The Synthesis of a Class of Wide-Band Lattice Crystal Filter With Symmetrical Insertion Loss characteristics

A general synthesis procedure based on the Darlington technique is described for the lattice-crystal-filter which incorporates shunt inductors to widen the bandwidth. Specifically, it is shown how equivalent low-pass insertion functions may be obtained for all filters with (approximately) symmetrical band-pass insertion functions; these low-pass functions may be expressed by the ratio of two polynomials of even degree in complex frequency with the degree of the numerator polynomial exceeding that of the denominator by at least two. Starting with two such polynomials, corresponding to the desired insertion function, it is shown how a set of crystal constants may be found.