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Microwave spatial power combining using MESFET oscillator array

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MICROWAVE SPATIAL POWER COMBINING USING MESFET
OSCILLATOR ARRAY
The members of the Committee approve the masters
thesis of Ali Alikoozehgaran
W. Alan Davis
Supervising Professor
04fU>
Ronald L. Carter
Kambiz Alavi
- ■s
/ ' U? ^ -* 7
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Dedication
To my mother for all the sacrifice
and
To my family for all the support they gave me
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MICROWAVE SPATIAL POWER COMBINING USING MESFET
OSCILLATOR ARRAY
by
ALIALDCOOZEHGARAN
Presented to the Faculty of the Graduate School of
The University of Texas at Arlington in Partial Fulfillment
of the Requirements
for the Degree of
MASTER OF SCIENCE IN ELECTRICAL ENGINEERING
THE UNIVERSITY OF TEXAS AT ARLINGTON
December 1995
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UMI Number: 1377844
UMI Microform 1377844
Copyright 1996, by UMI Company. All rights reserved.
This microform edition is protected against unauthorized
copying under Title 17, United States Code.
UMI
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Ann Arbor, M I 48103
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ACKNOWLEDGEMENT
The author wishes to thank his supervising professor, Dr. Alan Davis for his help
and encouragement throughout the course of this research, and to Dr. Jonathan Bredow
for the comments about designing patch antennas. I would also like to thank committee
member Dr. Ronald Carter for allowing me to use the network analyzer and other co-op­
erations.
Sincere thanks are expressed to Sayyid A. Nadimi for letting me use the spectrum
analyzer, and to the EE department staff members for their support. Special thanks to my
office mate Abbas AmiriChimeh for his support.
November 27, 1995
_
iv
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ABSTRACT
MICROWAVE SPATIAL POWER COMBINING USING MESFET
OSCILLATOR ARRAY
Publication N o.__________
Ali Alikoozehgaran, M.S.
The University of Texas at Arlington, 1995
Supervising Professor: W. Alan Davis
The primary purpose of this thesis is to demonstrate that spatial power combining
is capable o f achieving combining efficiency greater than 70%. A microwave spatial
power combiner has been designed to operate at 10 GHz. It consists o f single transistor
microwave oscillators designed on RT Duroid 5880 with relative permitivity of 2.2. The
Oscillators use ATF-26836, and ATF-26884 MESFET transistors. Oscillator simulation
was performed using EEsof LIBRA. Simulations have been optimized to fulfill impedance
matching requirements. The oscillators are designed using S-parameters for a typical bias
condition o f Vds = 3 V, and Ids = 10 mA. The operating frequency for the oscillators was
within 15% of the designed value. Combining efficiency of 80% to 90% was obtained.
The tuning bandwidth was 2.65 MHz or only 0.0265%.
v
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TABLE OF CONTENTS
ACKNOWLEDGMENTS ............................................................................................
iv
ABSTRACT .................................................................................................................
v
LIST OF ILLUSTRATIONS .......................................................................................
ix
LIST OF TABLES ........................................................................................................ xiii
CHAPTER 1. INTRODUCTION ...............................................................................
1
CHAPTER 2. POWER COMBINING TECHNIQUES .............................................
5
2.1 Resonant Cavity Combiners ...............................................................
5
2.1.1 Rectangular Waveguide Resonant Cavity Combiners .................
7
2.1.2 Cylindrical Resonant Cavity Combiners ......................................
12
2.2 Corporate Combiners .........................................................................
14
2.2.1 Hybrid Combiner ........................................................................
14
2.3 N-way Nonresonant Combiners ..........................................................
16
2.3.1 Wilkinson Combiner ...................................................................
16
2.3.2 Radial-Line Combiner .................................................................
17
2.3.3 Rucker Combiner ........................................................................
20
2.4 Chip-Level Combiners ........................................................................
20
2.5 Spatial Combiners ............................................................................... 23
2.6 Distributed Circuit Combiner ............................................................. 25
2.7 Multiple-Level Combining .................................................................. 27
CHAPTER 3. OSCILLATION THEORY ..................................................................
31
3.1 Resonators ......................................................................................... 31
3.1.1 Quality Factor ...........................................................................
32
vi
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3.2 Concept of Negative Resistance ......................................................... 33
3.3 Oscillation Condition Using Reflection Coefficient ............................ 36
3.4 Oscillation and Stability Condition ...................................................... 40
CHAPTER 4. POWER COMBINER DESIGN .......................................................... 49
4.1 Waveguide and Horn Antenna Design ................................................ 49
4.2 Oscillator Design ................................................................................. 52
4.3 Microstrip Patch Antenna Design ....................................................... 59
4.4 Drain-Side Transmission Line Design ................................................. 65
4.5 Source-Side Transmission Line Design ............................................... 67
4.6 Design Layout ..................................................................................... 67
CHAPTER 5. SINGLE OSCILLATOR SIMULATION ............................................ 71
• 5.1 MCOVER (Microstrip Cover Height) ................................................ 71
5.2 MSUB (Microstrip Substrate) ............................................................. 71
5.3 TAND (Dielectric Loss Tangent) ....................................................... 72
5.4 TEMP (Physical Temperature) ........................................................... 72
5.5 MWALL and PERM ........................................................................... 72
5.6 Drain-Side Simulation ......................................................................... 72
5.7 Source-Side Simulation ....................................................................... 74
5.8 Oscillator Simulation ........................................................................... 76
CHAPTER 6. MEASUREMENT AND CONCLUSION ............................................ 80
6.1 Combining Efficiency .......................................................................... 82
6.2 Bandwidth ......................................................................................... 89
6.3 Conclusion .......................................................................................... 92
APPENDIX A. ATF-26836 MESFET TRANSISTOR DATA SHEETS ..................... 96
APPENDIX B. ATF-26884 MESFET TRANSISTOR DATA SHEETS ..................... 99
vii
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APPENDIX C. LAYOUTS OF OSCILLATOR GRID .............................................. 102
APPENDIX D. LIBRA SIMULATION TEST BENCHES ........................................ 105
APPENDIX E. LIBRA SIMULATION DATA ITEMS ............................................ I l l
APPENDKF. RT/DURIOD 5880 DATA SHEET .................................................. 118
REFERENCES ........................................................................................................... 120
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LIST OF ILLUSTRATIONS
Figure
Page
1-1. Oscillator power combining techniques ............................................................
3
2-1. Rectangular waveguide resonant cavity combiner configuration
and cross-sections .....................................................................................
7
2-2. Modified circuit to double-diode capacity ......................................................
8
2-3. Equivalent circuit of the Kurokawa-Megalhaes combiner ................................
9
2-4. Coaxial waveguide diode mounting structure: (a) Top view,
(b) Side view ............................................................................................. 10
2-5. Equivalent circuit of coaxial waveguide diode mounting structure ................. 11
2-6. Cylindrical resonant cavity combiner, (a) Cross-section, (b) Top view ........... 13
2-7. Hybrid combiner schematic ............................................................................. 15
2-8. Output characteristics of hybrid combiner ....................................................... 17
2-9.
Power combining efficiency of hybrid-coupled combiner ............................... 18
2-10. Wilkinson N-way combiner circuit ................................................................. 18
2-11. Radial N-way combiner .................................................................................. 19
2-12. Schematic of a 12-way combiner circuit ..................................
21
2-13. Rucker's 4-way combiner ............................................................................... 22
2-14. Four IMPATT chip combiner ......................................................................... 23
2-15. Power combining through diode array ............................................................ 24
2-16. RF power combining using an array o f closely spaced diodes ....................... 24
2-17. 35 GHz spatial combiner block diagram and antenna array layout ................. 26
ix
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2-18. Three-device distributed combiner: (a) MIC realization,
(b) equivalent circuit ................................................................................ 28
2-19. Test station for measuring the large-signal impedance
of a Gunn device ....................................................................................... 28
2-20. Multiple-level combiner schematic ................................................................. 29
3-1.
Generic oscillator ............................................................................................ 31
3-2.
Series lumped model of a microwave resonator ............................................. 34
3-3.
The classical model of a negative-resistance oscillator ................................... 35
3-4.
Tc and i y ' on the smith chart ......................................................................... 39
3-5.
Nonlinear microwave oscillator ....................................................................... 41
3-6.
Negative impedance versus negative admittance ............................................ 43
3-7.
Generalized oscillator configuration ............................................................... 43
3-8.
Two-port loaded with two impedances .......................................................... 46
4-1.
Waveguide and horn antenna configuration .................................................... 49
4-2.
Rectangular waveguide ................................................................................... 50
4-3.
Waveguide cross-section ................................................................................. 51
4-4.
Horn antenna top view .................................................................................... 51
4-5.
Horn antenna side view ................................................................................... 52
4-6.
Oscillator designed not including dc bias circuitry ......................................... 54
4-7.
Three transistor configuration ......................................................................... 55
4-8.
Oscillator equivalent circuit using reflection coefficients ................................ 58
4-9.
Microstrip patch antenna configuration .......................................................... 64
4-10. Drain side configuration .................................................................................. 66
4-11. Step discontinuity ........................................................................................... 66
4-12. Source side microstrip configuration .............................................................. 68
4-13. An oscillator cell ............................................................................................. 68
x
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4-14. Front-side layout ............................................................................................ 69
4-15. Back-side layout ............................................................................................. 70
5-1.
Drain-side microstrip simulation ..................................................................... 73
5-2.
Simulated source-side microstrip configuration ............................................. 75
5-3.
Source-side impedance plot at different frequencies ...................................... 77
5-4.
Drain-side impedance plot at different frequencies ......................................... 77
5-5.
Simulated oscillation power for ATF-26836 .................................................. 78
5-6.
Simulated MESFET common gate configuration ........................................... 79
6-1.
Test set up for measuring combining efficiency ............................................. 80
6-2.
Bias configuration for MESFET .................................................................... 81
6-3.
Spectrum of oscillation at 12.01 GHz ........................................................... 82
6-4.
Spectrum of oscillation at 11.66 GHz ........................................................... 83
6-5.
Spectrum of combined power ....................................................................... 84
6-6.
Oscillation spectrum at 11.93 GHz ................................................................ 85
6-7.
Oscillation spectrum at 11.66 GHz .............................................................. 85
6-8.
Spectrum of combined power ....................................................................... 86
6-9.
Oscillation spectrum at 11.31 GHz ................................................................ 87
6-10. Oscillation spectrum at 10.78 GHz ................................................................ 87
6-11. Combined spectrum at 11.97 GHz ................................................................ 88
6-12. Test set up for measuring bandwidth ............................................................ 89
6-13. Oscillation spectrum at 10.22 GHz ................................................................ 90
6-14. Oscillation spectrum at 10.46 GHz ................................................................ 90
6-15. Combiner spectrum at 10.51 GHz .................................................................. 91
6-16. Combiner output along with injection signal .................................................. 92
6-17. Lower limit of injection locking ..................................................................... 93
xi
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6-18. Upper limit of injection locking .................................................................
93
C-l.
Oscillator grid ffont-side layout ..............
103
C-2.
Oscillator grid back-side layout .................................................................. 104
D-l.
Test bench for impedance measurment ....................................................... 106
D-2.
Sweep frequency oscillator test bench ........................................................ 107
D-3.
Oscillator analysis mode test bench ............................................................ 108
D-4.
Sweep power oscillator test bench .............................................................. 109
D-5.
Oscillator template test bench .................................................................... 110
xii
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LIST OF TABLES
Table
Page
4-1.
Common source S parameters for ATF-26836 GaAs MESFET .................... 60
4-2.
Common gate S parameters for ATF-26836 GaAs MESFET ....................... 61
4-3.
Oscillation status, and oscillation required source impedance ........................ 62
5-1.
Drain-side impedance at different frequencies ................................................ 73
5-2.
Source-side impedance at different frequencies .............................................. 75
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CHAPTER 1
INTRODUCTION
From microwave to submillimeter frequencies, it is desirable to combine the power
generated from many individual solid state devices because, each one of those devices is
limited in the amount of power it can produce. Also, there is a need to produce RF power
from solid state sources. Because of this reason, the generation of high power levels using
solid state devices requires the combination of the outputs of many individual sources. [2,
3,4]
In recent years, spatial power combining has been used extensively in solid state
radar or communication systems in microwave bands and millimeter wave bands. The
goal of power combining is to add the microwave power of several devices as efficiently
as possible. In general there are four main types of combiners: [S, 6]
1) Chip level: The outputs from many separate device chips are combined in a
certain manner at the chip level.
2) Circuit level: Device outputs are combined via microwave circuit elements such
as waveguides or planar transmission lines. This type can be further divided into two
categories. For moderate power levels, power combining can be achieved using 3dB hy­
brid couplers or lange couplers. For higher power levels, cavity power combiners using
waveguides are prefered.
3) Spatial: In this case, power from multiple sources is radiated, and combined in
free space rather than in a circuit.
4) Multiple level: Making use of two or more of the above combining techniques
1
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2
to combine the outputs of other combiners.
The typical method used to combine microwave power from active devices utilizes
a technique to locally resonate the individual active elements which are connected together
in a guiding structure capable of combining their powers. However, at high microwave,
and millimeter wave frequencies, those guiding structures are lossy. Therefore, utilizing
quasi-optical or spatial techniques is preferable.
Quasi-optical, and spatial combiners require many active devices connected to­
gether via some sort of radiating elements or antennas. Active devices are preferably os­
cillators which oscillate at almost the same frequency as designed. The frequency shift of
oscillators can be compensated by applying a wider tuning bandwidth for oscillation, and
by using more oscillating elements. Assuming that small frequency shifts depend upon dif­
ferences due to fabrication of active devices, the bigger the number of active elements, the
closer the statistical medium of resonant frequencies is to the desired operating frequency.
The circuit level combiners can be divided into resonant, and nonresonant combin­
ers. Resonant combiners include rectangular, and cylindrical-waveguide resonant-cavity
combining techniques. The nonresonant combining techniques include hybrid-coupled
combiners, radial-line combiners, and Wilkinson-type combiners. Differences between
these combiners will be discussed in chapter 2.
Different types, and categories of power combiners are shown in a tree-type dia­
gram in Figure 1-1. Resonant cavity combiners with IMPATT diodes have generated the
maximum power, although over narrow bandwidths o f around 0.2% to 3% [8]. Nonreso­
nant combiners provide wider band operation. Spatial combining is employed in antenna
array application. Since we are discussing oscillator power combining, many o f the com­
biners in Figure 1-1 may be used to combine the outputs of amplifiers also.
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Combiner
types
Chip-level
Circuit-level
Spatial
Multiple-level
Nonresonant
Resonant cavity
Rectangular
waveguide
resonant cavity
Cylindrical
resonant cavity
Other
combiners
N-way
Radial
line
Wilkinson
Corporate
Hybrid
coupled
combiners
Chain
coupled
combiners
Figure 1-1. Oscillator power combining techniques. (After Holzman [8])
U>
The focus of this thesis is to design a spatial power combiner which is located in­
side a waveguide horn. The active part of the combiner consists of four microwave oscil­
lators in an array-type configuration. The design goal is first to make the individual oscil­
lators work at 10 GHz. Then, it will be shown that high efficiency (80% to 90%) can be
obtained using the spatial combinig method. It will be shown in chapter 2 that spatial
combining is one of the most efficient techniques to achieve higher efficiency. Besides, it
can be easily extended to utilize more active elements, and achieve higher output power.
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CHAPTER 2
POWER COMBINING TECHNIQUES
This chapter reviews different combining techniques, and their properties. The pri­
mary focus of this chapter is the problem of power combining in the millimeter-wave fre­
quency range Of 3 to 300 GHz. However, some microwave combining issues will be dis­
cussed, because those techniques can be scaled up to the millimeter-wave frequency range.
The active devices used in combiners are IMPATT or Gunn diodes, although three-termi­
nal devices like MESFETs might be developed for millimeter-wave operations. [1,2]
The continuing demand for millimeter-wave radar, and communication systems has
created the need for high-power solid-state transmitters. Millimeter-wave systems can
have smaller antennas, cover wider bandwidth, and have better resolution than microwave
systems. Compared with optical systems, millimeter-wave systems offer better penetration
through fog, clouds, and dust. Solid-state transmitters might not surpass the travellingwave tube in output power or efficiency, however, solid-state devices offer improvement
in reliability, reduction in size, reduction in weight, and low-voltage power-supply
requirements. The output power from a single solid-state device is limited by fundamental
thermal, and impedance problems. To meet many system requirements, it is necessary to
combine several diodes to achieve high-power levels.
2.1 Resonant Cavity Combiners
A resonant cavity combiner was first developed by Kurokawa, and Megalhaes [16]
with a twelve-diode power combiner at X-band. The circuit includes a rectangular
5
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waveguide cavity with diodes mounted in cross-coupled coaxial waveguide diode mount­
ing modules in the waveguide walls. Based on the oscillator circuit theory, it can be
shown why this circuit configuration gave a stable oscillation, free from the multiple diode
moding problem. Replacing the rectangular waveguide cavity with a cylindrical resonant
cavity increases packaging density to accommodate a large number of diodes in a small
volume. This technique has been used to construct solid state power combiners for vari­
ous applications. The resonant cavity combiner has the following advantages:
a) high combining efficiency because of no path loss.
b) capability of combining a number of diodes up to 300 GHz.
c) compact size which can be used as a building block for multiple-level combin
ing.
d) built-in isolation between diodes to avoid mutual impedance variation by cou
pling to the cavity mode.
