 | X-Parameters: Characterization, modeling, and design of nonlinear RF and microwave components / D.E.Root, J.Verspecht, J.Horn, M.Marcu. - Cambridge; New York: Cambridge university press, 2013. - (The Cambridge RF and microwave engineering series). - Incl. bibl. ref. and ind. - ISBN 978-0-521-19323-8
Шифр: (И/З.84-X10) 02
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Preface ...................................................... xiii
Acknowledgments ................................................ xv
1 S-parameters - a concise review ............................... 1
1.1 Introduction ............................................... 1
1.2 S-parameters ............................................... 1
1.3 Wave variables ............................................. 2
1.4 S-parameter measurement .................................... 5
1.5 S-parameters as a spectral map ............................. 7
1.6 Superposition .............................................. 8
1.7 Time invariance of components described by S-parameters ... 10
1.8 Cascadability ............................................. 11
1.9 DC operating point ........................................ 12
1.10 S-parameters of a nonlinear device ........................ 12
1.11 Additional benefits of S-parameters ....................... 15
1.11.1 S-parameters are applicable to distributed
components at high frequencies ..................... 15
1.11.2 S-parameters are easy to measure at high
frequencies ........................................ 15
1.11.3 Interpretation of two-port S-parameters ............ 15
1.11.4 Hierarchical behavioral design with S-parameters ... 16
1.12 Limitations of S-parameters ............................... 16
1.13 Summary ................................................... 18
Exercises ...................................................... 18
References ..................................................... 18
Additional reading ............................................. 19
2 X-parameters - fundamental concepts .......................... 20
2.1 Overview .................................................. 20
2.2 Nonlinear behavior and nonlinear spectral mapping ......... 20
2.3 Multi-harmonic spectral maps .............................. 22
2.4 Load- and source-mismatch effects ......................... 25
2.5 Cascading DUTs ............................................ 25
2.6 Example: cascading two RF power amplifiers with
independent bias .......................................... 27
2.7 Relationship to harmonic balance .......................... 29
2.8 Cross-frequency phase ..................................... 30
2.8.1 Commensurate signals ............................... 30
2.8.2 Definition of cross-frequency phase ................ 30
2.9 Basic X-parameters for multi-harmonic multi-port
stimulus .................................................. 34
2.9.1 Time invariance and related properties of Fpk(.)
functions .......................................... 35
2.9.2 Definition of X-parameters and X-parameter
behavioral model ................................... 36
2.9.3 Example: a set of X-parameters ..................... 37
2.10 Physical meaning of the basic X-parameters ................ 38
2.10.1 Reference stimulus and response .................... 38
2.10.2 Physical interpretation ............................ 39
2.11 Using the X-parameter behavioral model .................... 39
2.11.1 Example: amplifier with source and load mismatch ... 40
2.12 Summary ................................................... 43
Exercises ...................................................... 44
References ..................................................... 44
Additional reading ............................................. 44
3 Spectral linearization approximation ........................ 45
3.1 Simplification of basic X-parameters for small mismatch ... 45
3.1.1 Non-analytic maps .................................. 46
3.1.2 Large-signal operating point ....................... 48
3.2 Adding small-signal stimuli (linearized nonlinear
spectral mapping) ......................................... 50
3.2.1 Small-signal interactions: the RF terms ............ 51
3.2.2 Small-signal interactions: the DC terms ............ 52
3.3 Physical meaning of the small-signal interaction terms .... 55
3.4 Discussion: X-parameters and the spectral Jacobian ........ 60
3.5 X-parameters as a superset of S-parameters ................ 60
3.6 Two-stage amplifier design ................................ 64
3.7 Amplifier matching under large-signal stimulus ............ 68
3.7.1 Output matching and hot-S22 ........................ 69
3.7.2 Input matching ..................................... 78
3.8 Practical application - a GSM amplifier ................... 80
3.9 Summary ................................................... 84
Exercise ....................................................... 84
References ..................................................... 87
Additional reading ............................................. 87
4 X-parameter measurement ................................... 88
4.1 Measurement hardware ...................................... 88
4.1.1 Hardware requirements .............................. 88
4.1.2 Mixer-based systems ................................ 88
4.1.3 Sampler-based systems .............................. 91
4.1.4 Stimulus requirements .............................. 93
4.2 Calibration ............................................... 93
4.2.1 Scalar-loss correction ............................. 94
4.2.2 S-parameter calibration ............................ 94
4.2.3 NVNA calibration ................................... 96
4.3 Phase references ........................................... 97
4.3.1 Phase-reference signals ............................ 97
4.3.2 Measurement considerations ......................... 99
4.3.3 Practical phase references ........................ 100
4.4 Measurement techniques .................................... 101
4.4.1 Large-signal response measurements ................ 101
4.4.2 Small-signal response measurements ................ 101
4.4.3 Practical measurement considerations .............. 105
4.4.4 Simulation-based extraction ....................... 106
4.5 X-parameter files ........................................ 106
4.5.1 Structure ......................................... 107
4.5.2 Naming conventions ................................ 107
4.5.3 Example file ...................................... 108
