Computer Aided Analysis of Nonlinear Analog Microwave Circuits using Frequency Domain ...

197 Pages·2007·1.14 MB·English

Computer-Aided Analysis of Nonlinear Microwave Analog
Circuits Using Frequency-Domain Spectral Balance
by
Chao-Ren Chang
A thesis submitted to the Graduate Faculty of
North Carolina State University
in partial fulfillment of the
requirements for the Degree of
Doctor of Philosophy
Department of Electrical and Computer Engineering
Raleigh, NC
1990
Approved By:
Michael B. Steer
Chairman of Advisory Committee
ii
Table of Contents
List of Figures v
List of Tables viii
List of Symbols ix
List of Abbreviations xiii
1 Introduction 1
1.1 Motivations and Objectives of This Study . . . . . . . . . . . . . . . 1
1.2 Thesis Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Review of Frequency-Domain Nonlinear Analog Circuit Analysis
techniques 4
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Time-Domain Methods and Hybrid Methods . . . . . . . . . . . . . . 4
2.3 Frequency-Domain Methods . . . . . . . . . . . . . . . . . . . . . . . 7
2.3.1 Power Series Expansion Analysis . . . . . . . . . . . . . . . . 9
2.3.2 Volterra Series Analysis . . . . . . . . . . . . . . . . . . . . . 15
2.3.3 Algebraic Functional Expansion . . . . . . . . . . . . . . . . . 20
2.3.4 Frequency-Domain Spectral Balance . . . . . . . . . . . . . . 20
2.3.5 Other Techniques . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3 Frequency-Domain Spectral Balance Using the Arithmetic Operator
Method 26
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2 System Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3 System Error Minimization Algorithm . . . . . . . . . . . . . . . . . 32
iii
3.4 Development of the Arithmetic Operator Method . . . . . . . . . . . 36
3.4.1 Basic Theories . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.4.2 Some Useful Spectral Operators and Equations . . . . . . . . 48
3.5 Simulation Examples and Discussion . . . . . . . . . . . . . . . . . . 49
3.5.1 The Curtice MESFET Model . . . . . . . . . . . . . . . . . . 51
3.5.2 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . 55
3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4 Computer-Aided Analysis of Nonlinear Microwave Amplifiers Using
Frequency-Domain Spectral Balance 60
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.2 Simulations with Power-Series-Based MESFET Models . . . . . . . . 61
4.2.1 Device Characterization . . . . . . . . . . . . . . . . . . . . . 62
4.2.2 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . 64
4.3 Simulations with Modified Curtice MESFET Models . . . . . . . . . 74
4.3.1 Device Characterization . . . . . . . . . . . . . . . . . . . . . 74
4.3.2 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . 80
4.4 Comparisons of AOM and APDFT Harmonic Balance methods . . . 83
4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5 Computer-Aided Analysis of Free-Running Microwave Oscillators
Using Frequency-Domain Spectral Balance 93
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.2 System Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.2.1 Kurokawa Condition . . . . . . . . . . . . . . . . . . . . . . . 97
5.2.2 Formulation of the System Equations . . . . . . . . . . . . . . 98
5.3 System Error Minimization Algorithm . . . . . . . . . . . . . . . . . 101
iv
5.3.1 Formulation of the Jacobian Matrix . . . . . . . . . . . . . . . 103
5.3.2 Convergence Considerations . . . . . . . . . . . . . . . . . . . 105
5.4 Oscillator Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.5 Active Device Characterization . . . . . . . . . . . . . . . . . . . . . 115
5.6 Simulation Results and Discussion . . . . . . . . . . . . . . . . . . . . 118
5.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
6 Conclusion 130
6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
6.2 Recommendations for Further Study . . . . . . . . . . . . . . . . . . 132
References 134
Appendices 143
A. Formulation of the Modified Nodal Admittance Matrix . . . . . . . . . 143
B. FREDA2 User Manual . . . . . . . . . . . . . . . . . . . . . . . . . . 149
C. Organization of FREDA2 . . . . . . . . . . . . . . . . . . . . . . . . . 168
D. Simulation Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
E. Simulation Example 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
v
List of Figures
3.3.1The backtracking technique. . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.3.2Algorithm of the convergence iterations used in the general purpose non-
linear microwave analog circuit simulator FREDA2. . . . . . . . . . 35
3.4.1The multiplication between limited spectra s and s results in limited
