line characteristic impedance at the antenna, in many cases
iteration o f the original antenna design is not required to apply this stub design directly.
However in narrow bandwidth cases and particularly with the proximity coupled case,
often Z0i must be much larger than Z02 to satisfy the requirements given in (2.16) and
(2.23). For Z0i = 50 Q , Zq2 m ust be a much lower characteristic impedance, therefore as
the wide lines loop around below the patch antenna as shown in Figure 2.28c, alteration
of the original antenna characteristics is possible. As a practical rule, 50 Q lines are the
minimum characteristic impedance used for these designs. Two consequences arise from
this fact. One is that we may wish to feed the antenna using a higher Z0i than 50 Q. The
second is that an even sim pler expression for (2.23) results. In cases where Afmax/fr is
small, (2.24) can be written as
(2.24)
ft
V.Afmax
max Jy
Using (2.23) or (2.24) results in the feed line characteristic impedances that can be
used to satisfy the requirement given by (2.16). However, further comments on these
design equations are warranted. As shown in Figure 2.28c, the stubs often contain a
number o f discontinuities, including bends, junction, and the open end. In addition, the
bonding film present for a multilayered printed circuit board fabrication needs to be
accounted for in any actual design. The actual lengths of L[ and h 2 are not exact quarter
44
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and half-wavelengths as assumed in the derivation due to these discontinuities. Also due
to the num ber o f approximations, a practical guide is that (2.23) has been found to work
well for bandwidths < 10 %, and (2.24) works well between 10 and 25 %. Regardless,
equations (2.23) and (2.24) give an excellent starting point for use with EM simulations,
and an EM solver can be used for design optimization.
2.3.1.3 Proximity Coupled Patch Example
The proximity coupled microstrip antenna incorporating the stub design of Figure
2.28c demonstrates the advantages of this technique. First, the tuning stub takes up no
excess substrate real estate since the reactive tuning takes place directly under the patch.
Second, since the stub is under the patch, any radiation from the stub is shielded and
potentially re-radiated by the patch. Third, the symmetry of the dual stub design avoids
exciting asymmetric cross polarization currents on the patch, leading to low cross­
polarization levels. Fourth, achieving excess bandwidth in this manner, instead of by
increasing the thickness of the substrate, results in antennas with higher radiation
efficiencies and more attractive scanning capabilities. Finally, the use of thinner
substrates leads to reduced material costs and weight.
Three conventional microstrip antenna designs with the layouts shown in Figure
2.28 are considered to illustrate the use of this technique. The baseline design of a typical
proximity-coupled microstrip antenna with a quarter-wavelength stub yields 4.8 %
bandwidth. The second design is a proximity coupled patch with a three quarterwavelength stub which results in 6 .1 % bandwidth. The third case uses the dual stub
design for enhanced bandwidth performance and achieves 8.4 % bandwidth. The input
45
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
impedances o f these three designs are plotted in Figure 2.30. The equivalent return loss
data is shown in Figure 2 .3 1.
The method described in Section IH o f optimizing the novel dual stub design can
be effectively illustrated with this example. Beginning with the baseline design, the
R n0nn
is 1.3 as illustrated in Figure 2.30. The Q found by (2.13) for S=2 is 15.6, and Afmax/fr
using (2.15) is 0.041. Applying the design procedure should yield a new bandwidth of
1.7 times the original 4.8% according to (2.18). Therefore, jX pric(fr+Afmax) or Zstub of
(2.16) is found to be j31 Q. For the dual stub feed line characteristic impedance of Z oi =
82 Q, the calculated Zo2 from the narrow band approximation of (2.24) is 56 Q. These
line characteristic impedances have much more realistic values than the approximately
500 - 600 Q. that would otherwise be necessary with a quarter-wavelength stub. The
actual fabricated characteristic impedances are Z0i = 82 £2 and Zo2 = 59 Q.. The measured
results, shown in Figure 2.30, demonstrates the anticipated 1.7 times increase over the
original design for a total bandwidth of 8.4 %.
It should be noted that to achieve this result, the actual
R n o rm
of the dual stub
design is slightly higher than the original. The equivalent circuit model for the proximity
coupled patch assumes no interaction between the stub and the patch, which is not
rigorously true. The currents on the patch are perturbed by the stub discontinuities as the
EM solver predicts, however its overall effect can be quite small. The increase of R
n 0 rm
from the baseline design value of 1.3 to the dual stub design value of 1.4 is a direct
consequence o f this effect. Due to this, the achieved bandwidth was increased from 1.7
to 1.75 times the original for this design.
46
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The gain was measured for the three designs and is shown in Figure 2.32. The
theoretical directivity was found to be 6.4 dBi [26] which leads to a measured radiation
efficiency o f 91 % for these designs. The predicted radiation efficiency is 85 % [21].
Surface wave diffraction from the finite sized substrate may have led to slightly higher
measured results. The results o f Figure 2.32 demonstrate two points. First, the gains of
all three designs are the same so the extra line lengths under the patch do not add extra
losses. Second, the extra impedance bandwidth shows up in the gain bandwidth as would
be expected. Also note that to achieve the 8.4 % bandwidth in the traditional quarterwavelength design by increasing the substrate thickness would require a substrate
thickness o f 0.055 XQwhich has a corresponding calculated radiation efficiency of 76 %.
Therefore, bandwidth is increased using the dual stub design while not degrading the
radiation efficiency. The radiation patterns were measured across the bands for co- and
cross-polarization levels. In all designs, the measured cross-polarization is below -20 dB
from co-polarized levels over its impedance bandwidth.
47
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
11 GHz
9 GHz
11 GHz
-CM
//©
Quarter Wave Stub
3-Quarter Wave Stub
Dual Stub
9 GHz
9 GHz
Figure 2.30. Smith chart plot of measured input impedance for three stub cases for
proximity coupled patch. Dimensions: Lp=W p=0.800 cm, t=0.1067 cm, Er=2.94,
hf=0.0508 cm, W(=0.066 cm, Lstub=0.400 cm, Ljnset=0.038 cm.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ffl
T3
-10
-15
Quarter Wave Stub
- - - - 3-Quarter Wave Stub
Dual Stub
-20
9
9.5
10.5
10
11
F r e q u e n c y (GHz)
Figure 2.31. Measured Sn for three stub cases for proximity coupled patch.
7
6
5
\
4
3
Q uarter W ave S tu b
- - - - 3 Q uarter W ave S tu b
D ual S tu b
2
1
0
9
9.5
10
10 .5
Frequency (GHz)
Figure 2.32. M easured gain for three stub cases for proximity coupled patch.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
11
■10
■20
H -C o p o l
E -C o p o l
* - - - H -C r o ssp o l
E -C r o ss p o l
Figure 2.33. M easured patterns for quarter wavelength feed at 10.1 GHz.
•20
- f.r .,
=30
H -C o p o l
E -C o p o l
- - - - H -C r o ssp o l
E -C r o ss p o l
Figure 2.34. M easured patterns for three quarter wavelength feed at 10.1 GHz.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
■20
-40'
H -C op ol
E -C o p o l
- - - - H -C r o ssp o l
E -C r o ss p o l
Figure 2.35. M easured patterns for dual stub feed at 10.1 GHz.
2.3.1.4 Aperture Coupled Patch Example
The dual stub matching technique can also be applied to other EM coupled feed
methods such as aperture coupling. A wideband aperture coupled patch design is
examined that uses stacked patches to achieve large bandwidths [27]. The stub
bandwidth enhancement is applied to this design to further improve the resulting
bandwidth. However, using the dual stub design with aperture coupling eliminates some
o f the advantages inherent in the proximity coupled patch case. First, radiation from the
stubs should be examined with the use of this technique, since an increased backlobe is a
potential consequence o f stub radiation. Second, the stub can use more substrate space
than the quarter-wavelength stub in this topology.
51
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The design [27] was simulated using an EM simulator [19] at a reference plane
0.05 Xo from the center o f the slot. The simulated impedance is shown in Figure 2.36 and
compares well with the predictions [27]. The calculated bandwidth (VSWR<2) is 27.5%.
W hen applying the design technique to this problem, the accuracy of the parallel RLC
circuit assumption may be deficient due to the complication of the double tuned response
o f the stacked patches. However, since the stub and patch are assumed to be independent,
the patch impedance can be found using the theory [27] or de-embedded from the EM
simulation. Values of Afmax/fr = 0.1 7 and -jXpr[c(fr+Afmax) = 46 Q are obtained directly
from Figure 2.36. Using equation (2.23) for the stub characteristics, we calculate Z ol =
50 Q and Z 0 2 = 85 Q. Using the EM simulator leads to an optimum value of Z 0 2 = 110 Q.
The anticipated increase is 1.24 times the original 27.5 % bandwidth. The simulated dual
stub design had a bandwidth o f 34.5 %, resulting in a 1.25 times increase. The magnitude
of the reflection is shown in Figure 2.37.
As mentioned above, using the dual stub with aperture coupled patch antennas has
the potential to increase backlobe radiation. This arises from spurious radiation from the
stub due to the half wavelength sections. In Figure 2.38 the simulated backlobe level for
the original and dual stub designs are shown. In this example, using the dual stub design
creates an increase of about 1.5 dB to the backlobe.
52
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25 GHz
15 GHz
7
25 GHz
0
Croq and Pozar [27]
Dual Stub
15 GHz
Figure 2.36. Smith chart of simulated results for original aperture coupled stacked patch
[27] and case with optimized dual stub design. Dimensions as defined in [27]: W] = 3.5
mm, W 2 = 3.8 mm, erl = er2 = £rf = 2.20, Hi = 0.50 mm, H2 = 1.0 mm, Ai = 3.2 mm, Aw =
0.4 mm, Hf = 0.508 mm, W f = 1.55 mm, Ls = 1.8 mm.
53
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0
C roq a n d P o za r [27]
D u al S tu b
•5
-10
-15
-20
-2 5
14
16
18
20
22
24
26
Frequency (GHz)
Figure 2.37. Calculated Sn o f the original design [27] and dual stub design.
0
2
•4
6
Croq a n d P ozar [27]
Dual S tu b
8
-10
-12
-1 4
-1 6
-18
-20
17
18
19
20
21
22
Frequency (GHz)
Figure 2.38. Backlobe levels for Croq [27] and dual stub design.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
23
2.3.2 Single Feed Circular Polarization Design using Proximity Coupling
In this section the transmission line model provides an excellent demonstration of
combining equivalent circuit models or simple transmission line models with moment
method simulators to attain a desired performance. These concepts will be used to design
a single feed circularly polarized (CP) microstrip antenna. There are variety of methods
to achieve CP [13]; here a compact method with a proximity coupled feed is used.
2.3.2.1 Design
Given the equivalent circuit model of Figure 2.16, the proximity coupled patch
acts as a series loading to the line. If the line were to feed both polarizations with the
proper amplitude and phase, then CP could be attained. Figure 2.39a shows the concept.
For proper circular polarization behavior, the amplitude excitation must be equal for each
radiating direction and quadrature phase must be present.
The quadrature phase is achieved by making the length of line a multiple of a
quarter wavelength: quarter, three-quarter, etc. The amplitude excitation is attained by
proper matching with the new equivalent model shown in Figure 2.39b.
2.3.2.2 Measured Results
An example is presented that demonstrates the use of the model and commercial
moment method codes in order to achieve CP performance. A proximity coupled
microstrip antenna has measured and calculated input impedance shown in Figure 2.40.
The antenna has a measured and calculated input impedance at each edge of 60 Q shown
55
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Zp
Zp
_
Microstrip Patch
Zin
Feed Line
3A g/4
,-<A-g/4 ►
Zp
□X g/4
a)
b)
Figure 2.39. a) Layout of single feed CP antenna, b) equivalent circuit model.
originally in Figure 2.20. Therefore, the line needs a characteristic impedance of
approximately 60 Q. Versions using feed line characteristic impedances of 55 - 66 Q.
were used. Best results occured with 60 L>. The axial ratio is shown in Figure 2.40 and a
spinning linear pattern at 10 GHz is shown in Figure 2.41.
Properties of this antenna include the fact that the sharp bends in the design in
Figure 2.39a are not ideal since the approximation that the line under the patch does not
interact with the patch is not completely correct. The bends create errors and make it
difficult to achieve very low axial ratios (<0.5 dB), at least with these parameters. A
better design would have a circular large radius bend, but even with sharp bends,
adequate axial ratios are achievable.
56
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As illustrated in Figure 2.40, the accuracy o f the moment method solver even for
this relatively complex antenna and feed is very good compared to measurements.
However, the solver in no way points the designer into this direction. The design of this
antenna element is aided by the equivalent circuit model that has been developed.
•CNJ
oi
-•— Measured
* — TL Model
* — Momentum
Figure 2.40. Measured and calculated input impedance of single feed CP design.
57
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20
18
16
m 14
o
(0
cc
x
<
12
10
8
6
4
2
0
9.5
9.7
9.9
10.5
10.3
10.1
F r e q u e n c y (GHz)
Figure 2.41. Axial ratio of single feed CP antenna.
90
-10
135
45
-20
-30
.-40
-30
> 10
180
315
225
270
Figure 2.42. Spinning linear pattern at 10.0 GHz of single feed CP antenna.
58
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References
[1]
Tummala, R.R., Rymaszewski, E J . and Klopfenstein, A.G., ed., Microelectronics
Packaging Handbook, second edition., New York: Chapman & Hall, 1997.
[2]
Pozar, D.M., “Considerations for M illimeter Wave Printed Antennas,” IEEE
Trans. Antennas Propag., vol. 31, no. 5, September 1983.
[3]
Duffy, S.M. and Gouker, M.A., “Experimental Comparison of the Radiation
Efficiency for Conventional and Cavity Backed Microstrip Antennas,” 1996 IEEE
Antennas Propag. Int. Symp. Dig., pp. 196-199, July 1996.
[4]
Pues, H. and Van de Capelle, A., “Accurate Transmission-Line Model for the
Rectangular Microstrip Antenna,” Proc. IEE, vol. 131, pr. H, no. 6, pp. 334-340,
December 1984.
[5]
Duffy, S.M. and Gouker, M.A., “A M odified Transmission Line Model for Cavity
Backed Microstrip Antennas, ” 1997 IEEE Antennas Propag. Int. Symp. Dig., pp.
2139-2142, July 1997.
[6]
Chang, E., Long, S.A. and Richards, W.F., “An Experimental Investigation of
Electrically Thick Rectangular Microstrip Antennas,” IEEE Trans. Antennas
Propag., vol. 34, no. 6, pp. 767-772, June 1986.
[7]
Schaubert, D.H. and Yngvesson, K.S., “Experimental Study of a Microstrip Array
on High Permittivity Substrate,” IEEE Trans. Antennas Propag., vol. 34, no. 1,
pp. 92-97, January 1986.
[8]
Bhattacharyya, A.K. and Garg, R., “Effect o f Substrate on the Efficiency of an
Arbitrarily Shaped Microstrip Patch Antenna,” IEEE Trans. Antennas Propag.,
vol. 34, no. 10, pp. 1181-1188, October 1986.
[9]
Bhattacharyya, A.K., “Effects of Ground Plane Truncation on the Impedance of a
Patch Antenna,” Proc. IEE, vol. 38, pt. H, no. 6, pp.560-564, December 1991.
[10]
Maci, S., Borselli, L. and Rossi, L., “Diffraction at the Edge of a Truncated
Grounded Dielectric Slab,” IEEE Trans. Antennas Propag., vol. 44, no. 6, pp.
863-873, June 1996.
[11]
Pozar, D.M. and Kaufman, B., “Comparison of Three Methods for the
Measurement of Printed Antenna Efficiency,” IEEE Trans. Antennas Propag.,
vol. 36, no. 1, pp. 136-139, January 1988.
[12]
Wheeler, H.A., “The Radiansphere Around a Small Antenna,” Proc. IRE, pp.
1325-1331, Aug. 1959.
59
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[13]
Pozar, D.M. and Schaubert, D.H., ed., M icrostrip Antennas, New York: IEEE
Press, 1995.
[14]
Pozar, D.M., Microwave Engineering, 2nd edition, New York: John W iley &
Sons, 1998.
[15]
Zhang, Q., Fukuoka, Y., and Itoh, T., “Analysis of Suspended Patch Antenna
Excited by an Electromagnetically Coupled Inverted Microstrip Feed,” IEE E
Trans. Antennas Propag., vol. 33, pp. 895-899, August 1985.
[16]
Splitt, G. and Davidovitz, M., “Guidelines for Design of Electromagnetically
Coupled Microstrip Patch Antennas on Two-Layer Substrates,” IEEE Trans.
Antennas Propag., vol. 38, pp. 1136-1140, July 1990.
[ 17]
Karmakar, N.C. and Bhattacharyya, A.K., “Electromagnetically Coupled Patch
Antenna-Theoretical and Experimental Investigations,” Microwave and Optical
Technology Letters, vol. 5, no. 3, pp. 115-118, March 1992.
[18]
Pozar, D.M., “A Reciprocity M ethod of Analysis for Printed Slot and SlotCoupled Microstrip Antennas,” IE E E Trans. Antennas Propag., vol. 34, no. 12,
pp. 1439-1446, December 1986.
[19]
Momentum, HPeesof, version 2.5, Santa Rosa, CA.
[20]
Pozar, D.M. and Kaufman, B., “Increasing the Bandwidth of a M icrostrip Antenna
by Proximity Coupling,” Electronics Lett., vol. 23, no. 8, pp. 368-369, April 1987.
[21]
Pozar, D.M., “Rigorous Closed-Form Expressions for the Surface W ave Loss of
Printed Antennas,” Electronics Lett., vol. 26, pp. 954-956, 1990.
[22]
Pathak, P.H. and Kouyoumjian, R.G., “Surface Wave Diffraction by a Truncated
Dielectric Slab in a Perfectly Conducting Surface,” Radio Science, Vol. 14, no. 3,
pp. 405-417, May-June 1979.
[23]
Fano, R.M., “Theoretical limitations on the broadband matching of arbitrary
impedances,” /. Franklin Inst., vol. 249, nos. 1-2, pp. 57-83 and 139-154, Jan.February 1950.
[24]
Pues, H.F. and Van de Capelle, A.R., “An impedance-matching technique for
increasing the bandwidth of microstrip antennas,” IEEE Trans. Antennas and
Propag., vol. AP-37, no. 11, pp. 1345-1354, November 1989.
[25]
Gouker, M.A., Delisle, J.T., and Duffy, S.M., “A 16-element subarray for hybridcircuit tile-approach spatial power combining,” IEEE Tran. Microwave Theory
Tech., vol. 44, no. 11, pp. 2093-2098, November 1996.
60
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[26]
PCAAD, version 3.0, Antenna Design Associates, Inc., Leverett, MA, 01002.
[27]
Croq, F. and Pozar, D.M., “M illimeter-wave design of wide-band aperturecoupled stacked microstrip antennas,” IE E E Trans. Antennas Propag., vol. AP39, no. 12, pp. 1770-1776, December 1991.
61
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CHAPTERS
FULL-WAVE MODEL FOR STRIPLINE-FED RECTANGULAR
APERTURES WITH AND WITHOUT CAVITY BACKING
A full-wave model for the cavity backed patch is developed in this chapter. In
addition, several other antenna geometries are investigated that provide further insight
into the characteristics of the cavity backed patch. The four basic antenna structures
studied here are the stripline fed slot (SLS), cavity backed slot (CBS), stripline fed patch
(SLP) and cavity backed patch (CBP) as shown in Figure 3.1. All antennas use slots in a
ground plane and are fed using a proximity coupled stripline feed. As with the cavity
backed patches considered in the previous chapter, the cavity is constructed using
multiple shorting vias.
The SLS and CBS use a simple rectangular slot as the radiating element.
Advantages from a numerical point of view are the easy, fast calculations possible either
with the custom full-wave model developed in this chapter or using commercial EM
simulators. However, several disadvantages exist from a practical point of view: the high
input impedance, low radiation efficiency and small bandwidth make these difficult
antennas to work with compared to microstrip antennas. The SLP and CBP use a square
annular ring slot in the ground plane as the radiating aperture. The SLP and CBP provide
better radiating characteristics than the simple slots. However, the computational burden
is increased with these and therefore the simplifications to the analysis and model
outlined below become very useful and important.
The reciprocity method [1] has been applied successfully to many planar antennas
[l]-[4], and can be extended to the geometries examined here. It has the advantage of
62
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being numerically efficient and intuitively satisfying, since the feed interacts only in a
region of discontinuity. Also, the equivalent circuit model derived from this technique is
similar to the transmission line model developed in the previous chapter, so the improved
feeding methods for enhanced bandwidth and CP presented in Chapter 2 are directly
applicable.
The model developed in this chapter, albeit a full-wave solution, provides a tool
for understanding the antenna behavior but not necessarily the final design tool. A prime
advantage the model holds is the fundamental understanding of the dominant wave
mechanisms which lead to better designs and faster iterations. The model will be shown
to have understandable limitations that result from some of the assumptions. Therefore,
final design iterations typically utilize commercial electromagnetic solvers that possess
adequate speed and good accuracy.
a)
b)
c)
d)
Figure 3.1. Geometries o f the four antennas, a) stripline fed slot (SLS), b) cavity backed
slot (CBS), c) stripline fed patch (SLP), and d) cavity backed patch (CBP).
63
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'inset
Reference
Plane
Figure 3.2. Layout and parameters of antennas.
3.1 Theory
Several assumptions are made in the analysis that significantly increase the
numerical efficiency and provide physical insight. The cavity is assumed to be a smooth
perfectly conducting metal wall which reduces the number of unknowns since each
individual via does not have to be modeled. The opening for the feed is assumed not to
affect the cavity, and the slotted regions are assumed square with an equal number of
modes along each edge. The stripline substrates are homogeneous.
3.1.1 Method of Analysis
The method o f analysis is equivalent to that outlined in [1] and others [2]-[4], so
additional details may be found in those references. Initially, a TEM wave is assumed to
64
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exist on an infinite feed line (in this case a stripline) expressed with incident, reflected
and transmitted waves. At a slot discontinuity, the equivalence principle [5] is applied to
divide the problem into two regions, the radiating free space side and the internal stripline
or cavity side, by placing perfect electric conductors with equivalent magnetic currents
over the aperture. Magnetic currents in the aperture are represented by basis function
expansions
iV,
m (x, y) =
,v,
(x, y) + y J X nmvn (x, y ) .
n=I
(3.1)
n=\
The unknown basis function coefficients in (3.1) can be written as
'7 = K
v >-]
(3-2)
and mxm and myn are PWS modes defined in Appendix C.
In the vicinity of the slot discontinuity and the feed line, the reciprocity analysis is
applied [1]. A pictorial representation is shown in Figure 3.3 that demonstrates some of
the simplifications. The first assumption is that the feed line does not interact with the
shorting vias. A second assumption is that the feed line does not interact with all regions
of the aperture for the SLP and CBP. For purposes of excitation and application of the
reciprocity method [1], the aperture region of the SLP and CBP are assumed to be
reduced into a single rectangular slot. This is an important approximation that makes the
application of the reciprocity method possible. The coupling of the feed line to the
aperture then involves the conventional application of [1]. However, the rest of the
aperture is accounted for by the full interaction o f the slot modes in the solution for the
aperture admittance.
65
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Application of the reciprocity method [1] gives the expression that relates the feed
line reflection coefficient to the magnetic currents in the aperture
R=
(x, y ) - m(x, y)dSa = ^ V A v
“
(3.3)
S'
and h f is the field of the feed line [1]. The TEM assumption necessitates that h f has a
zero x component. Therefore, coupling of the feed line to the aperture is through y
directed magnetic currents only.
i z
In c id e n t
T ra n s m itte d
R e fle c te d
h*
►!
R egion of
D iscontinuity
Figure 3.3. Reciprocity analysis [I] application at single region of the aperture for SLP
and CBP.
Application o f the boundary condition that H is continuous in the slot results in
the following expression
(1 - R )h { + H in[(M ) = H fs( - M ) .
Galerkin testing with the aperture basis functions yields the matrix equation
66
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(3.4)
(3.5)
where the admittance matrices are written as
(3.6)
The matrix Yfs is the admittance of the aperture in free space and Yint is either Ysi or Ycav,
where Ysi is the admittance of the aperture looking into stripline while Ycav is the
admittance o f the aperture looking into the cavity. These admittance matrices are defined
shortly. The voltage vector, V, can be found from (3.5) to be
—
V =
~1
-A
va/
T 1
— [i ; , ] - | V f, ]
A v.
