Digital Circuit Boards: Mach 1 GHz

1.3 The Role of Circuit Analysis

We are used to thinking in terms of sinusoids. The language of circuit analysis is closely related to these sine wave signals. The words impedance or reactance are defined in terms of sine waves. We are married to circuit symbols and sinusoidal measures and somehow we must stretch these meanings to fit a high speed digital world. We certainly are not going to invent a new language or use new symbols to describe our needs. The old words and symbols will have to do. Usage defines meaning and eventually usage may change. We will use the word impedance without regard to sinusoids.

In digital circuitry, the signals are usually in the form of step functions of voltage. These voltage level changes are applied to traces that carry information (energy) between components. We will refer to these traces as transmission lines. It will come as a surprise to some readers that a 1/16-in-long trace should be considered a transmission line. Also that a vias associated with a trace can modify the character of the transmission path. The reflections on sections of the energy path can result in radiation and limit performance.

Repetitive wave forms are equivalent to a group of sine waves with a harmonic relationship. For example, a square wave can be equated to a group of sine waves consisting of a fundamental and all the odd harmonics of this frequency. The amplitude of each harmonic is inversely proportional to the number of the harmonic. Digital signals are not repetitive ...