S-Parameters for Signal Integrity

Contents......Page 7
Preface......Page 14
Abbreviations......Page 17
Introduction......Page 18
Part I Scattering Parameters......Page 22
1.1 The Concept of Network Parameter Models......Page 24
1.2 Network Parameter Models of Circuit Elements and Circuit Models......Page 33
1.3 Network Parameter Conversions......Page 38
1.4 Network Simulation......Page 42
1.5 Cascading Networks......Page 43
1.6 Network Parameter Summary......Page 45
2.1 Wave Relationships to Voltage and Current......Page 46
2.2 Wave Definition Requirements......Page 48
2.3 Power and the Normalization Factor......Page 51
2.4 Wave Equations......Page 54
2.5 Power Wave Equations......Page 55
3.1 S-Parameter Definition......Page 58
3.2 Method of Determining S-Parameters of Circuits......Page 59
3.3 Example S-Parameter Circuit Calculations......Page 63
3.4 S-Parameter Conversions......Page 72
3.5 Power Wave Based S-Parameters......Page 79
3.6 T-Parameters......Page 82
3.8 Inverse and Identity Sections......Page 86
3.9 De-embedding S-Parameters......Page 87
3.10 Network Parameters of Common Elements......Page 88
3.11 Advanced Cascade Parameters – Multi-Port T-Parameters......Page 90
3.12 S-Parameter File Format......Page 94
4 S-Parameter System Models......Page 99
4.1 Interconnection of S-Parameter Networks......Page 100
4.2 Signal-Flow Diagram Representation of Systems......Page 104
4.3 S-Parameters of Systems......Page 115
4.4 Block Matrix Solution of S-Parameter Systems......Page 120
4.5 System Reduction Through Node Removal......Page 126
4.6 Node Removal Using Graphical Equation Methods......Page 139
4.7 Examples......Page 143
4.8 Summary......Page 150
5.1 Basic Reference Impedance Transformation......Page 151
5.2 The Reference Impedance Transformer......Page 153
5.3 Reference Impedance Transformers in Wave Measurements......Page 158
5.4 Reference Impedance Transformation Using Transformers......Page 163
6.1 Source Elements......Page 169
6.2 Sense Elements......Page 173
6.3 Dependent Sources......Page 176
6.4 Amplifiers......Page 179
6.6 Ideal Transformer......Page 193
7.1 The Transmission Line Model......Page 195
7.2 Simulation Example of Single-Ended Transmission Line......Page 208
7.3 Differential Signaling......Page 211
7.4 Differential Transmission Lines......Page 217
7.5 Mixed-Mode Terminations......Page 226
Part II Applications......Page 232
8 System Descriptions......Page 234
8.1 System Descriptions......Page 235
8.2 System Description Example......Page 242
8.3 Symbolics......Page 245
8.4 The System Description Parser......Page 257
8.5 Numeric Solutions......Page 262
8.6 Subcircuits......Page 273
8.7 Summary of Python Code Arrangement......Page 276
9.1 Simulation Solutions......Page 277
9.2 The Simulator Class......Page 281
9.4 The SimulatorParser Class......Page 283
9.5 Numeric Solutions......Page 288
10 De-embedding......Page 299
10.1 One-Port De-embedding......Page 300
10.2 Two-Port De-embedding......Page 301
10.3 Fixture De-embedding......Page 304
10.4 Two-Port Tip De-embedding......Page 306
10.5 Extensions to the Fixture De-embedding Problem......Page 307
10.6 The Deembedder Class......Page 319
10.7 Symbolic De-embedding Solutions......Page 321
10.8 The DeembedderParser Class......Page 327
10.9 Numeric De-embedding Solutions......Page 329
10.10 Numeric De-embedding Example......Page 331
11.1 A Simple Case of Virtual Probing......Page 336
11.2 A Multiple Input and Output Example......Page 340
11.3 A Degree of Freedom Example......Page 344
11.4 The Virtual Probe General Case Equations......Page 346
11.5 Virtually Probing a Virtual Circuit......Page 348
11.6 Programmatic Methods......Page 351
11.7 Virtual Probing Numeric Example......Page 361
Part III Signal Processing and Measurement......Page 372
12 Frequency Responses, Impulse Responses, and Convolution......Page 374
12.1 Discrete-Time Waveforms......Page 375
12.2 Discrete-Frequency Responses......Page 381
12.3 The Discrete Fourier Transform......Page 385
12.4 Frequency Responses and Impulse Responses......Page 401
12.5 Resampling......Page 412
13.1 Convolution and Time......Page 421
13.2 Upsampling and Interpolation......Page 431
13.3 Fractional Delay Filters......Page 440
13.4 Waveform Adaption......Page 446
13.5 Transfer Matrices Processing......Page 453
14.1 Impedance and Time-Domain Reflectometry......Page 457
14.2 Impedance Profile Approximation with the Step Response......Page 460
14.3 Impedance Profile Approximation from S-Parameters......Page 462
14.4 Impedance Profile Calculation Using Peeling......Page 465
14.5 Python Impedance Profile Software......Page 467
14.6 Problems with the Impedance Profile......Page 473
15 Measurement......Page 474
15.1 The Twelve-Term Error Model......Page 476
15.2 Calibration......Page 479
15.3 Calculation of the Device Under Test......Page 491
15.4 Calibration and Measurement Summary......Page 492
15.5 Calibration Standards......Page 496
15.6 Time-Domain Reflectometry......Page 502
15.7 S-Parameter Checking and Conditioning......Page 515
16 Model Extraction......Page 529
16.1 Linear Equations......Page 530
16.2 Newton’s Method......Page 534
16.4 Python Fitting Code......Page 538
16.5 Transmission Line Model Fitting......Page 541
Part IV SignalIntegrity......Page 550
17.1 Package Organization......Page 554
17.2 Universal Modeling Language Diagrams......Page 558
17.3 SignalIntegrity Applications......Page 559
17.4 Waveform Processing......Page 574
17.5 Measurement......Page 578
18.1 Project File Format......Page 579
18.2 SignalIntegrityAppHeadless Application Programming Interface......Page 582
18.3 Calculation Properties......Page 583
18.4 S-Parameter Viewing and Transfer Matrices......Page 585
18.5 SignalIntegrityApp Equalization Example......Page 587
Afterword......Page 607
Appendix A Terminology and Conventions......Page 609
Appendix B Telegrapher’s Equations......Page 612
Appendix C Matrix Algebra......Page 615
Appendix D Symbolic Device Solutions......Page 625
References......Page 648
Index......Page 653