(3.7)
The series impedance of the aperture is
where R has been defined in (3.3) and Zc is the characteristic impedance o f the stripline
found from a full-wave solution [6 ].
3.1.2 Mode Layout
PWS modes are used to model the magnetic currents in the direction of current
flow, while uniform pulses are employed along the width. For the SLP and CBP, x and y
directed magnetic currents are used around the square annular slot. For the SLS and
CBS, only y directed currents are employed, since the slot is assumed narrow enough so
that the aperture field Ey = 0 [1]. Detailed expressions for the basis functions are given in
Appendix C. The layout illustrated in Figures 3.4 and 3.5 is used since it easily handles
67
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multiple modes along the slot width, an important condition for accurate frequency
prediction for large slotted regions.
As mentioned above, for the CBP and SLP the stripline feed couples into the y
directed slot modes on the slot section directly above, the excited modes are shown in
Figure 3.6. Coupling from the feed line to other modes on the slotted region is
approximated as zero.
x d ire c te d m o d e s
y d ire c te d m o d e s
Figure 3.4. Layout of modes for SLP and CBP. Single mode along slot width, five
modes along slot length.
68
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x d ire c te d m o d e s
y d ire c te d m o d e s
Figure 3.5. Layout o f modes for SLP and CBP. Tw o modes along slot width, seven
modes along slot length.
Figure 3.6. Excitation of slot from feed line.
69
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3.1.3 Matrix Elements
The voltage discontinuity elements Avn can be written for a centered cavity [1] as
c o s /3
(
(L - W ) \
x n
+ — s— ~— — c o s k
v
-
r y n d
( 3 .9 )
k v
/
where Fu and Fp are the Fourier transforms of the uniform and PWS basis functions
defined in Appendix C. Equation (3.9) is valid for xn=-(Ls-Ws)/2 as shown in Figure 3.6,
but Avn = 0 for other xn. The spectral domain Green’s function Q™ represents the Hy
component in the aperture due to a unit electric current source Jx, as defined in Appendix
D.
The aperture admittance matrices for Yfs and YS[ are composed of four individual
admittance matrices with elements defined by
= j p - j j F- <-k, '2h^ Fp
>5"" (*„*,)
F .
( k ,
£ jkt(-.r,)e Jk>(
,2
h , , ) F
p
(fc,
>dkxdk v
, h
„
)
(3.10)
Y ^ = ^ ] ] F S k y 2 h v )Fp ( . k ' J i „ ) Q " * \ k ' , k y) F , ( k , ? - K . ) F p( k ! ,h.! )
e ikz(~x. )e jk>(-v«~-v«>dkxdk v
Y „
, .
=^ T
J J
F
, ( k x ,
2h
„
) F
„
i k
, , h
„
) Q
"
(3.11)
"
(3.12)
Yx x.mn = x x F
mn
.m n
(3.13) /
v
70
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G reen’s functions Quv gives the H u com ponent due to a unit v directed magnetic current
source. The explicit forms for Q™uv and <2™*v used to determine YfS and Ysi,
respectively, are defined in Appendix D. The integration for (3.10)-(3.13) is perform ed in
polar coordinates as in [7]. The symmetry o f the G reen’s functions simplifies the number
of unique matrix elements. Further reduction of the number of calculations is
accomplished using a smaller integration domain [8 ].
The solution for the cavity aperture adm ittance matrix Ycav is solved using a
spatial domain procedure similar to [4], so that
C L = I l Q
(q, y n , 2 hyn)Cp ( p , x n ,hxn) g xx ( p , q ) C u(q, y m, 2 hym)Cp(pqcm, h m)
p= I q = 0
(3.14)
C L = i l Q
(q , y„ ,2hyn )Cp ( p , x n, h xn) g ™ ( p , q ) C u (p,.rm,2hxm)Cp (q,ym, hym)
p-1 ? =I
(3-15)
x a ,2hm )Cp( q , y n, h yn ) g
C L
( p , q ) C u( p , x m,2hxm) Cp (q,ym, hym)
p = 0 <y=I
(3.16)
C L = C L
(3-17)
where Cu and Cp are the Fourier series coefficients for the uniform and PWS modes,
respectively, and g ™ is a portion of the G reen’s function defined in Appendix E.
The solution o f the components for an equivalent circuit model can be found
using the induced electromotive force (emf) method [4], [5] where
71
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so that Y,-nt and YfSbecome
(3-19)
4,
=-Ar{v')[%„,y
(3.21)
I °I
while the circuit voltage discontinuity is given by
- ,'v 1 /2
Avc =■
1
fr-r -1
[ v r Av] (v*) A v
(3.22)
The equivalent circuit parameters combined with equation (3.8) results in the input
impedance
Av;
c -y
i y
I fs~t
int
(3.23)
stub
where Zstub is the input impedance of the stub defined in (2.7). The equivalent circuit
model is shown in Figure 3.7. Note the similar form of the equivalent circuit model for
the transmission line model shown in Figure 2.16 and the full-wave model.
AV
-in
Zstub
Figure 3.7. Equivalent circuit model for proximity coupled aperture.
72
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3.2 Validation
This section will show some comparisons of the full wave model to measured
results or Momentum simulations for the four aperture geometries.
3.2.1 Stripline Fed Slot
Two examples will be shown to compare the results obtained with the full-wave
model to other calculated solutions. Momentum [9] will be used for comparison as in
many cases in this dissertation. The second example compares with a moment method
solution that models the feed line currents in addition to the slot currents [ 1 0 ].
The first antenna element is a simple rectangular slot in stripline (SLS) shown in
Figure 3.1a. An example using Momentum [9] and the full-wave model is shown in
Figure 3.8. A second example is a case presented in [10] and calculated results are shown
in Figure 3.9. In each case for the full-wave model, 3 PWS modes in the slot are used.
Similar results are obtained with 1 and 5 modes.
These two examples demonstrate the validity of using the reciprocity method [1]
for finding the input impedance of a stripline fed slot since M omentum and the analysis
of [ 1 0 ] use slot and feed line modes.
3.2.2 Cavity Backed Slot
The cavity backed slot has been studied extensively in the literature [11]-[13].
For example, the effect of the cavity dimensions on the overall resonant frequency has
been well documented [12], [13]. Recent results have begun to treat the interaction of
individual shorting vias with the slot [14]. The CBS considered in this work uses a
73
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10 GHz
// O
4 GHz
•- - Full-wave model
* — Momentum
Figure 3.8. Calculated data for SLS. Dimensions: t=0.6 cm, £r=l .08, Ls=2.245 cm,
Ws=0.318 cm, hf=0.3 cm, Wf=0.8 cm, Lstub=0.965 cm, LinSet=0.183 cm. Step freq: 0.3
GHz.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
m
TJ
-10
Full-wave model
Momentum
1-
03
-15
-20
2
3
4
5
6
7
8
F r e q u e n c y (GHz)
Figure 3.9. Calculated full wave model and Momentum results and [10]. Dimensions:
Ls=3.0 cm, Ws=0.2 cm, t= 0.314 cm, £,-=2 .2 , hf=0.157 cm, Wf=0.26 cm, LstUb= 1.0 cm.
proxim ity coupled stripline feed as shown in Figure 3.1b. Shorting vias are used to
construct the cavity wall. Two cases are considered that were measured and compared to
the full-wave model.
The first antenna is a CBS constructed on a substrate with relative dielectric
constant of 2.94. Sixty shorting vias were used to construct the cavity. The measured
and calculated results are shown in Figure 3.10. A second antenna built on a higher
dielectric constant o f 6.15, was measured and compared to calculations, with results
shown in Figure 3.11.
It should be noted that in the calculations of the full-wave model, the substrate
was assumed to be homogeneous. In reality, a bonding film exists to construct the 10
GHz multilayered printed circuit boards. Typical parameters for the bonding film are a
thickness of 0.00508 cm and dielectric constant of 2.3. In addition, the printed circuit
75
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boards are constructed with three duroid (in this case Rogers RT/6002) layers and two
bonding film layers. The effective dielectric constant used in the calculations is
^ d u ro id ^ d u ro id
et = —
:—
duroid
^ film ^ film
r;
film
■
(3-24)
which has been found to provide good results. Therefore in Figure 3.10, for duroid
thickness o f 0.1905 cm and 8r=2.94 and bonding film o f 0.01016 cm and £r=2.3, the
effective dielectric constant is 2.91.
These cases demonstrate that treating the cavity as a perfect electric conductor is a
useful approximation. This incorporates two approximations: that the shorting vias are a
smooth wall and the opening in the cavity does not exist. The cavity for a CBS has a
strong effect on the input impedance as will be shown in Figure 3.12. Therefore,
deficiencies in the cavity solution would be present in the results.
It should be mentioned that only electrically small diameter vias were considered
in this dissertation. The definition of the length of the cavity wall may have been more
complicated had electrically large diameter vias been used.
The analysis of the cavity backed slot found by solving the SLS and eliminating
(numerically) the residue of the parallel plate mode has been found to be incorrect [15].
The case in Figure 3.10 was calculated using an analysis o f the SLS with a discarded
residue contribution with the input impedance shown in Figure 3.12. The discarded
residue prediction has a resonant resistance not too far from the actual measured CBS, but
the resonant frequency is off by 20 %. In this case, the cavity resonant frequency is much
lower than the slot, such that the combination YfS+Ycav is resonant around 9.6 GHz. By
discarding the residue, the size of the cavity is not a parameter. This contrasts with
76
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experimental and theoretical studies [1 1]-[13] that have shown that the size of the cavity
to have a significant effect on the resonant frequency and input impedance of a CBS.
Also shown in Figure 3.12 is the input impedance of the SLS (including the residue)
which demonstrates the strong effect of the parallel plate mode.
9 GHz
11 GHz
-CM
‘O
:a
kffli- -tfxc.WU V 9 .6 GHz:
,V .
• — Measured
■ Full-wave model
Figure 3.10. M easured and calculated results of proximity coupled CBS. Dimensions:
Lcx=1.473 cm, Lcy=1.638 cm, t=0.2007 cm, £ ^ 2 .9 1 , Ls=1.067 cm, Ws=0.0432 cm,
hf=0.0635 cm, W f=0.1143 cm, Lstub=0.437, Lopen=0.572 cm. Step freq: 0.2 GHz.
77
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GHz
•CM
/ ‘/ ' O
:©
s’
11 GHz
— Measured
■ Full-wave model
Figure 3 .1 1. Measured and calculated results of proximity coupled CBS. Dimensions:
Lcx=1.016 cm, Lcy=1.219 cm, t=0.2007 cm, Seff=5.96, Ls=0.787 cm, W s= 0.0315 cm,
hf=0.0635 cm, Wf=0.066 cm, Lstub=0.302, Lopen=0.445 cm. Step freq: 0.2 GHz.
78
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11 GHz
13 GHz
11 GHz
• — Without Residue
*- - With Residue (SLS)
13 GHz
Figure 3.12. Calculated results of proximity coupled CBS using residue and without
residue o f SLS solution. Dimensions: Lcx= 1.473 cm, Lcy= l.638 cm, t=0.2007 cm,
£eff=2.91, Ls= 1.067 cm, Ws=0.0432 cm, hf=0.0635 cm, W>=0.1143 cm, Lstub=0.437. Start
freq: 11 GHz, stop freq: 13 GHz, step freq: 0.4 GHz.
79
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3.2.3 Stripline Fed Patch
The stripline fed patch (SLP) is actually a square annular ring aperture in stripline,
as shown in Figure 3.1c. Although modeled as an aperture, this antenna acts very similar
to a normal patch and leads to good insight into the cavity backed patch presented next.
Two SLP examples are shown in Figures 3.13 and 3.14 and compared with
M omentum and the full-wave model calculations. The SLP in Figure 3.13 uses a thin slot
width that results in fairly good frequency prediction, 9.6 GHz for a single slot mode
along the width, 9.8 GHz for two slot modes along the width, and 10 GHz measured. The
SLP in Figure 3.14 uses a wider slot, which is almost twice the substrate thickness, and
leads to less accurate frequency prediction.
A stationary phase evaluation [16] is used to calculate the patterns. The radiation
patterns are calculated and plotted in Figure 3.15 for the SLP with dimensions given in
Figure 3.14. The calculated directivity of this antenna at 10.1 GHz is 6.45 dBi.
The SLP is a useful antenna element to study for its practical applicability and for
its validation o f the model. Since the coupling of the feedline to the slot has been
investigated with the SLS, errors in treating the square annular ring slot analysis would
appear, if present. In general, the results are adequate. A frequency shift arises with the
analysis that is studied in more depth later. For a single mode along the width, 9 modes
are used along the length and for two modes along the width,
1 1
modes are used along the
length.
80
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9 GHz
9.6 GHz
10 GHz
11 GHz
:cc
Measured
* • - One mode
♦ Two modes
Figure 3.13. Measured and calculated results of proximity coupled SLP. Dimensions:
t=0.1118 cm, £eff=2.88, Ls=0.979 cm, Ws=0.0895 cm, hf=0.0508 cm, Wf=0.066 cm,
Lstub=0.400 cm, LinSet=0.038 cm. Step freq: 0.2 GHz.
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9 GHz
9.2 GHz
10 GHz
11 GHz
C4
9.6 GHz
«
♦
Measured
One mode
Two modes
Figure 3.14. Measured and calculated results of proximity coupled SLP. Dimensions:
t= 0 .1118 cm, £eff=2.88,Ls=1.158 cm, Ws=0.179 cm, hf=0.0508 cm, Wf=0.066 cm,
Lstub=0.400 cm, LjnseFO-038 cm. Step freq: 0.2 GHz.
82
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•20
•30
-40
-30
-1 0
H-Plane
E-Plane
Figure 3.15. Calculated radiation patterns for SLP of Figure 3.14. Freq: 10.0 GHz.
3.2.4 Cavity Backed Patch
The cavity backed patch (CBP) shown in Figure 3. Id remains the central theme
throughout this work due to its many desirable features. In the process of developing 45
GHz antenna designs, the arrays presented in Chapter 7, and the various circuit elements
presented in the rest o f this work, many cavity backed microstrip antennas were built and
measured. Just a few representative samples are included here to compare the full-wave
model to measurements.
Calculations for two CBP antennas are shown in Figures 3.16 and 3.17 for both
one and two modes along the slot width. Figure 3.16 represents a thin slot case and
83
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Figure 3.17 represents a wide slot case. Radiation patterns are shown in Figure 3.18 for
the CBP given in Figure 3.17. The directivity is 6.5 dBi at 10.15 GHz for this antenna.
With the CBP, the utility o f reducing the analysis to the dominant wave
mechanisms is illuminated. For a CBP antenna using the dual stub design as shown in
Figure 1.2, a moment method solution incorporating all slot modes, feed modes and via
modes presents an impractical and unnecessary numerical computation. Therefore, usin
reciprocity to separate the slot from the feed and assuming the cavity wall is smooth, an
accurate solution can be found in an efficient, computationally fast manner.
9 GHz
,
9.8 GHz '/>
^ 9 . 4 GHz U
11 GHz
f t 9.6 GHz f t
UAtm-v
— • — Measured
- - One mode
• ♦ - Two modes
Figure 3.16. Measured and calculated results for proximity coupled CBP. Dimensions:
LCx=LCy= 1.08 cm, t=0.1753 cm , £efi=2.90, Ls=1.041 cm, Ws=0.14 cm, hf=0.0762 cm,
W f=0.117 cm, LstUb=0.381 cm, Linset=0-057 cm. Step freq: 0.2 GHz.
84
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9.2 GHz
9.6 GHz
10 GHz
CM
■CX.
O
Measured
■ • One mode
• Two modes
Figure 3.17. Measured and calculated results for proximity coupled CBP. Dimensions:
Lcx=Lcy=1.196 cm, t=0.1118 cm, ^^= 2.88, Ls=1.158 cm, Ws=0.179 cm, hf=0.0508 cm,
W{=0.066 cm, LstUb=0-400 cm, Linset=0.038 cm. Step freq: 0.2 GHz.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
•
■
H-PIane -M easured
E-Plane - M easured
H-PIane - Calculated
E-Plane - Calculated
Figure 3.18. M easured and calculated radiation patterns for CBP in Figure 3.17. Freq:
10.1 GHz.
3.3 Discussion of Antenna Designs and Model
Several comments regarding the antennas are made in terms of their practicality
and use. Also, several problems are illuminated that are not apparent in the above cases.
3.3.1 Numerical Speed
The calculated results from the full-wave model are compared with Momentum
for the four antenna geometries. The computer workstation used to compare times is an
HP 735/125. A Sun Ultra60 360 MHz was used to compute many cases in the
dissertation with run times three times faster than the HP workstation.
86
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Run times for the four antennas using the full-wave model and M omentum are
show n in Table 3.1. The full-wave model uses 3 modes for the SLS and CBS and 9
m odes along the length and one along the width for the SLP and CBP. M omentum uses a
default setting of 30 cells/wavelength. Also, the Momentum results use a smooth cavity
wall, therefore, the individual vias are not modeled. In reality, either code can adjust the
num ber o f modes used for increasing or decreasing the accuracy or speed o f the solution.
In fact, tricks like using triangular modes around the comers of the SLP and CBP (which
incidentally provides identical results to rectangular rooftop modes) or edge modes along
the edges of the lines and apertures can be used.
Therefore, either code is useful as a design tool. The term “design tool” is given
to a code that can be run while working on a design without having to wait long for
results. It is unrealistic to place a hard number on length, since under some design
situations, 15 minutes may be too long, but under other situations, several hours may be
too long. Understand that the run times listed in Table 3.1 are for specific set of
conditions. In reality, these conditions change and blanket statements about the speed of
solution are not possible.
Full-wave
model
M om entum
SLS
(Figure 3.8)
CBS
(Figure 3.10)
SLP
(Figure 3.14)
CBP
(Figure 3.17)
1 - 2 seconds/
data point
18 seconds/
data point
1 - 2 seconds/
data point
1 1 minutes/
data point
26 minutes/
data point
2 minutes/ data
point
minutes/
data point
15 minutes/
data point
1 2
Table 3.1. CPU time for the full-wave model and Momentum for the four antenna
geometries.
87
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3.3.2 Comparison of YfS, Yst and Ycav
The high input impedance and narrow bandwidth of the SLS and CBS limit their
use as individual radiating elements, although the feed could be offset to reduce the input
impedance [12]. However, the CBS does provide an attractive means of constructing
stripline fed aperture coupled microstrip antennas since back radiation is eliminated and
high coupling levels are possible (small slot lengths) [14].
A comparison of Yfs, Ys[ and Ycav are shown for the SLS and CBS in Figures 3.19
and 3.20 and for the SLP and CBP in Figures 3.21 and 3.22. For the SLS and CBS, Ysi
and Ycav are very different, thus suggesting that the cavity has a large effect on the slot
behavior. However, for the SLP and CBP, YS[ and Ycav are close, particularly near the
resonant frequency of 9.65 GHz. Thus, the cavity does not have much effect on the
overall slot behavior.
0.01
0.009
G fs
G cav
Gsl
0.008
^
0.007
g
0.006
2
0.005
■|
0.004
c
O
O
0.003
0.002
Gcav
0.001
0
9
9.5
10
10.5
11
Frequency (GHz)
Figure 3.19. Conductance of SLS and CBS. Dimensions: Lcx=Lcy=1.30 cm, t=0.1118
cm, Seff=2.88, Ls= 1.19 cm, Ws=0.0895 cm, hf=0.0508 cm, Wt=0.066 cm, Lstub=0.438 cm.
88
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0.008
0.006
0.004
®
0.002
o
-0 .0 0 2
- Bs
C/5 -0.004
-0.006
-0.008
Frequency (GHz)
Figure 3.20. Susceptance of SLS and CBS. Dimensions: Lcx=Lcy=1.30 cm, t=0.1118 cm,
Eefl=2.88, Ls=1.19 cm, W s=0.0895 cm, hf=0.0508 cm, Wf=0.066 cm, Lstub=0.438 cm.
0.01
0.009
G fs
G cav
- - - G sl
0.008
0.007
ao> 0.006
c
<a 0.005
u
3
■a 0.004
c
o
0.003
G fs
0.002
Gcav
Gsl
0.001
0
9
9.2
9.4
9.6
9.8
10
10.2
Frequency (GHz)
Figure 3.21. Conductance of SLP and CBP. Dimensions: Lcx=Lcy= 1.033 cm, t=0.1118
cm, £eff=2.88, Ls=0.979 cm, Ws=0.0895 cm, hf=0.0508 cm, Wf=0.066 cm, LstUb=0.438
cm.
89
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0.01
0.008
0.006
B sl
55 * 0.004
g 0.002
c
«
n
u
O.
0)
o -0 .0 0 2
co
B fs
B ca v
B sl
CO -0.004
-0.006
-0.008
-
0.01
9
9.2
9.4
9.6
9.8
10
10.2
Frequency (GHz)
Figure 3.22. Susceptance o f SLP and CBP. Dimensions: Lcx=LCy= l .033 cm, t= 0.1118
cm, Sefi=2.88, Ls=0.979 cm, Ws=0.0895 cm, hf=0.0508 cm, Wf=0.066 cm, LstUb=0.438
cm.
3.3.3 Finite Sized Ground Plane of Stripline Fed Patch
It is noticed from the calculations and measurements shown in Figures 2.20, 3.14,
3.15, 3.17 and 3.18 that the conventional microstrip antenna, the CBP and the SLP all
behave similarly in terms of input impedance and patterns. However, a potential problem
arises with the SLP.
It should be noted from a practical/measurement point of view that the parallel
plate mode excitation onto a substrate must be carefully considered. For the results of
Figures 3.13 and 3.14, absorber was placed along the edge of the substrate to simulate the
behavior of an infinite ground plane. This was also demonstrated in Chapter 2 when the
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thick, high dielectric constant substrate microstrip antennas used absorber along the edge
o f the substrate since it was very important to the input impedance measurement.
Therefore, care in measurements need be taken when using the SLP. For
comparison, the same antenna shown in Figure 3.14 is measured without the absorber
with the results shown in Figure 3.23. The actual response will be a function of the
ground plane size and antenna placement.
Similar behavior is illustrated in the measured results o f Figure 13 in [10].
9 G H z:
in; •
:
:
l i GHz]
Measured
Figure 3.23. Measured results of proximity coupled SLP without absorber at the substrate
edge. Dimensions: same as Figure 3.14, Lsub=10.16 cm (E-plane), Wsub=7.62 cm (Hplane).
91
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3.3.4 Brief Discussion of the Opening in the Cavity Wall for the Feed
The opening of the cavity wall for the stripline feed is kept below a half-guide
wavelength to eliminate possible TEio waveguide modes from propagating energy from
the cavity. Marcuvitz [17] found an equivalent circuit m odel of the discontinuity effect of
an above cutoff waveguide junction with a below cutoff waveguide, where the below
cutoff waveguide section looks like an inductor. Essentially, the opening provides a
length extension to an ideal short.
However, a problem can arise with the opening. The cavity is considered to be
asymmetric since it has an opening where the feed enters but is shorted at the other end of
the cavity, as shown in Figure 3.24. Viewing the excitation o f the slot into the cavity as
done in Chapter 2 as a transmission line along the x direction, the cavity wall with the
opening presents a quarter wave length of line with an inductor load at one end and a
perfect short at the other end. A narrowband resonance close to the resonant frequency of
the cavity can be excited and explained below.
A very simple solution to the problem is to construct cavities (for the CBS) with
symmetric openings at each end of the cavity. It is also possible to avoid the resonance
by constructing a cavity with a resonant frequency much higher or lower than the slot
resonance as done in Figures 3.10 and 3.11.
92
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• •
• •
Asymmetric opening
Symmetric opening
Figure 3.24. Layout o f asymmetric and symmetric opening in cavity.
3.3.4.1 Asymmetric Cavity Opening - Transmission Line Analogy
A brief demonstration of the resonance possible by using an asymmetric cavity is
illuminated using a transmission line and equivalent circuit model calculation.
For a slot, the cavity may be viewed as series transmission lines. Therefore, for a
centered slot with an asymmetric cavity due to the boxed stripline opening, the equivalent
circuit model is shown in Figure 3.25. The input admittance is
- j f
Y
______ Z—
Z wco t1 _p_______________
i - c o L cot —_______
pi
tisym
imm “ Z„ [coLcot2 pi + 2 Z Wcot pi —coLJ '
where Y^ym is equivalent to Ycav-
93
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(3.25)
Figure 3.25. Equivalent circuit model for asymmetric cavity.