x z
spectrum s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
y
3.5.1Equivalent circuit of the Curtice MESFET model. . . . . . . . . . . . . . 50
3.5.2Schematic of the multistage MESFET amplifier. . . . . . . . . . . . . . . 51
3.5.3Comparison of the simulated output power of the single-tone test for
the multistage MESFET amplifier using AOM and Harmonic Balance
method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.5.4Comparison of the simulated IF output power of the two-tone test for
the multistage MESFET amplifier using AOM and Harmonic Balance
method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.2.1Circuit used to model the MESFET which includes linear as well as non-
linear elements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.2.2The transconductance as a function of intrinsic drain-source voltage. . . 66
4.2.3The drain-source current as a function of intrinsic gate-source voltage for
the Avantek AT-8250 GaAs MESFET. . . . . . . . . . . . . . . . . . 67
4.2.4The drain-source current as a function of intrinsic drain-source voltage for
the Avantek AT-8250 GaAs MESFET. . . . . . . . . . . . . . . . . . 68
4.2.5The results of the single-tone test using AOM and GPSA-TM. . . . . . . 70
4.2.6The results of the two-tone test using AOM and GPSA-TM. . . . . . . . 71
4.2.7The relative gain of the common source amplifier as a function of input
power using the Avantek AT-8250. . . . . . . . . . . . . . . . . . . . 72
vi
4.3.1The calculated i as a function of the intrinsic drain-source voltage for
ds
the dc modified Curtice model. . . . . . . . . . . . . . . . . . . . . . 76
4.3.2The calculated g as a function of the intrinsic drain-source voltage for
m
the ac modified Curtice model. . . . . . . . . . . . . . . . . . . . . . 78
4.3.3The calculated g as a function of the intrinsic drain-source voltage for
ds
the ac modified Curtice model. . . . . . . . . . . . . . . . . . . . . . 79
4.3.4The results of the single-tone test using AOM of FDSB. . . . . . . . . . 81
4.3.5The results of the two-tone test using AOM of FDSB. . . . . . . . . . . . 82
4.4.1Comparison of the simulated output power versus the number of anal-
ysis frequencies at the second harmonic frequency for the MESFET
amplifier with single-tone input excitation. . . . . . . . . . . . . . . . 85
4.4.2Comparison of simulation run time and the maximum memory require-
ment for the MESFET amplifier with single-tone input excitation. . . 87
4.4.3Comparison of the simulated IF (50 MHz) output power versus the in-
termodulation order for the MESFET amplifier with two-tone input
excitation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.4.4Comparison of simulation run time and the maximum memory require-
ment for the MESFET amplifier with two-tone input excitation. . . . 91
5.2.1An equivalent circuit of a general oscillator (after [111]). . . . . . . . . . 97
5.2.2One-port equivalent circuit of an oscillator circuit. . . . . . . . . . . . . . 99
5.3.1The sequence of the initial fundamental frequency settings. . . . . . . . . 107
5.3.2Algorithm for the fundamental frequency searching. . . . . . . . . . . . . 108
5.4.1Device layout of the TI EG8132 GaAs varactor-tuned FET oscillator. . . 110
5.4.2Schematic of the TI EG8132 GaAs varactor-tuned FET oscillator. . . . . 111
5.4.3Schematic of the block “drain network” in Fig. 5.4.2. . . . . . . . . . 112
5.4.4Schematic of the block “gate bias network” in Fig. 5.4.2. . . . . . . . 113
vii
5.4.5Schematic of the block “source bias network” in Fig. 5.4.2. . . . . . 114
5.4.6Schematic of the block “drain bias network” in Fig. 5.4.2. . . . . . . 114
5.5.1The calculated equivalent capacitances from the models and the measured
data for both gate and source varactors of the TI EG8132 oscillator. . 117
5.5.2Equivalent circuit of the MESFET of the TI EG8132 oscillator. . . . . . 118
5.5.3The calculated i from the MESFET model as a function of v . . . . . . 119
ds ds
5.6.1The simulated fundamental oscillation frequency vs. the total tuning volt-
age V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
T
5.6.2Thesimulatedoutputpoweratthefundamentalfrequency,andthesecond,
third, and fourth harmonics. . . . . . . . . . . . . . . . . . . . . . . . 122
5.6.3The simulated v and v curves at V = 10 V. . . . . . . . . . . . . . . 123
gs ds T
5.6.4The simulated output power spectrum of TI EG8132 oscillator at V = 10 V.124
T
5.6.5The simulated i vs. v locus at V = 3 V. . . . . . . . . . . . . . . . . 126
ds ds T
5.6.6The simulated i vs. v locus at V = 10 V. . . . . . . . . . . . . . . . . 127
ds ds T
5.6.7The simulated i vs. v locus at V = 21 V. . . . . . . . . . . . . . . . . 128
