9

NETWORK ANALYSIS FOR DIGITAL ENGINEERS

9.1 High-Frequency Voltage and Current Waves

9.1.1 Input Reflection into a Terminated Network

9.1.2 Input Impedance

9.2 Network Theory

9.2.1 Impedance Matrix

9.2.2 Scattering Matrix

9.2.3 *ABCD* Parameters

9.2.4 Cascading S–Parameters

9.2.5 Calibration and De–embedding

9.2.6 Changing the Reference Impedance

9.2.7 Multimode S–Parameters

9.3 Properties of Physical *S*-Parameters

9.3.1 Passivity

9.3.2 Reality

9.3.3 Causality

9.3.4 Subjective Examination of S–Parameters

References

Problems

Historically, the techniques used to analyze signal integrity for digital designs required the use of equivalent circuits to describe components such as vias, connectors, 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 negligible phase change in the voltage and current across the circuit. In other words, the signal frequency is low enough so that the electrical delay of the circuit is small compared to the switching rate of the digital waveforms. However, as system data rates increase, the delay of the interconnects becomes significant. In fact, in many modern digital designs, such as in high–speed computers, the delay of the system ...