A Taylor series expansion for the cotangent function is used as in Chapter 2, such
that the cotangent function can be written as
cot pi =
7z A f
2
(3.26)
/
J re
Equation (3.25) is expressed in terms of Af and fres and manipulated. Near the resonance
A f « f rcs and so (3.25) reduces to
r Af V
4
Yasym = —
^
Z„.
A/
fn
\
+ LAf
\ f res J
(3.27)
+ 2Lfn
/
Therefore, Yasym=0 when Af=0, however Yasym becomes infinite when the denominator
goes to zero. That is when,
2L
,
(3.28)
As an example, a 1 nH inductor is placed at the end of a quarter wave length (at 10 GHz)
150 Q transmission line. The resonance is predicted to be at 8.67 GHz from (3.28). The
94
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circuit simulation is shown in Figure 3.26. The predicted resonance from the figure is
approximately 8.87 GHz. The step frequency is 0.05 GHz in the figure so the resonance
is very narrow band.
The inductance o f the opening can be found in Marcuvitz [17]. A junction of an
above cutoff waveguide section with a below cutoff section creates an inductive
reactance. For typical cavity sizes and boxed stripline geometries used in this work, the
reactance, X, of the opening can be close to 0.5 Zw. This gives an inductance around 1
nH. Therefore, at a frequency very close to where Yasym=0 is a frequency where Yasym
approaches infinity. A very narrowband short occurs at the slot that causes the input
impedance to go to zero.
8 .9 0 G H z
5 GHz
15 GHz
8 .8 5 G H z
Figure 3.26. MDS calculation o f equivalent circuit model for fres=10 GHz, L=1 nH and
(31=90 degrees (at 10 GHz), step freq: 0.5 GHz.
95
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3.3.4.2 Symmetric Cavity Opening - Transmission Line Analogy
For a symmetric cavity, the equivalent circuit model shown in Figure 3.27 holds
and represents an opening at each end of the cavity. The input impedance is
Y
1 Z u. cot Bl - coL
= ---------- 51----- -2 j Z K coL cot pi + Z H.
(3 ?9)
^ '
which can be reduced with (3.26) and the input admittance expressed as
Y
Z Af
2L (f + A /)+ — —
.
res
J
2 f
——-------------------------------- L*L2Zlr
—7tz L A f ( f res + A f )
C3 30")
which for A f«fres becomes
Y .=
JTC
(3.31)
Therefore, Ysym=0 when
A f _ ~ 4 L f res
/J res
z
(3.32)
if
For L = 1 nH, Zw = 150 £> and fres = 10 GHz, Ysym equals zero when Af/fres= -0.27.
However, unlike Yasym, Ysym does not become infinity near fres. Around the resonance
Ysym is smooth (ie., doesn’t go to infinity). A small frequency shift is predicted by using
two openings (ie., the cavity effectively looks longer).
The problem is elucidated using Momentum calculations for an asymmetric and
symmetric cavity and shown in Figure 3.28. Other measured results shown in Figure
5.27 - 5.31 demonstrate the same effect.
96
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Figure 3.27. Equivalent circuit model for symmetric cavity openings.
9.5 GHz
10.5 GHz
— • — Asymmetric cavity
— **— Symmetric cavity
- - - Full-wave model
Figure 3.28. M omentum and reciprocity calculation of opening in via wall. Dimensions
Lcx=Lcy= 1.207 cm, t=0.2286 cm, £r=2.94, Ls= 1.143 cm, Ws=0.127 cm, hf=0.0762 cm,
Wf=0.086 cm, Lstub= 0 .3 11 cm, Linset=0.0895 cm. Step freq: 0.05 GHz.
97
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3.4 Convergence
For the CBP and SLP, the full-wave model predicts resonant frequencies lower
than measured. This effect is directly related to the magnetic current expansion mode
spacing given by (3.1) and Figure 3.4. A pictorial representation of the current in the
aperture for the SLP and CBP is given in Figure 3.29 using Momentum for the case of
using an edge mesh (very thin modes along the edge) and for two equal sized modes
along the slot width. Relative current strength at the edge of the patch to that away from
the edge o f the patch is approximately 10 to 1 in each case. The advantage of using fewer
modes along the slot width as in the full-wave model is the reduction in computation time
that is required when using many modes in the aperture.
A
y-directed
magnetic current
strength
Two modes
Four modes
(with edge mode)
Aperture for SLP and CBP
x Side view o f SLP and CBP
Figure 3.29. Pictorial representation of Momentum calculations of y directed magnetic
current strength along slot width using edge modes and two modes.
98
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The convergence along the length is demonstrated clearly. The CBP given in
Figure 3.16 is calculated for a single slot mode along the width and 5, 7, 9 and 11 modes
along the length, as shown in Figure 3.30. A general rule of thumb derived is that for a
single mode along the width the number of modes along the length should be
approximately Ls/W s-1 and for two modes along the width the number of modes along the
length should be approximately 2LS/W S-1. These result in approximately square PWS
modes. Overly long or wide PWS modes tend to lead to less accurate calculations.
o
■9 GHz
— • — 3 Modes
— ■— 5 Modes
—
7 Modes
— at- 9 Modes
- r - - 1 1 Modes
Figure 3.30. Convergence test for CBP with 3, 5, 7, 9 and 11 modes along the slot length.
Dimensions: same as Figure 3.16.
99
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3.5 Number of Vias
An analysis studying the effect of several shorting vias around a rectangular slot
was considered recently [14]. As the results showed above with the SLS and CBS in
Figure 3.19 and 3.20, the input impedances were significantly different depending on
whether the cavity was present or not. Thus the number of vias are predicted to have a
strong effect as one case tends to the other. Due to our main interest in the CBP, the
effect of the number o f vias for a CBS is not considered further.
For the SLP and CBP, each antenna tends to be dominated by the microstrip
antenna behavior and the cavity effects are negligible. For example, the SLP and CBP
results shown in Figures 3.21 and 3.22 had similar input impedances. AJso, a conclusion
drawn in Chapter 2 was the similarity of cavity backed and conventional patches.
Therefore, in general, the presence and number of vias is not expected to change the
impedance much except for thick, high dielectric constant substrates.
A series of measured CBPs using 0, 2, 4, 6 and 14 vias along a side are shown in
Figure 3.31. This is a thin (0.034 X0) low dielectric constant (£^2.94) case. The input
impedance difference between the varying number of vias is minor. A second case uses a
thick (0.051 X0) high dielectric constant (£^10.2) substrate. Using Momentum, the CBP
with a smooth wall, SLP with no wall and CBP with 2 vias on a side are calculated and
shown in Figure 3.32.
Based on the results presented in this chapter, from a numerical analysis
viewpoint, assuming that the cavity was a perfect, smooth wall is a good assumption.
The extra numerical computation of treating the individual interaction of each via
provides no added physical insight and accuracy for the CBP.
100
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14 Vias (CBP)
6 Vias
4 Vias
2 Vias
0 Vias (SLP)
Figure 3.31. M easured results of antennas with 0, 2, 4, 6 and 14 vias along a side.
Dimensions: given in Figures 3.14 and 3.17. Step freq: 0.2 GHz.
101
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9.5 GHz
10.5 GHz
.'7 o
• — Full wall (CBP)
- 2 vias
— No wall (SLP)
Figure 3.32. M omentum simulations of full CBP, SLP and with 2 shorting vias a side.
Dimensions: Lcx=Lcy=0.546 cm, t= 0 .1524 cm, e^lO .2, Ls=0.521 cm, Ws=0.0635 cm,
hf=0.0508 cm, Wf=0.0254 cm, Lstub=0.222 cm, L;nset=0.044 cm. Step freq: 0.1 GHz.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
3.6 Radiation Efficiency of Slots in Stripline
The radiation efficiency of apertures in stripline is investigated in this section.
The SLS and SLP radiation efficiency is calculated over a wide range of substrate
thicknesses. This is an important consideration since the SLS generally has poor
radiation efficiency.
The radiation efficiency has been defined as [18]
(3.33)
where
(3.34)
n
m
(3.35)
n
m
The rectangular slot in stripline is calculated and shown in Figure 3.33 for the lowest
order TMo parallel plate mode, t < XJ2. The simple slot acts opposite to microstrip
antennas in terms o f substrate thickness. As the substrate thickness is increased, a
microstrip antenna suffers reduced radiation efficiency, but a stripline fed slot achieves
higher radiation efficiency.
A second calculation is a finite array solution [19] for the radiation efficiency of
two slots. The SLP may be viewed as possessing two slots separated by approximately a
half wavelength. In fact, this is precisely the basis of the transmission line model. For
two slots spaced by XJ2 in the E-plane on £r=l, the radiation efficiency is calculated and
shown in Figure 3.34. The change in efficiency of multiple elements is similar to dipole
results [19].
103
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Finally, the radiation efficiency of the SLP is calculated and compared to a
conventional microstrip antenna [20]. The calculated data is shown in Figure 3.35. For
thin substrates, the SLP acts similarly to a m icrostrip antenna. These calculations assume
perfect electric conductors and no dielectric loss.
0.9
0.8
>.
o
c
<u
o
LLI 0.5
c
o
4-^ 0.4
5
er=1
er=2.5
er=10
T3
to
CC
0.2
0.1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
S u b str a te T h ic k n e s s tA .0
Figure 3.33. Radiation efficiency of SLS.
0.9
>.
g
0.8
0.7
.2
£
0.6
|
0.5
o
’■<50 °-4
'-o „ „
ca 0.3
1x1
CC
0.2
0.1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
S u b str a te T h ic k n e s s tM.0
Figure 3.34. Radiation efficiency of 1 x 2 E-plane array o f SLS.
104
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0.5
0.9
0.8
>»
g 0.7
a>
0.6
3=
^ 0.5
O
*
.s °-4
*5
—•— er=2.5 - SLP
—
e r =10 - SLP
er=2.5 - Conventional
- - - - er=10 - Conventional
ro 0.3
CC
0.2
0.1
0
0.05
0.15
0.1
0.2
0.25
S u b s tr a te T h ic k n e s s tM.0
Figure 3.35. Radiation efficiency of SLP and conventional microstrip antenna.
References
[1]
Pozar, D.M., “A Reciprocity Method of Analysis for Printed Slot and SlotCoupled Microstrip Antennas,” IEEE Trans. Antennas Propag., vol. 34, pp. 14391446, December 1986.
[2]
Das, N.K. and Pozar, D.M., “Analysis and Design of Series-Fed Arrays of
Printed-Dipoles Proximity-Coupled to a Perpendicular Microstripline,” IEEE
Trans. Antennas Propag., vol. 37, pp. 435-444, April 1989.
[3]
Herscovici, N. and Pozar, D.M., “Full-W ave Analysis of Aperture-Coupled
M icrostrip Lines,” IEEE Trans. Microwave Theory Tech., vol. 39, pp. 1108-1114,
July 1991.
[4]
Haddad, P.R., A Study o f Microstrip Antennas fo r Use in Millimeter Wave Phased
Arrays, Ph.D. Dissertation, Department of Electrical and Computer Engineering,
University o f Massachusetts, Amherst, MA, 1995.
[5]
Harrington, R.F., Time-Harmonic Electromagnetic Fields, New York: McGrawHill, 1961.
[6]
Das, N.K. and Pozar, D.M., “A Generalized spectral-domain Green’s Function for
M ultilayer Dielectric Substrates with Application to Multilayer Transmission
Lines,” IEEE Trans. Microwave Theory Tech., vol. 35, pp. 326-335, March 1987.
105
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[7]
Pozar, D.M., “Input Impedance and Mutual Coupling of Rectangular Microstrip
Antennas,” IEEE Trans. Antennas Propag., vol. 30, pp. 1191-1196, November
1982.
[8]
Targonski, S.D., personal communication.
[9]
Momentum, HPeesof, version 2.5, Santa Rosa, CA.
[10]
Chen, C., McKinzie, HI, W.E. and Alexopoulos, N.G., “Stripline-Fed Arbitrarily
Shaped Printed-Aperture Antennas,” IEEE Trans. Antennas Propag., vol. 45, pp.
1186-1198, July 1997.
[11]
Long, S.A., “Experimental Study of the Impedance of Cavity-Backed Slot
Antennas,” IEEE Trans. Antennas Propag., vol. 23, pp. 1-7, January 1975.
[12]
Hadid, A. and Hamid, M., “Aperture Field and Circuit Parameters of a CavityBacked Slot Radiator,” IEE Proc., vol. 136, pt. H, pp. 139-146, April 1989.
[13]
Lee, J., Homg, T. and Alexopoulos, N.G., “Analysis of Cavity-Backed Aperture
Antennas with a Dielectric Overlay,” IEEE Trans. Antennas Propag., vol. 42, pp.
1556-1561, November 1994.
[14]
Bhattacharyya, A., Fordham, O. and Liu, Y., “Analysis of Stripline-Fed SlotCoupled Patch Antennas with Vias for Parallel-Plate Mode Suppression,” IEEE
Trans. Antennas Propag., vol. 46, pp. 538-545, April 1998.
[15]
Herscovici, N.I., Analysis o f Aperture Coupled Microstrip Transmission Lines
and Antennas, Ph.D. Dissertation, Department of Electrical and Computer
Engineering, University of Massachusetts, Amherst, MA, 1992.
[16]
Collin, R.E. and Zucker, F.J., Antenna Theorv (part 1), New York: McGraw-Hill,
1969.
[17]
Marcuvitz, N., Waveguide Handbook, MIT Radiation Laboratory Series, vol. 10,
New York: McGraw-Hill, 1951.
[18]
Pozar, D.M., “Considerations for M illimeter Wave Printed Antennas,” IEEE
Trans. Antennas Propag., vol. 31, pp. 740-747, September 1983.
[19]
Pozar, D.M., “Analysis of Finite Phased Arrays of Printed Dipoles,” IEEE Trans.
Antennas Propag., vol. 33, pp. 1045-1053, October 1985.
[20]
Pozar, D.M., “Rigorous Closed-Form Expressions for the Surface Wave Loss of
Printed Antennas,” Electronics Lett., vol. 26, pp. 954-956, June 1990.
106
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CHAPTER 4
ARRAYS OF STRIPLINE-FED RECTANGULAR APERTURES
WITH AND WITHOUT CAVITY BACKING
The antennas presented in the previous chapter are studied for array behavior here.
The specific antenna geometries considered are the stripline fed slot (SLS), the cavity
backed slot (CBS), the stripline fed patch (SLP) and the cavity backed patch (CBP). As
demonstrated in the previous chapter, the basic physical behavior of radiating slots in
stripline are demonstrated by the simple rectangular slots (SLS, CBS). However, the
square annular apertures (SLP, CBP) generally have more desirable characteristics, such
as lower radiation resistance and higher efficiency.
The basic characteristics of printed arrays have been extensively studied in the
literature [l]-[4]. In this chapter, infinite array models are developed for the antennas to
predict active reflection coefficient, active element pattern and the active impedance of
“large” arrays [1]. The transition from isolated element to infinite array from a theoretical
and numerical point of view is facilitated by the spectral domain formulation used in
Chapter 3. M ost commercial codes do not currently incorporate infinite array analyses, so
developing this model provides a unique computational tool.
Following the infinite array model, a study of active impedance is undertaken for
“small” arrays o f CBPs. The importance o f these measurements and calculations will
become clear in Chapter 7 when a high efficiency, spatial power combined array is
designed and built. In this study, the edge and inner elements of an array are shown
generally to have different input impedances, as expected. For maximum output power
from an amplifier, this non-uniform impedance must be accounted for to achieve proper
107
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load matching. This chapter closes with the presentation of a gain matching technique,
based on individual element directivity and spacing, that can be used to minimize the
non-uniformity o f the active impedance for small arrays.
4.1 Infinite Array Model
4.1.1 Method of Analysis
The details o f the infinite array analysis have been presented clearly in [1]. The
G reen’s function is found for a periodic array o f magnetic sources with x direction
spacing, ax, and y direction spacing, by. The p., v source positions are expressed as
= X o +V&Z
(4.1)
y v = y a +vby
where —
< j i ,v < °° .
For scanning at angle (0, 0), the magnetic sources must be phased as
- j k 0 (fia zu+ vbyv)
(4.2)
where
u = sin 9 cos (j)
(4-3)
v = sin d sin 0
The solution for the elements of the aperture admittance matrix for an infinite
array is simplified by application of the Poisson sum formula [I]. Therefore, equations
(3.10)-(3.13) can be written as
F c r .™
= ^T ~ X
a A n ^ v=-
(k x * y)Fu( k y2 h ay) Fp {k x ,h„ )
eA
- x .) g y*» c.'m->Vi)
108
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( 4 .4 )
r->- =T T
a xD\
Z
t K * , ^ F , « M Q ™ ( k ' . k r)F.ik'ahJFr{kr,hv )
ejX-z<*m-X«)e Jk^>m-yn)
^
r „ „ = - r - S t K i K ^ y F r(k,,hv )a^(kx,k,)F.{kxai^)Fr(k,,hv )
a z y
n=-*>v=-~>
e ik s i x „ - x J g j k y l y m- y . )
Fv.r.m/i = F.n-.mn
(4.7)
v 7
where
£ = 2 K i l l a T + k nii
ky
=
2 tuv / b v + k av
'
( 4
' 8 )
Yfs and YS[ are found from (4.4)-(4.7) with the appropriate Green’s function in Appendix
D, while Fu and Fp are defined in Appendix C. The solution for Ycav is given by (3.14)(3.17).
The active reflection coefficient as defined in [I] is simply
r (0, <p) =
Z. ( 0 ,0 ) - Z. (0,0)
------. - - m
z inw,<t>)+zinm )
(4.9)
as referenced to the broadside active impedance.
The rest of the solution, Av, equivalent model and parameters are identical to
those given in Chapter 3. An assumption inherent in this analysis isthat the feed does not
interact with neighboring antennas [1].
4.1.2 Scanning - Stripline Fed and Cavity Backed Slots
The fundamental characteristics of arrays of simple slots in stripline, with (CBS)
or without cavities (SLS), was presented in [5]. W ithout cavities separating the slots in
109
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the parallel plate region, excitation o f the parallel plate mode can cause serious scan
blindnesses [5]. More investigation on the use o f stripline (without cavity backing) for
infinite arrays was performed in [6] with similar conclusions. The use of a cavity around
the slot was shown to provide good scanning characteristics even for large dielectric
constant materials [5]. In this and the next section, several cases are presented to
demonstrate some o f the salient points of scanning when using cavities.
The first example of simple slots in stripline is a case that was considered in [5].
Calculated results for the formulation presented here are compared against [5] in Figure
4.1. An example of using a cavity around a slot [5] is presented in Figure 4.2. The power
transmission factor used in Figures 4.1 and 4.2 is defined as
= i —l r| ’ .
(4.io)
Multiplying the power transmission factor by cos 0 results in the active element pattern.
Some variation of this result with that o f [5] appears for high scanning angles. In
this solution, the active reflection coefficient is unity at 0 = 90° while it appears that the
result in [5] is not. Certainly, in the H-plane (u scan), one would expect due to the
element pattern that zero power could be transmitted along the surface of the ground
plane since the E field should short (Etan=0). However, good agreement from 0 to 60° is
obtained for the two solutions.
An example showing the active reflection coefficient for the SLS and CBS for a
thin, low dielectric constant substrate is given in Figure 4.3. The SLS due to the parallel
plate mode has a scan blindness at an angle close to broadside in the E-plane (17°), while
the CBS displays good scanning characteristics. A similar case will be demonstrated for
the SLP and CBP in the next section.
110
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0 0*8
co
u.
c
‘35 0-6
co
1
c
•
■
V Scan
U Scan
V S c a n [5]
U S c a n [5]
0.8
1
CO
CC
0.4
(2*.
a>
3
o 0.2
a.
o
0.2
0.6
0 .4
U or V
Figure 4.1. Calculated power transmission factor results for infinite array o f SLS. s
t= 0 .1265 A-o, Ls=0.340 X0, ax=by=0.5 X0.
k.
o
o 0.8
CC
u_
c
o
'(A 0.6
•M
CO
E
CO
co
0.4
k.
Ik.
(U
•
■
O 0.2
V S can
U S can
V S can [5]
U S ca n [5]
Q.
0
0.2
0.6
0.4
0.8
1
U or V
Figure 4.2. Calculated power transmission factor for infinite array of CBS. £r=2.5,
t=0.163 X0, L s=0.354 X0, ax=by=0.5 XQ-
111
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c
.2
o
0.8
"5 0.6
O
O
c
o
■■5 °-4
©
©
CC
CBS - E-plane
CBS H-plane
- - - - SLS E-plane
— - - SLS H-plane
0.2
0
10
20
30
40
50
60
70
80
90
S c a n A n g le (d e g r e e s )
Figure 4.3. Scanning behavior of CBS and SLS. CBS: Lcx=Lcy=1.389 cm, Ls=1.08 cm,
W s= 0 .179 cm. SLS: Ls=0.85 cm, Ws=0.1 cm. CBS/SLS: t=0.1067 cm, £,=2.94,
hf=0.0508 cm, Wf=0.066 cm, LstUb=0.438 cm, ax=by=1.5 cm. Freq: 10 GHz.
4.1.3 Scanning - Stripline Fed and Cavity Backed Patches
The stripline fed patch (SLP) and cavity backed patch (CBP) scanning
characteristics are calculated in this section. Scanning behavior of the CBP is expected to
be similar to results in [7]. For comparison o f the scanning of the SLP and CBP, a thin,
low dielectric constant substrate is used for the calculation with results in Figure 4.4. The
SLP suffers from the scan blindness at 17°, sim ilar to the SLS in Figure 4.3. However,
the scan blindness is a narrow band resonance for the SLP similar to that seen in the
stripline fed aperture coupled patches in [6]. The CBP, as expected, has good scanning
behavior.
A waveguide simulator experiment was performed on the CBP for further
validation of the model. The waveguide simulator has been well documented [3], [4] and
112
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shown to work well for microstrip antennas [8], [9]. A center CBP with two half shorted
antennas are placed in an X-band waveguide. The effective scan angle in the H-plane is
sin0 = -^4b
(4.11)
where b is the inner dimension of the waveguide wall for a single center element with two
halves. Measured and calculated results are compared in Figure 4.5. For the CBP
resonant frequency of 10 GHz, the scan angle is 19.2 degrees. From 9.5 to 10.5 GHz, the
scan angle changes from 20.2 to 18.2 degrees.
^
c
.£
CBP E-plane
CBP H-plane
SLP E-plane
— - - SLP H-plane
0.8
//
o
a
O
O
0.6
/ /
c
o
•■s °-4
0)
0)
*♦—
DC
0.2
0
10
20
30
40
50
60
70
80
90
S c a n A n g le ( d e g r e e s )
Figure 4.4. Scanning behavior of CBP and SLP. CBP: Lcx=Lcy=1.196 cm. CBP/SLS:
t=0.1067 cm, £r=2.94, Ls=1.08 cm, Ws=0.179 cm, hf=0.0508 cm, Wf=0.066 cm,
Lstub=0.438 cm, ax=by=1.5 cm. Freq: 10 GHz.
113
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9.5 GHz
>o
:a
* — Measured
■ Calculated
10.5 GHz
Figure 4.5. Smith chart plot of m easured and calculated input impedance of waveguide
simulator for a CBP antenna. Lcx=Lcy= 1.069 cm, Ls=1.016 cm, Ws= 0 .108 cm, t=0.1067
cm, 8eff=2.90, hf=0.0508 cm, Wf=0.066 cm, Lstub=0.438 cm, ax= 1.069 cm. Step freq: 0.1
GHz.
114
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4.2 Active Impedance for Broadside, Small Arrays
The active impedance as defined in [2] is the impedance of an antenna element in
an array with all o f the other elements excited (or activated). The term scan impedance
[3] is also used in the literature to distinguish the antenna from active devices (a power
amplifier for example). The terms active impedance (and sometimes active antenna
impedance), edge elem ent impedance and inner elem ent impedance will be used in this
work.
In this section, the active impedance problem deals with properly matching the
antenna input impedance to the ideal load impedance of an amplifier. In particular,
matching an isolated antenna or an infinite array element is straightforward since all
elements have the same input impedance. However, for small arrays, such as the 4 x 4
array used in Chapter 7, the edge and inner elements may possess different input
impedances (active impedance). This investigation deals specifically with 0° or broadside
scan, since this is used for the spatial power combined arrays discussed in Chapter 7.
Measurements and calculations demonstrate that for ideal matching, the mutual coupling
in a small array requires consideration.