The disadvantages o f resonant combiners are:
a) bandwidth is limited to less than a few percent.
b) number o f diodes to be combined in a cavity is limited by moding problems
since the number of modes increases with the cavity dimensions.
c) electrical or mechanical tuning is difficult.
The combiner can be used as an oscillator, injection locking amplifier, or stable
amplifier. In the case of injection-locking amplifier, the normalized locking bandwidth
2 A/- / / q is proportional to the inverse of power gain (P0 / PL ), thus: [1]
2A/
fo
2
f
P
\-l/2
1n
(2.1)
a In J
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Where / 0 is the free-running frequency, A f is the one-sided locking bandwidth, P0 is the
free-running oscillator power, and PL is the injection -locking signal power. In most cases
Q. has a value that varies from 20 to 100, and (P0 / PL)from 10 to 20 dB. The locking
bandwidth therefore ranges from 0.2 to 3 percent.
2.1.1 Rectangular Waveguide Resonant Cavity Combiners
The rectangular waveguide resonant cavity combiner described by Kurokawa, and
Megalhaes [16] is shown in Figure 2-1. Each diode is mounted at one end of a coaxial
line which is coupled to the magnetic field at the side wall of a waveguide cavity.
Wave guide cavity
f To bias supply
Tapered termination
To load
Quarter-wave transformer
/
Diode
Magnetic field
f \ Lf \
L
L
I
A
Xg/4
Section through B-B
RF absorber
Coaxial center conductor
Section through A-A'
Transformer
— Diode
Figure 2-1. Rectangular waveguide resonant cavity combiner configuration, and crosssections. (After Holzman [8])
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8
This type of combiner is best suited for two-terminal devices. Like the SDO (single-de­
vice oscillator), the device is mounted at one end of the coaxial line, the device port, and
the center conductor is used to deliver dc bias.
To stabilize the oscillation, the other end of the coaxial line is terminated by a ta­
pered absorber. The coaxial circuits should be located at the magnetic field maxima of the
cavity in order to be properly coupled to the waveguide cavity. Therefore the diode pairs
must be spaced one-half wavelengh apart along the waveguide. In order to increase the
diode capacity, more diodes can be located on either side of the peak magnetic field. (Fig.
2-2)
v« V* V* V* V* V* V* V1 V4
66 A i d i 66 o'4"66 o o ’oo
oo c o oo OO
0 0 (00)00
oo
IM
« A V IO U IM
PU W M
MOQUUI
■Ml
VI
M
OIQOf
Figure 2-2. Modified circuit to double-diode capacity. (After Chang [1])
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The combiner equivalent circuit near the resonant frequency o f the cavity can be
modeled (Fig.2-3).
N identical
circuits
Port j
npl
jth device
admittance
Poit 1
Cavity model
Port N
Figure 2-3. Equivalent circuit o f the Kurokawa-Megalhaes combiner.
(After Holzman [8])
GL,GC, and C are the coupling coefficients between each coaxial module, and the
cavity. G„ represent the Eccosorb resistance, and YN the device admittance.The resona­
tor frequency is given by:
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(2 .2)
where a is the waveguide width, b is the waveguide height, and c is the resonator length,
with the corresponding eigen values n, m, and p. The resonant frequency can be easily
calculated for given resonator dimensions. The combiner building block is a cross-coupled
coaxial waveguide diode mounting structure. This structure is shown in Figure 2-4.
r
"H i
a
-o
ULC
(b)
Figure 2-4. Coaxial waveguide diode mounting structure: (a) Top view, (b) Side view.
(After Chang [1])
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11
A theoretical analysis of this configuration was first developed by Lewin [17,18].
The equivalent circuit was modified, and verified experimentally by Chang, and Ebert [19]
for the power combiner design. The equivalent circuit for a coaxial waveguide diode
mounting structure is demonstrated in Figure 2-5.
2INt
;:v.
IN
mu
2IN4
2IN3
Figure 2-5. Equivalent circuit of coaxial waveguide diode mounting structure.
(After Chang [1])
The coaxial line is of different diameters in the upper, and lower sections, and Zl,
Z2, Z3, and Z4 are the load impedances at each port, respectively. Z0 is the characteristic
impedance of the waveguide, and Z0I, and Zra are the characteristic impedances of the
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12
coaxial lines. Z0p is inductance caused by the post in waveguide excited by TEn0 modes.
Y', and Ylp,Y2p represent the effects of waveguide coaxial junctions. The rectangular
resonant cavity combiners can be used for CW or short-pulse operation. Diode heat dissi­
pation can not make any problem but the pulse shape of the bias current to each diode
ought to be tuned to reduce the frequency chirp which consequently increases combining
efficiency. The output power is only partially combined across the pulse duration unless
the above condition is provided. Thermal dissipation due to the closeness of the diodes
imposes severe thermal stress on diodes, and thus decreases reliability. Heat sinking, and
proper thermal control are key design prameteres to be kept in mind for CW combiners.
2.1.2 Cylindrical Resonant-Cavity Combiners
The cylindrical resonant-cavity combiner was first proposed by Harp, and Stover
[1]. The combiner shown in Figure 2-6 consists of a number o f identical coaxial modules
on the periphery of a cylindrical resonator. The output power of each diode is combined
by making use of a the cross-coupling of the coaxial module, and cylindrical resonator.
The combined power is then coupled to the load by means of a coaxial probe in the
resonator, and a coax-to-waveguide transition. This has been a well established, and
successful combining scheme for its small size, and symmetrical geometry. However, at
high frequencies, the cylindrical resonator is less desirable for the following reasons:
a)
The number of modes in a given frequency band increases rapidly when the
resonator diameter increases to accomodate more diodes. So, moding limits the number
of diodes which can be used at high frequencies because the diameter of the resonator af­
fects the number of diodes in a cylindrical combiner.
On the other hand, the rectangular resonant cavity combiner can be made longer to
accomodate more diodes while keeping the other two dimensions unchanged. The result
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is a slower increase in the number of higher order modes in the rectangular resonant cavity
combiner. Higher power can be obtained using a higher order mode cavity.
dc bias
RF absorber
[L
RFoutput
J
1
Bias
port
Coaxial
probe
E-field ‘
lines
m
a t t t
n
Device
port
Tuning
rod
(a)
Device
Magnetic
field lines
(b)
Figure 2-6. Cylindrical resonant cavity combiner: (a) cross-section, (b) Top view.
(After Holzman [8])
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b)
Input-output coaxial probe is hard to fabricate at high frequencies, and unless
precisely designed, and fabricated, it limits the operating bandwidth, and combining effi­
ciency.
2.2 Corporate Combiners
The corporate combiner adds the RF outputs of several oscillators through a cir­
cuit which isolates the oscillators from each other. Since this type of combiner does not
utilize any resonant cavity circuit to combine the outputs of the devices, it is known as a
nonresonant combiner. As a result, corporate combiners have the ability to operate over a
wider bandwidth than resonant combiners.
2.2.1 Hybrid Combiner
The hybrid combiner consists of a hybrid 2-dB coupler, and two oscillators as
shown in Figure 2-7. Three different configurations for the couplers have been used,
those with ports 2, and 3 in phase, or 90° out of phase (quadrature as shown in figure),
and 180° out of phase. Only the quadrature coupler will be discussed here. The oscillator
may be a SDO (single-device oscillator) or combiners. The moding problem associated
with resonant cavity combiner design is eliminated because the isolation between the
oscillators is provided by the hybrid coulper.Consequently, the oscillator, and the hybrid
circuit can be designed independently.
The hybrid coupler is quite suitable for both waveguide, and planar implementa­
tions. The coupler can be designed easily using commercially available CAD programs.
In general, the hybrid combiner is operated injection locked to make sure that the two
oscillators are synchronized in phase, and frequency.
The 3-dB coupler plays a crucial role in the operation of the combiner. Refering to
Figure 2-7, and applying the locking signal to port 1, the output is received at port 4. The
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
hybrid coupler is designed in a way that the port 1 signal power will be split evenly be­
tween ports 2, and 2. The distance from port 1 to port 3 is adjusted so that the signal re­
ceived at port 2 is 90° ahead in phase to the signal received at port 2. The coupler is de­
signed so that no power is transfered from port 2 to port 4. The coupler behaves identi
cally when power is applied at any of the other ports. For example, if a signal is applied at
port 2, it is split evenly between ports 1, and 4 with no power delivered to port 2.
Ports 2, and 3 are terminated with a pair of identical oscillators. Each oscillator
amplifies, and reflects its half of the locking signal. The signal reflected from the oscillator
Hybrid coupler
RF output
RF input
A©
-3 d B
-3dB
A©
Oscillator
Oscillator
Figure 2-7. Hybrid combiner schematic. (After Holzman [8])
at port 2 splits evenly between ports 1, and 4, but the phase o f the signal at port 4 is 90°
delayed in phase behind the signal at port 1. A similar group of signals is created by the
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signal reflected from the oscillator at port 2. Output characteristics of a hybrid-coupled
combiner are shown in Figure 2-8. Figure 2-9 shows the variation in combining efficiency
associated with hybrid combiners.
2.3 N-way Nonresonant Combiners
The N-way nonresonant combiner is an extension of the hybrid combiner. Instead
of having two oscillators combined at a time, N oscillators are combined with a single cir­
cuit. There are plenty of configuration varieties. The N-way combiner has a wide band
width, although it is difficult to isolate the oscillators. Moding problems can also happen.
Resistive materials are usually placed between devices or in the waveguide hous­
ings to increase the isolation among the devices, and minimize higher order mode excita­
tions. Because of these reasons, the N-way nonresonant combiner is difficult to operate
above 60 GHz.
2.3.1 Wilkinson Combiner
The Wilkinson N-way combiner / divider is shown in Figure 2-10. N oscillators
are combined through quarter wavelength transmission lines into one input-output port
with the characteristic impedance of Z0. The characteristic impedance of the N lines is
-v/ n Z0. The isolation among oscillators is done by resistors connected in a star pattern to
a common point. An injection locking signal is applied to the input-output port, the signal
is then split N ways, amplified, recombined, and directed back to the input-output port.
The problem with the Wilkinson isolation resistors is that at high frequencies it is
not possible to connect all resistors in a planar circuit. Gysel [20] proposed an improve­
ment to the Wilkinson design that eliminates the star pattern for the isolation resistors, and
uses conventional coaxial terminations for the ports.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
17
JLO
XP
j 1.0
•»
>2.0
-IJ0
U
II
U
U
M M I W W iM N C t IN 00
(a)
XP
m
cmi
o
8
z
MP
.1 0
>2.0
>1.0
OlO
M
22)
n u n otFFCMNCt m «
10
(b)
Figure 2-8. Output charactristics of hybrid combiner. (After Chang [1])
2.3.2 Radial-Line Combiner
Cohn, and co-workers [21,22] modified Wilkinson's design. They proposed
radial-line combiner shown in Figure 2-11. The oscillators are mounted in a radial
configuration, and the isolation resistors are connected between adjacent transmission
lines. Therefore the radial-line combiner can operate at microwave frequencies. The
radial-line combiner can be used with two, and three-terminal device oscillators.
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18
100
6p
------------------------ =
5
0
5
20
90
.1 $
X> w
-------------- _
e >* 80
----------------------3° =
u
b *§
70 Pi £4)
Cl
60
.5
40
60
|
a
&
80
SO
1
-3.0
1
-1.0
1
_J_.......
1.0
3.0
Power difference (in dB)
Figure 2-9. Power combining efficiency of hybrid-coupled combiner.
(After Holzman [8])
Oscillator
Oscillator
HA
Oscillator
Floating common
point
Figure 2-10. Wilkinson N-way combiner circuit. (After Holzman [8])
Circulators might be needed at the ports to improve combiner stability.
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Hanna, and Jumeau [23] have designed, and built a 12-way power combiner circuit
entirely in microstrip circuitry. A modification of the radial-line combiner is the 12-way
Oscillator
Oscillator
^
Input/output
----------------------
Oscillator
Figure 2-11. Radial N-way combiner. (After Holzman [8])
combiner that consists of two stages of resistors, and quarter wavelength transmission
lines (Figure 2-12).
The values of the circuit elements are calculated so that:
a) The insertion loss from any of the ports 1 through 12 to the output port is
maximally flat.
b) The output port is perfectly matched at the center frequency of operation.
c) The isolation, and match of the input ports are optimal at the center frequency.
If the device impedance is Zd = 50 Q, a circuit analysis shows that R, = 50Q,
R 2 = 166Q,Z01 = 131.5Q, Zra = 690., and Z ^ = 15.1Q. Two quarter wavelength lines
with characteristic impedances of 20.5 Q, and 36.9 Q can be used to match the output to
50 O.
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Hanna, and Jumeau built a test combiner using a 10-mil-thick Duroid substrate.
The resistors were provided using commercially available chip resistors. Over the fre­
quency band of 10-14 GHz, a minimum isolation of 17 dB was achieved.
2.3.3 Rucker Combiner
Another N-way nonresonant combining technique was proposed by Rucker [24],
and later analyzed by Kurokawa [25], Figure 2-13 demonstrates Rucker combiner. This
technique makes use of five transmission lines for a five diode combiner. Each transmis­
sion line is approximately one quarter wavelength long, and terminates a device. Trans­
mission lines are arranged radially a common bias network, and a common output net­
work. a resistor R 5tab is added into each coaxial center conductor to eliminate instabilities.
The capacitance Cc between the output coupling disk, and each coaxial center conductor
provides the necessary coupling to the common load R L. CW power output exceeding 4
W at 7 GHz, and 3W at 9 GHz has been accomplished using 0.5-1 W diodes [26], No ef
fort has been made to generalize this circuit to millimeter-wave frequencies.
2.4 Chip-Level Combiners
To accomplish power combining, a multichip configuration consisting of two or
more separate active device chips can be connected together to achieve stable oscillation
or amplification with higher power output. The chip level combining concept was first
proposed by Josenhans [27] to combine three IMPATT diodes electrically in series, and
thermally in parallel on a diamond heat sink. This configuration results in high overall im­
pedance, and low thermal resistance. An output power of 4.5 W at 13 GHz with an effi­
ciency of 6.4 percent was achieved.
The basic limitation of chip-level combining is device interactions, and the circuit
impedance. As frequency increases, lateral dimensions need to become small, and thermal
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21
Impedance
transformer
to
output
_
mm
V
2) 2d
Figure 2-12. Schematic of a 12-way combiner circuit. (After Holzman [8])
interactions occur among devices. This can limit the number of diodes to be combined.
The most successful chip-level combining technique was proposed by Rucker [24]. Figure
2-14 shows the combining geometries. To avoid the instability problems associated with
multichip interactions, quartz capacitors are placed in parallel with each diode. Most re­
sults reported are at X-band. However, recent experiments have extended this technique
to 40 GHz [28],
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•VPASS CAPACITOR
Figure 2-13. Rucker's 5-way combiner. (After Chang [1])
A similar technique using the parallel diode array method was suggested by Swan
[29]. In this technique, diodes put together in a small area are combined as a single diode
from the RF point of view (Figure 2-15). Therefore, a single tuning circuit can make it
operate. The diode array can be fabricated using batch processing to improve reliability.
Impedance matching between the array, and circuit becomes more intricate as fre­
quency increases. That is due to the low impedance of the multidiode array. Besides, at
higher frequencies, the lateral dimensions of the diode array are no longer small compared
to the wavelength, and each diode does not share the same electromagnetic environment.
In the millimeter-wave region, the lateral dimensions of the array become comparatively
small resulting in thermal interference among diodes. Suzuki [30] examined a 70 GHz
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two-diode array arranged unsymmetrically with respect to a standoff to reduce the lateral
dimensions of the array. An output power of 380 mW at 70 GHz has been achieved from
two silicon double-drift IMPATT diodes. This is 1.7 times the power of a single diode.
2.5 Spatial Combiners
The spatial combiner adds the microwave power of oscillators in free-space
through constructive interference of the outputs. The combined power can be collected
either by another antenna or simply reflected off a target in a radar system. For example, a
large number of power amplifiers are used to build an array of active radiating apertures in
a phased array antenna. A spatial combiner was first successfully proposed at 140 MHz
by Staiman [31] to combine one hundred transistor amplifiers with a net gain of 4.75 dB,
and output power of 100 W. Figure 2-16 displays the array arrangement of this work.
Quartz post
Capacitor
Gold foil
Diamond
Diode chip
Figure 2-14. Four IMPATT chip combiner. (After Holzman [8])
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24
Figure 2-15. Power combining through diode array. (After Chang [1])
.CONDUCTING
ac*«N
ARRAY ELEMENT
Figure 2-16. RF power combining using an array of closely spaced dipoles.
(After Chang [1])
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Power is accumulated by using an array of very small radiating elements, put
closely together with each element fed by an active device. The output power of each
device is then radiated, and combined with others in free space. In another approach, a 35
GHz active array was developeded by Durkin [32]. It spatially combines the power from
pulsed IMP ATT oscillators integrated with a printed circuit antenna. Figure 2-17 shows a
block diagram, and its antenna array circuit of this combiner.
