Optimum Design of Broadband Microwave Transistor Amplifiers, A Thesis Presented to The Faculty ...

104 Pages·2007·3.72 MB·English

Optimum Design of Broadband
Microwave Transistor Amplifiers,
A Thesis Presented to
The Faculty of the College of Engineering and Technology
Ohio University
In Partial Fulfillment
of the Requirements for the Degree
Master of Science
March 1981
I would like to thank my adviser, Dr. Wai K a i Chen,
for his guidance and encouragement during the course of this
work. I have benefited considerably from his lectures on the
theories of broadband matching, which brought up this subject
and served t o carry out a systematic study into this problem.
I would also like t o express my indebtedness to the
many individuals who have helped me during my studies,
. .
particularly Dr. James C G i l fe rt
Thanks are also due to Dr. Tomoyasu Tanaka for
several useful discussions on nonlinear programming problems.
Finally, I must thank my parents for their support
and encouragement.
TABLE OF CONTENTS
CHAPTER I* BASIC DESIGN THEORY OF BROADBAND MICROWAVE
TRANSISTOR AMPLIFIERS
..................................
1. Introduction 1
..............
2. Characterization of Transistors 4
3. General Broadband Matching Problem for Microwave
.........................
Transistor Amplifiers 4
4. Approximate version of the Broadband Matching
.......................................
Problem 7
CHAPTER 2 GAIN-BANDWIDTH RESTRICTIONS
...........................
1. Transistor Modeling 9
..........
2. Series Resonant Reactive Constraints 10
....
3. Double-Order Low-Pass Reactive Constraints 14
CHAPTER 3. DESIGN OF BROADBAND DISTRIBUTED NATCHING NETWORKS
WITH ARBITRARILY TAPERED GAIN CHARACTERISTICS
1. Realizability of the Distributed Network
....................................
structures 16
2, Chebyshev Approximation of Tapered Gain
...............................
Characteristics 18
..................
3. Matching Network Realization 24
....
4. Evaluation of the Gain-Bandwidth Integrals 29
CHAPTER 4. DESIGN OF BROADI3AND DISTRIBUTED MATCHING NETWORKS
WITH A FLAT GAIN CHARACTERISTIC
1. Chebyshev Approximation .of a Flat Gain
.................................
Characteristic 43
. . . . .
2. Evaluation of the Gain-Bandwidth Integrals 54
CHAPTER 5. ILLUSTRATIVE EXAMPLES
1. 4-8 GHz GaAs FET Amplifier
..............
1 1 The Input Matching Network 63
......,......
1.2 The Output Matching Network 66
2. 8-12 GHz Low-Noise GaAs FET Amplifier
..............
2.1 The Input Matching Network 71
.............
2.2 The Output Matching Network 73
CHAPTER 6. CONCLUTION . . . . . .. . . . . . .. . . .. . . . . . . .. . . . . . . . . . 77
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
BIBLIOGRAPHY , , , , 80
AFPENDIX A.
A Computer Program for the Synthesis of Tapered Gain
Matching Networks 83
APPENDIX B.
A Computer Program for the Synthesis of Zero-Slope
Chebyshev Functions 89
.
APPENDIX C
A Computer Optimization Program 93
CHAPTER 1
BASIC DESIGN THEORY OF BROADBAND MICROWAVE
TRANSISTOR AMPLIFIERS
1. Introduction
The design of broadband microwave transistor ampli-
fiers has been the subject of considerable research effort.
A number of authors have discussed the subject using computer-
.
aided optimization techniques [I] , [2] Such direct optimiza-
tion of the elements of matching networks is difficult and
often inadequate for very broad bandwidths, since these ele-
ments relate to the amplifier gain in highly nonlinear combi-
nations. Furthermore, the techniques require a suitable
empirical network topology to be initially assumed for computer
optimization. Several designs based on an analytical method
have been reported in [3] -[6] , where the broadband matching
theories of Fano [?] and Youla [8] are applied to the synthesis
of matching networks. This procedure relies upon certain ap-
proximate models of transistor, but has proved successful in
the design of microwave transistor amplifiers and in the
problem of choosing an appropriate design which can be used in
conjunction with computer-aided optimization techniques.
The difficulties of designing microwave transistor
amplifiers stem from the fact that the matching network must
provide not only,broadband matching the transistor reactive
constraints but also broadband impedance transformation since,
for most practical microwave transistor amplifiers, broadband
impedance transformers are often either not available or
unacceptable because of circuit complexity or high insertion
loss. In addition, the matching networks with tapered magni-
tude characteristics are required to compensate for the in-
herent transistor gain rolloffs with respect to frequency.
