Transformed-variable synthesis of narrow-bandpass filters

A bilinear frequency transformation can be used to synthesize low-pass-prototype networks for narrow-bandpass filters. The lowpass prototype is based on the narrow-band approximation of circuit theory, which allows the use of the constant reactance elements and results in a lowpass frequency response that may not be symmetric about zero frequency. With an appropriate transformed variable, the numerical accuracy of the synthesis procedure is enhanced and the approximation problem is simplified. This technique is applicable to a broad class of filters using microwave cavity, mechanical, crystal or lumped-element resonators. Synthesis on an insertion loss basis is described for lossless doubly terminated filters, with an example of a coupled-resonator filter realization.