The antenna array includes 32 radiating elements in a S.S-in diameter aperture.
The array is divided into quadrants for monopulse operation, and each quadrant is fed by
an injection locked pulse IMP ATT oscillator. The injection locking signal is provided by a
two-stage exciter, and distributed to the aperture oscillators through the monopulse com­
parator. An injection-locked pulse power output o f 36 W has been achieved with an array
gain of 29 dB.
2.6 Distributed Circuit Combiner
In a distributed combiner the devices are treated as elements of the resonant cir­
cuit. Mortazawi, and Itoh [33] have developed injection-locked planar distributed com­
biners with Gunn devices at X-band. Their circuit configuration is shown in Figure 2-18.
The Gunn devices are located on a transmission line, one half wavelength apart, in a peri­
odic fashion.
The large signal impedance Zd of the Gunn device is required if an accurate theo­
retical needs to be performed. Figure 2-19 shows the test station which was used by
Mortazawi, and Itoh. A single device is connected to a 50 Cl microstrip line. Delivering
dc bias to the circuit is done by a bias tee, and a triple-stub tuner is used to adjust the cir­
cuit impedance presented to the Gunn device until maximum power was obtained at the
desired frequency. Now, the device is connected, and a coaxial cable was inserted in its
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26
Radiating elements
IMPATT
Comparator
Exciter
£ A az A el to receiver
Oscillator coupling slots
Radiating slots
Comparator coupling slots
Figure 2-17. 35 GHz spatial combiner block diagram, and antenna array layout.
(After Holzman [8])
place. The impedance of the circuit is then measured at the end o f the coaxial line. The
impedance is translated to the reference plane occupied by the Gunn device to give the
impedance of the circuit as seen by the device.
Figure 2-18 (b) demonstrates the equivalent circuit of the distributed circuit com­
biner while MIC realization is shown in part (a).
The device is modeled as a negative resistance in parallel with a capacitance. The
device impedance of the RC circuit changes as the frequency changes. For an N-device
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oscillator, it is obvious that the impedance seen by each device is the negative of the large
signal impedance Zd of a single device if the periodic structure is terminated by a load
R l = - R d/ N . A quarter wavelength transformer can be implemented to convert R L to
50 Q. As the number of devices increases, RL decreases. Transmission line losses, and
load matching put a limit on the size of the combiner.
Mortazawi, and Itoh built distributed combiners with two to six devices. The
i
devices were not chosen to be particularly well matched in characteristics. In practice,
once the devices are dc biased, they injection lock to each other. The output power is
maximized by adjusting the bias voltage. Injection locking was maintained over ±25%
variations in the bias voltage. The oscillation frequency variation with dc bias voltage
seemed to be unaffected by the number of devices. Combining efficiencies reached 100%
for combiners with up to five devices.
2.7 Multiple-Level Combining
In practice the maximum number of devices that can be combined is limited by
moding, device interactions, and loss problems. By employing multiple-level combining,
we can further increase the number of devices that may be combined. As illustrated in
Figure 2-20, a multiple-level combiner is a combiner built from combiners. As shown, the
chip-level combiners serve as the first level combining technique. The resonant combiners
can be used to combine several chip-level combiner modules, and serve as second-level
combining. The resonant combiner modules can then be joined by nonresonant combining
techniques such as hybrid-coupled combining or conical waveguide combining methods.
The last level, spatial combining, combine several nonresonant combiners. Therefore,
output powers o f hundreds of diodes can be combined together. The frequencies of com­
biner modules have to be aligned or injection-locked to accomplish a coherent output.
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Gunn devices
Quarter wave
Microstrip-to-coax
)— transition
Inductive stub
Figure 2-18. Three-device distributed combiner: (a) MIC realization, (b) equivalent
circuit. (After Holzman [8])
Gunn device
Microstnp
To power
meter and
spectrum
analyzer
Figure 2-19. Test station for measuring the large-signal impedance o f a Gunn device.
(After Holzman [8])
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29
Chip-level
combiner
Chip-level
combiner
Resonant
combiner
Chip-level
combiner
Resonant
combiner
Nonresonant
combiner
Resonant
combiner
Nonresonant
combiner
Spatial
combiner
Output
Resonant
combiner
Resonant
combiner
Nonresonant
combiner
Chip-level
combiner
Chip-level
combiner
Resonant
combiner
Chip-level
combiner
Figure 2-20. Multiple-level combiner schematic. (After Holzman [8])
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
30
Among different techniques of power combining, spatial combining has been a
reliable and efficient method. The primary advantage of spatial combining is the fact that
combining takes place in free space as a result of radiation. It does not have the comlexity
o f resosnant cavity combiners. It also has less power loss than chip combiners.
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CHAPTER 3
OSCILLATION THEORY
In this chapter Kurokawa's oscillation conditions for steady-state stable oscillation
will be reviewed. In most cases, microwave oscillators have very low phase noise, and
high dc-RF efficiency. Bipolar transistor oscillators are usually preferred at frequencies
below approximately 10 GHz. Oscillators using MESFETs, and MESFET variants
(HEMT) can operate at much higher frequencies, even into the millimeter-wave region.
However, their phase-noise level are significantly greater than those of bipolar transistors.
IMPATT, and Gunn oscillators are capable of operation at frequencies well above 100
GHz, but these oscillators often have high noise levels, and poor dc-RF efficiency [9]. A
generic oscillator is shown in Figure 3-1.
Circuit
Transition
Device
Figure 3-1. Generic oscillator. (After Holzman [8])
31
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32
3.1 Resonators
The oscillator circuit provides dc bias for the oscillator, induces oscillation, and
sets its frequency, and power level of the oscillation. From the oscillation point of view,
the RF power level increases from zero until it reaches a level at which point steady-state
operation starts. As the oscillation level approaches its steady state value, the frequency
also changes, often in a nonmonotonic, and discontinuous fashion. The frequency of oscil­
lation is invariant with time in an ideal oscillator in steady-state operation. The frequency
at which the oscillator operates is related to the microwave circuit resonance.
In electrical circuits, resonance is a balance of inductive, and capacitive energy
storage elements. At low frequencies, these are coil inductors, and parallel plate capaci­
tors. At high frequencies, electrical and magnetic energy is described as being stored in
fields. It means that inductive, and capacitive energy storage is achieved with steady-state
fields set up between conductors. A configuration of conductors used as an energy stor­
age device is called a resonator. The dimensions of a resonator can be chosen so energy is
stored at a particular resonant frequency. Because the resonator plays an important role in
an oscillator circuit, the oscillator's name usually derives from the type of resonator it em­
ploys. Four common microwave resonators are:
a) Dielectric
b) TEM transmission line
c) Waveguide
d) YIG (yttrium iron garnet) sphere
3.1.1 Quality Factor
When an RF signal drives a microwave resonator at its resonant frequency, the
resonator stores some o f the energy in the signal. The amplitude of the stored energy will
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decay because of the resonator circuit electrical resistance. The rate of decay depends on
the resonator's quality factor (Q) which is the ratio between an electrical circuit reactance,
and resistance or, equivalently,
q _ Qj(time- averaged energy stored in the resonator)
energy loss per second in the resonator
^
The lower the resonator's Q, the greater the rate of decay. Low-Q resonators are
employed in tunable oscillators while high-Q resonators are used to build very stable, lownoise fixed oscillators. Cavities that are entirely enclosed by electrical conductors like the
rectangular cavity tend to have very high Q values because little energy is lost over time.
Conversely, dielectric, and YIG resonators are not fully enclosed by conductors, and lose
energy through radiation effects, so they have lower Q values. At microwave, and milli­
meter wave frequencies, waveguide resonators can be used.
The external quality factor, Q ^ , is the Q factor that would result if a resonator
were lossless, and only subject to loading by a coupling element. A simple model for a
resonator is the series lumped circuit shown in Figure 3-2. The load R L represents losses
in the cavity, and C, and L describe the cavity’s energy storage ability. For the series
model, [8]
3.2 Concept of Negative Resistance
Work done by Kurokawa [34] is the basis for the design of modem microwave
oscillators. In this work a microwave oscillator is modeled as a one-port in which the real
part of the port impedance is negative. The one-port can be replaced by a two-terminal
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o —
1 |—
'T f l f l P —
'V W —
A /W — o
Figure 3-2. Series lumped model of a microwave resonator. (After Holzman [8])
solid-state device that shows negative resistance such as a tunnel diode, or a two-port that
has feedback such as a potentially unstable transistor or amplifier.
An oscillator modeled in this fashion is shown in Figure 3-3. The load impedance,
ZL(<o), is linear but the source impedance, Z ,(/0,o ) (the output impedance of the oscilla­
tor), is modeled in an unusual fashion: it is a linear impedance that is a function of 70 , the
magnitude of the fimdamental-frequency component of the output current. The real part
of Zs is negative, and decreases with an increase in 70. Although no linear impedance be­
haves in this manner, a nonlinear impedance can behave this way if the current, and volt­
age harmonics are ignored. An example of such an impedance is the LO input quasi-im­
pedance o f a pumped mixer diode. The small-signal source v(t) in Figure 3-3 represents
a perturbation in the voltage across the combined impedances; in practical circuits, it rep­
resents noise, an injection-locking signal, or the turn-on transient o f the circuit. If the total
resistance in the loop is negative (i.e., if ReJZ,}+Re(ZL) < 0), the circuit is unstable: if
v(t) is perturbed, the response i(t) increases exponentially with time, and will become
sinusoidal at some frequency, eop, where Im{ZJ} = -Im{Zt }.
This response is a
consequence of the fact that the poles of the total admittance in parallel with v(t) are in the
right half of the s plane. As the amplitude of the oscillation increases, |Re{Z,}| decreases,
If 70 were to increase beyond the point at which (3.3) is satisfied, 70 would decrease, and
eventually |Re{Z^}| would rise to the point where (3.3) would again be valid. Thus, the
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Zs Oo1
Zl M
~ ) v(I)
o
Figure 3-3. The classical model of a negative-resistance oscillator. (After Maas [9])
and eventually reaches a point where: [9]
Z3(I0,<op) = -Z L( a p)
(3.3)
value of 70 that satisfies (3.3) is stable, so 70 remains at that level, and oscillation contin­
ues at a constant amplitude. The decrease in |Re{Zf}| with increasing /„ is an inevitable
consequence of the inability of the amplitude of i(t) (Figure 3-3), in practice, to become
infinite. The source could also be described by a nonlinear conductance then, the oscilla­
tion condition is: [9]
Y1(V0,cop) = -YL(G>p)
(3.4)
This is the case o f a parallel resonance having a total negative conductance, in which the
transient excitation comes from a shunt small-signal current source, and V0 is the magni­
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tude of the shunt voltage. The oscillation begins when the real part of the shunt conduc­
tance is negative, and |Re{l^}| decreases as the oscillation increases until (3.4) is satisfied.
In practice, Y3 or Zs is realized by a solid-state device, which usually includes non­
linear capacitances.
The average values o f those capacitances, and hence Im{y,} or
Im{Zs}, vary at least slightly with V0 or /„. Thus, the frequency at which oscillations be­
gin (when V0 , /„ are small) is not necessarily the same as that for which (3.3) or (3.4) is
satisfied (where V0 , I0 are large). However, if a transistor oscillator circuit includes a
high-Q resonator, that resonator, not the reactances of the solid-state device, will domi­
nate in establishing the imaginary part of Ys, and the frequency shift will be minimal.
Similarly, if the load itself includes a high-Q resonator, Im{7t } varies rapidly close to
resonance. Therefore changes in Im{]^} do not cause much frequency deviation.
3.3 Oscillation Condition Using Reflection Coefficient
Oscillation conditions have been derived in terms of the device, and circuit imped­
ances. Some people prefer to work with reflection coefficients because they are easily
measured on network analyzers, and more applicable to analysis with a Smith chart. In
this section, oscillation, stability, and noise criteria will be derived in terms of the device,
and circuit reflection coefficients. These criteria are equivalent to those derived in Section
3.2.
Consider the oscillator schematic o f Figure (3-3). The reflection coefficient seen
from the device terminals looking into the circuit is Tc, r d is the reflection coefficient
looking into the device from the circuit. We want to determine the relation between these
reflection coefficients for steady-state oscillation.
By substituting into equation 3.3
expressions for Zd, and Zc in terms of the reflection coefficients, our desired result will be
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obtained.
Now, considering the relation between the reflection coefficient, and
impedance, [8]
Z + Z0
(3.5)
Where Z0 is the characteristic impedance of the oscillator system. In this case Z may be
the impedance o f either the device or the circuit. The above equation can be changed into:
[8]
(3.6)
With equation (3.6), the oscillator equation can be rewritten as [8]
(3.7)
This results in [8]
(3.8)
For a passive circuit
|rc| will be between 0, and 1 in magnitude.
Thus, in order to have
oscillation, r rf will require a magnitude that is greater than 1.
Stability, and noise conditions cannot be derived so easily. Esdale, and Howes [41
employ an approach that is based on Kurokawa's method. They assume that the device
reflection coefficient is a function of the RF current amplitude A only, and that the circuit
reflection coefficient is a function of the frequency <o only. Like Kurokawa they ignore all
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harmonics, and other frequencies except the fundamental by assuming that the circuit re­
flection coefficient is zero for all frequencies except the fundamental. Working with nor­
malized waves, and flow graphs, they derive expressions for stability, and noise in terms of
the complex reflection coefficients [8]
r e(fi>) = r e(®)eM(<0)
(3.9)
T M ) = Y M ) sMA)
(3.10)
where yc, and Yd ar® the magnitudes of the reflection coefficients, and thus, positive, and
real-valued. For an oscillator operating at ( 4 ,,0 „ ) t0 be stable, its reflection coefficients
must satisfy the stability condition: [8]
By plotting r c, and T / 1 on a Smith chart, the performance of an oscillator in the
complex R - X plane can be graphically analyzed. Figure 3-4 shows the intersection of
the two reflection coefficient loci. Employing cylindrical coordinates, Esdale, and Howes
rewrite the stability condition as [8]
S=
d r /'
sin0>O
dco dA
(3.12)
With S in this form, an oscillator is clearly stable when the angle 0 is between 0°, and
180°. Expressions for the AM, and phase noise spectra at the modulation frequency com
are: [8]
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39
drc
dto
|5/t(wm)|2 =
2\bm\
drr
i l da)
1 d r i'
2|M J y? dA
W
+ 3rc
o>l
(3.13)
d rc
dot
drc
dto
(3.14)
dA
Figure 3-4. Tc, and r / 1on the smith chart. (After Holzman [8])
where [8]
e 2l - r 12
b =—
"
V
4z0| r ; 2
(3.15)
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Based on these expressions, we conclude that good noise performance can be achieved if
a)
The circuit, and inverse device reflection coefficient loci intersect in an orthogo­
nal fashion.
b)
i arc
Yc da>
-1
i ard
takes on its minimum value.
c)
Yc dA
3.4 Oscillation, and Stability Condition
Any oscillator can be represented in an arbitrary plane on the output line by a non­
linear impedance ZnI, which is dependent on the current /„, and has a negative real part, in
series with a load impedance Z, (Fig. 3-5). It is assumed that the circuit has a sufficiently
high Q factor to suppress the harmonic currents. If a current
/(/) = IQcos(6y)
(3.16)
flows in the circuit, we can apply the Kirchhoff voltage law, and write in the plane
PP'(Fig. 3-5) assuming [10]
Z„\ + Ze —
+ J ^ir
(3.17)
Since / 0 is not equal to zero, equation (3.3) is satisfied by
R,(I0,<o0) = 0
(3.18)
(3.19)
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41
1
1
MESFET
+
Associated
Circuit
|
zt
T
1
_ i_
I
-
im
I
1
Figure 3-5. Nonlinear microwave oscillator. (After Soares [10])
Since Re(Z,) is greater than zero, eqn. (3.18) implies that Re(Znl) is less than zero.
Hence the device needs to present a negative resistance in order to be able to oscillate.
The frequency of the oscillations is determined by eqn. (3.19), i.e. by the requirement
that the load reactance is equal, and opposite to the device reactance. Oscillators can also
be represented by a nonlinear admittance Ynl. In this case the oscillation conditions are
determined using the Kirchhoff current law, and equation (3.4). Assuming: [10]
Yn,+ Y c = Yt =G t + }Bt
(3.20)
Since Vi is not equal to zero, from negative resistance argument [10]
G,(I0,0}o) = 0
B,(I0,(oq) = 0
(3.21)
To ensure that oscillation will start when d.c. bias is applied to the device, it is necessary
for the instantaneous r.f voltage of the device to be superior to that across the load. Thus
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which leads to the necessaty oscillation start-up conditions [10]
|Gnl(4>®o)L <|Gc(<ao)|
(3.23)
From the above equations, and considering Figure 3-5 it can be seen that at start up the
negative resistance (Fig. 3-6(a)) is greater than the load resistance but the negative admit­
tance (Fig. 3-6(b)) is less than the load admittance. It is more convenient to express
equations 3-19 to 3-22 in terms of corresponding reflection coefficients Tnl, and r c: [10]
(3.24)
Zrni+ZTe= 2nn
(3.25)
Equation (3.25) mentions that the device reflection coefficient |rn,| should be greater than
unity since |rc| is one or less.