4.2.1 Active Impedance of 1 x 4 Array of Cavity Backed Patch
The basis of the study is represented by the measured results of a 1 x 4 E-plane
array o f cavity backed patches with 0.8 XQspacing. The active impedance is found by
summing the measured S parameters [3]. Repeatability of the connection on the 8510 is
required for accurate measurements, and the ports not terminated by the two port network
115
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analyzer are terminated in matched loads. The active impedance o f the four antennas and
the corresponding input impedance of an isolated element are shown in Figure 4.6.
The isolated resonant resistance is 68 Q , the edge element resonant resistance is
81 Q. and the inner elem ent resonant resistance is 95 Q. The VSW R referenced to the
isolated antenna is 1.4 for the inner element. For normal passive antenna array designs,
this variation is usually ignored. However, a load-pull measurement taken of 10 GHz
MMICs and described in more detail in Chapters 6 and 7 is shown in Figure 4.7. This
result demonstrates that for these high gain amplifiers, the load impedance is fairly
unforgiving to errors in antenna impedance for maximum output power. The VSW R of
the load impedance result for an output power drop of 0.25 dB is approximately 1.4.
MMIC designs other than those used in this work might have more forgiving load
impedances, but these amplifiers, discussed in more depth in Chapter 6, did not.
For the CBP design o f Figure 4.6, designing the antenna matching network to maximize
the isolated antenna impedance instead of the active impedance leads to an overall 0.15 0.25 dB degradation to the overall amplifier power, corresponding to a 3.4 - 5.6 % drop in
efficiency. This contrasts with the assumption that the amplifier output power is
independent of load impedance as in the passive array mismatch equation,
Pou! = Pin (1 —|T["). In this case, the active impedance leads to 0.03 - 0.12 dB loss or 0.8 2.7 % drop in efficiency.
116
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GHz
V /',
GHz
o
:a
-•—
■*—
—
▼- ♦- -
Isolated
Active S11 Active S22 Active S33 Active S44 -
edge
inner
inner
edge
Figure 4.6. M easured active antenna impedance of isolated and array elements, 1 x 4 E
plane array. Dimensions: Lcx=Lcy= l.l9 6 cm, t=0.1067 cm, £r=2.94, Ls=1.08 cm,
W s=0.179 cm, hf=0.0508 cm, Wf=0.066 cm, LstUb=0.438 cm, ax=2.4 cm.
117
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25.00.
Figure 4.7. Load-pull measurement of typical M M IC amplifier at 10 GHz. Contour
values are given in dBm.
118
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The approach taken in Chapter 7 is to use the freedom of the quarter wave
matching section on the antenna layer shown in Figure 1.2 and in more detail in Figure
7.4b to adjust for the amplitude variations that the active impedance causes. A second
approach presented in more detail in the next section is to use the array spacing to
minimize the amplitude variation.
As an example o f the effect of spacing on the active impedance, the measured
active impedance o f a 1 x 4 E-plane array of CBP antennas with 0.59 Xo spacing is given
in Figure 4.8. In order to better understand the active impedance, the isolated and infinite
array input impedance are calculated for a CBP with 0.8 ?iQspacing and 0° scan. These
results are shown in Figure 4.9. An observation based on the results of Figures 4.6 and
4.9 is that the inner elements tend to approach the infinite array impedance while the edge
elements tend to be somewhere between the isolated and infinite array impedance.
Therefore, if the infinite array impedance were made close to the isolated impedance,
then the active impedance should be similar to the isolated case. This is demonstrated by
an array with 0.59 X0 spacing with the calculated isolated and infinite array impedance
shown in Figure 4.10.
119
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9 GHz
/ /;■
11 GHz,
//* ©
—
*—
-♦—
▼- -
Isolated
Active S11
Active S22
Active S33
Active S44
- edge
- inner
- inner
- edge
Figure 4.8. Measured active antenna impedance of isolated and array elements, 1 x 4 E
plane array with 0.59 X0 spacing. Dimensions: same as Figure 4.6, ax=1.77 cm.
120
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
9 GHz
11 GHz
■CM
— Isolated
■*— Infinite - 0.8 lo
Figure 4.9. Calculated input impedance using full-wave model for isolated and infinite
CBP antenna. Dimensions: same as Figure 4.6, ax=by=2.40 cm.
9 GHz
11 GHz
9.8 GHz
<M
i rmi '
9.9 GHz
sc
__
Isolated
Infinite - 0.59 lo
Figure 4.10. Calculated input impedance using full-wave model for isolated and infinite
CBP antenna. Dimensions: same as Figure 4.6, ax= b y= 1.77 cm.
121
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4.2.2 Comparison of Isolated and Infinite Cavity Backed Patch
Several curves shown in Figures 4.11 - 4.13 are calculated for isolated and infinite
antenna impedance for varying dielectric constant (1.08, 2.94 and 6.15) CBP antennas (ie.
varying directivity) and spacing at a particular frequency. The element spacing is
calculated over the range of minimum size based on the antenna dimensions and
wavelength. These calculations demonstrate the variation of the active impedance for an
infinite array with the equivalent isolated antenna. This change in input impedance as a
function o f spacing is exploited in the gain matching technique presented in the next
section.
0.55 A.
\ 0.95 A.0
"
V • ' - •**. '
‘
•;
W r
•
Isolated
? —■— Infinite
Figure 4.11. Variation of infinite array impedance with array spacing for CBP.
Dimensions: LCX=LCV=1.65 cm, t=0.15 cm, £r=1.08, Ls=1.53 cm, Ws=0.2 cm, hf=0.075 cm,
Wf=0.235 cm, LstUb=0.8 cm. Freq: 10 GHz. Step spacing: 0.05 X0.
122
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•
Isolated
hi— Infinite
0.95 A.
Figure 4.12. Variation of infinite array impedance with array spacing for CBP.
Dimensions: Lcx=Lcy=1.133 cm, t=0.1118 cm, £r=2.88, Ls=0.996 cm, Ws=0.108 cm,
hf=0.0508 cm, W(=0.066 cm, LstUb=0.438 cm. Freq: 10 GHz. Step spacing: 0.05 Xa.
•
Isolated
■*— Infinite
0.95 V q.
Figure 4.13. Variation of infinite array impedance with array spacing for CBP.
Dimensions: Lcx=Lcy=0.823 cm, t=0.076 cm, Er=6.15, Ls=0.708 cm, Ws=0.076 cm,
hf=0.0254 cm, Wf=0.0254 cm, LSWb=0.31 cm. Freq: 10 GHz. Step spacing: 0.05 Xq.
123
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4.3 Gain Matching Technique for Reducing Active Impedance Effects
The results plotted in Figures 4.6 - 4.13 demonstrate that a CBP in an array has a
different input impedance than an isolated CBP due to mutual coupling. This section
presents a simple procedure for array design to accomplish the goal of achieving the same
real part o f the input impedance near resonance whether in an isolated element, finite
array or infinite array. A similar observation was made in [10] that placing antenna
elements matched to the array characteristics would minimize input mismatch. A simple
CBS example will be derived to demonstrate the theory and examples of CBP antennas
are used as an extension.
4.3.1 Design Procedure
The directivity o f an array based on the physical aperture is [11]
4nA
arra y
=
4 itN
A
)}
yv D
c e ll^ c e ll
(4 [?)
^
where Aceu is the area of a unit cell, Ncen is the number of unit cells and Dcen is the
directivity of each cell. In (4.12) it is assumed that array spacings in each direction are
less than a wavelength or ax, by < Xo.
Classic phased array results demonstrate that the active element pattern can be
expressed in terms of the active reflection coefficient, die isolated element pattern and
active impedance [3], In fact, for broadside matched antennas with a broadside scan, the
active element gain, active element resistance, isolated element gain and isolated element
resistance are related as [3]
124
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(4.13)
Furthermore, the active element gain can also be expressed as [2]
8 a
(0.0) = ~
(4.14)
- lr (0 ,0 )|2]c o s0 .
Confining our attention to efficient antenna elements allows the use of the
directivity for the isolated gain at broadside. The advantage of using the directivity is that
for patches, the directivity is well known and found by commercial CAD programs [12].
A disadvantage of using the directivity is that for scanned conditions or inefficient dipole
and slot elements, this approach will not work properly. For broadside matched
conditions with broadside scan, equating equations (4.13) and (4.14) gives
R is o g js o W
* a (0,0)
_
4 ™
A
(4.15)
A;
If the isolated gain is replaced by the directivity (efficient antenna) and Dceu in (4.12) is
used,then
R a (0,0) Diso,aud ~ Dc'“
(-4 ' 16-)
Therefore, by making the directivity of the cell equal to the directivity of the
isolated element, the active antenna resistance will equal the isolated antenna resistance.
That is Dceii = DiS0[ated implies that R;so = Ra- In addition, as seen in the results o f Figures
4.6 and 4.9, the edge and inner element impedances will not vary greatly from the isolated
and infinite array impedance. Therefore, the array spacing condition that will satisfy
(4.15) is
125
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( 4 .1 7 )
The design procedure taken to achieve the spacing of 0.59 X0 for the case in
Figure 4.9 is illuminated for broadside arrays.
1) Choose efficient antenna element
2) Calculate directivity of single isolated element
3) Apply equation (4.17) to determine array spacing
The result of this procedure is an array design that limits the active impedance
effects of the previous section and further eliminates the edge and inner element
resistance differences. For example, the CBP shown in Figure 4.8 has a calculated
directivity o f 6.4 dBi. Equation (4.17) gives that the Acen should be 0.347 A^2 or, for a
square unit cell, the length should be 0.59 X0.
In the following, closed form expressions for the real part of the isolated and
infinite array impedance are derived for a sim ple slot, a CBS for example. By using the
relation that the conductance (or resistance) is equal at resonance, the directivity for an
isolated slot is found. The derived directivity is found to be compatible with full-wave
results o f Chapter 3. This demonstrates the validity o f the condition of (4.17).
4.3.2 Conductance of Cavity Backed Slot
In this section closed form expressions for the real part of the isolated and infinite
array impedance are derived for a simple slot. The free space admittance for a simple slot
with a single mode expansion as given in equation (3.12) is
126
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Y
fs
^isolated
if/i/
(4.18)
where Fu, Fp, Qyy are defined in Appendices C and D.
The free space admittance of an infinite array of simple slots with a single mode
expansion as given in equation (4.6) can be written as
(4.19)
infinite
where kx and ky are given by equation (4.8).
The proposed situation then is for what set o f values axby (Aceu) makes
= G*m u
(4.20)
As shown in Figures 4.6 - 4.13, the active impedance of an infinite array is shifted by
resistive and reactive components. The reactive shift (ie, frequency change) is ignored
and a solution for (4.20) is undertaken.
4.3.2.1 Infinite Radiation Conductance
Finding the radiation conductance of the infinite array for a slot is simple since for
array spacings less than X0, only the m = n = 0 Floquet mode contributes real power.
Therefore, the radiation conductance is
(4.21)
infinite
The Fu is a sine function which becomes unity for kx=0. The Fp function, the Fourier
transform of the PWS mode, is approximated in the following manner. For ky=0,
127
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Taking Taylor series expansions for the cosine term, retaining the first three terms, and
rearranging results in
\2 k h ~ - k ]h 4
F> g
1 2 s in M
'
(4'23)
An identical expression is found in the next section and validated for small ky.
The G reen’s function is given in Appendix D and becomes
Q fiy (0 ,0 )= — .
(4.24)
Therefore, the radiation conductance for a CBS is an extremely simple expression
F;
G fs- ■ ---- -—
m!m“' ~ a X b rito
(4 25)
V
4.3.2.2 Isolated Radiation Conductance
The real part o f the admittance for an isolated slot (CBS) is only contributed for
0<p<ko. Thus, (4.18) becomes
lx k„
= 7 r r ! I F .\k „ W ,X 2 % ,{k l,.k,)F H k,,h ,)ficl< xlp.
a=013—
Q
.
(4.26)
Using a polar transformation as in [13] such that
k t = k a sind?cos0
k y = k 0 sin 8 sin 0
(^—^)
results in the Green’s function becoming
128
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Q ? ,M
=
sin2 6 sin2 <p— 1
VaC0Sg
(«
8
)
The Fu calculation lends a worst case, ie. when kx=ko, value of approximately 0.98 and so
Fu is assumed to be approximately unity. The Fp is approximated again using a Taylor
series expansions of the sine and cosine terms and rearranging
k eh 2
Fp(K ,h ) =
9
sin k eh
k eh \ k ; + k ; )
'
12 sin k ht
(4.29)
This expression can be made equivalent to (4.23) since ke > ky and over most of the
integral ke »
ky, and therefore
12k eh z - k * h *
F = -----2-------- £---------------------------.
p
12 sin k eh
(4.30)
^
}
The Fp term will add error into the calculation of G£olaled. A more accurate expression for
Fp can be found by taking ky= 0.4 ko which is approximately the average in the integral
(4.26),
„
\2 k h 1 —klh *
k k 2h*
F = -----£-------- 2---- --— —
.
9
12sin k eh
1 5 s m k eh
(4.31)
Therefore, after converting (4.26) to polar coordinates results in
lc1f 1 2k k!Z
Gisolated ~ A—Zi r \ K 1—sin2 0 s in 2 <p)sin8d6d(p
Wo o=O0=O
(4.32)
which can be directly integrated to
k 2F 2
(4-33)
3tct70
129
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4.3.2.3 Comparison of Isolated and Infinite Radiation Conductance
These closed form expressions, equations (4.25) and (4.33), for the infinite and
isolated radiation conductance, respectively, are compared for several cases to check the
validity of the analysis and assumptions.
Comparison o f the closed form expression (4.33) using the two Fp approximations
(4.30) and (4.31) with the full-wave solution are calculated in Figure 4.14. This figure
demonstrates that the improved Fp approximation (4.31) does lead to very close
agreement with the full-wave solution, however, the Fp approximation (4.30) is adequate
for demonstration purposes.
A number o f CBS cases are calculated and shown in Figures 4.15 - 4.18 with
varying slot size (ie, dielectric constant in the cavity) and spacing. Figures 4.15 and 4.16
demonstrate 0.5 Xa spacing arrays. The isolated radiation conductance changes more
rapidly with frequency than the infinite radiation conductance since the k u2 appears in
(4.33). As shown in these two figures, for 0.5 XQspacing, the isolated and infinite
radiation conductance cross such that they are equal at a frequency. In contrast, Figures
4.17 and 4.18 demonstrate two CBS antennas with spacings greater than and less than 0.5
Xa. For the spacing case greater than 0.5 XQ, in Figure 4.17, the isolated radiation
conductance is much higher than the infinite radiation conductance. Likewise, for
spacing much less than 0.5 Xq in Figure 4.18, the isolated radiation conductance is lower
than the infinite radiation conductance.
130
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0.75
CO
m
fc>
x
'g
c
0.7
0.65
(0
3
0 .6
T3
C
o
°
c
o
0.55
”
0.5
ea
CC
Isolated - Full wave
Isolated - Fp from Eqn. (4.30)
- - - - Isolated - Fp from Eqn. (4.31)
0.45
9.4
9.6
9.8
10
1 0 .2
10.4
1 0 .6
F re q u en cy (GHz)
Figure 4.14. Comparison of Fp approximations for isolated slot with full wave results.
Lcx=Lcy= l.5 0 cm, t= 0 .15 cm, £,-=2.5, Ls= l . l 19 cm, Ws=0.15 cm, h(=0.075 cm, Wf=0.112
cm, LstUb=0.47 cm, ax=by=1.50 cm.
0.75
co
<b
CO
0.7
x
ao> 0.65
c
to
3
0 .6
T
3
C
o
°
c
o
0.55
Isolated - Full wave
Isolated - Eqn. (4.33)
Infinite - Full wave
Infinite - Eqn. (4.25)
0.5
0.45
9.4
9.6
9.8
10
10.2
10.4
1 0 .6
F re q u en cy (GHz)
Figure 4.15. Comparison of closed form expressions with full wave calculated results.
Dimensions same as Figure 4.14.
131
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0.35
(0
eo
<b
T“
0.32
X
<D
u
c
(0
0.29
o
3
■o
c
o
o
0.26
c
o
Isolated - Full w av e
Isolated - Eqn. (4.33)
- - - - Infinite - Full w av e
Infinite - Eqn. (4.25)
to 0.23
0 .2
9.4
9.6
9.8
10
1 0 .2
10.4
1 0 .6
F req u en cy (GHz)
Figure 4 .1 6 . Comparison of closed form expressions with full wave calculated results.
Dimensions: Lcx= L cy= 1 .0 cm, t= 0 .1 5 cm, £r=6.15, L s= 0 .7 6 3 cm, W s= 0 . 1 cm, ax= by= 1.50
cm.
W
co
*
x
CD
o
0.65
0 .6
0.55
£(0
0.5
a
0.45
o
0.4
~o
o
c
O
^
Isolated - Full w av e
Isolated - Eqn. (4.33)
Infinite - Full w ave
Infinite - E qn. (4.25)
0.35
0 .3
§■ 0.25
0 .2
9.4
9.6
9.8
10
1 0 .2
10.4
1 0 .6
F re q u en cy (GHz)
Figure 4.17. Comparison o f closed form expressions with full wave calculated results.
Dimensions: Lcx=Lcy=1.50 cm, t= 0.15 cm, £r=2.5, Ls= l .l 19 cm, Ws=0.15 cm, ax=by=2.0
cm.
132
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0.65
«
0 .6
eo
<b
t- 0.55
x,
n °-5
c
2 0.45
u
— Isolated - Full wave
— Isolated - Eqn. (4.33)
- • Infinite - Full wave
- Infinite - Eqn. (4.25)
3
■g
0.4
O
°
0.35
c
o
re 0.3
T
re3
QC 0.25
*—
<
0 .2
9.4
9.6
9.8
10
1 0 .2
10.4
1 0 .6
F req u en cy (GHz)
Figure 4.18. Comparison o f closed form expressions with full wave calculated results.
Dimensions: Lcx=Lcy= 1.0 cm, t=0.15 cm, £,=6.15, Ls=0.763 cm, Ws= 0 .1 cm, ax= b y = 1 .0
cm.
4.3.3 Relating Isolated Directivity to Cell Directivity
With expressions for the isolated and infinite radiation conductance, we can now
investigate when they are equal as equation (4.20) states, G?olaud = G ?finitc,
k 1F 1
F2
- t3K
F =—
fz r
a xbyrio
( « 4>
which can be solved for the area of the cell, Acen = axby as
3k
3
(« S )
and for a square cell this gives approximately 0.5 X0 spacing in each plane. The
calculated data shown in Figures 4.15 and 4.16 confirms this result.
The directivity enters the above equation by comparing equation (4.17) and (4.35)
written as
133
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A isolated
47r
3
(4-36)
47T
which finds that Delated = 3 for a simple slot. Actual calculated values for £,=1.08, 2.94
and 6.15 using the full wave model in Chapter 3 are 3.2, 3.1 and 3.1, respectively.
4.3.4 Extension to Cavity Backed Patch
The gain matching technique has been successfully applied to conventional and
cavity backed patches and to larger finite arrays (1 x 6). For CBP and conventional
patches, the inter-elem ent spacing using £r=l, £,=2.94 and £,=6.15 are 0.77 XQ, 0.59 X.0,
and 0.54 ?i0, respectively.
The first exam ple of the gain matching method was applied for a 1 x 4 E-plane
array of CBP with m easured data in Figure 4.9. A second example uses a 1 x 6 E-plane
array with measured results in Figure 4.19. Therefore, the technique can be extended to
larger finite arrays. A third example uses a 1 x 4 array of conventional patches on a
higher dielectric constant (£,=6.15) but thin substrate for high radiation efficiency (0.025
X0). Three cases are used to illustrate the small array effects and gain matching technique.
The calculations from Momentum of an E-plane array with 0.54 Xq spacing are shown in
Figure 4.20. By comparison, the results of an E-plane array with 0.8 Xq spacing are given
in Figure 4.21. The significant variation in input impedance from isolated to small array
is seen with these results. The gain matching technique drastically reduces the inner
element resistance from 100 Q to 55 Q for the 0.8 Xq to 0.54 X0 spacing, respectively.
Finally, this conventional patch is calculated for an H-plane array. These results in Figure
4.22 demonstrate that the H-plane mutual coupling effects can be ignored.
134
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GHz
GHz
;CN
// O
^ __ 1
U
I
-
L t ___
-•— Isolated
■- - Active S11 - edge
♦ • • Active S22 - innerl
a— Active S33 - inner2
Figure 4.19. Measured active antenna impedance of isolated and array elements, 1 x 6 E
plane array with 0.59 XQspacing. Dimensions: same as Figure 4.6, ax= l.77 cm.
135
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10 GHz
- • — Isolated
-■— Active - S11
- A ctiv e-S 2 2
Figure 4.20. Calculated active antenna im pedance using Momentum of isolated and array
elements, 1 x 4 E plane array with 0.54 XQspacing. Dimensions: Lp=W p=0.569 cm,
t=0.0762 cm, Sr=6.15, hf=0.0254 cm, W(=0.0254 cm, Lstub=0.284 cm, L;nset=0.0254 cm,
ax=1.61 cm. Start freq: 9.5 GHz, stop freq: 10.5 GHz, step freq: 0.1 GHz.
-• — Isolated
Active S11 - ed ge
- Active S22 - inner
Figure 4.21. Calculated active antenna impedance using Momentum of isolated and array
elements, 1 x 4 E-plane array with 0.8 Xq spacing. Dimensions: same as Figure 4.20,
ax=2.40 cm.
136
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9 .5 G Hz
1 0 .5 G Hz
*— Isolated
■«— Active S11 - edge
— Active S22 - inner
Figure 4.22. Calculated active antenna impedance using Momentum of isolated and array
elements, 1 x 4 H-plane array with 0.8 ^.0 spacing. Dimensions: same as Figure 4.20,
by=2.40 cm.
References
[1]
Pozar, D.M., “Analysis and Design Considerations for Printed Phased-Array
Antennas” , in Handbook o f Microstrip Antennas, J.R. James and P.S. Hall, ed.,
London: Peter Peregrinus Ltd., 1989.
[2]
Hansen, R.C., ed., Microwave Scanning Antennas, Los Altos: Peninsula
Publishing, 1985.
[3]
Hansen, R.C., Phased Array Antennas, New York: John Wiley & Sons, Inc.,
1998.
[4]
M ailloux, R.J., Phased Array Antenna Handbook, Boston: Artech House, 1994.
[5]
M ailloux, R.J., “On the Use of M etallized Cavities in Printed Slot Arrays with
Dielectric Substrates,” IEEE Trans. Antennas Propag., vol. 35, pp. 477-487, May
1987.
137
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[6]
Das, N.K. and Pozar, D.M., “M ultiport Scattering Analysis of General
M ultilayered Printed Antennas Fed by Multiple Feed Ports: Part II Applications,” IEEE Trans. Antennas Propag., vol. 40, pp. 482-491, May 1992.
[7]
Zavosh, F. and Aberle, J.T., “Infinite Phased Arrays of Cavity-Backed Patches,”
IEEE Trans. Antennas Propag., vol. 42, pp. 390-398, March 1994.
[8]
Pozar, D.M. and Schaubert, D.H., “Analysis of an Infinite Array of Rectangular
M icrostrip Patches with Idealized Probe Feeds,” IEEE Trans. Antennas Propag.,
vol. 32, pp. 1101-1107, Oct. 1984.
[9]
Aberle, J.T. and Pozar, D.M., “Analysis of Infinite Arrays of One- and TwoProbe-Fed Circular Patches,” IEEE Trans. Antennas Propag., vol. 38, pp. 421432, April 1990.
[10]
Allen, J.L., “Gain and Impedance Variation in Scanned Dipole Arrays,” IRE
Trans. Antennas Propag., vol. 10, September 1962.
[11]
Kraus, J.D., Antennas, 2nd edition, N ew York: McGraw-Hill, 1988.
[12]
PCAAD, version 3.0, Antenna Design Associates, Leverett, MA 01002.
[13]
Pozar, D.M., “Rigorous CIosed-Form Expressions for the Surface Wave Loss of
Printed Antennas,” Electronics Lett., vol. 26, no. 13, pp. 954-955, 21 June 1990.
138
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER 5
MULTILAYERED RF INTERCONNECTS
The use o f a multilayered packaging architecture requires a means of transferring
signals from layer to layer. Potentially, there are many ways of achieving this, including
aperture coupling [1], proximity coupling [2] and via connection [3]-[9] methods.
Several requirements exist for the transitions in this work based on the goals of the
packaging architecture. The transition should be capable of operating at millimeter wave
frequencies, be compact, efficient and provide isolation from other circuit structures.
