8
MATHEMATICAL REQUIREMENTS FOR PHYSICAL CHANNELS
8.1 Frequency-Domain Effects in Time-Domain Simulations
8.1.1 Linear and Time Invariance
8.1.2 Time and Frequency–Domain Equivalencies
8.1.3 Frequency Spectrum of a Digital Pulse
8.1.4 System Response
8.1.5 Single–Bit (Pulse) Response
8.2 Requirements for a Physical Channel
8.2.1 Causality
8.2.2 Passivity
8.2.3 Stability
References
Problems
Modern high–speed digital design requires extensive signal integrity simulations to assess the electrical performance of the system prior to fabrication of prototypes. To ensure accurate results from the simulations, careful attention must be given to system component models such as transmission lines, vias, connectors, and packages. For a model to be physically consistent with the laws of nature, certain mathematical constraints must be obeyed to ensure proper balance between signal propagation, energy storage, and losses. For example, the vast majority of engineers designing high–speed digital systems today utilize simplified modeling techniques that employ frequency–invariant values of dielectric permittivity, loss tangent, and inductance for transmission–line models. A review of Chapters 5 and 6 will remind the reader that transmission–line models have frequency–dependent properties that must be modeled correctly if a realistic response is expected. Such assumptions, although valid at low frequencies or for very short electrical structures, induce amplitude and phase errors for digital data ...