An oscillator can be considered as a combination of an active multiport, and a pas­
sive multiport, as illustrated in Figure 3-7. If the active device, and the embedding circuit
are characterized by their scattering matrices, we have for the active device, [10]
b = Sa
(3.26)
and for the embedding circuit [10]
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43
16.6 mS
(a)
20 mS
(b)
Figure 3-6. Negative impedance versus negative admittance. (After Soares [10])
(3.27)
b'=S'a'
when the active device, and the embedding network are connected for oscillation to occur
we have:
ai
Embedding
Network
Active
Device
Figure 3-7. Generalized oscillator configuration. (After Soares [10])
b'= a
(3.28)
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44
b = a'
(3.29)
From equations (3.27)-(3.30) we can derive [10]
b = SS'a'
(3.30)
a'= SS'a'
(3.31)
(SS'-U)a'= 0
(3.32)
or
or
Where Uis an identity matrix. Since aV 0, it leads to [10]
M = SS'-U
(3.33)
det Af = 0
(3.34)
is a singular matrix or [10]
which represents the generalized steady state oscillation condition for an n-port oscillator.
As a matter of fact, since the scattering matrix of the active device is defined at small
signal level, the n-port oscillation condition for small signals can be shown by [10]
|d e t(» -P ) | > 0
(3 .35)
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45
and [10]
argdet(5iS"-17) = 0
(3.36)
The oscillation can start when these relations are satisfied, and go on building up until the
device nonlinearities lead to the steady state condition. For instance, consider an active
two port loaded by two passive impedance as shown in Figure 3-8. The active device can
be described by the scattering matrix [10]
*S|l ^12
S2t S22
S=
(3.37)
and the embedding circuit is described by [10]
S’ =
r, o
o r,
(3.38)
From equation (3 .35) the oscillation condition is
detM = det
5,1^
. *^21^1
1
<^12^
(3.39)
*^22^2 —V
which gives [10]
(s1Ir1- ix v a- i ) - W ’,ra=o
(3.40)
From the above the same result can be obtained as equation (3.8) which is satisfied for
oscillation.
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Z,
Two-port
Figure 3-8. Two-port loaded with two impedances. (After Soares [10])
The oscillations are considered to be stable if any disturbance in the voltage or the
current o f the oscillator circuit at any instant decays, bringing the oscillator back to its
point of equilibrium. Oscillator stability is analyzed quasi-optically by applying a small
perturbation to the amplitude I0 (Figure 3-4). The impedance Zt defined in equation
(3.18) which is the function of 70, and the complex frequency p = a + j/?, is developed in
a Taylor series about I0,o)0. Since the perturbed current is non zero the oscillations con­
tinue to exist after the perturbation, and we should have in the plane PP' [10]
op
a0
(3.41)
Since Zt(/0, o 0)= 0 we obtain [10]
(d zj Ya?.
da J
a —
'da
(3.42)
where dp can be decomposed into its real, and imaginary parts as follows: [10]
5p = a + j S a
(3.43)
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The oscillator will be stable if, for a positive variation in the current amplitude, the real
part of the variation in the complex frequency is negative. If a is negative, it indicates a
decreasing wave returning to its point of equilibrium /„. From the above expression for
Sp this condition is derived as [10]
cR, dX.x 3Xt cRt
3Ia dto c%n <?<»> 0
(3-44)
This relation represents the stability condition for an oscillator around an amplitude /0,
and an angular frequency <o0. Moreever, from eqn. (3.46), the imaginary part So disap­
pears if the condition [10]
c^
[ 3Xt 3Xt _ q
do 3f0 do
(3-45)
is fulfilled. This indicates that a variation <570 in the amplitude will not cause any variation
in the oscillator's real angular frequency o 0. It can also be realized from eqn. (3.48) that,
for maximum stability, the device impedance Znl(/0), and the load impedance Zc(<»)
should intersect at right angles at the oscillation equilibrium point (IQ,eo0).
To verify Kurokawa's condition for the source side, equation (3.44) can be rewrit­
ten [9] as equation (3.47). Considering the common gate S parameters for Ids of 10 mA
and 30 mA, the input impedance of the MESFET can be calculated using equation (3.48).
r^.and r s are defined using equations (4.12), and (4.13).
p
Zdrain~5® p _ ZJou^e~ 50
L 'Zdn,in+ 50 * Zsource+ 50
(3 4 6 >
Zin(10 mA) = 33.073-j78.636
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Zin(30 mA) = 24.116-J37.437
8RS dXL
a xs aRL
a; so
a/ so
-
(3-47)
r _ p . *S'l2‘S2lr L
r '“ - S |l+ T ^ ;
^ = - .4 4 8
(3 48)
^ - = 2.06
dl
81
And from Figure 5-4, and by substituting into equation (3.47)
So
15 S t - 1 .
So
-,488*1.5-2.06*(-10) = 13.28> 0
so the condition is satisfied. To examine the stability for the drain side the following
equation will be used. The output impedance of the MESFET can be calculated.
8So 8XS 8X0 8RS
! T i 5 ~ “ T r i ^ >0
P -« )
5
ro=:% 2+T ^ J ;
(3-50)
Zo(10 mA) = -12.155-Hjl09.966
Zo(30 mA) = 31.33-Hj94.561
^ - = 2.174
81
81
= -0.77
From Figure 5-3, and by substituting into equation (3.49), the stability condition is met.
SAT,
So
8R,
So
— - = 17 —- = -25
2.174*17-(-0.77)*(-25) = 17.71> 0
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CHAPTER 4
POWER COMBINER DESIGN
4.1 Waveguide, and Horn Antenna
The microwave spatial power combiner functions by combinig power in the space
inside an X-band horn antenna. The power is delivered through a waveguide to a coaxial
adapter. A spectrum analyzer is used in monitoring the output power. Waveguide and
horn antenna configuration is illustrated in Figure 4-1.
Figure 4-1. Waveguide, and horn antenna configuration.
49
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
50
Rectangular waveguide is usually constructed with a height b which is almost half
the width a (Figure 4-2). The basic advantage of using waveguide is its low loss, and high
power delivering capability. However at the lower microwave frequencies, it is bulky. It
is also dispersive, and, does not propagate transverse electromagnetic waves. The operat­
ing frequency of waveguide is limited at low frequencies by its cutoff frequency, and at
high frequencies by the support of higher order propagating modes.
b
a
Figure 4-2. Rectangular waveguide.
The basic configuration of the power combiner can be obtained by putting the os­
cillator grid at the end of the horn antenna, and observe the power from the waveguide
end. The configuration of the oscillator grid inside the horn antenna is placed in a way
that there is a gap between the oscillator grid, and the reflector or the back plate. This
distance is close to a quarter effective wavelength. The gap can be adjusted to get the
maximum oscillation amplitude, and power.
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The waveguide cross-section of the cavity is shown in Figure 4-3. The top view,
and side view of the waveguide horn along with the corresponding dimensions are shown
in Figures 4-4, and 4-5.
0.4
Figure 4-3. Waveguide cross-section.
0.9
*
Figure 4-4. Horn antenna top view.
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52
*
0.4
*
Figure 4-5. Horn antenna side view.
4.2 Oscillator Design
Small-signal linear considerations are usually sufficient to ensure that oscillation
conditions are met, and to establish very closely the operating frequency. However, oscil­
lators are in fact large signal nonlinear components. A design based on linear theory is
valid because the oscillator, when it is about to start oscillation (before the input level rises
to the steady-state value), is in fact a linear small-signal component. If the frequency does
not change much as the amplitude of the oscillation increases, and if exact knowledge of
the output power is not needed small-signal design may be adequate by itself. However,
by using nonlinear analysis, the output power can be accurately predicted. The voltage
waveforms across critical components in the circuit such as a tuning varactor can also be
determined. The classical approach to the design of oscillators includes four steps:
a) selecting the circuit topology.
b) choosing bias conditions that provide adequate output power.
c) adding feedback to maximize the reflection coefficient at least one port.
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d) selecting source, and load impedances that satisfy the oscillation conditions, and
provide sufficient output power.
These steps make sure that the oscillation will begin at the desired frequency.
They do not exactly specify the amplitude or frequency of the large-signal steady-state
oscillation. Without using nonlinear analysis, accurately estimating the output power can
be difficult because the factors that limit the output voltage range are not easy to deter­
mine. However, if the oscillator's small-signal output-reflection coefficient can be made
very high, a wide range of values of the load-reflection coefficient will satisfy the oscilla­
tion conditions, and the output power usually can be maximized within this range.
Transistor oscillators usually consist of a positive-feedback amplifier that has a
resonator as an input termination. Selecting the oscillator circuit topology basically in­
cludes selecting the type of amplifier, and the choice of amplifier depends primarily on the
application of the oscillator. For instance, a common gate circuit is usually preferred for
VCOs but, for fixed frequency oscillators using dielectric resonators, a common-source
configuration is often preferred.
Selecting an appropriate bias condition has to be done in a manner similar to that
used for the Class-A power amplifier. V^, and 4 are chosen to allow a wide range of
variation for the RF voltage, and current so as to provide acceptable output power.
is
often made equal to the drain voltage that the MESFET would have when used as an
amplifier, and 4 is often set to approximately 0.5/dss.
An added inductance in series with the MESFET's common terminal (in series with
the gate in a common-gate configuration or with the source in a common-source configu­
ration) usually improves the magnitude of the input, and output reflection coefficients to
values well above 1.0. Its effect is to improve positive feedback. If these reflection coef­
ficients are high, the designer has a large degree of freedom in choosing the load imped­
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ance, and usually obtains well behaved operation. It is also important to adjust the feed­
back, and to design the load-side network so that oscillation can occur at only a single fre­
quency, so that there are no additional resonances between YX&), and YL(co) within the
frequency range for which Re{y,} < 0.
Satisfying the oscillation conditions in a small signal amplifier at either the input or
the output is sufficient to ensure oscillation. Therefore, the load is usually chosen to ac­
commodate enough output power, and the input termination is chosen to satisfy the oscil­
lation conditions. A design example is illustrated in Figure 4-6.
MICROSTRIP
RESONATOR
|
r
I
L . * _J
r 4
45 a —
O
1.54 nH
Figure 4-6. Oscillator designed not including dc bias circuitry.
The S parameters of a MESFET are usually measured with the source grounded.
Since in this case the common gate configuration is chosen for the oscillator, the device S
parameters have to be determined. Different configuration for MESFET oscillators are
shown in Figure 4-7.
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o
o
o
o
(b)
o
o
o
(C)
Figure 4-7. Three transistor configuration. (After Soares [10])
The conversion from common source S parameters to common gate S parameters
is accomplished by first converting the S parameters to Y parameters, since they are de­
fined with shorted output ports. This conversion was done by Kurokawa [35], The con­
version procedure is as follows:
a) Convert two-port common source S parameters to two-port common source Y
parameters.
b) Convert two-port common source Y parameters to three-port Y parameters.
c) Convert three-port Y parameters to three-port S parameters.
d) Convert three-port S parameters to common gate S parameters.
In step a) the matrix equation describing the transformation from S parameters to Y pa­
rameters is [33]
Y = F"'G_1(I+ S)~'(I-S)F
(4.1)
The variable I is the identity matrix, and F, and G are diagonal matrices containing the port
characteristic impedances [35].
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56
0
1
F=
0
(4.2)
2 ^
1
0
2-\/Z03
0
Z0,
G= 0
0‘
Z02
0
0
0
(4.3)
Zq3.
Knowing the two port Y matrix, the indefinite Y matrix is easily formed. This is
done by providing a third row, and column such that the sum of the rows, and sum of the
columns are zero. Now the three-port Y matrix is converted back to a three-port indefi­
nite S matrix using Kurokawa's transformation. [15].
T7-1
S = F(I- G*Y)(I+ GY) 1F
(4.4)
The rows, and column of this indefinite S matrix sum to 1. Making use o f this
three-port indefinite S matrix, the two port common gate, common drain or again com­
mon source parameters can be found. For instance, common gate S parameters can be
derived as follows, [15]
e
_ o . S21S12
a Ug ~
22
1
(4.5)
- - S li
S
- S
+ _ § 3lS l2 _
21g “ a 3 2 +
1
--s„
(4.6)
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57
(4.7)
(4.8)
Where
(4.9)
In the above formulas, the assumption is made that an impedance Zg is put in the
gate circuit. For a grounded gate rg = -1. The calculated stability factor based on these
transformed S parmeters, must be smaller than one for oscillation to take place.
The next step in the design process is choosing the source, and load impedance
values that will assure oscillation. As shown in Figure 4-8, if the correct load is connected
to one of the ports, oscillation will occur at both ports. When this occurs
YaYi
=
Y0Yh = 1
(4.10)
YG,Y\,Yt), and yL are the respective generator and load reflection coefficients.
The design procedure is basically aimed to closely estimate the generator (or load)
impedance, and calculate the output (input) reflection coefficients. Oscillation can occur
only if the magnitude of this calculated reflection is greater than one. The design load is
derived as follows [15]
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58
O
Zd
Zc
'C ---------------- o --------------------
rd
Figure 4-8. Oscillator equivalent circuit using reflection coefficients. (After Holzman [8])
(4.11)
A program was used to calculate the S parameter conversion, and minimum values
for source impedance, and drain impedance. The program can be run on DOS. The user
needs to insert the common source S parameters, and ask the program to convert them to
common gate S parameters. The user would also have to specify the common terminal
impedance, and the load impedance (in this case drain impedance). The program would
then calculate the impedance seen by the source, and the oscillation status at different fre­
quencies. In this case the drain impedance of 70 ohms with no reactance was chosen. The
transistor which was used is a GaAs MESFET with operating frequency range of 2-16
GHz. The transistor is manufactured by Avantec company, and its part number is ATF26836. For more specific reasons, the bias level of VDS = 3 V, and IDS = 10 mA was se­
lected. The common source S parameters for the transistor are sorted versus frequency in
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table 4-1. The modified common gate S parameters using S parameter conversion pro
gram are indicated in Table 4-2.
TABLE 4-1
COMMON SOURCE S PARAMETERS FOR ATF-26836 GAAS MESFET
! FILENAME:
ATF-26836
! DATE:
10/95
! BIAS CONDITIONS:
VDS=3V
IDS=10mA
Ta=25 C
! f=GHz
MAG
ANG
Z0=50
2
.94
-38
2.57
138
.044
60
.74
-26
3
.90
-55
2.45
120
.057
51
.71
-35
4
.84
-72
2.41
102
.072
44
.71
-44
5
.75
-92
2.5
82
.093
30
.66
-53
6
.64
-117
2.55
61
.109
15
.60
-64
7
.52
-155
2.6
37
.124
5
.51
-78
8
.49
163
2.47
14
.133
-12
.41
-92
9
.52
126
2.30
-7
.143
-21
.30
-106
10
.56
100
2.1
-28
.144
-32
.24
-125
11
.61
78
1.91
-47
.140
-41
.18
-154
12
.67
58
1.71
-66
.139
-49
.15
168
13
.69
45
1.57
-83
.137
-61
.17
134
14
.72
35
1.42
-98
.138
-66
.19
107
15
.72
22
1.33
-115
.138
-77
.23
89
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
60
TABLE 4-1 [cont.]
16
.72
13
1.26
-128
.135
-85
.27
71
TABLE 4-2
COMMON GATE S PARAMETERS FOR ATF-26836 GAAS MESFET
* Common b Data
* Series RLC:
R =.0000
L =.00Q0nH
C = *****pF
! FILENAME:
ATF-26836
! DATE:
10/95
! BIAS CONDITIONS:
VDS=3V
IDS=10mA
Ta=25C
! f=GHz
MAG
ANi
Z0=50
2
.190
170.3
1.209
-14.0
.149
43.4
.931
-11.6
3
.186
164.7
1.238
-21.2
.186
47.6
.958
-16.5
4
.203
157.3
1.305
-29.0
.218
54.5
1.026
-21.6
5
.284
144.3
1.498
-37.8
.242
63.8
1.131
-27.0
6
.435
134.4
1.871
-47.8
.294
77.0
1.344
-33.8
7
.901
131.2
3.023
-57.9
.436
106.1
2.000
-41.3
8
3.388
137.2
10.127 -60.6
1.734
144.8
6.134
-43.1
9
2.345
-74.8
6.502
78.1
1.524
-43.0
3.633
94.2
10
.877
-77.8
2.521
69.1
.747
-27.2
1.354
84.0
11
.546
-83.2
1.671
57.1
.595
-21.5
.904
69.7
12
.390
-87.4
1.305
44.0
.528
-18.6
.726
56.4
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
61
TABLE 4-2 [cont.]
13
.304
-96.3
1.148
34.3
.483
-16.9
.666
46.6
14
.239
-99.6
1.055
27.6
.449
-14.0
.634
38.9
15
.215
-109.1
.998
19.7
.421
-14.1
.618
31.8
16
.196
-113.4
.961
14.4
.393
-13.4
.624
26.3
The oscillation status, and source side calculated impedance are derived based on
the assumed drain impedance which is 70 ohms. This is shown in Table 4-3.