ds ds T
A.1.1Schematic of the circuit example. . . . . . . . . . . . . . . . . . . . . . . 144
viii
List of Tables
2.3.1An example of a GPSA-TM transform table. . . . . . . . . . . . . . . . . 14
3.4.1An example of the spectrum mapping function for the basic operation
y(t) = x(t)z(t). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.5.1Some useful frequency-domain spectral operators . . . . . . . . . . . . . 50
3.5.2The element and parameter values of the MESFET equivalent circuit in
Fig. 3.5.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.2.1The linear element values used in the model of the Avantek AT-8250 GaAs
MESFET (after [100]). . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.2.2The power series coefficients used in the model of the Avantek AT-8250
GaAs MESFET (after [100]). . . . . . . . . . . . . . . . . . . . . . . 64
4.2.3The bivariate power series coefficients used for I in the model of the
ds
Avantek AT-8250 GaAs MESFET. . . . . . . . . . . . . . . . . . . . 65
4.2.4The comparisons of computer run time for the single-tone test. The 1D
model was used for GPSA-TM and the 2D model was used for AOM. 73
4.3.1The parameter values of the MESFET equivalent circuit for the dc modi-
fied Curtice model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.3.2The parameter values of the MESFET equivalent circuit for the ac modi-
fied Curtice model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.4.1The processes executed in each time segment of Figs. 4.4.2 and 4.4.4. . . 88
5.5.1The parameter values of the gate and source varactor models in the TI
EG8132 oscillator.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
5.5.2The parameter values of the MESFET model in the TI EG8132 oscillator. 116
A.1.1Node number assignments for the circuit in Fig. A.1.1. . . . . . . . . . . 146
ix
List of Symbols
ω — Radian frequency.
τ — Time delay.
φ — Phase.
A, a, b, c — Coefficients, real or complex number.
C — Drain-to-source capacitance.
ds
C — Drain-to-gate capacitance.
gd
C — Gate-to-source capacitance.
gs
E (ix) — Element of f(ix) at branch n and radian frequency ω , where s = r or
n,k,s k
i indicates the real or imaginary part respectively.
E — Source voltage phasor at branch n and radian frequency ω (E = E +
n,k k n,k n,k,r
jE ).
n,k,i
E(ix) — System objective function at the i th iteration.
F (x) — A regular homogeneous functional defined for the Volterra series analysis.
n
f , f — Fundamental oscillation frequency.
1 osc
f — The k th harmonic oscillation frequency.
k
f(ix) — Error vector at the i th iteration.
f (ix) — The component vector of f(ix) at the radian frequency ω .
k k
G(x) — A continuous functional defined for the Volterra series analysis.
G , g — Gate-to-drain transconductance.
m m
g (x) — The n th order kernel of the functional F (x) defined for the Volterra series
n n
analysis.
H (f) — Volterra nonlinear transfer function of order n.
n
h (τ) — The n th order Volterra kernel.
n
Im{} — Imaginary part of the expression in braces.
I — Variable branch current at branch n and radian frequency ω , where s = r
n,k,s k
or i indicates the real or imaginary part respectively.
x
I — Variable current phasor at branch n and radian frequency ω (I = I +
n,k k n,k n,k,r
jI ).
n,k,i
I — Reverse diode saturation current.
0
I , i — Drain-to-source current.
ds ds
i — Drain-to-gate avalanche current.
dg
i — Forward-biased gate-to-source current.
gs
i — Drain-to-source current through R .
rds ds
J (ix) — Element of f(ix) at node n and radian frequency ω , where s = r or i
n,k,s k
indicates the real or imaginary part respectively.
J — Source current phasor at node n and radian frequency ω (J = J +
n,k k n,k n,k,r
jJ ).
n,k,i
J (ix) — Component of the induced current at frequency ω flowing into the
L(n,k,s) k
linear subcircuit from node n.
J (ix) — Component of the induced current at frequency ω flowing into the
NL(n,k,s) k
nonlinear subcircuit from node n.
J(ix) — Jacobian matrix of f(ix).
J−1(ix) — Inverse of J(ix).
J (ix) — Block Jacobian matrix with input frequency index k, and output fre-
q,k
quency index q.
J (ix)—x-dependentblockJacobiansub-matrixcontainingallthex-dependent
D(q,k)
entries generated from the nonlinear elements.
J — Block Jacobian sub-matrix generated from M .
ID(q,k) ID(q,k)
J (x)—Jacobianmatrixofthespectralvectorywithrespecttothevariablespectral
y
vector x.
M — Circuit matrix of a linear analog circuit.
M — Circuit matrix of a linear analog circuit at radian frequency ω .
k k
M(x) — Circuit matrix of a nonlinear analog circuit.
M(ix) — Circuit matrix of a nonlinear analog circuit at the i th iteration.