4.6 Summary .................................................. 110
References .................................................... 110
Additional reading ............................................ 111
5 Multi-tone and multi-port cases .......................... 112
5.1 Introduction ............................................. 112
5.2 Commensurate signals - large A1,1 and large A2,1:
load-dependent X-parameters ............................. 113
5.2.1 Time invariance, phase normalization, and
commensurate two-tone LSOP ........................ 114
5.2.2 Spectral linearization ............................ 115
5.3 Establishing the LSOP using a load tuner: passive load
pull ..................................................... 116
5.4 Additional considerations for commensurate signals ....... 118
5.4.1 Extraction of X-parameter functions under
controlled loads .................................. 118
5.4.2 Harmonic superposition ............................ 118
5.4.3 Limitations of passive load pull for load-
dependent X-parameters ............................ 119
5.4.4 Sampling of the three-RF-variable space defining
the reƒLSOPS ...................................... 119
5.4.5 Hardware setup for load-dependent X-parameters .... 119
5.4.6 Calibrating out uncontrolled harmonic impedances .. 119
5.5 Arbitrary load-dependent X-parameters of a GaAs FET ...... 120
5.5.1 Load-dependent X-parameter model of a GaN HEMT:
estimating the effect of independent harmonic
impedance tuning .................................. 123
5.6 Design example: Doherty power amplifier design and
validation ............................................... 129
5.6.1 Doherty power amplifier ........................... 129
5.6.2 X-parameter characterization of the transistors ... 130
5.6.3 X-parameter model validation ...................... 132
5.6.4 Doherty power amplifier design using
X-parameters ...................................... 135
5.6.5 Results ........................................... 136
5.7 Incommensurate signals ................................... 138
5.7.1 Notation for incommensurate two-tone
X-parameters ...................................... 138
5.7.2 Time invariance for incommensurate two-tone
X-parameters ...................................... 140
5.7.3 Reference LSOP .................................... 141
5.7.4 Spectral linearization ............................ 141
5.7.5 Discussion ........................................ 143
5.7.6 When intermodulation frequencies are negative ..... 143
5.7.7 X-parameter models of mixers ...................... 144
5.8 Summary .................................................. 147
Exercises ..................................................... 148
References .................................................... 148
Additional reading ............................................ 148
6 Memory ................................................... 150
6.1 Introduction ............................................. 150
6.2 Modulated signals: the envelope domain ................... 151
6.3 Quasi-static X-parameter evaluation in the envelope
domain ................................................... 151
6.3.1 Quasi-static two-tone intermodulation distortion
from a static one-tone X-parameter model .......... 152
6.3.2 ACPR estimations using quasi-static approach ...... 159
6.3.3 Limitations of quasi-static approach .............. 160
6.3.4 Advantages of quasi-static X-parameters for
digital modulation ................................ 161
6.4 Manifestations of memory ................................. 161
6.5 Causes of memory ......................................... 163
6.5.1 Self-heating ...................................... 163
6.5.2 Bias modulation ................................... 163
6.6 Importance of memory ..................................... 167
6.6.1 Modulation-induced baseband memory and carrier
memory ............................................ 167
6.6.2 Dynamic X-parameters .............................. 168
6.6.3 Identification of the memory kernel: conceptual
motivation ........................................ 171
6.6.4 Step response of the memory kernel ................ 172
6.6.5 Application to real amplifier ..................... 173
6.6.6 Validation of memory model ........................ 175
6.6.7 Interpretation of dynamic X-parameters ............ 181
6.6.8 Wide-band X-parameters (XWB) ...................... 182
References .................................................... 187
Additional reading ............................................ 188
Appendix A: Notations and general definitions ................. 189
A.1 Sets ..................................................... 189
A.2 Vectors and matrices ..................................... 189
A.3 Signal representations ................................... 190
A.3.1 Time-domain representation (real signal) .......... 190
A.3.2 Complex representation (complex envelope signal) .. 190
A.4 Fourier analysis ......................................... 191
A.5 Wave definitions ......................................... 192
A.5.1 Generalized power waves ........................... 192
A.5.2 Voltage waves ..................................... 194
A.6 Linear network matrix descriptions ....................... 194
A.6.1 S-parameters ...................................... 195
A.6.2 Z-parameters ...................................... 195
A.6.3 Y-parameters ...................................... 195
References .................................................... 195
Appendix B: X-parameters and Volterra theory .................. 196
B.1 Introduction ............................................. 196
B.2 Mathematical notation and problem definition ............. 196
B.3 Application of the Volterra theory ....................... 197
B.4 Derivation of the McLaurin series ........................ 198
B.5 McLaurin series for the DC output ........................ 200
B.6 Conclusions .............................................. 200
References .................................................... 201
Appendix C: Parallel Hammerstein symmetry ..................... 202
References .................................................... 203
Appendix D: Wide-band memory approximation .................... 204
Appendix E: Solutions to exercises ............................ 206
Index ......................................................... 216
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