TABLE 4-3
OSCILLATION STATUS, AND OSCILLATION REQUIRED SOURCE IMPEDANCE
Oscillation requires postive real impedances
Freq. (GHz)
Source impedance Zg
2.000 GHZ
.70000E+02
.00000E+00
-.13652E+03
.51124E+03
3.000 GHZ
.70000E+02
.00000E+00
-.21147E+02
.37792E+03
4.000 GHZ
.70000E+02
.00000E+00
.46659E+02
.27979E+03 OSC
5.000 GHZ
.70000E+02
.00000E+00
.74921E+02
.20281E+03 OSC
6.000 GHZ
.70000E+02
.OOOOOE+OO
.86001E+02
.13266E+03 OSC
7.000 GHZ
.70000E+02
.00000E+00
.85791E+02
.67161E+02 OSC
8.000 GHZ
.70000E+02
.00000E+00
.71256E+02
.15138E+02 OSC
9.000 GHZ
.70000E+02
.00000E+00
.52450E+02
-.24845E+02 OSC
10.00 GHZ
.70000E+02
.OOOOOE+OO
.27842E+02
-.57034E+02 OSC
Loac impedance ZL
Oscillation?
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
62
TABLE 4-3 [cont.]
11.00 GHZ
.70000E+02
.00000E+00
.33728E+01
-.80125E+02 OSC
12.00 GHZ
.70000E+02
.00000E+00
-.24243E+02
-.97779E+02
13.00 GHZ
.70000E+02
.00000E+00
-.47577E+02
-.10940E+03
14.00 GHZ
.70000E+02
.OOOOOE+OO
-.71185E+02
-.11619E+03
15.00 GHZ
.70000E+02
.OOOOOE+OO
-.98114E+02
-.12077E+03
16.00 GHZ
.70000E+02
.00000E+00
-.12251E+03
-.12551E+03
It can be seen from the above data that oscillation occursin frequency range of 4
GHz to 11 GHz.Since the power combiner desired frequency is 10 GHz, it is possible to
get oscillation from this device at 10 GHz. To satisfy oscillation conditions the source
side impedance at 10 GHz is then
Zjoure* = 27.842 - j 57.0340
(4.12)
Z * , ^ 70.00
(4.13)
These impedances will be used to design microstrip transmission lines, and proper micros­
trip patch antennas.
4.3 Microstrip Patch Antenna Design
The microstrip patch antenna has been widely used in microwave power combin­
ers. The antenna configuration is shown in Figure 4-9. The Antenna's input impedance is
mostly determined by the feed location, yp. The substrate is RT Duroid 5880 with
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
er = 2.2, and with thickness of 20 mils (h = 20 mils). The effective relative permitivity in
microstrip is as follows, [14]
2
(4.14)
w
where w is antenna width. The effective wavelength is then,
(4.15)
Antenna resonant frequency is, [13]
f =
r (L+2A/)
(4.16)
where A1 in this case is [13]
,4 1 2 ( ^ + 0 .3 )f^ + .2 6 4 l
a/ =
---------------r iJ ? —
( ^ - . 2 5 8 ) f ^ + 0.813j
(4.17)
The characteristic impedance for microstrip is, [14]
-i
(4.18)
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64
W
I
Figure 4-9. Microstrip patch antenna configuration.
Three more parameters are needed to complete the design. [13]
J
I = sin2
tan2 0sin 0d 6
R =
P=
120 a*
(4.19)
(4.20)
2n
(4.21)
Therefore, the input impedance is, [13]
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
|2
+ (J3AI)2 sin2(y5yp) - /3A1sin(2/?yp)
y
z * ( y ,) = - j R ,W ( / ! y ,) +
(4-22)
The drain-side, and source-side antennas' characteristics can be calculated using Mathcad.
Drain-side:
L= 385"
w = 0.5"
yp = 0.3" Zh = 70.0Q
fr =10GHz
Source-side:
L=.3875"
w = 0.4"
yp = 0.157" Zm=24.6Q
fr = 10 GHz
4.4 Drain-Side Transmission Line Design
Based on the analysis presented in chapter 4, the generator-side impedance was
derived using oscillation theory.
Zdnin=70.0Q
(4.23)
A microstrip patch antenna is needed to radiate microwave power. Microstrip
lines are used to connect the MESFET drain to the patch antenna. Another important is­
sue is to find a way to dc bias the drain. Referring to the microstrip line characteristic im­
pedance provided in the previous section, microstrip lines with smaller width offer greater
characteristic impedance. Thus, the drain is fed through a 10-mil thick microstrip line. In
practice, microstrip lines narrower than 10 mils are difficult to fabricate.
The drain-side circuit is shown in Figure 4-10. The output resistance of the power
supply is assumed to be zero. Then the transmission line heading to the supply is consid­
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ered as a short-circuit stub. The open-circuit stub is added to bring down the imaginary
part of the impedance to approximately zero.
The patch antenna is replaced by its input impedance (70.OQ). The step disconti­
nuity between the narrow and wide line is shown in Figure 4-11, and it acts as a low pass
filter. This high and low impedance line reduces microwave loss through the bias line. It
also prevents unwanted high frequency signals from entering the combiner.
Drain
Figure 4-10. Drain side configuration.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
I
I
Figure 4-11. Step discontinuity. (After Gupta [11])
4.5 Source Side Transmission Line Design
Referring to Table 4-3, the value of impedance seen by the source to satisfy
oscillation condition is
Zjource = 2 7 .8 4 2 -j57.034£2
(4.24)
The microstrip patch antenna is again employed to make radiation stronger, and to make
power combinig more efficient. The bias line design follows the same reasoning used in
the last section. The microstrip patch antenna is of course substituted by its input imped­
ance which is a resistor. The power supply output resistance is assumed to be almost
zero. Then the last transmission line on the right in Figure 4-12 is a short circuit stub.
The open circuit stub in Figure 4-12 is employed to help optimize for the desired value of
impedance seen by the MESFET source.
4.6 Design Layout
The layout design for the MESFET oscillator is drawn using AUTOCAD software
version 12 on a PC. The design is done for both sides of the printed circuit board. The
type of substrate used is RT Duroid 5880 with relative permitivity of 2.2 and
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
thickness o f 20 mils. The front side is the oscillator grid, and consists of four oscillator
cells (Figures 5-13, and 5-14). They are arranged in an array of two rows, and two
Source
Figure 4-12. Source side microstrip configuration.
columns. The distance between rows is chosen to be 0.3" while the distance between col­
umns is 0.2". The ground plane occupies the vacant space outside the cells. The back
side is mostly occupied by ground plane except for oval windows which face microstrip
patch antennas. These windows are employed to deliver oscillation power through the
waveguide to achieve power combining. Figures 4-14, and 4-15 show the front, and the
back side of the printed circuit board. Figure 4-13 shows one oscillator cell.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
69
Figure 4-13. An oscillator cell.
♦
m
[JO
A 1i
k
r
i
r
m
A Ii
Ii
r
_____
n
r
k
Figure 4-14. Front-side layout.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 4-15. Back-side layout.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER 5
SINGLE OSCILLATOR SIMULATION
Simulation of the oscillation was done using EEsof LIBRA. The first step to simu­
late a microwave circuit is to set data items in the default bench. The substrate is RT Duroid S880. Data items will be described in the following sections.
5.1 MCOVER (Microstrip Cover Height)
The parameters for this item are HC, and H. HC is the height of the cover above
the top surface of the substrate, and H is the substrate thickness. The following inequality
should be satisfied
HC;>H
(5.1)
The value of HC is set to zero which means that the cover is placed at an infinite height.
5.2 MSUB (Microstrip Substrate)
The parameters involved here are listed as the following:
ER = substrate dielectric constant
H = substrate thickness
T = metal thickness
RHO = metal bulk resistivity (relative to gold)
RGH = rms surface roughness
71
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Bulk resistivity for copper is assumed to be 0.94. For RGH, the default value was
used. So, the parameters for RT Duroid S880 are:
ER = 2.2
H = 20 mils
T = 1.414 mils
RHO = .95
RGH = Default
5.3 TAND (Dielectric Loss Tangent)
Dielectric loss tangent can be ignored in this case, and the parameter TAND is as­
sumed to be zero.
5.4 TEMP (Physical Temperature)
The default value used for physical temperature is 15.85 ° C (290 K).
5.5 MWALL, and PERM
Default values for MWALL (microstrip sidewalls), and PERM (permeability, and
magnetic loss tangent) are used because they are not applicable in this case.
5.6 Drain-Side Simulation
Optimization technique was used to achieve the desired value for drain-side im­
pedance. This technique functions by changing the characteristics o f microstrip lines, and
other elements until the desired value is achieved. Figure 5-1 shows the simulated drainside configuration with all the information needed for layout design. Table 5-1 lists the
impedance seen by the drain in the frequency range of 2-16 GHz. Data items are based on
what were discussed in sections 5.1 to 5.4.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
73
^MLSC
TL4
W=2 1 5
L= 3 0 0
MSTEP
STEP1
W1= 2 1 5
{?
W2 = 1 0
ML I N
TL 3
W=1 0
L=1 8 0
"ra b s
CR0S1
°W1= 3 5 . 9
13PORT
P1
ML I N
TL1
por t= 1
W = 3 5 .9
W2= 1 0
W 3 = 3 5 .9
W4= 1 0
L= 590
R= 7 0
W = 3 5 .9
L= 1 5 0
MLOC
TL 5
W= 1 0
L = 9 9 .7
Figure 5-1. Drain-side microstrip simulation.
TABLE 5-1
DRAIN-SIDE IMPEDANCE AT DIFFERENT FREQUENCIES
EEsof LinA tb EEsof LinA tb
ZI1
ZI1
test70
test70
Z1
Zl
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
74
TABLE 5-1 [cont.]
Frequency
Re
Im
GHz
Ohm
Ohm
2.000000000
139.8703
141.1150
3.000000000
114.0955
-70.1187
4.000000000
55.1634
-32.5915
5.000000000
54.0319
-4.9576
6.000000000
74.1318
-4.8637
7.000000000
12.0475
-30.9113
8.000000000
68.0535
45.8559
9.000000000
84.5965
3.6207
10.000000000
70.0584
-0.0300
11.000000000
71.4898
8.5309
12.000000000
87.1923
5.3192
13.000000000
90.2064
-20.7096
14.000000000
61.0098
-32.4114
15.000000000
38.8366
-15.5565
16.000000000
31.2218
7.6341
5.7 Source-Side Simulation
Using the same procedure as in section 5.6, optimization to obtain 27.842 - j
57.034 for impedance seen by the source has been successful. Figure 5-2 shows simulated
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
75
source-side configuration, and Table 5-2 lists impedance seen by the source at frequency
range of 2-16 GHz. Optimization error is set to be less than 0.1 %.
R =24.6
w=35.9
L = 195
0—
PORT
PI
por t=
w = 3 5 . 9 MCROS
W=35.9
L=36.5
ML IN
TL6
W=35.9
L=100
MSTEP ML IN
ST E P 1 TL3
W1= 3 5 . 9 W=10
W 2 = 10 L = 9 5
ML IN
TL2
W=1 0
L=20
MLSC
MSTEP
T L5
STEP 2
W = 2 15
W1= 2 1 5 ^ L = 1 4 1 . 5
W 2 = 10 r
Figure 5-2. Simulated source-side microstrip configuration.
TABLE 5-2
SOURCE-SIDE IMPEDANCE AT DIFFERENT FREQUENCIES
EEsof LinA tb EEsof LinA tb
ZI1
ZI1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
76
TABLE 5-2 [cont.]
test27
test27
Z1
Z1
Frequency
Re
Im
GHz
Ohm
Ohm
2.0000000
10.4409
18.4118
3.0000000
13.7625
24.6940
4.0000000
18.6418
34.0838
5.0000000
27.8620
47.4933
6.0000000
48.6016
63.2844
7.0000000
101.1818
68.9167
8.0000000
154.1070
-19.0694
9.0000000
74.2875
-78.3293
10.0000000
27.8511
-57.0882
11.0000000
11.5470
-34.3235
12.0000000
4.2550
-17.1402
13.0000000
0.3714
7.6116
14.0000000
107.3894
-34.9815
15.0000000
13.3619
-24.1424
16.0000000
5.5781
-10.3728
5.8 Oscillator Simulation
To complete the oscillator simulation, the common gate MESFET transistor is
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
200 . 0
50.0
too.o
50.0
-50.0
100.0
-
20.0
f r e q u e n c y 5 . 0 GHz / DI V
Figure 5-3. Source-side impedance plot at different frequencies.
211
211
150.0
100.0
50.0
0.0
-50.0
-
100.0
20.0
Frequency 5 . 0 GHj /Ol V
Figure 5-4. Drain-side impedance plot at different frequencies.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
simulated. The common gate MESFET can be modeled as a three-port device in EEsof
LIBRA. Then source-side, and drain-side configurations can be connected to source, and
drain of the three-port device to form a complete simulation of the MESFET oscillator.
The simulated oscillation power for the GaAs MESFET ATF-26836 for the frequency
range of 2-16 GHz is plotted in Figure 5-4. Complete oscillator simulation is shown in
Figure 5-5.
QEEsof_OscFswp_tb
. OscPower
t e s t 26 8 3 o
PF
dBm
o.o
0.0
-
20.0
-30.0
-40.0
-50.0
-60.0
20.0
Frequency
5.0
GHz/DIV
Figure 5-5. Simulated oscillation power for ATF-26836.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
79
'A A A H 11'
MSTEP
MLSC
ML I N
STEP1
W=2 15 W1=215 W=10
L= 300
W2 = 1 0
L = 18 0
H Z J'
ML I N
W=35.9
L = I 50
MLSC
TL 1 2
W = 2 15
L=14 1 .5
MCR( !S
c r o :;i
MSTEP
p|STEP3
r W I =215
U W 2 = 10
\
ML I N
TL 1 1
W=10
L= 20
rA/W ni
RES
R2
R=24.6
ML I N
TL 1 0
W= t0
L=95
ML I N
TL6
W = 3 5 .9
L= 19 5
ML I N
W=35.9
L= 590
m P O R -T
por t=2
S2P
SNP2
F t lrE- = ^ 2 6 8-3-q
MSTEP
STEP2
W1= 3 5 . 9
W2=10
MLOC
TL 8
W = 3 5 .9
L = 3 6 .5
MLOC
TL5
W= 10
L=99.7
a
PORT
P3
por t = 3
ML I N
[ JPORT
L= 1 0 0
por t= 1
MCROS
CROS2
“W1='35t 9
W 2=35.9
W 3=35.9
W 4=35.9
ML I N
TL7
W =35.9
1 = 20
Figure 5-6. Simulated MESFET common gate configuration.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER 6
MEASUREMENT AND CONCLUSION
To examine the performance of the microwave power combiner, a measuring in­
strument is required. The power combiner consists of oscillators that require a dc bias for
the MESFET transistors. The test bench shown in Figure 6-1 is used. The HP 8553
spectrum analyzer used to display oscillations covers frequencies from 90 kHz to 26.5
GHz. Each transistor requires two power supplies.
Power
Supply
Oscillator
Grid
Spectrum
Analyzer
Power
Supply
Figure 6-1. Test set up for measuring combining efficiency.
80
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81
Each MESFET requires a negative gate to source voltage, and a positive drain to
source voltage. Since the gate terminal is grounded, positive voltages should be applied to
source, and drain terminals. Drain voltage to source voltage is maintained positive to al­
low positive current flow from drain to source. Chip resistors are added to maintain DC
bias stability. A chip resistor is connected from the source to ground to help maintain the
dc operating point. The bias configuration for a MESFET is shown in Figure 6-2.
Ids
< ---------
S
D
Vs g
C
Vdg
Figure 6-2. Bias configuration for MESFET.
Typical values for R, C, Vdg, and Vdg are:
R = 50 f t
Vdg = 4 V
C = 150 pF
Vsg = 1 V
Ids = 10 mA
Bias voltages, and drain-source currents are according in Table 4-2 o f chapter 4. Due to
fabrication, and mounting differences among MESFET transistors, the operating bias point
differs from one MESFET to another one. The bias condition of Vds = 3 V , and Ids = 10
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
82
mA, a typical bias point given by the manufacturer, cannot be easily reached. In cases
using two power supplies, bias condition is set by the device, and every attempt to force a
certain bias condition would damage the device. As a result, one power supply was not
used to bias two or more transistors. Therefore, in most cases, every oscillator requires
two separate power supplies.
6.1 Combining Efficiency
To achieve power combining, at least two oscillators need to work at the same
time. That means four power supplies are needed to meet the minimum requirement.
