NETWORK ANALYSIS FOR DIGITAL ENGINEERS - Advanced Signal Integrity for High-Speed Digital Design - page 344

NETWORK ANALYSIS FOR DIGITAL
ENGINEERS

9.1 High-frequency voltage and current waves 349

9.1.1 Input reflection into a terminated network 349

9.1.2 Input impedance 353

9.2 Network theory 354

9.2.1 Impedance matrix 355

9.2.2 Scattering matrix 358

9.2.3 ABCD parameters 382

9.2.4 Cascading S -parameters 390

9.2.5 Calibration and de-embedding 395

9.2.6 Changing the reference impedance 399

9.2.7 Multimode S -parameters 400

9.3 Properties of physical S -parameters 406

9.3.1 Passivity 406

9.3.2 Reality 408

9.3.3 Causality 408

9.3.4 Subjective examination of S -parameters 410

References 413

Problems 413

Historically, the techniques used to analyze signal integrity for digital designs
required the use of equivalent circuits to describe components such as vias, con-
nectors, sockets, and even transmission lines for low-data-rate applications. At
low frequencies where the interconnects between the components of a digital
system are small compared to the wavelength of the signal, the circuits can be
described with lumped elements using resistors, capacitors, and inductors. In
general, circuit theory works well for these types of problems because there is