Two transition geometries are studied in this chapter: an “RF via” connection and
aperture coupled striplines with cavity backing. Both of these transitions fulfill the above
criteria.
5.1 RF Via
The RF via is a cylindrical metal connection of the center conductors of stacked
striplines. The geometry is shown in Figure 5.1. Shorting vias are placed around the
periphery of the transition in order to short the parallel plate mode otherwise excited. In
this work, via construction was high yield and had little cost or time impact, thus multiple
shorting vias were used around each RF via connection.
5.1.1 Equivalent Circuit Model
In this section, a simple equivalent circuit model will be developed for the RF via.
139
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Stripline
Out
*
f
*
W,
Stripline
In -*
h,
^gap Dwali
I
i '■X
RF Via
Shorting Via
j
.' -1 ( s'*-3 L . L
Dv
Figure 5.1. Side and top view of RF via geometry.
5.1.1.1 Coaxial Line
Several investigators have looked at similar via configurations [3]-[9]. The
equivalent circuit model shown in Figure 5.3 provides the basis of the transition’s
characteristics.
For the RF via transition, the shorting vias are placed somewhat removed from the
center conductor of the stripline in order to preserve the field structure of the stripline.
Since the vias do not provide a smooth wall, the field lines from the center conductor of
the stripline are desired to terminate on the top and bottom ground planes. Therefore, the
wall spacing o f the shorting vias is kept greater than the strip-to-ground spacing, so Dwaii
should be approximately greater than 3 t - 4 t. The other limitation on the shorting via
140
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spacing is keeping the region below cutoff, Dwau < XJ2. Since the transition being
developed is a compact one, making a resonant cavity region around the via was not
investigated. A resonant cavity will be used however, when discussing the aperture
coupling transition. Finally, in the model, the gap spacing, Dgap, is used as the coaxial
outer conductor diameter. Therefore, deviations of the gap spacing from the actual
shorting wall spacing are anticipated to lead to less accurate results.
The key to the model is considering the RF via as a section of coaxial line
connecting the two stripline traces. This is illustrated in Figure 5.2. For simplicity, only
symmetric stripline (hf = Vi t) is considered in the dissertation. Symmetry is added to the
model by assigning half of the resulting capacitance to either side of the center pin
inductance as in Figure 5.3. Static equations for the inductance and capacitance are
simply [10]
f D gap A
(5.1)
K£r£„t
C' coax
_ r = - 7f ^ X
gap
In
(5-2)
v D,,a j
where t is the height of the stripline, D gap is the diameter of the slotted region
(approximately the via wall spacing) and DVja is the via diameter. These equations are for
symmetric stripline, such that the total via height is t.
141
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Top Ground
Top Stripline
Trace
Center G rou nd -^
Bottom
Stripline Trace
Bottom Ground
Coaxial Region
Figure 5.2. Section of coaxial line.
Figure 5.3. Equivalent circuit model for RF via.
5.1.1.2 Capture Pads
Manufacturing considerations of these transitions can be a key driver in the
physical layout. For example in the layout of Figure 1.2, a finite sized capture pad
142
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necessary where the via touches the metal layers. This is needed to allow for alignment
and drilling tolerances.
To account for variable sized capture pads and make the equivalent model slightly
more accurate for realistic designs, this capacitance m ust be considered. One effect that
seems to account for the dominant wave mechanisms is modeling the capture pad as a
parallel plate capacitor. This is illustrated in Figure 5.4. The electrostatic equation for
this is [10]
£r£pApad
(5.3)
Cpad ~
h
f
where Apad is the area o f the pad. Another useful approximation is considering the
capture pad as a short section of open ended transmission line which adds capacitance.
The capture pad capacitance is also important for via widths much greater than the
feedline width. Therefore, on higher dielectric constant materials, the capacitance of the
via can become dominant. This will be illustrated in the next section.
Figure 5.4. Circuit components of cross section.
143
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5.1.2 Validation with Measurements
Several measurements will be used to validate the circuit model and simulations
using HFSS [11]. HFSS is a finite elem ent method solver that can model complex 3-d
circuit structures. The shorting vias will be assumed to be numerous and closely spaced
so that a smooth perfect electric conductor is an adequate approximation. The RF via
design shown in Figure 1.2 used 12 vias around the periphery. The center conductor via,
however, is rigorously modeled with this EM simulator.
The first result is the RF via with measurements, circuit model, HFSS and
Momentum predictions given in Figures 5.5 and 5.6. M omentum calculations include the
12 shorting vias around the RF via. Identical results are obtained using a smooth wall
approximation and using the actual shorting via geometry with Momentum. The second
result is given in Figure 5.7, and the third result is given in Figure 5.8. These results
demonstrate the good accuracy of the calculations using HFSS and the circuit model.
Both solutions provide very usable S parameter information. Several observations can be
made about the RF via based on the results. The transition is compact, the shorting via
wall spacing is 3 x 3 mm. The transition is efficient, - 0.05 -0 .1 dB excluding mismatch
at 10 GHz. The transition has an input impedance that is relatively close to 50 Q and
does not change quickly (resonant) with frequency. These wideband characteristics will
be looked at in more detail later.
144
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Frequency
5 GHz
7
9
11
13
15
M easured
0.130Z-96.40
0 .1 5 4 Z -1 16.2°
0 .1 8 9 Z -1 19.9°
0.219Z-131.20
0 .2 4 2 Z -138.2°
0.235Z-145.30
HFSS
0 .1 12Z -105.5°
0.154Z -110.3°
0 .1 7 3 Z -115.4°
0 .2 2 6 Z -120.8°
0 .2 5 5 Z -126.2°
0 .278Z -132.0°
Circuit Model
0.123Z -105.4°
0.168Z -111.4°
0 .207Z -117.4°
0 .242Z -123.2°
0 .270Z -127.0°
0.291 Z -134.7°
Momentum
0.064Z-103.7°
0.102Z-109.2°
0.148Z -114.9°
0.200Z -120.7°
0.254Z -126.5°
0.302Z-132.20
Table 5.1. Measured and calculated S n for RF via of Figure 5.5.
15GHz.
.'- £ 0
- - • - Measured - S11
—
H F S S -S 1 1
- - ♦ - - Circuit model - S11
—
Momentum -S 11
Figure 5.5. Measured and calculated Sn data for RF via. Dimensions: Dwaii=3.18 mm,
Dgap=2.03 mm, DVia=0.787 mm, Dpacj=1.14 mm, t= 1.067 mm, £r=2.94, Wj=0.66 mm.
145
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Frequency
5 GHz
7
9
11
13
15
Measured
0.992Z-16.50
0.984Z-22.30
0.976Z-28.40
0.973Z-35.2 0
0.970Z-41.60
0.961Z-47.80
HFSS
0.994Z-14.20
0.988Z-19.90
0.981Z-25.40
0.974Z-31.10
0.967Z-36.80
0.961Z-42.60
Circuit Model
0.992Z-15.40
0.986Z-21.40
0.978Z-27.40
0.970Z-33.20
0.963Z-39.00
0.957Z-44.7 0
M omentum
0.998Z-13.80
0.995Z-19.50
0.989Z-25.20
0.979Z-31.10
0.967Z-36.90
0.952Z-42.70
Table 5.2. Measured and calculated S 2 1 for RF via of Figure 5.6.
I tttf
Y
' 5 GHz
— •— Measured - S21
■ H F S S -S 2 1
— ♦— Circuit model - S21
- - a - - Momentum - S21
Figure 5.6. Measured and calculated S 2 1 data for RF via of Figure 5.5. Start: 5 GHz,
stop: 15 GHz, step: 2 GHz.
146
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// o
■t - ;csS :
5 GHz
15 GHz
Measured
HFSS
Circuit Model
Figure 5.7. M easured and calculated Sn data for RF via. Dimensions: Dwan=3.i8 mm,
Dgap=3.05 mm, Dv;a=0.787 mm, D pad=1.14 mm, t= 1.067 mm, £^=2.94, Wf=0.66 mm.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-CM
:©
5 GHz
15 GHz
-•— Measured
»- - HFSS
* Circuit model
Figure 5.8. Measured and calculated Sn data for RF via. Dimensions: Dwaii=3.18 mm,
Dgap=3.05 mm, Dvia=1.016 mm, Dpad=1.27 mm, t=1.65 mm, £r=2.94, Wf= 1.067 mm.
148
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5.1.3 Results of Varying Via Diameter and Height
The following series of graphs compare the circuit model to simulated results
using HFSS. These calculations will show the effect of varying the via diam eter and
height.
The first set o f calculations use a fixed stripline geometry, the substrate thickness
and dielectric constant, stripline trace width, the via wall spacing and slot size are held
constant while the via diameter is varied from 0.06 mm to 2.35 mm. In all cases
considered in this section, the pad is assumed to be the same size as the via diameter and
therefore is not included in the circuit model. The substrate thickness is 1.524 mm and
the dielectric constant is 2 for these calculations. The input impedance for different via
diameters is shown in Figures 5.9 - 5.12 for the HFSS and circuit model calculations.
Notice that for very narrow RF vias, the input impedance is very inductive but becomes
increasingly capacitive as the width of the via approaches the width of the feed line.
Using these input impedance results, a least squares fit to the HFSS data is
performed using the circuit model of Figure 5.3. The curve fit values for L and C are then
compared to the predicted L and C of equations (5.1) and (5.2) and shown in Figures 5.13
and 5.14. A second series of calculations using a dielectric constant o f 4 are curve fit to L
and C values and given in Figures 5.15 and 5.16. The third series of calculations varies
the via height and correspondingly the substrate height (since only symmetric stripline is
considered) while holding the via diameter, via wall spacing and slot size constant. Using
the narrow via of 0.06 mm and dielectric constant of 2, L and C are found from curve fits
to HFSS data. The results of this case are shown in Figures 5.17 and 5.18. The final
series of calculations varies the via height but uses a wider via (1.97 mm).
149
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•18 GHz
2 GHz
HFSS
Circuit Model
Figure 5.9. Input impedance of HFSS and circuit model calculations for RF via.
Dimensions: Dwan=5.08 mm, Dgap=4.45 mm, Dvia=0.064 mm, Dpad=0.064 mm, t= 1.524
mm, £^=2.0, Wf= 1.346 mm.
•18 GHz-
HFSS
Circuit Model
Figure 5.10. Input impedance o f HFSS and circuit model calculations for RF via.
Dimensions: Dwaii=5.08 mm, Dgap=4.45 mm, Dvia=0.825 mm, Dpad=0.825 mm, t= 1.524
mm, £r=2.0, Wf= 1.346 mm.
150
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2 G H z/
.VS(F
HFSS
Circuit Model
Figure 5.11. Input impedance of HFSS and circuit model calculations for RF via.
Dimensions: Dwan=5.08 mm, Dgap=4.45 mm, DVia=1.589 mm, Dpad=1.589 mm, t=1.524
mm, £r=2.0, Wf= 1.346 mm.
2 GHz
HFSS
Circuit Model
18 GHz
Figure 5.12. Input impedance of HFSS and circuit model calculations for RF via.
Dimensions: Dwaii=5.08 mm, Dgap=4.45 mm, Dvia=2.35 mm, Dpad=2.35 mm, t= 1.524 mm,
£r=2.0, Wf= 1.346 mm.
151
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1.4
1.2
X
c,
H FSS
* — C ircuit m od e!
o 0.8
c
ca
4-*
o 0.6
3
■u
c
0)
0.4
0.2
0.5
0
1.5
1
2
2 .5
Via diameter, CVja (mm)
Figure 5.13. Comparison o f HFSS and circuit model inductance calculation.
Dimensions: Dwan=5.08 mm, Dgap=4.45 mm, t= 1.524 mm, £,=2.0, Wf= 1.346 mm.
0.14
0.12
uT
a
g
c
<B.
o
(Q
a.
ra
O
°-1
0.08
0.06
HFSS
Circuit m od el
0.04
0.02
0
0.5
1.5
1
2
2.5
Via diameter, D^a (mm)
Figure 5.14. Comparison o f HFSS and circuit model capacitance calculation.
Dimensions: Dwau=5.08 mm, Dgap=4.45 mm, t= 1.524 mm, £,=2.0, Wf= 1.346 mm.
152
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0.8
0.7
X
0.6
c
— HFSS
* — C ircuit m o d e l
0.5
o
c
n
*4
o 0.4
3
T3
c
0.3
0.2
0.1
0.2
0
0.4
0 .6
0.8
1
1.2
Via diameter, Dyja (mm)
Figure 5.15. Comparison of HFSS and circuit model inductance calculation.
Dimensions: DwaU=3.05 mm, Dgap=2.54 mm, t= 1.016 mm, £r=4.0, Wf=0.508 mm.
0.14
0.12
LL
a.
0 .1
CD
o
n 0.08
o
CO
Q.
co 0.06
H FSS
Circuit m o d el
O
0.04
0.02
0
0 .2
0.4
0 .6
0.8
1
1.2
Via diameter, D^ia (mm)
Figure 5.16. Comparison of HFSS and circuit model capacitance calculation.
Dimensions: DwaU=3.05 mm, Dgap=2.54 mm, t= 1.016 mm, £r=4.0, Wf=0.508 mm.
153
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1.6
1.4
)
o
c 1.2
CB
4*i
o
3
TJ
1
0
* — H FSS
« — C ircuit m o d el
C
0.8
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
Via height, t (mm)
Figure 5.17. Comparison of inductance of RF via versus via height. Dimensions:
DWaii=3.81 mm, Dgap=3.18 mm, D vja=0.064 mm, £[-=2.0, Wf=0.883 t.
0.045
ll
0.035
n
0.025
O
0.015
Circuit Model
0.005
1.2
1.4
1.6
1.8
Via height, t (mm)
Figure 5.18. Comparison o f capacitance of RF via versus via height. Dimensions:
Dwaii=3.81 mm, Dgap=3.18 mm, D via=0.064 mm, £^=2.0, W>=0.883 t.
154
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0.22
0.2
0.18
X
0.16
c
. °-1 4
o
£ 0.12
(C
o
3
0.1
■o
c 0.08
HFSS
Circuit M odel
0.06
0.04
0.02
0.8
1
1.2
1.4
1.6
2.2
2
1.8
Via height, t (mm)
Figure 5.19. Comparison o f inductance of RF via versus via height. Dimensions:
DWaii=3-81 mm, D2ap= 3 .18 mm, Dvia= l-97 mm, £^2.0, Wf=0.883 t.
0.26
0.24
^
U?
^a)
0,22
0.2
o
«
HFSS
Circuit M odel
0.18
a . 0.16
03
O
0.14
0.12
0.1
0.8
1
1.2
1.4
1.6
1.8
2
2.2
Via height, t (mm)
Figure 5.20. Comparison o f capacitance of RF via versus via height. Dimensions:
DWaii=3.81 mm, Dgap= 3 .18 mm, Dvja= 1.97 mm, £t=2.0, Wf=0.883 t.
155
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5.1.4 Wideband Designs
The RF via can be used for wideband applications. As the calculated impedances
in Figures 5.9 - 5.12 demonstrate, the transition is matched with a certain maximum
desired VSWR from 0 GHz until some upper limit frequency, Fmax. In fact, the
equivalent circuit model o f Figure 5.3 is recognized as a low pass filter network. The
circuit model provides a useful tool for understanding the transition’s performance.
The following calculations vary the diameter of the via for a given substrate
height and find maximum usable bandwidth, Fmax, defined as 0 - Fmax GHz such that
VSWR < 1.5. The data in Figure 5.21 uses a substrate with dielectric constant of 2 and
heights of 0.102, 0.152 and 0.203 cm. The data in Figure 5.22 uses a substrate with
dielectric constant o f 4 with these same substrate heights. In Figures 5.21 and 5.22, a
realizable line is indicated. Beyond the frequency marked as realizable, the via wall
spacing exceeds Xz/2 such that the circuit model is no longer valid. The data at these
higher frequencies is included to demonstrate the inherently wide bandwidth that is
possible.
The calculations demonstrate that for thin substrates, 50 D. matched transitions
can be constructed over the full stripline bandwidth. This 50 Q. transition is a function of
the height of the via, dielectric constant, via wall and slot gap spacing. However,
manufacturing considerations often dictate what DVia/t ratio is allowable. For example, in
the printed circuit board construction used in this work (discussed in more detail shortly),
the minimum DVia/t ratio allowable was approximately 1.5. This is a result of the process
steps to achieve the construction technique used in Chapters
6
and 7. A different set of
process steps could have allowed a much lower Dvia/t ratio.
156
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50
45
*— t = 0.102 cm
■— t = 0.152 cm
— t = 0.203 cm
40
35
N
X
30
^
25
0
CO
E
U-
20
Realizable
10
o
0.5
1
2
1.5
2.5
Via Diameter/Height (Qria/t)
Figure 5.21. M aximum frequency for VSWR < 1.5 for 0 G H z to Fmax. Dimensions:
Dwaii=0.381 cm, Dgap= 0 .3 8 1 cm, Sr=2.0, feed line impedance=50 £>.
50
45
— •— 1 = 0.102 cm
1 = 0.152 cm
— •— t = 0.203 cm
40
35
N
X
0
30
^
25
co
E
u.
20
Realizable
0
0.2
0.6
0.4
0.8
1
1.2
Via Diameter/Height (fyia/t)
Figure 5.22. M aximum frequency for VSWR < 1.5 for 0 G H z to Fmax. Dimensions:
DWaii=0-254 cm, Dgap=0.254 cm, 8^4.0, feed line impedance=50 Q .
157
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5.1.5 High Frequency Resonance
The equivalent circuit model given in Figure 5.3 is essentially a low pass filter
network. For the symmetric stripline considered here, the capacitances are identical. The
input impedance is
Z0 + 760(1 - to2LQ[L-CZ; ( 2 - or LC)]
(1 —orLC)2 +£o2C2Z;(2-orLC)2
(5.4)
The input impedance will equal Z q when f = 0, but also when
(5.5)
This resonance exists when 2C Z 2 > L . An example of the behavior of equation (5.4) is
demonstrated using L = I nH and C = 1 pF with a 50 Q. line impedance and shown in
Figure 5.23. The input impedance equals Zq at f = 0 GHz and 6.37 GHz, as equation
(5.5) predicts. The reactance equals zero at three frequencies: 0, 5.0 GHz and 6.37 GHz.
The 5.0 GHz case is where f 0 = (2K^jLC)~X .
However, L and C are linked by equations (5.1) and (5.2) for symmetric stripline
without a large pad contribution. The following equations assume that the pad
capacitance can be ignored, and therefore would only be applicable for via diameter less
than the feedline width. Therefore,
(5.6)
158
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Figure 5.23. Input impedance of pi network for L = 1 nH and C = 1 pF.
For low frequencies and electrically short via lengths, an approximate expression
for Dgap/Dyia tS
Dgap
= exp
27tZ0JfTr
(5.7)
lo
The £rk ^ t2 / 4 term of (5.6) results in a maximum 10 % error in the argument of the
exponential for
/ A„) < 0.14. For example, a 0.1016 cm substrate with £,=2.94,
fo=10 GHz, and 50 Q. feed lines, equation (5.6) gives D 2ap/D Via = 4.07 and equation (5.7)
gives Dgap/Dvia = 4.17. Therefore, for a 0.066 cm via, the gap diameter should be 0.269
cm. HFSS and circuit model calculations of this transition are shown in Fisure 5.24.
159
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One important consequence of equations (5.5) - (5.7) is that the resonance can be
used to achieve matched (narrow band) transitions at high frequencies. For example with
the 0.0508 cm substrate, a matched transition at approximately 38 GHz can be achieved
by calculating through equation (5.6) Dgap/D via to be 3.78 so that the gap for a 0.033 cm
via should be 0.125 cm. HFSS and circuit model calculations for this case are also shown
in Figure 5.24. It is also interesting to note that (5.7) describes the characteristic
impedance of a coaxial line [10] where Zq is the coaxial impedance. Therefore, for
electrically thin substrates ~ < 0.14 \ g, the R F via can be simply constructed using a
Dgap/Dvia ratio that makes a.50 Q. coaxial line.
—•— HFSS - 10 GHz
—■— Circuit model - 10 GHz
—♦— HFSS - 38 GHz
—* — Circuit model - 38 GHz
-10
-20
“
-30
T“
-40
£0
-50
-60 1 /
-70
0
5
10
15
20
25
30
35
40
45
50
F r e q u e n c y (G H z)
Figure 5.24. Matched transitions at 10 GHz and 38 GHz using proper Dgap/Dvia ratio.
160
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5.1.6 Construction Technique
The construction technique for the multilayered transitions is described in this
section. The construction of the multilayered circuits was investigated in depth for the
development of the package architecture. Hard substrate approaches using laminated
ceramics with polyimides and cyanoacrylates were investigated for millimeter wave
frequencies. Methods and procedures of constructing multilayered packages are still
developmental and expensive using these technologies. Therefore, much of the
experimental circuits in this dissertation used a printed circuit board technology,
sometimes called MCM-L (laminate). The disadvantage of using this technology is the
decreased performance at high frequencies caused by line etching and layer-to-layer
registration tolerances. However, improvements in processing techniques continue to
enhance the resolution of the line definition, making it compatible with millimeter wave
tolerances. These techniques have been successfully used for multilayered boards at 45
GHz [13] and single layer designs at 77 GHz [14].
The manufacturing process used to construct the multilayered circuits is a slightly
modified version of standard printed circuit board process with plated through holes and
blind vias. The basic configuration of a single signal level is stripline. In the actual
construction, the board was made using three laminated circuit boards to accommodate
the routing and blind via formation. The multilayered package is constructed by stacking
individual stripline slices. The mating surfaces of two layers are the top ground plane
from one layer and the bottom ground plane from another. Thus the connected surface is
metal-to-metal with annular regions which define the slotted region of the vias for the
layer-to-layer transitions.
161
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The connection between the two ground planes could be accomplished in many
ways, but two m ethods were used with success. The first uses a screen print mask with a
squeegied thin layer o f silver epoxy to selectively place conductive adhesive around the
regions that contained the buried cavity and RF via. The second placement method used
a dry epoxy film with the thickness of a piece of paper that is cut, placed and aligned
between the metal ground planes and cured. These attachment techniques are suitable
where alignment tolerances of 0.127 mm or greater is acceptable. These methods are
likely to be less expensive than conventional solder or eutectic solder approaches.
5.2 Aperture Coupled Striplines with Cavity Backing
The use o f the buried via in the RF via construction of the previous section has
many advantages. However, if the fabricational technology has difficulty with buried
vias, a multilayered transition using aperture coupling may be necessary. In this section,
an aperture-coupled stripline approach is investigated to provide power transfer between
layers. Previous work [1], [16], [17] demonstrate the feasibility of using this approach,
particularly for microstrip lines. However, it has also been shown in [16] and in Chapter
3 that using slots in the ground plane of stripline without a cavity lead to low efficiency
and poor coupling levels. Therefore, cavity backing is used and provides an efficient,
easily designed transition with total power transfer from layer-to-layer.
A full-wave model will be developed for the aperture-coupled stripline with cavity
backing transition shown in Figure 5.25 using the same technique as [17] and that
presented in Chapter 3. The advantages of using the reciprocity method [17] are the
enhanced numerical speed and derivation of equivalent circuit model. In fact, the
162
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equivalent model will be reduced to demonstrate the choice of physical parameters for the
transition.
5.2.1 Development of Equivalent Circuit Model
The method o f analysis proceeds exactly as in [17] and in chapter 3. The result is
the equivalent circuit model shown in Figure 5.26.
Stripline
Out Stripline
In —
Figure 5.25. Layout and geometry of aperture coupled stripline with cavity backing.
163
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Z s tu b c
y2
n::1
Yi
H.
Zin ^
Figure 5.26. Equivalent circuit model for aperture coupled stripline.
The circuit parameters are as defined in [17]
Avc
<
II
1
1 ~~ Z
Av/
1 Kc
In this Avf and Avc represent the voltage coupling factor from the stripline to the slot, as
determined by equation (3.9). In equations (5.8) - (5.10), the subscript f refers to the feed
line side and c refers to the coupled line side, where for example, f can refer to the bottom
stripline and c can refer to the top stripline. Yaf and Yac are the cavity aperture
admittances as defined by equation (3.16). Zof and Z qCare the stripline characteristic
impedances and Zstubc and Zstubf are the input impedance o f the open ended stubs.
