Prototype Filter - Impedance Scaling

Impedance Scaling

Impedance scaling is invariably a scaling to a fixed resistance. This is because the terminations of the filter, at least nominally, are taken to be a fixed resistance. To carry out this scaling to a nominal impedance R, each impedance element of the filter is transformed by:

It may be more convenient on some elements to scale the admittance instead:

It can readily be seen that to achieve this, the non-resistive components of the filter must be scaled as:

and,

Impedance scaling by itself has no effect on the transfer function of the filter (providing that the terminating impedances have the same scaling applied to them). However, it is usual to combine the frequency and impedance scaling into a single step:

and,