Referring to the grid array in Figure 4-14, more power combining efficiency can be ob­
tained by putting two transistors in a diagonal manner. Figure 6-3 shows the spectrum of
the power combiner with one active MESFET oscillator with the following bias condition:
Vds = 3.23 V '
Ids = 14.97 mA
ATTEN
lO d B
RL
lO O .O m V
MKR
1 2 . 31
9 1 . 3-4
L IN
MKR B 1 . 3 4 m V
lE .O lG H z
GHz
ft V
j
I
CENTEH
1 3.S B G H Z
RBW
1 . OMHz
VBW
1 . OMHZ
SPAN 3 6 . BOGHz
SWP S 3 0 m s
Figure 6-3. Spectrum of oscillation at 12.01 GHz.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The spectrum of the combiner with another MESFET is plotted in Figure 6-4. The
bias conditions are:
Vds = 2.3 V
Ids = 20.18 mA
The RF output of the first device is 51.54 mV at 12.01 GHz, and the RF ouput of the sec­
ond device is 86.49 mV at 11.56 GHz.
A T TE N
lO O B
RL
ISO .O fflV
MKR
1 1 . 56
B 6 . 49
L I N
MKR B B . 4 9 m V
l l . B B B H z
GH z
IT V
C E N TER
1 3 .2 9 Q H Z
RBW
l.O M H Z
VBW
1 . OMHZ
SP A N
S B . 50Q H Z
SM R
E 3 0 m o
Figure 6-4. Spectrum of oscillation at 11.66 GHz.
Now, if the above transistors work together, their powers combine in the space in­
side the waveguide. This combined power is plotted in Figure 6-5. Its voltage is 91.62
mV, and its frequency is 11.93 GHz. Combiner efficiency can be easily calculated. Since
the input impedance of the spectrum analyzer is 50Q, the efficiency is:
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
91.622
EffiCimCy=i M F 5W
50 + 50
A T T E N
lO d B
R L
lO O .O m V
MKR
± 1 . 33
9 1 . 3 2
= 82'97%
MKR B 1 . 6 2 m V
1 1 .9 3 G H z
L I N
GH z
rr V
C E N T E R
1 3 .2 G G H Z
RBW
a . OMHZ
VBW
1 . OMHZ
SP A N
2 6 . BOSHZ
SW P
S 3 0 m s
Figure 6-5. Spectrum of combined power.
In another experiment with two different transistors, the bias conditions for the re­
sults shown in Figure 6-6 are:
Vds = 3.46 V
Ids = 25.41 mA
and for the results shown in Figure 6-7 are:
Vds = 2.383 V
Ids = 20 66 mA.
The power spectrum of the combination of the devices is plotted in Figure 6-8.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
85
ATTEN lOdB
RL SOO.OmV
MKR
1 1 . 9 3
t 1 9 .
7
LIN
MKR 119.7mV
11.93QHZ
GH z
rr V
1
CENTER
1 3 >2 3 G H z
RBW
X . OMHZ
VBW
1 . OMHz
SPA N
S 6 .3 0 G H Z
SW P
SSOmas
Figure 6-6. Oscillation spectrum at 11.93 GHz.
ATTEN
lO d B
RL S O O .O m V
MKR
1 1 . SB
1 IB . O
MKR
L IN
H B .O m V
XX, B 6 G H Z
GHz
rr V
1
CENTER
1 3 .3 9 G H z
RBW
1 . OMHz
VBW
1 . OMHZ
SPA N
S B . SOQ Hz
SW P
930(im
Figure 6-7. Oscillation spectrum at 11.66 GHz.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
86
ATTEN lOdS
RL SOO.OmV
MKR
1 1 . 33
1ST . O
LIN
MKR 1S7.OmV
11.93GHz
GHZ
ITV
1
CENTER
1 3 . 35GHZ
RBW
1 . OMHz
VBW
1 . OMHz
SPAN S B . SOGHz
SWP S 3 0 m s
Figure 6-8. Spectrum of combined power.
Combining efficiency in this case is similar to that found previously:
157.02
Efficiency = ------ ^ ------ r = 87-25%
J
118.0
119.7
50 + 50
In this last experiment, the bias conditions for oscillator shown in Figure 6-9 are:
Vds = 3 V
Ids = 23.95 mA
And oscillation plotted in Figure 6-10 requires following bias conditions:
Vds = 2.383 V
Ids = 23.95 mA.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
87
ATTEN
lO d B
RL. g s .a s m v
MKR
l in
u
79.61m V
.sishz
•
MKR
1 1 . 31
7 9 . 31
GH z
IT V
1
CENTER 1 3 . SSG H z
RBW 1 . O M H z
VBW
1 . OMHz
SPAN 2 5 . SOQHz
SWP S S O m a
Figure 6-9. Oscillation spectrum at 11.31 GHz.
ATTEN lO d B
Rl_ B B . S l m V
MKR
lO . 78
4 4 . 3S
GHz
IT V
L IN
MKR 4 4 . O Sm V
1 0 .7 6 G H z
.
1
CENTER
1 3 .2 9 G H z
RBW 1 . OMHZ
VBW
1 . OMHz
S P A N 2 5 . SOGHZ
SWP 5 3 0 m a
Figure 6-10. Oscillation spectrum at 10.78 GHz.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Finally, combination of these two oscillations results in Figure 6-11.
ATTEN lOd B
Rl_ lOO.OmV
MKR
1 1 . 37
7 9 . 98
MKR 7 9 . 98mV
1 1 .3 7 G H z
L IN
GHz
rr V
CENTER 1 3 . 25G H z
RBW 1 . OMHz
VBW
1 . OMHz
SPAN S6 .SO G H Z
SWP 53 0m s
Figure 6-11. Combined spectrum at 11.97 GHz
Power combining efficiency can be found as before:
79.982
Efficiency = -------^ ------ r = 77.27%
3 79.61
44.05
50 + 50
Power combining efficiency depends on two parameters. The first parameter is
frequency difference between the two free running oscillators. The closer these two fre­
quencies are, the more combining efficiency can be achieved (comparing Figures 6-3, and
6-4 to Figures 6-9, and 6-10). The second parameter is the oscillation amplitude. Higher
efficiency occurs under higher oscillation amplitude for both oscillators. Comparing
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
89
Figures 6-6, and 6-7 to Figures 6-3, and 6-4 indicates that higher oscillation amplitude
leads to greater combining efficiency.
6.2 Bandwidth
To measure power combiner bandwidth, a different test setup is required. This
setup is shown in Figure 6-12.
-3 0
-2 0 dB
Supply
D irectional Coupler
D irectional Coupler
Supply
Figure 6-12. Test setup for measuring bandwidth.
The injection locking method is used. In this method, the injection frequency is
swept until it locks on to the power combiner output. The frequency range over which the
injected signal locks on to the oscillator is the injection locking bandwidth. Figures 6-13,
and 6-14 show two oscillator outputs used for measuring the bandwidth. The bias condi­
tions for Figure 6-13 are:
Vds = 1.57 V
Ids = 24.5 mA.
The bias conditions for Figure 6-14 are:
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
90
ATTEN
rl. a .
lO d B
ooomv
MKR
l O . 33
1 . B 34
G
MK R A • B 8 4 m V
io .a a Q H z
l i n
HZ
ITV
.
START S.O O G H z
RBW 1 . OMHZ
VBW
STOP
1 . OMHz
30.0 0 G H Z
SWP 3 B O m a
Figure 6-13. Oscillation spectrum at 10.22 GHz.
ATTEN lO d B
RL. S . O O O m V
I -1
*0
.2*
4B
1 . B 32
LIN
M KR 1 . S 3 S m V
lO • 4BGHZ
G HZ
ITV
START S.O O G H Z
RBW 1 . O M H Z
VBW
STOP
1 . OMHz
SO .O O G H z
SWP 3 6 0 m i
Figure 6-14. Oscillation spectrum at 10.46 GHz.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
91
Vds = 1.9 V
Ids = 23 mA.
The power spectrum of the combination of the devices is plotted in Figure 6-15.
ATTEN
lO d B
S . OOOmV
MKR
lO . 31
a . B IS
L IN
MKR S . B l S m V
lO . 51G H z
GHz
IT V
•»
------- — m r
CENTER
1 3 . 25QHZ
RBW 1 . O M H z
VBW
1 . OMHz
SPAN S B .S O Q H z
SW P 3 3 0 m o
Figure 6-15. Combiner spectrum at 10.51 GHz.
The power combiner output along with external injection signal are shown in Fig­
ure 6-16. The higher amplitude signal is the injection signal. Increasing the frequency of
injection signal to 10.46055 GHz gives it the capability to lock on the combiner output as
shown in Figure 6-16. The spectrum analyzer is calibrated before taking the measurments.
As frequency increases to 10.46320 GHz, the external signal generator looses the
ability to lock on to the output of the combiner. This is shown in Figure 6-18. The differ­
ence between these two frequencies is the combiner bandwidth.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
92
ATTEN
lO d B
RL- l g . O O m V
MKR a . 6 4 B i n V
lO . 4 6 4 0 0 G H z
L IN
1
MKR
lO . 4B4C O
a . b 4 8 nr V
G Iz
/
V
I
—
START
l O . 49QOOGHZ
STOP
RBW 3 0 0 k H Z
VBW B O O k H z
1 0 .4 0 0 0 0 G H z
SWP S O . Oma
Figure 6-16. Combiner output along with injection signal.
BW = 10.46320 GHz - 10.46055 GHz = 2.65 MHz
This means that combiner has a narrow bandwidth. The narrower the bandwidth
for oscillation indicates a better performance for fixed oscillators.
6.3 Conclusion
A microwave spatial power combiner has been designed to operate at 10 GHz.
The common-gate MESFET configuration was used for the individual oscillators. MESFET oscillators were designed on RT Duroid 5880 substrate with relative permitivity of
2.2. Oscillator simulation was done on EEsof LIBRA. Since it is not possible to simulate
power combining on EEsof LIBRA, it is not possible to predict power combining effi­
ciency based on simulation. The circuit was optimized to fulfill impedance matching re­
quirements.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
93
A T T E N lOdB
RL. l H . O O m V
M K R 13.S3HIV
10.4609S6HZ
LIN
MKR
1 0 . 4 6 0 ! B Gl'Z
1 3 . 3 3 rr V
i
*
—J
START 1 0 . 4 9 0 0 0 G H Z
STOP
RBW 3 0 0 K M Z
VBW 3 0 0 k H z
1 0 .4 8 0 0 0 B H Z
SWP
S O . Oma
Figure 6-17. Lower limit of injection locking.
ATTEN lO dB
RL. l S . O O m V
MKR 1 3 . 7 4 m V
1 0.463a0G H z
LIN
MKR
l O . 4 6 3 2 O GH 1 2
1 3 . 7 A IT V
V,
S T A R T l O . 4SOOOOHZ
STOP
RBW 3 0 0 k H z
VBW 3 0 0 k H Z
10.46000G H z
SWP B O . Oma
Figure 6-18. Upper limit of injection locking.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
94
The oscillator design was done using S parameters measured under the bias condi­
tion of Vds = 3 V, and Ids = 10 mA. However, it has been difficult to apply the above
bias to the MESFETs. That is one reason the operating frequency for oscillators are not
exactly as designed. Two power supplies were needed to bias each transistor: One for the
source and one for the drain. This is a practical restriction, since, to combine four oscilla­
tors, eight power supplies are required.
Power combining efficiency has been investigated in three different cases. In each
case, different devices were used. The efficiency was found to be 80% to 90%. In gen­
eral, spatial power combining has been shown to be efficient. Since each individual device
and circuit are not fabricated exactly the same, differences in oscillation frequencies oc­
curs. Furthermore, each circuit is in a different environment. When individual free run­
ning frequencies are nearly the same, combining efficiency is highest.
It was found that combining efficiency depends on both frequency, and amplitude.
It was also noticed that if one oscillator has a significantly larger amplitude than the other,
its frequency dominates when combined with a weaker oscillator. That means the fre­
quency of the combined signal would be almost the same as the frequency o f the high am­
plitude oscillator.
It was found that tuning bandwidth of oscillation is not affected by injection lock
signal level. The amplitude of the injection lock signal is 13.2 mV. The tuning bandwidth
of an oscillator, and therefore, the bandwidth of combined signal was narrow (2.65 MHz).
This has been verified by calculating
was found to be 4400.
It is desirable to predict oscillator frequency. That will be possible through a more
accurate large signal S parameter design for oscillators. Reaching a desirable bias condi­
tion will also help maintain a smaller tolerance for oscillator frequency. Since radiation
cannot be simulated on EEsof LIBRA, more precise simulation for oscillator can be ob-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
tained by taking the radiation effect of patch antennas into account. Work will need to be
done to improve power combining efficiency. It is desirable to simulate power combining,
and then to predict power combining efficiency based on simulation results. The next step
will be to make three or more oscillators work together to see how power combining can
be achieved at that level. Future works might include ways to maintain a desirable DC
bias, and to obtain a more accurate oscillation frequency.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
APPENDIX A
ATF-26836 MESFET TRANSISTOR DATA SHEET
96
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
97
Q a v a n te k
ATF-26836
2-16 GHz General Purpose
Gallium Arsenide FET
F eatures
A v a n te k 3 6 m lcro-X P a c k a g e '
•
H igh (m ax : 6 0 G H z ty p ic a l
•
•
H igh O u tp u t P o w e r: 18 .0 d B m ty p ic a l P i ob
at 12 GHz
H igh G a in : 9 .0 d B ty p ic a l G ss a t 1 2 G H z
•
•
C o st E ffe ctiv e C e ra m ic M lc ro strlp P a c k a g e
T a p e -a n d -R e e l P a c k a g in g O p tio n A v a ila b le 1
SOURCE
□RAIN —
D escription
Avantek's ATF-26836 is a high performance gallium
arxanide Schottky-berriar-gate field effect transistor housed
in a cost effective microstrip package. This device Is
designed for use in oscillator applications up to 25 GHz and
general purpoee amplifier applications in the 2-16 GHz
frequency range.
( u n l c u o t h f f w i M » p«clH *d)
1. OtoiMMlons art Jjk
i. TolanncM
.057 X.010
t.«tffl-* sjy
This GaAs FET device has a nominal 0.3 micron g ate length
with a total gate periphery of 250 microns. Proven gold
based metallization system s and nitride passivation assure
a rugged, reliable device.
rn
.022
jT
a-
.110 1.010
“
In j u u ■ *.003
mm ju ta *.13
n
4.57 1 a s “
I
.004 1.001
.IS * .05
n e w now ro w ix o ju a m rn m m avaxaxlx qaih
AMOMUDMUU kTASll OJUN<*. mOUINCV
V a a .e v .io o M M iT i.irc
IU
AS
Electrical Specifications, Ta » 28*C
Symbol
Piremelers end Test CondlUone
Units
Min.
Typ.
hlAX
QSJ
GHz
dB
7.0
60
g.o
dBm
15.0
18.0
Qa
Maximum Frequency of OscUetlcn: Vds • 5 V. Ids • 30 mA
Tuned Smal Signal Qaki:
• 1.12.0 GHz
Vos • 5 V. Id s - 30 mA
! • 12.0 GHz
OutputPower® 1 dB Qain Compression:
Vos • 5 V. los< 30mA
1.12.0 GHz
Optimum Noise Figure: Vos - 3 V, Ids ■ 10 mA
I • 12.0 GHz
Gain 0 NFo: Vos » 3 V, los ■ 10mA
Sm
loss
VP
Transconduetance: Vos « 3 V. Vos ■ 0 V
Saturated Drain Current: Vos * 3 V. Vos • 0 V
Pincholf Voltage: Vos ■ 3 V. Ids - 1 mA
16
20
-3.5
2.2
6.0
35
50
-t.5
Pi dB
NFo
dB
dB
mmho
mA
V
Hex.
too
-0.6
Nome 1. long leeded 35 rrKro-XpecMoeewuue upon reque«.
I M t t to PACXAQMG McSonTlpe^nd-Reel PicXxging lor Sudan Mount Senwonduoonr.
A rm * . Me. •
sueOn— ! Am.. 1—
cun.CAMOM .
Phone(400) 7270100 •
FAX: (404) 727-0634 • 1WX:2105714717ar 5103714474
•
TELEX:244337
M 4
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
98
ATF-26836,2-16 GHz
General Purpose Gallium Arsenide FET
Absolute Maximum Ratings
A bsolute
M axim um'
Param eter
Symbol
Orain-Source Voltage
Gale-Source Voltage
Drain Currant
Total Power Dissipation*9
Channel Temperature
Storage Temperature*
VOS
Vos
♦7V
-4 V
ids
loss
275 mW
I7S*C
-65*C to *175*0
Pt
Tch
TSTO
Part Number Ordering Information
Pan Number
Devfcea Per Reel
ATF-26838-TR1
ATF-26836-TR2
ATF-26536>STR
1000
4000
Reel Size
r
tr
1
STRIP
Thermal Resistance: 0je • 3S0*C/W; Tch ■ 150*0
Liquid Crystal Measurement: 1 urn Spot Size9
NoMt:
1. Operation of this device above any one of these parameters
may cause permanent damage.
2. Case Temperature ■ 25*C.
Typical Performance, Ta a 25°C
(unless otherwise noted)
inssmion rowin asnt tumauu svailsbli osm
amo MA&smii sta sis tuuNn. fumuincv
VosaSV.IgaatOnA
3. Derate at 2.9 mW/*C for TcasE>79*C.
4. Storage above *I50*C may tarnish the leads of this package
difficult to solder into a circuit Attar a device has been soldered
into a circuit it may be safety stored up to 175*C.
5. The smell spot site ol this technique results in a higher, though
more accurate determination of 8jc than do alternate methods.