164
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For a multilayered transition, a two port network is considered unlike the four port
in [17]. Therefore, two o f the ports are terminated with open end stubs leading to the
input impedance equation
z„ =
—
n
7
-------------Y,+
7
+
Z,,„„
(5.11)
+y,
Z uc -t^ Z siubc y
which can be written for a single PWS mode in the slot as
Z ofA V f
"=
zZ
Z
A v2
+ Z ‘”4/
<3' l2 )
Y- * t Y^ Z ^ r ~
uc
oc
stubc
For quarter wavelength open ended stubs at ports 2 and 3,
and Zst u b 3 are 0 at
resonance. Therefore, the input impedance reduces to
A v;-Z «/
VZ„. Av„
a *'•
, ) = --------7
Z,
Y . + — Y + — ---- a}
ac Z oc
OCZ
(5-l3)
If the admittance seen by the slots in the cavity were zero, that is if Yac=Yaf=0 , then the
above equation becomes
Avc
Z i n ( f r 's ) = ~ ^ t Z oc
(5.14)
which for symmetric stripline, Avc = Avf, results in
Z in( f res) = Z ac.
(5.15)
Therefore, for 50 Q. feed and coupled lines results in total power transfer from port i to
port 4, R=0, T = l.
The result of equation (5.15) is important since aperture coupled striplines can
potentially provide efficient multilayered signal transfer without a matching network.
165
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However, the key is in providing equation (5.13) with Yac = Yaf = 0. Using a cavity
around the slot provides a method of producing this result since the admittance is purely
reactive (for small conductor and dielectric losses) as shown in Chapter 3.
5.2.2 Results
Several transitions were measured and calculated with the full-wave model.
Momentum, and HFSS. The geometry and parameters of the aperture coupled striplines
with cavity backing are shown in Figure 5.25. The first case uses symmetric (almost)
stripline, with measured and calculated results shown in Figure 5.27 for input impedance
o f port I and Figure 5.28 for the input impedance of port 2. This first case used an
asymmetric cavity opening as discussed in Chapter 3. The same design using a
symmetric cavity opening has the measured results shown in Figure 5.29. A third
example with measured and calculated results is shown in Figures 5.30 and 5.31.
The narrow band resonance caused by the asymmetric cavity opening was
discussed in Chapter 3 and is demonstrated in Figures 5.27, 5.28, 5.30 and 5.31. Also,
the symmetric opening method of eliminating the resonance is confirmed by the
measurements of Figure 5.29. It should be remembered that since the cavity aperture
admittance is affected by the slot length and cavity dimensions, making the slot length
shorter and the cavity larger can achieve the same degree of matching while moving the
resonance lower in frequency (out of band). This technique was used in Figures 3.10 and
3.11.
For symmetric striplines (top and bottom substrate thickness equal), good
matching (-15 dB) is attained. Even the thin substrate of Figures 5.27 and 5.28, where as
166
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shown in Chapter 3 the bonding film of the printed circuit board process is important, has
good matching characteristics.
10.4 GHz
CM
/ - / 'i.J •'/
Measured
Momentum
Full-wave model
HFSS
Figure 5.27. Measured and calculated results for aperture coupled cavity backed stripline
for port 1. Dimensions: Lcx=Lcy=1.308 cm, t= 0.1118 cm, £ ^ 2 .8 8 , Ls=0.886 cm,
Ws=0.1016 cm, hf=0.0610 cm, Wf=0.066 cm, Lstub=0.438 cm. Freq: 8 - 1 2 GHz, step 0.4
GHz.
167
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-•— Measured
*- - Momentum
■ Fuii-wave model
Figure 5.28. iVIeasured and calculated results for aperture coupled cavity backed stripline
for port 2. Dimensions: Lcx=Lcy= 1.308 cm, t= 0.1118 cm, £-(2=2.88, Ls=0.886 cm,
W s=0.1016 cm, hf=0.0508 cm, W>=0.066 cm, LstUb=0.438 cm. Freq: 8 - 1 2 GHz, step 0.4
GHz.
168
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V -\1 2 GHz
7 0
*- - S21
8 GHz
Figure 5.29. Measured results for aperture coupled cavity backed stripline using
symmetric cavity opening. Dimensions: Lcx=Lcy= 1.308 cm, t=0.1067 cm, 8r=2.94,
Ls=0.886 cm, Ws= 0 .1016 cm, hf=0.0508 cm, Wf=0.066 cm, Lstllb=0.438 cm. Freq: 8 - 1 2
GHz, step 0.4 GHz.
169
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8 GHz
12 GHz
- • — Measured
-« — Momentum
- Full wave model
Figure 5.30. Measured and calculated results for aperture coupled cavity backed stripline
for port 1. Dimensions: Lcx=Lcy= 1.308 cm, t=0.1727 cm, £r=2.94, Ls=0.886 cm,
W s=0.1016 cm, hf=0.0965 cm, Wf=0.066 cm, LstUb=0.438 cm. Freq: 8 - 1 2 GHz, step 0.4
GHz.
V\ * \ \
w
tV*“ "
-• — Measured
-■ — Momentum
,
• Full-wave model '
Figure 5.31. Measured and calculated results for aperture coupled cavity backed stripline
for port 2. Dimensions: Lcx=Lcy=1.308 cm, t=0.1727 cm, £r=2.94, Ls=0.886 cm,
W s=0.1016 cm, hf=0.0762 cm, Wf=0.066 cm, LstUb=0-438 cm. Freq: 8 - 1 2 GHz, step 0.4
GHz.
170
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References
[1]
Herscovici, N.I. and Pozar, D.M., “CAD o f M ultilayer Feeding Networks,”
M icrowave Journal, pp. 84-96, June 1994.
[2]
Dietrich, F.J., Metzen, P. and Monte, P., “The Globalstar Cellular Satellite
System,” IEEE Trans. Antennas Propag., vol. 46, pp. 935-942, June 1998.
[3]
Ommodt, K., Sanzgiri, S., German, F. and Jones, T., “Vertical Interconnects for
Phased Array Packaging,” IEEE Antennas Propag. Int. Symp. Dig., pp. 13341337, July 1996.
[4]
Wang, T., Harrington, R.F. and Mautz, J.R., “Quasi-Static Analysis of a
M icrostrip Via Through a Hole in a Ground Plane,” IEEE Trans. Microwave
Theory Tech., vol. 36, pp. 1008-1013, June 1988.
[5]
Gu, Q., Yang, E. and Tassoudji, M.A., “M odeling and Analysis of Vias in
M ultilayered Integrated Circuits,” IEEE Trans. Microwave Theory Tech., vol. 41,
pp. 206-214, February 1993.
[6]
Pillai, E. and Wiesbeck, W ., “Derivation o f Equivalent Circuits for Multilayer
Printed Circuit Board Discontinuities Using Full Wave M odels,” IEE E Trans.
M icrowave Theory Tech., vol. 42, pp. 1774-1783, September 1994.
[7]
Kok, P.A. and De Zutter, D., “Prediction o f the Excess Capacitance of a Via-Hole
Through a M ultilayered Board Including the Effect of Connecting Microstrips or
Striplines,” IEEE Trans. Microwave Theory Tech., vol. 42, pp. 2270-2276,
December 1994.
[8]
Show-Gwo Hsu and Ruey-Beei Wu, “Full-W ave Characterization of a Through
Hole Via in Multi-Layered Packaging,” IEE E Trans. Microwave Theory Tech.,
vol. 43, pp. 1073-1081, May 1995.
[9]
Pillai, E.R., “Coax Via - A Technique to Reduce Crosstalk and Enhance
Impedance Match at Vias in High-Frequency M ultilayer Packages Verified by
FDTD and MoM M odeling,” IEEE Trans. M icrowave Theory Tech., vol. 45, pp.
1981-1985, October 1997.
[10]
Cheng, D.K., Field and Wave Electromagnetics, 2nd Edition, Reading: Addison
Wesley, 1989.
[11]
High Frequency Structure Simulator, version 5.2, HPeesof, Hewlett-Packard,
Santa Rosa, CA.
171
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[12]
Pozar, D.M., Microwave Engineering, 2nd edition, New York: John Wiley &
Sons, 1998.
[13]
Delisle, J.T., Gouker, M.A. and Duffy, S.M., “45-GHz MMIC Pow er Combining
Using a Circuit-Fed, Spatially-Combined Array,” IEEE M icrowave Guided Wave
Lett., vol. 7, pp. 15-17, Jan. 1997.
[14]
Pozar, D.M., Targonski, S.D. and Syrigos, H.D., “Design of M illim eter Wave
M icrostrip Reflectarrays,” IEEE Trans. Antennas Propag., vol. 45, pp. 287-296,
Feb. 1997.
[15]
Daigle, R.C., Bull, G.W. and Doyle, D.J., “M ultilayer Microwave Boards:
M anufacturing and Design,” M icrowave Journal, pp. 87-97, April 1993.
[16]
Das, N.K. and Pozar, D.M., “M ultiport Scattering Analysis of General
M ultilayered Printed Antennas Fed by M ultiple Feed Ports: Part U Applications,” IEEE Trans. Antennas Propag., vol. 40, pp. 482-491, May 1992.
[17]
Herscovici, N. and Pozar, D.M., “Full-W ave Analysis of Aperture-Coupled
Microstrip Lines,” IEEE Trans. M icrowave Theory Tech., vol. 39, pp. 1108-1114,
July 1991.
172
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C H A PTER 6
BURIED M M IC CAVITIES
This chapter explores the use o f a MMIC buried in an individual cavity in the
multilayered package. The concept was presented in Chapter 1 and is shown in Figure
1.1. The goal o f this investigation was to provide a method of using a cavity around the
M MIC that would provide isolation from other circuit structures and eliminate the need
for loss in the cavity [1], [2] to prevent oscillation from a MMIC amplifier. The circuit
element specifically addressed is shown as a close up in Figure 6.1. This chapter
provides just a cursory look at some o f the issues involved in using this circuit element.
A design capable of being used in the spatial power combined arrays of the next chapter
was desired.
In conventional and multichip module packaging, amplifiers and other active
devices are typically placed in metal housings for reliability concerns and environmental
protection. However, placing components within a metal enclosure can lead to
unintended propagation paths giving rise to crosstalk and oscillation. Often, a series of
components or cascade of amplifiers are placed in a metal channel with dimensions that
provide a below cutoff waveguide section. In addition, absorber is sometimes placed on
the back of the cover to further reduce the propagation of energy in the waveguide mode
[3]In this work, cavities are formed around individual MMIC amplifiers. Unintended
feedback is minimized by choosing the dimensions of the cavity to have resonances away
from the operating frequency o f the MMIC. However, as measurements will show,
173
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discontinuities in the substrate and wirebonds create a complicated response that is not
easily predicted. Therefore, measurements and experiments are used for cavity design.
Figure 6.1. Photograph of open cavity with MMIC carrier.
6.1 Passive Cavity
Several measurements were performed on passive cavities to provide initial
understanding. In addition, HFSS simulations and calculations were made for the cavity
resonances. The two passive cavity cases are shown in Figure 6.2. The cavity in Figure
6.2a has a through line and the cavity in Figure 6.2b has open ended stubs. The spacing
o f the stubs, Lgap, is the length of the M M IC carrier which is 1.143 cm long. Therefore,
coupling betv/een the lines is solely from cavity effects. The cavity is constructed with
many shorting vias around the periphery and an inhomogeneous substrate o f air over
174
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dielectric. For the measurements and HFSS simulations, a boxed stripline enters and
exits at the ends.
The first case is given in Figure 6.3 with the measured and calculated values. The
measured cavity resonance is 11.9 GHz. The lowest order mode for a short, partially
filled cavity, the TEno mode, can be solved using a field solution or transverse resonance
method [4]. The predicted resonant frequency is 12.1 GHz for the TEno mode. The TEio
mode for the boxed stripline is predicted to be excited at 15 GHz. In these results, a
version with a through line and a version with open ended stubs are used to demonstrate
potential problems of using a resonant cavity. A second case is the cavity size used for
the arrays in Chapter 7 and the open ended stub results are shown in Figure 6.4. The
predicted cavity resonance is 14.7 GHz and the measured result is 14.9 GHz.
Figure 6.2. Layout o f the passive cavity circuits, a) through line and b) open ended stubs.
175
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0
-10
r,
m
-o
-2 0
Through line-measured
Open stubs-m easured
- - -Through line-HFSS
CM
CO -30
w
/
-40
/
/
•
-50
Ji
l i t
7
L
9
11
'
'
’
»
13
15
F r e q u e n c y (G H z)
Figure 6.3. Measured and calculated data for through line and open ended stubs for large
cavity. Dimensions: t = 0.1118 cm, sr= 2.94, Lcx= 1.702 cm, Lcy= 1.336 cm, Wopen=
0.572 cm, W line= 0.127 cm, Lgap= 1.143 cm.
Open stubs-m easured
-10
-20
-30
-40
-50
-60
-70
-80
-90
-100
5
7
9
11
13
15
17
19
F r e q u e n c y (G H z)
Figure 6.4. M easured data for open ended stubs for small cavity. Dimensions: t = 0.1118
cm, £t=2.94, Lcx= 1.422 cm, Lcy= 0.991 cm, W open= 0.318 cm, W line= 0.114 cm, Lgap=
1.143 cm.
176
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The next two measurements are taken for the addition o f the MMIC amplifier and
carrier to the passive cavities of Figures 6.3 and 6.4. The presence and implementation of
the MMIC in this work causes a discontinuity in the ground plane, the substrate and bond
wires. A detailed but not precise representation is shown in Figure 6.5. The measured
S 2 1 with the MMICs unbiased for the two cavities are shown in Figure 6.6.
The 10 GHz MMICs were mounted on metal carriers that were screwed onto the
metal baseplate. This allows multiple measurements to be made since the interconnection
by wirebonds is done on the Alumina input and output sections that has thicker gold
metallization than the M M IC and may be repeatedly connected and disconnected. Also,
the large Alumina sections on the input and output creates a carrier size electrically
equivalent to the 45 GHz MMICs used in [5].
M M IC
Alumina section
W ire b o n d s
M M IC carrier
Baseplate
Figure 6.5. Side view o f MMIC in cavity.
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Small cavity
Large cavity
-10
-20
■o
CM
w
-30
-40
-50
5
7
9
11
13
15
F r e q u e n c y (GHz)
Figure 6.6. M easured S 2 1 of passive cavity with M M IC carrier.
6.2 Active Cavity
The results of the passive measurements demonstrate that the cavity and carrier
can have a significant effect on the overall behavior. The approach taken in this work is
to use a cavity far from resonance for providing stable operation. Other methods of
eliminating cavity effects include adding absorber (or loss) to the cavity [1], [2] and using
MMIC designs incorporating cavity effects [6], Eliminating the absorber from the cavity
removes what is typically a “hand crafted” process step. The other goal is to use off the
shelf components to minimize cost. These amplifiers are designed for operation in free
space and the package designer must deal with variations caused by the cavity.
The complicated MMIC carrier response of Figure 6.6 necessitates an
experimental technique to check for stability/oscillation. In general, the M M IC in a
178
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cavity can be view ed as a feedback amplifier. The cavity modes provide (from the ideal
M M IC design) undesired feedback that can result in unstable operation. For example, the
general feedback am plifier in Figure 6.7 has an output response given by [7]
A(cq)
\ —A{co)H {(d)
= ---------------- —
( 6 . 1)
-
V
V.t
—
for a matched input and output.
The Nyquist and Barkhausen criteria [7], [8] can be used to check for stability and
oscillation. The Barkhausen criteria can be used to determine oscillation frequencies, for
A{dB) + H {dB) > 0 dB
(6.2)
ZA(deg) + Z H { deg)= O(deg)
(6.3)
and
oscillation is predicted to occur. This can be found by measuring the small signal S 21
gain of the amplifier, A, with the cavity open and measuring the S 2 1 o f the closed cavity
with the amplifier unbiased but connected, H. As was shown in Figure 6.6, the wire
bonds can play a significant role.
V;I
Figure 6.7. Generalized feedback amplifier.
179
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Therefore, measurements for the small cavity with a M M IC amplifier was made
and shown in Figure 6.8. The large cavity with a MMIC amplifier has oscillations.
Figure 6.8 contains the small signal gain of the MMIC amplifier, A, and the unbiased
cavity measurement, H, from Figure 6.6. Plotted in Figure 6.8 is A+H (dB) which shows
that it is just below 0 dB and therefore not oscillating. Finally, the small signal gain of
the MMIC amplifier in the closed cavity is shown in Figure 6.8. The ripple in gain is
predicted since the phase of A(co)H(co) adds constructively and destructively in frequency
with unity in the denom inator of (6.1).
50
40
30
•"v.
20
CQ
■a
^
:______________
Vo/Vi - activ e cavity
— - - A - sm a ll sign al gain
- - - - H - c lo s e d cavity
A(dB)+H(dB)
10
-20
• N.
-30
-40
-50
5
7
9
11
13
15
F r e q u e n c y (G H z)
Figure 6.8. M easured results of small signal MMIC amplifier gain, closed cavity
unbiased MMIC, sm all signal closed cavity MMIC amplifier, and Barkhausen criteria
equation (6.1).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Since the amplifier is terminated with a patch antenna (viewed as a RLC circuit),
the response for the single element active antennas and arrays discussed in Chapter 7 is
different than that of Figure 6.8. For both the matched output and RLC output, the
stability is ju st barely achieved for this cavity design. In fact, several higher than normal
gain amplifiers do oscillate under these conditions. However, as higher input drive is
applied (reduced gain from nonlinear amplifier response), the oscillations disappear.
6.3 MMIC Characteristics
The MMIC amplifiers used in this work were originally Texas Instruments part
TGA8031-SCC. The amplifier is a four-stage device that consists of two 500 pm dual­
gate FETs and one 750 iim single-gate FET driving a 1500 (im output single gate FET.
The amplifier operated under bias conditions of drain voltage of 5.2 V, gate 1 voltage of 2.3 V and gate 2 voltages of -1.0, -0.75 or 0 V provides higher power added efficiency
(and less gain) than the bias conditions given in the data sheets. Small signal gain is
typically between 33 and 36 dB depending on device and gate 2 voltage. Since the
efficiency o f active devices is increased when operated in saturation [9] and modem
digital communication modulations use constant power [10], transmitters often operate in
saturation. A typical output power plot o f these amplifiers with varying input power at 10
GHz is shown in Figure 6.9. For this work, the input power operating point was chosen
to be -4 dBm (0.4 mW).
Typical large signal gains for the MMIC amplifier measured with the cavity open
and with the cavity closed are shown in Figure 6.10. This is a constant input power of -4
dBm at all frequencies in the band. For a linear device, the input power does not matter.
181
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40
35
E
CQ 30
TJ,
o 25
3
o
Q. 20
— M easured
- - Linear
3
Q.
15
1 dB
Compression
Point
10
5
-25
Operating
Point
-15
5
-10
Input Power (dBm)
-20
0
5
Figure 6.9. Output pow er characteristics of MMIC amplifier.
40
O pen cavity
C lo s e d cavity
30
20
m
TJ
10
CM
cn
0
-10
-20
5
7
9
11
13
Frequency (GHz)
Figure 6.10. Large signal conditions with cavity open and closed.
182
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15
A load-pull measurement [11] is typically used to characterize nonlinear
amplifiers, such as pow er amplifiers. The load-pull technique is a measurement method
that varies the load impedance presented to a device or amplifier and measuring the
output power and efficiency at a particular drive level and bias. Based on these empirical
results, optimum load matching for ideal output power or efficiency may be made. The
load-pull measurements made in this work use a reference plane outside the cavity in the
stripline section sim ilar to [5]. Therefore, ideal matching is approximately 95 - j 10 Q at
this reference plane with the measured result in Figure 6.11. The advantage of using this
measurement plane is that all of the discontinuities, MMIC mismatch, bond wires,
substrate changes, and cavity-stripline junction are included and referenced in a TEM
transmission line. This technique is used in the design of high output power spatial
power combined arrays discussed in the next chapter.
183
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25.00.
CM
// O
o.
Figure 6.11. Load-pull measurement of MMIC attached to carrier. Contour values are
given in dBm.
References
[ 1]
Williams, D.F., “Damping of the resonant modes of a rectangular metal package,”
IEEE Trans. Microwave Theory Tech., vol. 37, pp. 253-256, Jan. 1989.
[2]
Burke, J.J. and Jackson, R.W., “Reduction of parasitic coupling in packaged
M M IC’s,” IEEE M TT-S Int. Microwave Symp. Dig., pp. 255-258, 1990.
[3]
Kushner, L.J., personal communication.
184
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[4]
Pozar, D.M., Microwave Engineering, 2nd edition. N ew York: John Wiley &
Sons, 1998.
[5]
Delisle, J.T., Gouker, M.A. and Duffy, S.M., “45 GHz M M IC power combining
using a circuit-fed, spatially combined array,” IEEE M icrowave Guided Wave
Lett., vol. 7, pp. 15-17, Jan. 1997.
[6]
Jackson, R.W. and Wang, Z., “Circuit based model for coupling between MMIC’s
in multi-chip assemblies,” IEEE MTT-S Int. M icrowave Symp. Dig., pp. 13771380, 1997.
[7]
Clarke, K.K. and Hess, D.T., Communication Circuits: Analysis and Design,
Reading, MA: Addison-Wesley, 1971.
[8]
Gonzalez, G., M icrowave Transistor Amplifiers: Analysis and Design, 2nd ed.,
New Jersey: Prentice Hall, 1997.
[9]
Kushner, L.J., “Output Performance of Idealized M icrowave Power Amplifiers,”
Microwave Journal, pp. 103 - 116, October 1989.
[10]
Bums, L., “Digital Modulation and Demodulation,” in R F and Microwave Circuit
Design fo r Wireless Communications, L.E. Larson, ed., Artech House, Inc., 1996.
[11]
Takayama, Y., “A New Load-Pull Characterization M ethod for Microwave Power
Transistors,” IEE E M TT-S Int. Microwave Symp. Dig., pp. 218-220, 1976.
185
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CHAPTER 7
APPLICATION OF ARCHITECTURE AND MODELS TO SPATIAL
POWER COMBINED ARRAYS
7.1 Introduction
The multilayered packaging architecture of Figures 1.1 and 1.2 and the circuit
elements studied in the rest o f the dissertation enable the proper and efficient operation of
micro wave/millimeter wave active arrays. In particular, the specific type of active array
under consideration is spatial power combined arrays. In this chapter, design procedures
and analyses o f array results will be presented for several spatial power combining
examples.
This work is an outgrowth of an effort [l]-[3] to develop 45 GHz spatial power
combined arrays. The designs developed in this chapter retain several concepts from that
work. The basic approach uses a hybrid-circuit (or multichip module), tile architecture.
The tile approach utilizes multiple layers of circuitry that make up a subarray tile, and
then multiple tiles make up an overall array. Advantages o f using a tile approach are the
very low profile and compact architecture. Disadvantages include the increased
complexity o f the assembly and design caused by using multiple layers. The motivation
for this dissertation research has been to develop an array architecture that simplifies the
assembly and to develop design methodologies for the multilayer components.
The hybrid circuit or multichip module approach is used, as discussed in Chapter
I, and enables higher reliability and better performance o f an array since it can be
constructed with pre-tested MMIC devices. Choosing M M ICs with similar amplitude
186
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and phase characteristics helps reduce variation in the output of the array elements and
leads to higher performance.
A corporate feed is used to distribute the input signals to the MMIC amplifiers in
the array and possesses several advantages. First it provides isolation (> 20 dB) between
M M IC elements by using terminated power dividers (W ilkinson) in the feed network.
Second it provides an easy and accurate manner of providing an equal amplitude and
phase input signal to each MMIC element in the array. As will be discussed in the next
section, the antenna array efficiency degradation due to improper amplitude and phase
illumination is not discounted in this work and must be carefully assessed. The common
alternative to a corporate feed network is a spatial feed. This approach is used in the
plane wave am plifier arrays [4], [5] and the quasi-optical approaches normally associated
with spatial pow er combining. Achieving uniform amplitude and phase to each element
in a quasi-optic approach requires an external lens or phase shifters and leads to a
significantly more difficult design.
Finally, as discussed in Chapter 1, the thermal management of the waste heat
generated by the pow er amplifiers is a very important consideration for transmitting
arrays. Millimeter wave power amplifiers with Class A operation have an ideal
maximum dc-rf efficiency of 50 % [6], but typically more like 20 - 30 %. Therefore, for
each watt of RF power, more than one watt o f DC power (heat) is dissipated. High power
arrays (tens of watts) can generate significant amounts of heat (tens to hundreds of watts).
The array architecture used here incorporates a low thermal resistance path from the
M MIC to the heat sink with the whole back side of the array reserved for heat sinking.
