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 and a harmonic wave analysis may not be directly applicable. Some of the ideas expressed by harmonic analysis can still be of value. The most important factor that we must consider is the rise and fall time of the leading edges in step functions. Sometimes, the third harmonic of the fundamental (clock frequency) can be used as a reference frequency in describing or analyzing some aspect of performance. This makes sense if the rise and fall times are 20% of the clock period.

The materials used in board manufacture have been around for a long time. Progress is the process of using these same materials in new and better configurations to serve our needs. A lot of engineering is based on past practice. Every practice has its limitations. We must question everything so that when a practice needs changing we can act accordingly. A better design will most likely be a change in how we configure these available materials. Some of the material is given to us in the form of components and some of the material is used in mounting and connecting these components. Our job is to select the right components and configure them on circuit boards so that field energy flows to perform the task at hand.