The design based on conventional lumped Chebyshev
matching networks often requires ideal transformers i n the
realization. In one sense a solution to the problem can be
obtained by sjmthesizing matching networks directly i n the
distributed domain, as w i l l be seen i n Chapter 5. Fig. 1.1
shows the general ladder-type distributed matching network
configuration designed t o approximate a flat or tapered gain
characteristic. This circuit configuration has been used by
Bolhasson and Ku [6] ,[9].
Fig. 1.1 General band-pass distributed matching network
configuration.
The purpose of this thesis is t o develope a general synthesis
procedure, allowing arbitrary response parameters such as
slope, bandwidth, ripple, commensurate line length, and network
order, and t o evaluate the gain-bandwidth properties of micro-
wave transistor amplifiers by applying the fundamental gain-
bandwidth integral restrictions of Fano [7] to actual gain
characteristics. The matching networks must yield the best
approximation t o an ideal gain response i n Chebyshev's sense.
The thesis is organized i n the following manner.
This chapter discusses the basic problems of designing micro-
wave transistor amplifiers. The transistors are analyzed as
constrained two-port networks represented by a set of measured
scattering parameters. Based on the equivalent circuit models
of transistors, the integral gain-bandwidth restrictions are
derived i n Chapter 2. Chapter 3 describes a procedure for the
synthesis of tapered magnitude matching networks of the form of
Fig. 1.1. Gain-bandwidth limitations for tapered gain charac-
teristics are presented i n graphical form. Chapter 4 compli-
ments Chapter 3 by treating the corresponding synthesis method
for matching networks with no taper (flat-gain response).
Chapter 5 illustrates the methods by the broadband designs of
microwave Gaks FET amplifier based upon published scattering
parameter data and the gain-bandwidth limitations derived i n
Chapters 3 and 4. Computer-aided optimization techniques are
used i n the final step of designs only t o account for the inac-
curacy of transistor models. In addition to the gain-bandwidth
restrictions, we will further impose the restriction that
ideal transformers cannot be used.
-
2. characterization of ~ransistors
Transistors used at microwave frequencies are typ-
ically characterized using the measured scattering parame-
ters. At these frequencies, the conventional transistor
equivalent circuits are not adequate to characterize the
device behavior over a broad band of frequencies unless a
very complicated equivalent circuit is used.
The scattering relations of a general linear ac-
tive two-port are
where the a's represent the incident waves and b's represent
the waves reflected from the two-port. The scattering param-
eters are measured with the two-port imbedded between refer-
ence impedances which, under most conditions, are 5OQ. All
figures of merit may be derived from the scattering parame-
ters in order to evaluate a device including stability factor.
3. General Broadband Matching Problem for Microwave
Transistor Amplifiers
Fig. 1.2 shows a schematic representation of a
single transistor amplifier. The lossless two-port input
and output matching networks are denoted by M1 and M2, re-
--
spectively. The generator and the load resistance are
considered t o be 50 ohms.
-
5on *
INPUT OUTPUT
MATCHING TRAN- WIATC HIN G
*
NETWORK SISTOR NET WORK
IsI
M1
b
s- z
0' ql Sq2 ,z q2
Fig. 1.2 Schematic of general transistor amplifier
2
The transducer power gain Gt(U ), defined as the ratio of
average power delivered t o the load t o the maximum available
average power from the source, for the amplifier of Fig. 1.2
can be shown t o be [lo]
(1 *2)
where
ZO = reference impedance
fi
Throughout the thesis Z0 is considered to be 50 (real).
The Sij(j W ) , i . j = 1,2, are the measured transistor scattering
.
f2
parameters all normalized to 50 The impedances Z ( j Ic)) and
q l
Z ( j u ) o r, equivalently, the reflection coefficients S (j#)
q2 ql
and S (ju)r epresent the passive source and load matching
q2
networks. The scattering parameters of the transistor are pre-
scribed and the problem is that of designing the input and
output matching networks denoted by S ( j 13 ) and S ( J h ) such
ql q2
that the overall transducer power gain given by (1.2) has the
prescribed response.
To maintain a broadband match to the characteristics
of a transistor is at best a complicated problem. The main
complexity is that there exists coupling between the input and
the output of amplifier due to the internal reverse feedback in
transistor. In other words, the match a t port 1 is dependent
on the matching network at port 2 and vice versa. An addi-
tional complication of the current transistor amplifier matching
problem was pointed out at the beginning of this chapter.