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In this chapter, a brief discussion o f some salient points about spatial power
combining is given which provides some background motivation and introduces the
measurements and terminology used in the remainder o f the chapter.
7.1.1 Brief Discussion on Spatial Power Combining
A review o f spatial power combining is given here, with a full discussion found in
[7]-[9]. A primary motivation for using spatial power combining is generating high
power micro wave/millimeter wave sources or transmitters from solid state devices [7].
Solid state devices are preferred over tubes due to the potential for high reliability, low
cost and graceful degradation. However, the output power from a single solid state
device is limited [7]. Therefore, methods of combining the output from a number of solid
state devices is necessary.
The first method of combining power is found at the device level, where multiple
fingers, on a M ESFET for example, are combined. The second method of combining
power occurs at the circuit or MMIC level. Multiple devices can be combined in a
corporate com biner or on multiple MMICs. W ithout transmission line and combining
losses, there would be no other need than circuit combining. For example, given 0.5 W
output power MMICs, 8 W would be attained by combining 16 MMICs. However, the
presence o f loss acts to reduce the actual combined output power. Losses can be present
as improperly matched circuits, conductor and dielectric loss in the transmission lines and
amplitude and phase errors of combining. In addition, the loss grows with increasing
numbers o f devices, since interconnecting line lengths are greater and more levels of
combining exist [7].
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A basic figure o f merit that characterizes a spatial pow er combined array is the
effective isotropic radiated power (EIRP). The EIRP is found using the Friis transmission
formula [10] which is valid in the far field. For polarization matched antennas, the EIRP
is
EIRP = G.P.
t r =
uniform
r 4 7rPv
Prad, = 4
Gr l A ;
(7.1)
Therefore, using a m atched power meter on a standard gain horn results in an
unambiguous, directly measurable quantity since X, R, Gr and Pr are known. The radiated
power is related to the EIRP through the directivity of a uniformly illuminated aperture
[7],
EIRP
^ = 7 5 ------- •
uniform
0
7-2)
Defining the radiated power in this manner includes all sources o f possible loss. The DCRF efficiency is found by dividing the radiated power by the DC power. By accounting
for the available pow er of each MMIC device and comparing the radiated power of above
yields the combining efficiency [8] of
ric„mb= y j ^
•
/ -j 1n.available
(7-3)
n
This result has the advantage and the importance of including all array effects (amplitude
and phase variations, mutual coupling, etc.) into an efficiency result.
The combining efficiency can be further reduced into mismatch loss, circuit loss
and directivity loss,
^Icomb
mismatch^*circuit^directivity '
(7.4)
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The mismatch loss is the amount of power lost by not presenting the amplifier with its
optimum output impedance. The circuit loss accounts for conductor and dielectric loss of
the transmission lines and the radiation efficiency of the antenna. The importance of
using a high radiation efficiency antenna is shown since it is one component of many
possible loss mechanisms. The directivity loss is the loss due to not exciting all array
elements with equal amplitude and phase. The amplitude and phase variations of the
amplifiers and potential mutual coupling in the antennas contribute to this effect
The available power of the MMIC amplifier is defined as the output power
delivered to a matched load with a matched input [8]. This definition provides a
convenient method o f comparing several different spatial power combined arrays. It
assumes that the input and output of the MMIC have been matched to 50 Cl. In reality,
the output is not always matched perfectly to 50 Q. Defined in this way, the available
power does not completely account for all of the possible output power of the amplifier.
7.1.2 Shortcomings of 45 GHz Array
The development o f a 45 GHz spatial power combined transmitter [3] provided
the motivation for this research. The architecture for the array in [3] used a multiple layer
design with cavity backed patches for the radiating element and a corporate feed
constructed of covered microstrip. Ground pedestals provided the mechanical and
electrical contact for the antenna layer. The MMIC amplifiers were placed on the lower
level and a long bond wire was used to make contact between layers. A side view of the
architecture is shown in Figure 7.1 and an antenna layer layout is shown in Figure 7.2.
190
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There are several shortcomings of this array architecture. The large open cavity in
the input feed and exposure of the input feed to the cavity led to oscillation. The
oscillations generally were controlled by using high input drive levels. Driving the
amplifier far into saturation reduces the gain and likelihood of oscillation. The long bond
wire attachment was difficult to perform and repeat accurately. In addition, the transition
had losses on the order of 0.5 dB which immediately dropped the maximum possible
combining efficiency by 11 %. At the time, a suitable packaging technology was not
available, nor were the design methodologies devised, for transitioning the 45 GHz array
designs to the multilayered packaging approach studied in this work.
Long bond wire
Output layer
Input layer
MMIC
Figure 7.1. Cutaway view of architecture of 45 GHz array design.
191
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WILKINSON
DIVIDERS
PLATED THROUGH
HOLES
CUTOUTS FOR
RIBBON BOND
1_______________
MICROSTRIP
ANTENNAS
Figure 7.2. Antenna layer layout for 45 GHz array design.
These fundamental problems inevitably led to the development of the architecture
investigated throughout this dissertation. The oscillations have been kept under control
(even for the 10 GHz MMICs that have 35 dB small signal gain, as opposed to the 45
GHz MMICs that had 25 dB small signal gain) by placing amplifiers in individual
cavities and isolating circuit stmctures with shorting vias. The efficiency is improved by
removing the cutout, the long bond wire, and developing a design procedure to deal with
active antenna impedance.
L92
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7.2 Single Element Active Antenna Designs
The difficulty and cost of building 45 GHz array modules was circumvented by
studying scaled models at 10 GHz. In addition, the effort can be compared to previous 10
GHz work [I], [2]. The first two designs developed are single element active antennas.
The 10 GHz active antennas and arrays use the multilayered architecture described
in Chapter 1 and shown again in Figure 7.3. The architecture uses some of the circuit
elements developed in Chapters 2-6. The goal is to use the multilayered packaging
architecture with associated circuit elements of Figure 7.3 to design high combining
efficiency and stable single element and array designs. In addition, a design procedure is
developed by analyzing the components to allow formulation of designs that achieve the
desired performance.
7.2.1 Circuit Elements
The three primary circuit elements developed for this array have been discussed in
depth in previous chapters but are summarized here for completeness. These are the
cavity backed patch, the RF via and the buried M M IC cavity. The layout of the single
element active antennas including these circuit elements is shown in Figure 7.4.
The cavity backed patch is used in these array designs for its high radiation
efficiency and desirable mutual coupling characteristics. Further, since the antenna is
isolated from the antenna substrate by the cavity wall, other circuitry, for example the DC
bias distribution, can be routed on the antenna layer. The antenna used in this study is
fairly narrow band (~ 3 %). This resulted in a simplified analysis of its behavior and a
simple method o f calculating the radiated power.
193
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Cavity backed
patch
RF via
Load-pull reference
plane
MMIC Cavity
Figure 7.3. Side view of multilayered packaging architecture.
Matching
Network
Figure 7.4. Layout of single element active antennas, a) antenna layer without quarter
wave transformer, b) antenna layer with quarter wave transformer, c) MMIC layer.
194
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The multilayered transition in these designs use the RF via. As discussed in
Chapter 5, the RF via is a wideband, compact transition. The compactness is critical
when designing the corporate feed for the array. The RF via is also suitable for routing
the DC bias lines between layers and was used to minimize the number of circuit
elements needing development.
The MMIC amplifier was placed in a buried cavity as discussed in Chapter 6.
For the 10 GHz work, the MMICs are placed on a removable carrier which led to three
desirable traits: the size is now electrically comparable to the 45 GHz MMICs used in [3],
the whole MMIC assembly is made more rugged allowing many measurements to be
performed without risk o f damage, and some of the stabilization circuitry on the bias is
integrated on the carrier. The approach taken here in contrast to other designs using
absorber in the cavity is to move the cavity resonance so far from the amplifier gain that
the feedback effects will be minimized.
7.2.2 MMIC Matching
A photograph o f the M MIC in a cavity was shown in Figure 6.1. One of the
difficulties in providing the optimum load impedance to the MMIC is the number of
discontinuities on the am plifier output. Using a large signal load-pull measurement,
including these discontinuities at a well defined reference plane provides an experimental
technique to provide the optimum load impedance [3].
195
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7.2.3 Antenna Impedance
Utilizing the same reference plane o f the load-pull measurement, an equivalent
antenna impedance is defined looking into a section of transmission line, the RF via, a
section o f transmission line, quarter wave transformer and finally the actual antenna.
This is illustrated in Figure 7.3. The advantage of finding circuit models for the antenna
and RF via in previous chapters are clear, since the problem is reduced to straightforward
circuit optimization.
Two antenna designs are considered for the single element active antenna. One
uses a minimal length of 50 Q line between the antenna and the RF via as shown in
Figure 7.4a. The second design uses a quarter wave transformer as shown in Figure 7.4b.
The measured results of the two designs are shown in Figure 7.5. It should be noted that
the design without the transformer is actually matched to 50 Q, but the design with
transformer uses the enhanced bandwidth technique described in Chapter 2 and has a
resonant resistance of 80 Q. Discussion on calculation of the antenna impedance will
occur shortly.
7.2.4 Measured Results of Single Element Active Antenna
The design procedure presented above with the load-pull measurement and
antenna matching is validated with these two designs. The two antenna designs given in
the previous section are used with MMICs and measured to find the EIRP and radiated
power.
The EIRP was measured for the two cases and shown in Figure 7.6. The
directivity of the antenna was calculated to be 6.4 dBi. The radiated power is shewn in
196
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Figure 7.7. The DC-RF efficiency is shown in Figure 7.8. These results and the
calculations made in the next section lend confidence that the design procedure is sound.
These two single element active antennas are stable and since most circuit elements are
isolated in the array architecture, the array is expected to be stable.
•CM
10.2 GHz:
— • — With transformer
—
Wi t hout transformer
Figure 7.5. Measured input impedance for antenna with and without quarter wave
transformer. Start: 9 GHz, stop: 11 GHz, step: 0.1 GHz.
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6
4
2
0
2
■4
-6
8
With tr a n sfo r m er
W ith ou t tra n sfo rm er
-10
-12
9
10
9.5
10 .5
11
Frequency (GHz)
Figure 7.6. EIRP of single element active antenna designs.
0.6
0.5
5
tr
<D
3
0 .4
o
u
<D
0.3
/ \
CO
With transformer
Without transformer
=5
ra 0.2
cc
0.1
9
9.5
10
10.5
F r e q u e n c y (GHz)
Figure 7.7. Radiated power of single element active antenna designs.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
11
0.3
0 .2 5
>»
g
aj
o
£
0.2
0 .1 5
LL
DC
6
Q
o.i
With transform er
W ithout transform er
0.05
9
10
9.5
10.5
11
Frequency (GHz)
Figure 7.8. DC-RF efficiency of single element active antenna designs.
7.2.5 Calculation of Radiated Power
The results demonstrate some key concepts that lead to an ability to predict the
output power based on the load-pull results and calculated antenna impedances. The
ideal load impedance of a typical MMIC for frequencies 9.5, 10 and 10.5 GHz is
approximately 80 - j 35 £>, 90 -j 20 Q., and 90 Q, respectively. The output power over a
wide range of frequencies of a typical MMIC has been shown in Figure 6.10. Two
observations result. The output power and the load impedance of these MMICs are
constant over the antenna bandwidth. Therefore, overlaying the antenna impedance on a
load-pull measurement leads directly to the amount o f power supplied by the MMIC.
The calculated radiated power can be found by finding the amount of power
supplied by the MMIC due to load matching and accounting for circuit losses on the
output due to inevitable conductor and dielectric losses. In this case, the stripline is
199
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calculated to have 0.1 dB of loss, the RF via has been measured to have ~ 0.05 dB and the
antenna radiation efficiency is approximately 96 %. Therefore, the calculated radiated
power for the two cases is shown in Figure 7.9.
Urn
0.5
0)
3
o
Q.
"O
0)
0.4
”
0.3
(0
oc
T3
_<U
ra
3O
«
O
0.2
With transformer
Without transformer
0.1
9
9.5
10
10.5
11
F r e q u e n c y (GHz)
Figure 7.9. Calculated radiated power for single element active antenna designs.
7.3 4 x 4 Array Designs
The proper operation of the single element active antennas led to the development
of 4 x 4 array designs. The goal of these arrays was to provide high combining efficiency
and stable operation using the multilayered packaging architecture. Several errors in the
first array design were corrected in a second array design. The primary problems with the
first array design are an overly wide amplitude and phase variation amongst the MMIC
amplifiers and matching to the isolated antenna impedance.
The basic elements of the arrays are the same as the single element active
antennas. A cutaway view of the array design was given in Figure 1.2 and a layout with
200
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some o f the metal layers (6 in all) is shown in Figure 7.10. Photographs o f the bottom
and top layers are shown in Figures 7.11 and 7.12.
Figure 7.10. Layout of feed and antenna layers for arrays.
Figure 7.11. Input layer showing corporate divider and open MMIC cavities.
201
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Figure 7.12. Output layer showing cavity backed patches.
7.3.1 Design of Arrays
Several additional circuit elements were developed for the arrays. The corporate
feed network uses a straightforward layout as shown in Figure 7.10. A W ilkinson divider
was used in the feed network to increase the isolation between MMIC inputs. The
W ilkinson was optimized using M omentum [11] with first pass results close to predicted.
The DC bias distribution primarily uses the antenna substrate between cavity backed
patches for routing as demonstrated in Figure 7.10. Single bias inputs are routed around
to feed each of the MMIC elements.
The single bias point with via transition from the bottom to top layer causes a
couple of problems with the high DC current in the drain bias. A high current (> 5
Amps) passes through the single via on the drain input. The use of a single feed point is
202
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done to minimize the complexity of the array and bias circuitry. Feeding on the input
layer demonstrates that the package architecture is viable both from an RF and a DC point
o f view. A problem arises since the DC resistance of the via is 0.05 Q which leads to
0.25 V drop and 1.25 W o f lost power which correspondingly degrades the overall DCRF efficiency o f the arrays. Using multiple feed points or multiple vias w ould improve
this behavior. A second problem arose for the first array design, an assembly error at the
single via bias input caused one of the M M ICs to fail.
7.3.2 Antenna Impedance
The active antenna impedance was defined and presented in Chapter 4. For the
spatial power combined arrays, the first array design used the isolated antenna impedance
and the second array design used the active antenna impedance. M atching to the isolated
antenna impedance will be shown to provide good results, however improvements can be
obtained by matching to the active antenna impedance. These improvements include
better amplifier load matching and improved uniformity of the array elements.
The following antenna measurements are made with a reference plane on the
MMIC layer just outside the buried cavity. Therefore, the results include a quarter wave
matching transformer, short section of 50 £2 line, RF via and another short section of 50
Q. line. The measured and calculated edge element impedance and inner elem ent
impedance for the first array design are shown in Figures 7.13 and 7.14. U sing the active
antenna impedance and the quarter wave matching transformer, the matching transformer
can be used to alter the input impedance separately for the edge and inner elements. The
measured and calculated edge element impedance and inner element impedance for the
203
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second array design are shown in Figures 7.15 and 7.16. The characteristic impedance of
the matching transformer for the three cases are: 38 Q for the isolated antenna impedance,
43 Q for the edge element impedance and 47 Q. for the inner element impedance.
The structure from the reference plane through the RF via, through the quarter
wave transformer to the antenna is calculated using the circuit model approach taken
throughout this work. M om entum is used to calculate the active impedance as done in
Chapter 4 for a simple stub. A separate simulation calculates the dual stub input
impedance, which is then substituted using the equivalent circuit model in Chapter 2.
Circuit models are used for the rest of the elements, the RF via uses the model developed
in Chapter 5 and the transmission lines use ideal models in MDS [12]. The optimization
of the quarter wave matching network is now a simple circuit simulation. In contrast, it is
interesting to note that a code like Momentum does in fact handle the whole design for
isolated elements. The antenna, matching network, RF via and transmission lines can be
simulated with good results.
As an example, com parison of the measured, full calculated and circuit model
approach is given for the isolated antenna design shown in Figure 7.4b. The measured
isolated input impedance given in Figure 7.5 has a resonant frequency of 10.1 GHz and
resonant resistance of 80 Q. The calculated approach using a full M omentum calculation
(except for shorting vias which are simulated as smooth walls) has a resonant frequency
of 9.9 GHz and resonant resistance of 70 Q. The circuit model approach yields a
resonant frequency of 10.15 GHz and resonant resistance of 79 £2. Useful agreement for
design purposes is obtained with both approaches. However, the ran time for the full
calculated approach is an order of magnitude (10 X) longer than the circuit model
204
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approach, where run times were initially presented in Chapter 3. Active impedance
calculations using this approach are not practical from a memory and run time
consideration. However, the real problem is that a full calculation does not lead the
designer into understanding which parameter or component to change to affect a desirable
response. For the circuit model approach, the antenna can be calculated once and then a
multitude of circuit simulations can be run to improve the design. Circuit simulations
using MDS for example are nearly instantaneous calculations.
10.1 GHz-
« — Edge elem ent-m easured
* — Edge elem ent-calculated
9 .5 GHz
Figure 7.13. Smith chart plot of measured and calculated edge element active impedance
at load-pull reference plane for Array #1. Start: 9.5 GHz, stop: 10.5 GHz, step: 0.1 GHz.
205
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10.1 GHz;
{f/'ss:-- &
* — Inner elem ent-m easured
Inner elem ent-calculated
Figure 7.14. Smith chart plot of measured and calculated inner element active impedance
at load-pull reference plane for Array #1. Start: 9.5 GHz, stop: 10.5 GHz, step: 0.1 GHz.
10.1 G H z
* — Edge elem ent-m easured
-• — Edge elem ent-calculated
9 .5 G H z
Figure 7.15. Smith chart plot of measured and calculated edge elem ent active impedance
at load-pull reference plane for Array #2. Start: 9.5 GHz, stop: 10.5 GHz, step: 0.1 GHz.
206
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10.1 G H z
'eX
—■— Inner elem ent-m easured
- Inner elem ent-calculated
9 .5 GHz
Figure 7.16. Smith chart plot of measured and calculated inner element active impedance
at load-pull reference plane for Array #2. Start: 9.5 GHz, stop: 10.5 GHz, step: 0.1 GHz.
7.3.3 Measured Results
The measured results of the two arrays are shown in Figures 7.17 - 7.29. Figure
7.17 shows the EIRP results. Figure 7.18 shows the DC-RF efficiency results. Figures
7.19 and 7.20 show the available power and the measured and calculated radiated power
for arrays #1 and #2, respectively. Figure 7.21 shows the combining efficiency results.
Figures 7.22 - 7.25 show co- and cross-polarization patterns for the two arrays. Nearfield
plots o f the amplitude and phase at the array face are shown in Figures 7.26 - 7.29. Array
#1 was completely stable with or without RF drive. Array #2 was stable for normal drive
levels and with very low levels of input drive -8 dBm. The increased gain in the MMICs
of Array #2 cause several to oscillate without RF drive.
207
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30
29
28
27
m
26
25
o.
gc 2 4
UJ
Array #1
Array # 2
23
22
21
20
9 .7
9 .8
9.9
10
10.1
10.2
10.3
10.4
Frequency (GHz)
Figure 7.17. EIRP results of arrays.
30
27
24
Array #1
Array #2
21
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0
c
18
a>
'o 15
ie
in
LL 12
CC
1
o 9
a
6
3
0
9 .7
9.8
9.9
10
10.1
10.2
10.3
Frequency (GHz)
Figure 7.18. DC-RF efficiency of arrays.
208
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10.4
10
-
1—
o
3
o
Q.
TJ
0)
A vailab le P o w e r
- - C alcu lated Prad
M easu red Prad
05
T3
GJ
DC
T3
C
(a
a>
a
_ro
>
<
9 .7
9 .8
9.9
10
10.1
1 0 .2
10.3
1 0 .4
Frequency (GHz)
Figure 7.19. Available power, measured and calculated radiated power for Array #1.
10
1m
0)
3
o
Q.
■o
0)
C3
‘■05
5
DC
"O
c
03
O
.Q
as
re
>
<
— A vailab le P ow er
— M easu red Prad
—- C a lcu la ted Prad
9 .7
9 .8
9.9
10
10.1
10.2
10.3
1 0.4
Frequency (GHz)
Figure 7.20. Available power, measured and calculated radiated power for Array #2.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0.9
>*
0
0.8
1
° ‘7
£
0.6
A rray #1
Array # 2
LLI
O)
0.5
£
0.4
|
0.3
C
.a
O
0.2
0.1
9.7
9.8
9.9
10
10.1
10.2
Frequency (GHz)
10.3
10.4
Figure 7.21. Combining efficiency o f arrays.
o
E -C op ol
E -C r o ssp o l
-10
CQ
~D
a>
TJ -20
3
"q.
E
<
-30
-40
-100
-8 0
-60
-4 0
0
-20
20
40
60
Angle (degrees)
Figure 7.22. E-plane radiation patterns at 10.2 GHz for Array #1.
210
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80
1 00
0
H -C opol
H -C r o ssp o l
-10
5 -20
-30
-40
-1 0 0
-8 0
-6 0
-40
0
20
Angle (degrees)
-20
40
60
80
100
Figure 7.23. H-plane radiation patterns at 10.2 GHz for Array #1.
E -C op ol
E -C ro ssp o l
-10
-a
5 -20
Q.
-40
-100
-8 0
-60
-40
-20
0
20
40
60
Angle (degrees)
Figure 7.24. E-plane radiation patterns at 10.1 GHz for Array #2.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
80
100
0
H -C opol
H -C ro ssp o l
-10
5 -20
£L
-30
-40
-100
-80
-60
-4 0
0
20
Angle (degrees)
-20
40
60
80
1 00
Figure 7.25. H-plane radiation patterns at 10.1 GHz for Array #2.
2 .5 0 - ------------- 1-------------1-------------!------------- !------------- 1------------- 1------------- 1-------------1--------
2.00
1.50
1.00
0.50
0.00
-0.50
-
1.00
-1.50-
-
2.00-
II
-2.50-;-------------i-------------;-------------;------------- ;------------- ;------------- ;------------- |-------------;-------------2.50
-2.00
-1.50
-1.00
-0 .5 0
0.00
0.50
1.00
1.50
2.00
r
2.50
Figure 7.26. Amplitude excitation at 10.2 GHz for Array #1 from nearfield scan.
212
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2 .5 0
2.00
1 .5 0
1.00
r
0 .5 0 -
0.00•0 .5 0
- 1.0 0 -
- 1 .5 0 -
- 2.00
-2 .5 0 -2 .5 0
- 2 .0 0
-1 .5 0
- 1 .0 0
- 0 .5 0
0 .0 0
0 .5 0
1 .0 0
1 .5 0
2 .0 0
2 .5 0
Figure 7.27. Phase excitation at 10.2 GHz for Array #1 from nearfield scan.
2 .5 0 -
2 . 00 -
1 .5 0 J
1 . 0 0 -;
0.00- 0 .5 0 - t
- 1 .5 0 - r
-2.00-
-2 .5 0 - 2 .5 0
- 2 .0 0
- 1 .5 0
- 1 .0 0
- 0 .5 0
0 .0 0
0 .5 0
1 .0 0
1 .5 0
2 .0 0
2 .5 0
Figure 7.28. Amplitude excitation at 10.1 GHz for Array #2 from nearfield scan.
213
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2 .5 0 —
2 .0 0 -
1 .5 0 -
0 .5 0 -
0.00- 0 .5 0 -
-2 .00 ^
- 2 .0 0
- 1 .5 0
-
1 .0 0
- 0 .5 0
0 .0 0
0 .5 0
1.00
1 .5 0
2.00
2 .5 0
Figure 7.29. Phase excitation at 10.1 GHz for Array #2 from nearfield scan.
The peak EIRP results are 28.0 and 29.0 dBW or 631 and 794 W of effective
isotropic radiated power for arrays #1 and #2, respectively. These results are
improvements over the peak results of 27 dBW in [1]. The DC-RF efficiency peak
results of 23.7 and 24.7 % for arrays #1 and #2 are actually a DC-radiated power
efficiency since the losses o f the antenna are included in the measured data. The peak
MMIC DC-RF efficiency was 31 and 30 % for arrays #1 and #2, respectively. As
mentioned above, a full one percent was lost in the DC-RF efficiency due to the drain
bias via. The calculations o f the radiated power in Figures 7.19 and 7.20 are very
accurate considering the number o f circuit elements and number of MMICs (16). The
motivation o f constructing array #2 was based on a calculation showing that another 1
W att of radiated pow er was possible (plus another 0.5 W from a full 16 working
214
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MMICs). The calculation in Figure 7.19 discounts the lost MMIC power and additional
reduction in directivity. The combining efficiency results in Figure 7.21 represent the
greatest success o f this work. The closest reported combining efficiencies to date for CW
power have been under 68 % [1], [4], [5], [13].