See MEASUREMENTS section for more information.
u
sa
Ta a 25°C, Vos®3 V,los = to mA
Typical Scattering Parameters: Common Emitter, Zo = s o a
s„
Sai
Freq.
GHz
Meg
Ang
dB
Mag
Ang
dB
Mag
Ang
Mag
2.0
3.0
4.0
5.0
6.0
7.0
S.0
9.0
10.0
11.0
12.0
13.0
140
150
16.0
.94
90
.84
.75
.64
.52
.49
.52
.56
.61
67
.69
72
72
72
-38
-55
-72
-92
8.2
7.8
7.6
8.0
8.1
-155
163
126
100
78
58
4S
35
22
13
8.3
7.9
7.2
6.4
5.6
4.7
3.9
3.0
2.5
2.0
138
120
102
82
61
37
14
-7
-28
-47
-66
-83
-98
-115
-128
-27.1
-24.9
-22.9
-20.6
-19.3
-18.1
-17.5
-16.9
-16.8
-17.1
-17.1
-17.3
-17.2
-17.2
-17.4
044
.057
.072
.093
.109
.124
133
.143
.144
.140
.139
.137
.138
138
135
60
51
44
30
-117
2.57
2.45
2.41
2.50
2.55
2.60
2.47
^^0
2.10
1.91
1.71
157
1.42
133
126
.74
.71
.71
.66
.60
.51
.41
.30
.24
.16
.15
.17
.19
23
27
2.0
3.0
40
5.0
8.0
7.0
6.0
9.0
10.0
110
12.0
13.0
14.0
15.0
16.0
.94
.86
.78
68
57
.43
37
40
47
.55
61
71
.71
65
58
-44
-63
-81
-97
-118
-151
165
122
96
75
53
33
10
-10
-30
9.0
8.5
8.0
7.9
2.82
2.65
2.51
2.49
2.53
2.65
2.66
2.S2
2.42
2.37
2.35
2.34
2.17
193
1.62
130
110
89
71
51
28
3
-20
-42
-66
-88
-116
-143
-170
166
-30.2
-28.4
-26.9
-25.5
-24.4
-22.4
-20.6
-18.0
-16.4
-15.1
-13.6
-13.2
-13.5
-14.0
•149
.031
.038
045
.053
.060
076
093
126
152
176
205
220
212
200
180
IS
5
-12
-21
-82
-41
-49
-61
-66
-77
-85
Ang
-26
-85
-44
-83
-64
-78
-92
-106
-125
-154
168
134
107
69
71
K
0.39
0.51
0.59
0.78
0.91
0.98
1.05
1.07
1.11
1.16
1.16
1.20
1.20
1.24
1.31
Ta = 25°C, Vos = 5 V, 103 = 30 mA
8.1
8.5
8.5
8.0
7.7
7.5
7.4
7.4
6.7
5.7
42
65
56
47
41
39
38
30
15
3
-4
-19
-39
-56
-72
-93
.80
80
79
.78
.76
.73
69
64
.66
63
64
.71
.78
.85
98
-31
-43
-52
-58
-67
-80
-99
-119
-140
-166
168
132
104
79
61
0.28
0.49
0.72
0.89
0.98
0.90
0.82
067
047
0.39
030
0.11
0.06
0.04
-023
A model tor evs demos is avalafile in the DEVICE MODELS secson.
Swart, he.
3tneannAM>s«aciiiACAesos« • pnmiweim-oiM • P*x:i«t>7j7.04» • rwx:jiojiisri7oiji»s»i'eiie
3-55
• TELEX:344337
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
APPENDIX B
ATF-26884 MESFET TRANSISTOR DATA SHEET
99
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
100
© a v a n te k
ATF-26884
2-16 GHz General Purpose
Gallium Arsenide FET
Features
•
Avantek 84 Plastic Package
High (m ax: 60 GHz typical
•
High Output Power: 18.0 dBm typical Pi hb
at 12 GHz
• High Gain: 9.0 dB typical Gss at 12 GHz
• Low Cost Plastic Package
• Tape-and-Reel Packaging Option Available'
Notts:
I
u n lttt olhifwtM apaclHad)
I (,U
IDlm intlont a rt ~In
2.Tolarancia
In . x u a 2.005
nun
■ 2.13
Description
Avantek's ATF-26884 Is a high performance gallium
arsenide Schottky-barrier-gate field effect transistor housed
in a low cost effective plastic package. This device is
designed for use in oscillator applications up to 25 GHz and
general purpose amplifier applications in the 2-16 GHz
frequency range.
mm
.0002.002
L
.20 X .060
i_ e =
This GaAs FET device has a nominal 0.3 micron gate
length with a total gate periphery of 250 microns. Proven
gold based metallization system s an d nitride passivation
assure a rugged, reliable device.
T.020IC
• ASA
»
.51
MERTON FOWtR CAIN. MAXIMUMAVAIUXIB GAIN
ANO MAXIMUMSTABLE GAM VL FREOUENCV
VM ■ * V. lot • » mA. T* a JS*C
MUimON FOWSR GAIN. MASMUMAVAiLAXlfOAlN
ANOMAXIMUMSTABUi GAINv*. FREQUENCY
It
m
MM
it
to
•u
40
40
40
100 140
140
40
40
140 140
Etoctrtcal Specifications, T a » 25eC
Symbol
Peiemeiere and Teel Conditions
Units
Hln.
fUAX
GSS
Pi dB
Maximum Frequency of Oscillation: Vos* 5 V. Ids • 3 0 mA
Tuned Smal Signal Gain: Vos • 5 V. IDS • 30 mA
1• 12.0 GHz
Output Power <91 dB Gain Compression:
t • 12.0 GHz
Vos • 6 V. IDS • 30 mA
GHz
d8
dBm
7.0
15.0
NFo
GA
Optimum Noise Figure: Vos • 3 V, Ids • 10 mA
Gain 9 NFo: VDS • 3 V, Ids* 10 mA
flm
Transconductance: Vos • 3 V. Vos • 0 V
Saturated Drain Currant: Vos • 3 V, Vqs • 0 V
Pincholf Vottaga: VOS • 3 V, Ids • 1 mA
loss
VP
1 . 12.0 GHz
1 .1 2 .0 GHz
Z2
6.0
dB
d8
mmho
mA
V
Max.
Typ.
60
9.0
18.0
15
20
-3.5
35
50
-1.5
too
-0.5
Not*: 1. R otf to PACXAGMQ tocOon T a p i and nt i i PocXiffng lor Surtsca M otfit Sanxconduapq’.
AvanMume. • 3176t o M A m .6 M a 0 * 4 CAtflfltt • PMna (401) 727-0700 •
3-66
FAX:MOO)727*0030 • TVflC310371-1717or3I0-37I-M7I
•
TELEX:34*337
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
101
ATF-26884,2-16 GHz
General Purpose Gallium Arsenide FET
Absolute Maximum Ratings
Param eter
Sym bol
Drain•Source Voltage
Gate-Souroe Voltage
Orain Currant
Total Powar Dissipation”
Channel Temperature
Storage Temperature
Vos
Voa
■os
Pt
Tch
Tsto
Absolute
Maximum1
Pan Number Ordering Information
*7 V
-4V
loss
275 mW
175*C
-C5*Cto+l50*C
Part Number
Oevicte Per Reel
Reel Size
ATF-26884-TR1
ATP-26884-TR2
ATF-26884-STR
1000
4000
1
r
13STRIP
.Thermal Retistanoe: 8|C«300*C /W ;Tch-15* ?.
llouid Crystal Measurement: 1 um Spot Size4
Notts:
1. Operation oltM idevietabovttnyorwolttiesoportmotorj
may cauie permanent damage.
2. Cate Temperature • 25*C.
3. Derate at 3.3 mW/*C lor Tc > 92.5*C.
4. Thetm alipot tizaol Blit teettnique retultt in a higher, though
more accurate determination ol 6jc than do alternate maBtodt.
See MEASUREMENTS tecaon tor more mtarmaMn.
Ta a 25°C ( Vo* a 3 V, Igs s 10 mA
T y p ica l S c a tte rin g P a r a m e te r s : C o m m o n S o u r c e , Z o s s o n
Meg
Ang
dB
Mag
96
.91
.86
.79
.73
.67
62
.57
.53
52
-36
6.9
7.4
7.6
7.2
6.8
6.4
6.4
6.2
5.8
5.2
4.9
4.6
4.0
3.3
2.9
2.3
1.3
2.21
2.35
2.39
2.30
2.20
2.10
2.08
2.03
1.96
1.81
1.76
1,70
1.58
1.46
1.40
1.30
1.16
dB
Ang
142
123
103
86
71
56
41
23
6
-10
-22
-36
-54
-72
-83
-99
-112
-26.6
-23.0
-20.6
-19.5
-18.9
-18,4
-17.9
-17.5
-17.3
-17.2
-17.1
-16.7
-16.3
-16.3
-16.3
-16.0
-15.9
-41
.94
9.2
2.0 .
2.88
138
87
9.5
30
-65
2.97
118
79
9.3
40
-89
2.93
97
.71
8.7
5.0
-109
2.73
79
.64
6.0
8.1
-128
2.54
64
70
.57
-142
75
2.38
50
8.0
52
-162
7.2
2.30
35
174
6.9
90
48
221
16
too
149
65
48
2.11
1
11 0
48
59
130
197
-14
12.0
49
5.6
108
191
-25
13.0
S3
5.2
88
182
-39
47
14.0
57
69
1 71
-55
62
4.1
15.0
56
160
-75
.70
44
16.0
3.7
153
-87
33
75
17.0
3.0
1 41
-103
74
24
18.0
2.3
-117
1 30
A model lor ms de*ce»avaMOlenffie DEVICE MOOELS section.
-30.8
-27.3
-25.5
-24.9
-24.4
-24.0
-23.1
68
-56
-78
-97
-113
-127
-144
-168
166
147
124
103
80
65
52
40
.69
30
.49
.52
.56
.60
65
S»
S it
Meg
Ang
Mag
047
64
SO
81
071
093
106
.114
120
.128
.134
136
.138
36
25
16
9
1
-8
-16
-22
-26
-31
-37
-42
.140
.146
.153
.153
.153
.158
-48
-56
-72
.159
T* = 25°C ,
A « M ,K
#
3 in B 0 M fe A w fc .S M a C lM .C A MOM
•
-219
-20.4
-197
-18 1
-162
-15.2
-14 8
-138
-129
-13.6
Phone(401) 7270700
•
65
029
043
053
057
060
063
070
080
095
104
125
155
173
182
205
226
210
PAX:(408)727-Cttfl
51
40
35
33
31
30
28
24
22
20
18
5
-1
-16
-28
-44
•
Ang
-25
-38
-80
-61
-70
-78
-68
-101
-116
-133
-143
-154
-171
173
132
101
77
.70
66
62
61
56
.54
.47
.41
.39
.37
.35
.35
.37
41
47
II
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0
12.0
13.0
14.0
15.0
16.0
17.0
18.0
3 *i
<
a
(A
S ii
Freq.
GHz
87
K
0.22
0.33
0.44
0.57
0.70
0.81
0.88
0.94
1.07
1.19
1.26
1.21
1.17
1.16
1.10
1.07
1.03
5 V, Ids = 30 mA
84
80
74
-23
-34
-44
71
-53
69
69
69
67
63
57
55
-60
-67
-76
-122
54
52
52
52
54
63
-132
-146
-165
165
135
114
TW X:3t0.371S7l7of 3IM 71.M 7B
-87
•too
-114
•
029
043
063
0.82
099
1.12
1 07
1 05
098
i to
096
0 78
0.72
065
051
0 45
0.41
7EIEX;344337
3-57
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
APPENDIX C
LAYOUTS OF OSCILLATOR GRID
102
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
103
Figure C-l. Oscillator grid front-side layout.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure C-2. Oscillator grid back-side layout.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
APPENDIX D
LIBRA SIMULATION TEST BENCHES
105
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
106
L i n e a r T w o - p o r t G e n e r i c S - p a r a m e t e r Te s t Bench
S u b s t i t u t e N e t w o r k ( DUT)
with term inations
Meosuremen ts
( Sc at te rin g Parameters)
Z i n = 50 Ohms
Zoul = 50 Ohms
REFGAMMA
TERM 1
MAG=0
ANG=0
tes t70
XI
Stim ulus Controls
O utput Equat ion
Equotion for Uaiimum Stabl e Coin
.FREQUENCY
FPLAN
v a l u e = S WE E P 2 16 1
Figure D-l. Test bench for impedance measurment.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
107
Swept Frequency O s c i l l a t o r Test Bench
Stim u lu s
Test C i r c u i I
and S i m u l a t i o n C o n t r o l s
FREQUENCY
FPLAN
Rierm
OSCTtST
P*_power
’ F= _ lr e a l
ANG=0
— RsRsource
volue=SWEEP 2 16 0.1
na
POWER
PPLAN
volue=STEP 40
NH
NH
VALUE=1
Rlood
R=O.OOI
The e t c i l l o t e r n e tv o tk i i a ttu n e d
to be o Ih te e - p o r t. elth s o M t t end
2 d l» ld l» e the o i c i l l o l o ' t i# io n o to »
and p a r i 3 b e in g th e a t c l I t o l o r lea d.
Measurements and O u tp u t
E q u a t io n s
OUTPUT
EQUATION
PF
OscPower
TP1ID=TP3
TP2ID=gnd
ELEU=R food
H1=1
VFC
Vinject
TP1I0=TP2
TP2IO=qnd
HI = 1
H2=0
H2=0
H3=0
VFC
Vrel ur n
TP1I0=TP1
TP2ID=gnd
HUI
H2=0
H3=0
SAMPLE
SAMPLE
VALUE=2
f— 5
3
OUT.EON
FOSC
.0UTE0N1
FOSCt
Comple«Vratio= V r et ur n /
RatioAngIe= onq (V re lu rn
RotioMoq= maq(Vreturn /
FOSC
F0SC2
Vinject
/ V inject)
Vinject)
The o b je c tiv e here i | t o U nd the freq ue ncy o t »M < h "R a tlo A n g ie *
goes to i t f o .
T hi» i t th e o p p ro tim o le de queeey o l e s c i I l o t io n .
H3-0
Figure D-2. Sweep frequency oscillator test bench.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
108
O s c i l l a t o r A n a l y s i s Mo de T e s t B e n c h
Tesl
S t i m u l u s and S i m u l a t i o n
C irc u it
AAArn
RES
Rlerm
R=50
Rsource
OSCTEST
□s
OSCMODE
OSCMODE
TPID=TP3
V01TACE=0
PS
Pi nj ect
P*_power
F -.Ire g l
ANG=0
H=t
th» oscuooc voiracc
s p e c i f i c s Ibe lim a - ie r o
v o lt e a * o t TPJ. U se th*
r e s u l t s Irgm ( h e nqnOSOiOOC a n a l y s e s to
dariw e t h i s v a lu e . The
v o lu t s In in * frequ en cy
and p e v o i p l a n s sh o u ld
a p p ro e lm a le ly corr esp o n d
lo th e o e lu o l o p e r a tin g
p o in t.
□a
Resource
t es12683a
C o ntrols
FREQUENCY
FPLAN
volue=SWEEP 2 16 0.1
POWER
PPLAN
volueaSTEP 20
TD
xi i; res p
Rlood
>R=0.00t
□I
Tht o s c i l l a t o r n t lv o i h i s onum cd
t o bo 9 t h r o o -p o r t , v l l h t o i l s 1 and
J d i v id i n g th e o s c i l l a t o r ' s reson ator
and p a i l j b a in g Iho o s c i l l a t o r lo a d .
NH
NH
VALUE=1
□s
SAMPLE
SAMPLE
VALUE=2
Measurements and Ou tp ut E q u a t i o n s
OUTPUT
EQUATION
FOSC
OscF reguency
lijllk,.
PSPEC
OscSpectrum
TP1I0*TP3
TP2ID*gnd
ELEUoRload
PF
OscPower
TP1I0=TP3
TP2ID*gnd
ELEU=Rload
H1*1
H2»0
H3*0
VFC
Vi nject
TP1I0=TP2
TP2IO=gnd
HU1
H2»0
H3=0
VFC
Vreturn
TP110=TP1
TP2ID=gnd
H1 = 1
H?*0
H3*0
OUT.EQN
.OUTEONt
Comple*Vralio= Vreturn / V i n j e c t
RolioAngles ang(Vrelurn / V i n j e c t )
RotioUog* mog(Vreturn / V i n j e c t )
To m an u ally lin d l i e o a c fI lo to * o p e r a tin g c o n d i t i o n s ,
d e a c t iv a t e IK* OSCUOOE S im u la tio n C on trol Item
and th en a d ju s t Ihe frequ en cy and pover
u n t il ’ ftetioU eg* g a t s lo u n ity ond "R olloA n gla" g o e s
Figure D-3. Oscillator analysis mode test bench.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
109
Swept Power O s c i l l a t o r T e s t Bench
S t i m u lu s and S i m u l a t i o n C o n t r o l s
TPt
RES
Rterm
R»50
TP2
FREQUENCY
FPLAN
RES
Rsource
R»50
OSCTEST
0SC1
volue=STEP 10
□1
POWER
PPLAN
volue=SWEEP 2 16 O.t
□B
.JP< RT
Oscl el
NH
NH
VALUE*
RES
TPJ
Rload
R=0.00t
□B
lh« a s e illa lo r n«l»»ik i t o n im d
to 6* • Ik iM - p o r l, v ilh t o r l l I *nd
1 d iv id in g the o te iM a lo r 't resonator
and port j being Ik * o«ci11ator load.
