On the Synthesis of the Crystal-Capacitor Lattice-Filter with Symmetrical Insertion Loss Characteristics

A general synthesis procedure is described for the very narrow-bandwidth lattice crystal filter. Specifically, it has been shown that equivalent low-pass insertion functions for all (almost) symmetrical insertion functions of lattice, crystal-capacitor filters may be expressed by the ratio of two polynomials of even degree in complex frequency. Starting with two such polynomials corresponding to the desired insertion function, it is shown how a set of corresponding crystal constants may be found.