The response of mismatched prototype image impedance filters

A normalized low-pass prototype filter, terminated in equal value resistances, is considered and the insertion loss is given, as a function of normalized frequency and value of the terminating resistance. The root-locus of the poles of the insertion-loss function is plotted showing the effect of variation of the value of the termination and comparison is made with the pole locations of Butterworth and Chebyshev filters of the third order. The treatment is extended to two identical prototype filters in cascade and in this case the root-locus of the poles of the insertion-loss function is compared with the poles of fifth order Butterworth and Chebyshev filter functions. Insertion-loss curves are given for various terminations for both single and cascaded filters.