M easurem ents and 0
SAMPLE
SAMPLE
VALUE*
ut Equal ions
OUTPUT
PF
OscPower
TP1I0=TP3
TP2ID=qnd
£L£M=Rload
H1 = 1
H2=0
H3=0
VFC
V in je ct
TP1I0=TP2
TP2ID=gnd
Hl = t
H2=0
H3=0
1VFC
Vre turn
TPt!0=TPI
TP2ID=qnd
Ht=t
H2=0
H3=0
EQUATION
OUT.EON
JJUTEQNl
ComplexVrotio* Vreturn / V i n j e c t
RatioAngle= ang(Vrelurn / V i n j e c t )
RatioMag= mag(Vreturn / V i n j e c t )
Tltt o b |* e llv * hot* i t lo fin d Hi* p o o r ol nkiek “ RolioNaq'
goes lo u n ity . Vh*n tk i» condition it r r w l, and Ik * (r**u«ncy
volut dot o lto b«tn od |u tt*d tuck that "RatloAngt*" «guols
l* ro , Ik* e a c illo tio n condition* o’ * » « ll* li« d .
Figure D-4. Sweep power oscillator test bench.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
110
I MPORTANT
I f y o u r D e f a u l t s w i n d o w na me i s a n y t h i n g
o t h e r t h a n " d e f a u l t s . d s n " , i t must be ope ned
i n o r d e r t o be a s s o c i a t e d w i t h t h i s s i m u l a t i o n .
2) A t e s t bench r e f e r s to the D e f o u l t s window
f o r i t s u n i t s , v a r i a b l e s and e q u a t i o n s .
3 ) T h e " S i m u l a t i o n C o n t r o l O p t i o n " OSCMODE
i s r e q u i r e d f or the o s c i l l o t o r a n a l y s i s mode.
1)
FREQUENCY
FPLAN
value=SWEEP 2 16 1
POWER
PPLAN
vaIue=STEP 20
IBW
I
NH
OSCMODE
OSCMODE
TP ID=TP3
VOL TAGE=0
spco
XI
Dip -
TP2ID=gnd
H1 = 1
H2=0
0SC1
■ w
OUTPUT
W
RES
RGEN
<]
<\
TP1
TP2
TP
a
TPtID=TP2
TP4
OSCTEST
R=50
VALUE=2
VFC
Vs amp
< TP1
TP3
NH
TP
n
RES
RSAMP
H3=0
EQUATION
HU'
R=50
Te mp = »GROUND
OUT.EON
.OUTEON
l o o p q o i n = Vs a mp / V i n j
VFC
Vi nj
TPIID=TP 1
TP2ID=qnd
H1=1
H2=0
H3=0
Figure D-S. Oscillator template test bench.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
APPENDIX E
LIBRA SIMULATION DATA ITEMS
111
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Data Iterns
MWALL
Microstrip Sidewalls
Symbol:
Illustration:
D A T A
Parameters:
W1 = distance from near edge of microstrip transmission line to 1st sidewall,
in length units
W2 = distance from near edge of microstrip transmission line to 2nd sidewall,
in length units
Range of Usage:
W l> M A X [ H / 2 , W / 2 ]
W2> M A X [ H / 2 , W / 2 ]
where
H = thickness of associated MSUB
W = width of associated MLIN
Notes/Equations/References:
1.
To neglect the effect of sidewalls during analysis, set W1 and W2tozero.
2.
This Data Item is optional. It can be used with those microstrip elements that have
MWALL as one of the parameters.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
113
Data Items
Permeability and Magnetic Loss Tangent
PERM
Symbol:
D A T A
Parameters:
MUR a relative permeability
TANM = magnetic loss tangent
Range of Usage:
N/A
Notes/Equatlons/Referances:
Harrington, R.F. Time-Harmonic Electromagnetic Fields, McGraw-Hill, 1961.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
114
Dataltems
Dielectric Loss Tangent
TAND
Symbol:
D A T A
Purpose:
To specify dielectric loss tangent for certain transmission media.
Parameters:
TAND
= dielectric loss tangent value
Range of Usage:
TAND 2 0
Notes/Equations/References:
If TAND= 0, dielectric loss is ignored.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
115
Data Items
Physical Temperature
TEMP
Symbol:
D A T A
Purpose:
To specify physical temperature affecting noise analysis of circuit elements.
Parameters:
TEMP s physical temperature, in degrees Celsius
Range of Usage:
The default value of TEMP is 16.85°C (290K).
Use TEMP s -273.15°C (or less) to turn off noise contribution of passive elements.
Notes/Equations/References:
1.
Noise performance of lossy passive elements is calculated as a function of their
physical temperature.
2.
TEMP specifies physical temperature for one or more passive elements.
3.
TEMP as -273.15°C (zero Kelvin) is important when modeling noise in an active
device by noise sources so that noise generated by lossy passive elements of the model
is not accounted for twice.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
116
Data Items
MSUB
Microstrip Substrate
Illustration:
Symbol:
D A T A
_L
H
I
Parameters:
ER
H
T
RHO
RGH
s substrate dielectric constant
substrate thickness, in length units
> metal thickness, in length units
3 metal bulk resistivity (relative to gold)
3
mis surface roughness, in length units
3
Range of Usage:
N/A
Notes/Equations/References:
1.
Bulk resistivity (RHO) specified is relative to that of pure gold (2.44 microhm-cm)
Circuit resistivity = RHO • 2.44 microhm-cm
2.
Losses are accounted for when RHO > 0 and T > 0 . The RGH parameter modifies the
loss calculations.
3.
This Data Item specification is required for all microstrip elements.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
117
Data Items
Microstrip Cover Height
Symbol:
DATA
MCOVER
Illustration:
////////////////////
SjEr (from MSUB)
(from MSUB)
Parameters:
HC =* height of cover above top surface of substrate, in length units, substrate is specified
by an associated MSUB Data Item
Range of Usage:
HC£H
If HC = 0, cover is placed at infinite height
where
H s substrate thickness
Notes/Equations/References:
This Data Item is optional. It can be used with those miciostrip elements that have
MCOVER as one of the parameters.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
APPENDIX F
RT/DUROID 5880 DATA SHEET
118
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
RT ISB8Q
$ ROGERS
RT/durold 5880
PROPERTY
TEST METHOD
CONDITION
Dielectric c o n sta n t, Cr
1MHz, MIL-P-13949G Appendix B
10GHz, IPCTM 650. 2.5.5 5
tMHz, MILP-13949G Appendix B
10GHz, IPC-TM-650, 2.5.5 5
C 24(23/50
C 24/23/50
C 24/23/50
C 24/23/50
V olume resistivity
S u rfa ce resistivity
ASTM D257
ASTM D257
C 96 /3 5 /9 0
C 96 /3 5 /9 0
M o h m cm
M ohm
T en sile m odulus
ASTM D638
A
M Pa (kpsi)
D issipation factor, ta n 6
ultim ate s tr e s s
-
M Pa (kpsi)
%
ultim ate strain
C o m p ressiv e m odulus
u n it s m
ASTM D695
A
M Pa (kpsi)
ultim ate s tre s s
M Pa (kpsi)
ultim ate strain
%
DIRECTION
z
z
T e s t a l 150°C
1.0
X
Y
X
Y
X
Y
X
Y
Z
X
Y
z
D eform ation u n d e r lo ad
X
Y
ASTM D621
W ater a b so rp tio n
ASTM D570
T hickness = 0.8mm (0.031 in.)
T hickness = 1.6mm (0.062 in.)
S p ecific gravity
ASTM D792
ASTM D648
H eat distortion tem p e ra tu re
C
alculated
S pecific h e at
R o g ers TR2721
T herm al conductivity
T herm al ex p an sio n
ASTM D3386
(10 K /m in.)
(V alues given a re to ta l c h a n g e tram a
b a s e te m p e ra tu re o f 35°C )
24 hr/14M Pa(2 kpsl)
D 24 /2 3
%
1.82MPa(264 psi)
°C (°F)
X.Y
J /g /K ( B T U /lb /° n
W /m /K (B TU ln /ft* /h r/°F ) Z
—♦
m m /m
m g (•/.)
m g (*/»)
-1 0 0 °C
15
25
75
150
250
11181 unlit fiivtn firtt «nlh oitwr Irtquaniry uHd umlt In p titra h tttt
|2) R tftrtnctt: Intarnal TfTi 1430.2224,2884. T ttlt «mr« *1 23*C u ru tu ottunrtM
ncrttd- Typtcti raluti ihouM not to umo lo* tptcilieaNon fimitt.
RT/durold'
TYPICAL VALUE(2)
2.20
2.20 ± 0 .0 2 spec.
0.0004
0.0009
2 x 10'
3 x 10>
T est a t 2 3 °C
T e st a t 100°C
1070 (156)
450(65)
860 (125)
380(55)
29 (4.2)
20(2.9)
27 (3.9)
18 (2.6)
6.0
7.2
4.9
5.8
710(103)
500(73)
710(103)
500(75)
670(97)
940(136)
27 (3.9)
22(3.2)
28 (4.0)
21 (3.1)
52 (7.5)
43(6.3)
8.5
8.4
7.7
7.8
12.5
17.6
Z
z
z
z
z
X.Y
0.9 (0.02)
1.3(0.015)
2.2
> 2 6 0 (> 500)
0.96 (0.23)
0.26 (1.8)
X
Y
Z
-6 .1
-8 .7
-1 8 .7
-0 .9
-1 .8
- 6.9
-0 .5
-0 .9
- 4.5
8.7
1.1
1.5
2.3
3.2
28.3
3.8
5.5
69.5
TIm mbom lalonMUon It not InltnOtd to and do*i not c*Mla any wtrrtnUot, u p r n i o* Impiltd,
ladudtag any «Mrany of — rctitnltbiWy or lUnott to* • p trtlcUnr pwpoto. U tt ol RTMurtM
wtc w n * Unintto In your ptfticUtr oppUctUon may yftkl dlirtrtnt rttuflt.
lim m iti it a legitttito Irtdtmtm ol Rogers Coiportlion lor lit mciowavt m tltrttlt
A vtiidtito tapofi itcenst issued Oy ihe U S Oeperimeni ol Conwntrct it required lor trpon of these m altntlt from Ihe United Sialaa or Canada.
0«version contrary to U S ia« proh»twt«o
PrmledmUS A
1847-078-KLOWA
R«vi8«d3/61
Supenedet 1/78
VO
REFERENCES
[1] K. Chang and C. Sun, "Millimeter-Wave Power Combining Techniques", IEEE
Trans. Microwave Theory Tech., Vol. MTT-31, pp. 91-107, Feb. 1983.
[2] K.J. Russel, "Microwave Power Combining Techniques", IEEE Trans. Microwave
Theory Tech., Vol. MTT-27, pp. 472-478, May 1979.
[3] A. Mortazawi, and B.C. De Loach, "Spatial Power Combining Oscillators Based on
an Extended Resonance Technique", IEEE Trans. Microwave Theory Tech.,
Vol. MTT-42, pp. 2222-2402, Dec. 1994.
[4] X. Dong Wu and K. Chang, "Dual FET Active Patch Elements for Spatial Power
Combining", IEEE Trans. Microwave Theory Tech. Vol. 43, pp. 26-30, Jan.
1995.
[5] J. Birkeland and T. Itoh, "A 16 Element Quasi-optical FET Oscillator Power
Combining Array with External Injection Locking", IEEE Trans. Microwave Theory
Tech., Vol. MTT-40, pp. 475-481, March 1992.
[6] Z. Ding, L. Fan and K. Chang, "A New Type of Active Antenna for Coupled Gunn
Oscillator Driven Spatial Power Combining Arrays", IEEE Trans. Microwave
Theory Tech., Vol. MTT-5, pp. 264-266, August 1995.
[7] E. Pattenpaul, H. Kapusta, A. Weisgerber, H. Mampe, J. Luginsland, and I. Wolff,
"CAD Models of Lumped Elements on GaAs up to 18 GHz" IEEE. Trans.
Microwave Theory. Tech., Vol. MTT-36, pp. 294-304, Feb. 1988.
[8] Eric L. Holzman, Solid-State Microwave Power Oscillator Design, Chapter 9,
pp.401-451, Chapter 3, pp. 59-62, and 74-78, Massachusetts: Artech House
Inc, 1992.
120
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
121
[9] Stephen A. Maas, Nonlinear Microwave Circuits, Chapter 12, pp. 449-452, and 456461, Massachusetts: Artech House Inc., 1988.
[10] R. Soares, GaAs MESFET Circuit Design, Chapter 7, pp. 350-355, Massachusetts:
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[11] K. C. Gupta, R. Grag and R. Chadha, Computer Aided Design o f Microwave
Circuits. Dedham, Mass.: Artech House, 1981.
[12] EEsof LIBRA, Circuit Element Catalog, Chapter 5, pp. 5-6 to 5-28.
[13] P. Bhartia, K.V.S. Rao and R.S. Tomar., Millimeter-Wave Microstrip and Printed
Circuit Antennas, Boston, Artech House, 1991.
[14] J.R. James, P. S. Hall, and C. Wood, Microstrip Antenna Theory and Design, Peter
Peregrinus Ltd., New York, 1981.
[15] W. Alan Davis, Private Communications.
[16] K. Kurokawa and F. M. Megalhaes," An X-band 10-Watt multiple-IMPATT
oscillator" Proc. IEEE, pp. 102-103, Jan. 1971.
[17] L. Lewin," A contribution to the theory of probes in waveguides," Pro. Inst. Elec.
Eng., Managr. 259R, pp. 109-116, Oct. 1957.
[18] L. Lewin, Theory of Waveguides. New York: Wiley, 1975, ch. 5.
[19] K. Chang and R. L. Ebert, "W-band power combiner design," EEEE Trans.
Microwave Theory Tech. Vol. MTT-28, pp. 295-305, Apr. 1980.
[20] Gysel, U.H., "A New N-Way Divider/Combiner for High Power Applications,"
IEEE International Microwave Symposium Digest, 1975, pp. 116-118.
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122
[21] Schellenberg, J.M. and M. Cohn, "A Wideband Radial Power Combiner for FET
Amplifiers,” IEEE ISSCC Dig. Tech. Papers, 1978, Vol. 21, Feb. 1978, pp. 164165.
[22] Cohn, M., B.D. Geller and J.M. Schellenberg, "A 10-Watt Broadband FET
Combiner/Amplifier," IEEE International Microwave Symposium Digest, April
1979, pp. 292-297.
[23] Hanna, V.F. and J. Jumeau, "A Wide-Band 12-GHz 12-Way Planar Power
Divider/Combiner," IEEE Trans. Microwave Theory Tech., Vol. MTT-34, No.
8, August 1986, pp. 896-897.
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IEEE Trans. Microwave Theory Tech., vol. MTT-17, pp. 1156-1158, Dec.
1969.
[25] K. Kurokawa, "An analysis of Rucker's multidevice symmetrical oscillator," IEEE
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Force Avionics Lab, Wright Patterson Air Force Base, OH, Interim Tech. Rep.
no. 1, Mar. 1978.
[27] J. G. Josenhans, "Diamond as an insulating heat sink for a series combination of
IMPATT diodes," Proc. IEEE, vol. 56, pp. 762-763, apr. 1968.
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GHz," in 1981 IEEE MTT-S Int. Microwave Symp. Dig., June 1981, pp. 347348.
[29] C. B. Swan, T. Misawa and L. Marinacio, "Composite avalanche diode structures
for increased power capability," IEEE Trans. Electron Devices, vol ED-14, pp.
584-589, Sept. 1967.
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123
[30] H. Suzuki et al., "Power consideration on IMPATT diode arrays with incomplete
thermal oscillation," IEEE Trans. Microwave Theory Tech., vol. MTT-28, pp.
632-638, June 1980.
[31] D. Staiman, M. E. Breese and W. T. Patton, "New technique for combining solid
state sources," IEEE J. Solid-State Circuits, vol. SC-3, pp. 238-243, Sept. 1968.
[32] M. F. Durkin, "35 GHz active aperture," in 1981 IEEE MTT-S Int. Microwave
Symp. Dig., June 1981, pp. 425-427.
[33] Mortazawi A. and T. Itoh, "A Periodic Planar Gunn Diode Power Combining
Oscillator," IEEE Trans. Microwave Theory Tech., vol. MTT-38, No.l, Jan.
1990, pp. 86-87.
[34] K. Kurokawa, "Some Basic Characteristic of Broadband Negative Resistance
Oscillator Circuits," Bell Sys. Tech. J., vol. 48,1969, p. 1937.
[35] K. Kurokawa, "Power Waves and the Scattering Matrix," IEEE Trans, on
Microwave Theory Tech., vol. MTT-11, March 1965, pp. 194-202.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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