Analog design: Magnitude and frequency scaling in filter design

Not infrequently, filters are designed using a different scale for their component parts than the final requirement. For example a filter could be designed for a frequency of 1.0, inductors in Henries and capacitors in Farads. The Smith chart uses scaling as a matter of common usage. It becomes a vital part of the design engineer's repertoire to understand this concept. This post deals with the very basics of scaling in a cookbook fashion for simplicity. Here are the rules: (1) If each inductor and capacitor is multiplied by a quantity 1/alpha, then the network is said to be scaled in frequency by alpha. If every resistance and inductance is multiplied by a quantity beta, and every capacitor is divided by beta, then the network is said to be magnitude scaled by beta.