Explicit formulas for the synthesis of optimum bandpass Butterworth and Chebyshev impedance-matching networks

Abstract

Explicit formulas for computing the optimum design parameters of the bandpass impedance-matching networks having Butterworth and Chebyshev responses of arbitrary order for a class of most practical RLC load are derived. It is shown that using at most a second-order all-pass function for the equalizer back-end reflection coefficient, a bandpass impedance match is possible if and only if the series inductance of the given load does not exceed a certain critical value. This is in direct contrast to the low-pass situation where we showed earlier that any given RLC load can be matched using at most the rust-order all-pass function. The significance of the present results is that we reduce the design of these practical bandpass impedance-matching networks to simple arithmetic.