Magnitude and frequency scaling simplifies filter design by calibrating filter responses and circuit parameters to fit within usable ranges.

Magnitude scaling involves amplifying all impedances in a network by a factor, maintaining consistent frequency responses.

The scaled impedance and frequency values are then expressed using the scaling factor.

This process does not alter the circuit's resonance frequency, quality factor, bandwidth, or transfer functions.

Frequency scaling shifts the frequency response of a network either up or down the frequency axis while leaving the impedance unchanged. It is accomplished by multiplying the frequency by a scaling factor.

Frequency scaling influences the impedances of frequency-dependent reactive elements, but the resistor remains unaffected.

The scaling factor alters the resonant frequency and bandwidth, but the quality factor remains the same.

A general expression for impedance and frequency scaling accommodates simultaneous magnitude and frequency scaling.

For cases when magnitude scaling is not applied, the magnitude scaling factor is set to one. Similarly, without frequency scaling, the frequency scaling factor is set to one.