The far and near-field patterns demonstrate the relative uniformity of the array
excitation. In particular, as discussed next, the MMIC amplifiers have amplitude, phase
and optimum load variations since no two devices are exactly the same. Therefore,
similar amplifiers are typically binned and used in a particular array. The amplitude and
phase variation of Array #1 was an error caused by using amplifiers with a wide phase
variation, but also from not matching into the optimum load impedance. Variations in the
load-pull measurements are greater away from the optimum load impedance. The near­
field results o f Figures 7.26 - 7.29 demonstrate the improvement in array excitation from
array #1 to array #2.
7.3.4 Tabulation of Losses
This section will enumerate the causes of loss and tabulate them for these array
designs. Knowing where the losses occurred allowed improvements to be made for the
results of array #2.
A M M IC was lost on array #1 and was found to be an assembly error. The
nearfield diagram in Figure 7.26 shows this clearly. A gate connection was not made that
caused on initial DC testing high drain currents that damaged the MESFET device on the
MMIC and eventually burned out the 1 W att limited bond wires. The other fifteen
MMICs still operate as initial testing determined.
215
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In general for these arrays, the loss can be categorized into three main sources:
1. M ism atch loss - not presenting the proper impedance to amplifier for
maxim um output power
2. Circuit loss - conductor/dielectric loss o f output lines, RF via, and antenna
radiation efficiency
3. Directivity loss - amplitude and phase errors at array elements
The mismatch loss as discussed above occurs due to presenting a load impedance
that is not optimum for maximum output power. For an isolated antenna, the antenna
impedance can be designed to correspond with the load-pull measurements of the MMIC.
However, two problems arise with the use of an array. The first problem is that, although
similar, each M M IC has a slightly different best impedance match. Therefore, the loadpull data of Figure 6.11 represents a typical (or average) result. The second problem is
that the active antenna impedance plays a role in detuning the output power.
The circuit losses can be minimized by reducing the line lengths and/or the line
attenuation. The circuit loss can be calculated and/or measured usually to a fairly high
degree of accuracy. In many ways, circuit loss has been minimized by the package
architecture. The use of the antenna directly above the MMIC leads to very short output
line lengths. The line length from the output of the M M IC to the input of the antenna is
approximately half a wavelength, thus leading to minimal line loss. The use of the high
radiation efficiency cavity backed patch and the efficient RF via eliminate many potential
sources of loss.
The last significant contribution to reduced radiated power is referred to as
directivity loss and is the amplitude and phase errors that lead to reduced antenna gain.
216
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The use o f the radiated pow er definition o f (7.2) include array excitation errors that
actually can contribute significantly to reduced performance. This is clearly evidenced by
the nearfield plots in Figures 7.26 - 7.29. F or array #1, the amplitude and phase errors at
the antenna elements lead to a predicted 0.5 dB loss based on the nearfield results. The
error is clear when the classic equation [14] is elucidated
D.
D,uniform
(7.5)
1 + 8 2 + C 71
where delta is the phase error (in radians) and sigm a is the amplitude error. The
measured phase deviation o f the S 2 1 of the 16 M M IC elements are +/- 20 degrees. This
phase error leads to a predicted 0.5 dB loss from the ideal directivity of 20.65 dBi for a
uniformly illuminated array [15].
The directivity loss can be reduced by choosing M M ICs with less deviation of the
S 2 1 . The second array design uses MMICs w ith less phase deviation +/- 10 degrees for
better performance.
The characteristics of the MMICs used for the arrays are tabulated in Table 7 .1.
The overall peak results for the two array designs are summ arized in Table 7.2. The
tabulation of losses is shown in Table 7.3.
Gain (dB)
DC-RF efficiency (%)
Output Power (mW)
Phase Variation (degrees)
Array #1
30.5
31.2
447
+ /-20
A rray #2
30.9
29.7
490
+/- 10
Table 7.1. Typical (average) MMIC characteristics.
217
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EIRP (dBW)
DC-RF Efficiency (%)
Radiated Pow er (W)
Available Pow er (W)
Combining Efficiency (%)
Array #1
28.0
23.7
5.3
6.8
78
Array #2
29.0
24.7
6.8
7.8
87
Table 7.2. Sum m ary o f peak results for two array designs.
Array #1
Array #2
Input Power
Estimated loss in Input Feed
Amplifier Gain
10 dBm
2 dB
30.5 dB
10 dBm
2 dB
30.9 dB
Output line loss
RF via loss
Antenna radiation efficiency
0.1 dB
0.05 dB
0.15 dB
0.1 dB
0.05 dB
0.15 dB
Amplifier mismatch loss
Phase error loss
Total Output Losses
0.4 dB
0.4 dB
l.l dB
0.1 dB
0.2 dB
0.6 dB
Total Radiated Power
Total System Gain
5.3 W
27.3 dB
6.8 W
28.3 dB
Table 7.3. Tabulation o f losses for two array designs.
7.4 Discussion of Measurements
For proper thermal performance, the arrays were mounted to a 8” x 6” x 1.5”
thermal baseplate with I” fins and a 3” fan blowing. Without fins, the array baseplate
warmed to 36 C, 15 C over room temperature. Since power amplifiers lose
approximately 0.02 dB/C [16] and the individual MMICs were measured at
218
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approximately 27 C, it is important for an accurate combining efficiency result to
compare MMICs at similar temperatures. The results for these array designs are made
after having “warmed up” over the period of an afternoon. Therefore, the radiated power
quoted above is CW power, which is important for many system applications.
The input power at the array input connector is flattened across the frequency
band. The array is excited with 10 dBm at the array input. There is 12 dB o f fan out loss
plus 2 dB of circuit loss to each MMIC amplifier leading to -4 dBm as shown in Table 3.
Several steps were performed to improve the accuracy of the measurements. For
short far field ranges the multipath from transmit to receive either directly or from
scattering may limit accuracy [10]. Therefore, multiple measurements, in this case two,
were spaced quarter wavelength away and averaged. The variation in received power is
approximately 0.1 dB at 2 m spacing.
As a check for the EIRP measurement, two standard gain horns were used and
confirmed to within 0.2 dB accuracy.
7.5 Discussion of Results
The array results o f a combining efficiency of 87 % and radiated power of 6.8 W
are impressive. In fact, using circuit combining results in a best case (no amplitude and
phase errors) based solely on circuit loss of 78 % combining efficiency for the 16 MMIC
amplifiers. The results achieved here demonstrate the understanding of the individual
circuit components and the success of the multilayered packaging architecture.
219
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References
[1]
Gouker, M .A., Beudette, R.G. and Delisle, J.T., “A Hybrid-Circuit Tile Approach
Architecture for High-Power Spatial Power-Combined Transmitters,” IEEE MTTS Int. M icrowave Symp. Dig., pp. 1545-1548, M ay 1994.
[2]
Gouker, M .A., Delisle, J.T. and Duffy, S.M., “A 16-Element Subarray for HybridCircuit Tile-Approach Spatial Power Combining,” IEEE Trans. Microwave
Theory Tech., vol. 44, pp. 2093-2098, Nov. 1996.
[3]
Delisle, J.T., Gouker, M.A. and Duffy, S.M., “45 GHz MMIC Power Combining
Using a Circuit-Fed, Spatially Combined Array,” IEEE Microwave Guided Wave
Lett., vol. 7, pp. 15-17, Jan. 1997.
[4]
Popovic, Z.B., Shiroma, W.A. and Weikle II, R.M., “Grid oscillators,” in Active
and Quasi-Optical Arrays fo r Solid-State Pow er Combining, R.A. York and Z.B.
Popovic, eds., New York: John Wiley & Sons, Inc., pp. 293-330, 1997.
[5]
De Lisio, M .P. and Cheh-Ming Liu, “Grid amplifiers,” in Active and
Quasi-Optical Arrays fo r Solid-State Power Combining, R.A. York and Z.B.
Popovic, eds., New York: John Wiley & Sons, Inc., pp. 331-376, 1997.
[6]
Krauss, H.L., Bostian, C.W. and Raab F.H., Solid State Radio Engineering, New
York: John W iley & Sons, chap. 12, 1980.
[7]
York, R.A., “Quasi-optical power combining,” in Active and Quasi-Optical
Arrays fo r Solid-State Power Combining, R.A. York and Z.B. Popovic, ed., New
York: John W iley & Sons, Inc., pp. 1-48, 1997.
[8]
Gouker, M .A., ‘T ow ard Standard Figures-of-M erit for Spatial and Quasi-Optical
Power-Combined Arrays,” IEEE Trans. M icrowave Theory Tech., vol. 43, pp.
1614-1617, July 1995.
[9]
Brown, E.R. and Harvey, J.F., “Research Focus on Quasi-Optical Technology,”
Microwave Journal, pp. 22-35, Sept. 1998.
[10]
Balanis, C., Antenna Theory: Analysis and Design, 2nd edition, New York: J.
Wiley & Sons, 1997.
[11]
M omentum, HPeesof, Hewlett-Packard, Santa Rosa, CA.
[12]
Microwave Design System, HPeesof, Hewlett-Packard, Santa Rosa, CA.
220
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[13]
Alexanian, A. and York, R.A., “Broadband Spatially Combined Amplifier Array
Using Tapered Slot Transitions in W aveguide,” IEEE Microwave Guided Wave
Lett., vol. 7, pp. 42-44, February 1997.
[14]
Skolnik, M.I., “Nonuniform Arrays,” in Antenna Theory, R.E. Collin and F.J.
Zucker, ed., New York: McGraw-Hill Book Company, pp. 233, 1969.
[15]
PCAAD, Personal Computer Aided Antenna Design, Antenna Design Associates,
Leverett, MA.
[16]
Kushner, L.J., personal communication.
221
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CHAPTER 8
CONCLUSION
In this dissertation, a study of microwave/millimeter wave active arrays has been
undertaken. In particular, a multilayered packaging architecture was presented that
utilizes MCM techniques and resolves several difficulties associated with constructing
microwave/millimeter wave active arrays.
Several novel circuit elements are possible using the packaging architecture
studied in the bulk of the dissertation. The cavity backed patch was shown to possess
high radiation efficiency even on thick, high dielectric constant substrates. A
transmission line model and full-wave model were developed for this antenna element.
In addition, an enhanced bandwidth design technique was developed for
electromagnetically coupled microstrip antennas. The active impedance matching of
small arrays is improved using separate matching networks for inner and edge elements
and a gain matching technique for proper spacing in arrays was presented. Two
multilayered transitions are presented with design models that allow efficient transfer
from layer-to-layer. The MMIC in a buried cavity provides isolation from other circuit
elements and placement directly to the metal baseplate allows a low thermal resistance to
the heat sink.
Finally, the multilayered packaging architecture and circuit/antenna elements were
used in the demonstration o f spatial power combining. The goals of achieving high
combining efficiency, stability and ability to predict the output power were achieved. The
222
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high com bining efficiency (87 %) of the arrays proves the viability of spatial power
combining even for small arrays.
223
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APPENDIX A
Av APPROXIM ATION
The simple equation (2.5) for Av for a proximity coupled patch is validated using
Momentum. A series of simulations of proximity coupled patches with varying feed
height are used to compare M omentum predictions with (2.5). For two different
substrates, the feed height is adjusted from 0.1 t to 0.9 t, where t is the height of the patch
substrate. The case when hfeed = t is the edge fed case. The input resistance of the edge
fed patch is noted as
R p a tc h -
The general input resistance of the proximity coupled patches
is written as R;n. The Momentum results with dimensions are tabulated in Table A .I.
hfeed/t
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Rin - case #1
8r = 2.94
0.064
0.258
0.582
1.046
1.658
1.926
2.778
3.884
5.352
6.826
R,-n - case #2
£,= 10.2
0.113
0.457
1.045
1.903
3.057
3.701
5.906
8.303
11.304
14.472
Table A .I. Momentum calculations of resonant resistance (x 50 Q.) of patches as feed
height varies. Case #1: Lp=Wp=0.831 cm, t=0.0635 cm, 8r=2.94, Wf=0.0254 cm,
Linset=0.0254 cm. Case #2: Lp=Wp=0.447 cm, t=0.0635 cm, £,-=10.2, Wf=0.0191 cm,
Linset=0.0127 cm.
224
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From equation (2.5)
R , = A v -R patch
at resonance.
R p a tc h
(A .l)
is the input resistance o f the patch fed at its edge. Therefore, Av can
be written as
Av =
V
R,
D
\ i/fe e d
(A.2)
patch J
Figure A .l shows the ideal curve given by (2.5) and the simulated data of Table A .I. The
approximation o f (2.5) is useful.
0.9
0.8
0.6
o
5Q
.
0.5
%
0.4
£
0.3
•
■
er= 2.94
er= 10.2
E quation (2.5)
0.2
0.1
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
hfeed/htotal
Figure A .l. Comparison of equation (2.5) and Momentum simulations of input resistance
for varying feed heights.
225
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APPENDIX B
TRANSMISSION LINE MODEL
The input admittance for an edge fed coplanar microstrip patch with the
transmission line model [1] shown in Figure B .l is
T,
^
T, , Y; - Y ^ Y sYc coth{yLe) - 2 Y mYc cosh{yLe)
+
F ^ r c c o th (^ )
*
°* A)
In (B .l), the line parameters corresponding to the patch, the complex propagation
constant, y, the characteristic admittance o f the patch, Yc, and the feed line radiation
reduction, r, are stated clearly in [1]. The slot admittance, Ys, the mutual slot admittance,
Ym, and the patch length, L , have been altered in the transmission line model o f Chapter
2 and are discussed in more detail.
y,Yc
- p a tc h
Figure B .l. Transmission line model for microstrip antenna.
226
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The addition o f the cavity and the use of the surface wave term is discussed in
Chapter 2. The new equations for Ys and Ym are
Y m = G m .n t* + J B m
(B -2)
K = { g , m + G ^ ) + ]B,
(B-3)
where
=
G m
w
r lr a d G s
C B -4 )
= T lr a d G m
GW =
( B -5 )
(B .6)
+< W )~
and R is 0 for conventional patches and given by (2.10) for cavity backed patches. A
closed form expression for the radiation efficiency, r|rad, is given in [2]. The original slot
and mutual admittance equations (Gs, Gm, Bs and Bm) are found in [1].
A final expression was presented in [3] that accounts for the reduction in resonant
frequency prediction of the original model [1] for thick, high dielectric constant substrates
and is given by
Le = Lp + A /-^ — .
A.
(B.7)
[1]
Van de Capelle, A., “Transmission-line model for rectangular microstrip
antennas,” in Handbook o f M icrostrip Antennas, James and Hall, ed., London:
Peter Peregrinus, Ltd., pp. 527-578, 1989.
[2]
Pozar, D.M., “Rigorous Closed-Form Expressions for the Surface W ave Loss of
Printed Antennas,” Electronics Lett., vol. 26, pp. 954-956, June 1990.
[3]
Duffy, S.M. and Gouker, M.A., “A Modified Transmission Line M odel for Cavity
Backed Microstrip Antennas, ” IEEE Antennas Propag. Int. Symp. Dig., pp. 21392142, July 1997.
227
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APPENDIX C
BASIS FUNCTION EXPANSIONS
As given in (3.1), the magnetic currents in the aperture are expanded with basis
functions given by
m(x, y) = x £
(x, y) + y £ Vynm yn (x, y ) .
m—I
(C. 1)
n=I
PWS modes are used to model the magnetic current in the direction of current flow with a
uniform pulse width. Therefore, mxn and myn are
mxn U ’ >’) = fu (y. w P, s ) f P( x ~ x n, hm)
my n y ) = f u (-r -Wpm) f p{ y - y n,hyn) ■
(C.2)
fu is a uniform pulse across the width of the PWS mode,
fu O,
)=-5 pw-j
where /v/<W pws/2.
(C.3)
fp is a PWS mode given by
sin k ( h —U)
f 0( u , h ) = -------:—— ---p
sin k eh
where h is the half length and
w here/u/<h
(C.4)
is the effective wave number
€ +1
(C.5)
The layout of these modes has been shown in Figures 3.4 and 3.5 for the CBP and SLP.
Defining a Fourier transform as
228
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F { k ) = ] f ( u ) e ~ Jkudu
(C.6)
the spatial domain representations for fu and fp becom e in spectral domain
sin kW nK, / 2
(C.7)
and
2ke(coskhun —co skehun)
F 'p
p
’^un )
f r 2
I 2 i
•
7
7,
- £ )sm£e/z„,
229
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(C.8)
APPENDIX D
SPECTRAL DOMAIN G R E E N ’S FUNCTIONS
The spectral domain form of the G reen’s Functions for the free space and parallel
plate excitation by a unit magnetic current elem ent are listed. The two dimensional
Fourier transform definition relating the space domain and spectral domain Green’s
functions is defined as
G(x,y)
J J Q{kx, k y) e ^ x-x')e 1^ y- f)dkxd ky .
(DA)
The following list the components o f the G reen’s function.
For a unit magnetic current source on an infinite ground plane:
QfJ^x =
at (x,y,0) due to x directed unit magnetic current element at (x’,y’,0)
Q™' = Hx at (x,y,0) due to y directed unit magnetic current element at (x’,y’,0)
QftM
y.x ~
at (x>y>0) due to x directed unit magnetic current element at (x’,y’,0)
Q/s% =
at (X’Y’0) due to y directed unit magnetic current element at (x’,y’,0)
For a unit magnetic current source in a parallel piate waveguide:
g " " = Hx at (x,y,t) due to x directed unit magnetic current element at (x’,y’,t)
=
at (x,y,t)
dueto y directed unit magnetic current element at (x’,y’,t)
Q™\x = f^y at (x,y,t) due to x directed unit magnetic current element at (x’,y’,t)
= Ky at (x,yd)
dueto y directed unit magnetic current element at (x’,y’,t)
For a unit electric current source in a parallel plate waveguide:
230
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Q™ = Hy at (x,y,t) due to x directed unit electric current element at (x’,y’,hf)
Spectral domain representations:
Free Space Components
Ic~ lc~
r~ °
(D.2)
fc Jc
O f* (k ,k ) =
* --- ■
-r '
M A
(D-3)
O f* (k x,,k yj) =
=
( ° - 4>
(D -5 '
Stripline Components
k : —erkz cosAr.r
wu
^ ^
(D6)
Q “1 ( * ,. * ,) =
,k ' k ' ! ° s * 'f
j k 0T]0k x sin k xt
<D -7>
Q ™ A k *>ky) = Q Z ( k x , k y )
\HM
Q
{K
. K.
s
) =
-
Z
iM A
(C-8)
! ° 5M
sin M
OD-9)
Stripline Feed
sin/:,/!,
Q™( k x , k y) = J -/sin A:xr
(D.10)
k\ = ^ £ rko ~ P 2 where Imag(ki) < 0
(D .l 1)
where
231
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k 2 = -Jk 2 —p z where Imag(k2) < 0
(D.12)
P2 = k ;+ k ;
(D.13)
232
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APPENDIX E
CAVITY REPRESENTATIONS
The Green’s function for the cavity excitation due to a unit magnetic current
source are listed. The components o f the Green’s function are defined as
G “l/ = H Xat (x, y, t) due to unit x directed magnetic current element at (x’,y’,t)
G" M = Hx at (x, y, t) due to unit y directed magnetic current element at (x’,y’,t)
G ™ = Hy at (x, y, t) due to unit x directed magnetic current element at (x’,y’.t)
G[[s' = Hy at (x, y, t) due to unit y directed magnetic current element at (x’,y’,t)
k \ ~ ( p K / La ) co sk. t
(* ’ y . z ; x ’, y' , z' ) = - — 2/
X X
k n L L
k o o k c x k c \ p —I (7=0
sin-
pj t
G r u . y ; x ’. y ) =
x +'
2 j
. pKr
sinx'+
pn
qK
qK
2 j
COS-
'ey \
y-
COS-
y +-
sin
(E-1)
■'ey \
~ 4j ?
k o 7l a L l e L 'cy
sin-
sin&.r
x +-
P=lq=l k z S m k J
cos-
pK
qK
COSV
-
J
-cy V
qK
(E.2)
2 j
HM t
G™(x,y,x',y')=G™
xv { x , y ; x ' , y ' )
(E.3)
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2j
y y
k o nlo L cx L cx p - 0 <7=1 p
c
pit
cosx-
cos-
pK
1 L cy ) cos k.t
sin£.f
fe.
qit
siny7
Ucy \
sin-
qit
y +-
(E.4)
"'ey \
where
[ l,p = 0
|U = 0
e„ = i^
„ and e =
p [ 2 ,p ^ 0
q \2 ,q 0
it. =
r
p it
kz -
qn:
(E.5)
V
, Imag(kz) < 0
(E.6)
v Lcx J
An analytical integration over the source and field pairs are performed resulting in the
following elements of the cavity admittance matrix defined in (3.14) - (3.17),
2j
k ) - ( p i t / La )~ cos k. t
(E.7)
sin k. t
- 4 jit1
HM
pq cos k .t
(E.8)
Sx
k z
„
HM
§ v.t
„
S in k zt
HM
(E.9)
§ xv
Svv’ =
K lo k x ^ c v
(E. 10)
sin k .t
k z
and
X .+ W /2
Cu{p, xi , W ) =
\ f u( x , W ) cos
pit
clx
(E .ll)
x, -\vn
pitWs
p it
p it
p it
p it
Cu( p , x i , W) = ~Lc* sin
cos——cos—— x ; —sin——sin—— x ;
pitWs
2 La
234
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(E.12)
and
L„
Cp(.yn hyi, k e) = J f p( y ~ y , , h , k ' ) s in - y ^ ( y + ~ ) d y
y .- fi
(E.13)
^cy
, , , 2 keL„ c o s q x / L „ - c o s k 'h
^
L
C A y i , h , k e) = -.
— 7 ;— sin— (v,- + - r i-).
p
sin k eh {keLa y ~ { q K ) L„
2
235
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(E.14)
BIBLIOGRAPHY
Aberle, J.T. and Pozar, D.M., “Analysis o f Infinite Arrays of One- and Two-Probe-Fed
Circular Patches,” IEE E Trans. Antennas Propag., vol. 38, pp. 421-432, April
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Alexanian, A. and York, R.A., “Broadband Spatially Combined Amplifier Array Using
Tapered Slot Transitions in W aveguide,” IEEE Microwave Guided Wave Lett.,
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Allen, J.L., “Gain and Impedance Variation in Scanned Dipole Arrays,” IR E Trans.
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Patch Antennas with Vias for Parallel-Plate M ode Suppression,” IE E E Trans.
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Brown, E.R. and Harvey, J.F., “Research Focus on Quasi-Optical Technology,”
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Cheng, D.K., Field and Wave Electromagnetics, 2nd Edition, Reading: Addison Wesley,
1989.
Clarke, K.K. and Hess, D.T., Communication Circuits: Analysis and Design, Reading,
MA: Addison-Wesley, 1971.
Collin, R.E. and Zucker, F.J., Antenna Theory (part 1), New York: McGraw-Hill, 1969.
Croq, F. and Pozar, D.M., “Millimeter-Wave Design o f W ide-Band Aperture-Coupled
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12, pp. 1770-1776, December 1991.
Daigle, R.C., Bull, G.W. and Doyle, D.J., “M ultilayer Microwave Boards: Manufacturing
and Design,” Microwave Journal, pp. 87-97, April 1993.
Das, N.K. and Pozar, D.M., “A Generalized Spectral-Domain Green’s Function for
M ultilayer Dielectric Substrates with Application to M ultilayer Transmission
Lines,” IEEE Trans. Microwave Theory Tech., vol. 35, pp. 326-335, March 1987.
Das, N.K. and Pozar, D.M., “Analysis and Design o f Series-Fed Arrays of PrintedDipoles Proximity-Coupled to a Perpendicular Microstripline,” IEEE Trans.
Antennas Propag., vol. 37, pp. 435-444, April 1989.
Das, N.K. and Pozar, D.M., “Multiport Scattering Analysis of General Multilayered
Printed Antennas Fed by Multiple Feed Points: Part II - Applications,” IEEE
Trans. Antennas Propag., vol. 40, pp. 482-491, May 1992.
De Lisio, M.P. and Cheh-Ming Liu, “Grid Amplifiers,” in Active and Quasi-Optical
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