S-Parameters for Signal Integrity

Description

Master the usage of s-parameters in signal integrity applications and gain full understanding of your simulation and measurement environment with this rigorous and practical guide. Solve specific signal integrity problems including calculation of the s-parameters of a network, linear simulation of circuits, de-embedding, and virtual probing, all with expert guidance. Learn about the interconnectedness of s-parameters, frequency responses, filters, and waveforms. This invaluable resource for signal integrity engineers is supplemented with the open-source software SignalIntegrity, a Python package for scripting solutions to signal integrity problems. 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