Synthesis of multi-coupled resonator filters with frequency-dependent couplings

A procedure is presented for the synthesis of multi-coupled resonator filters with frequency-dependent couplings. The two-port parameters of the filter are obtained by circuit analysis with frequency dependent coupling coefficients. A numerical technique, valid for wideband applications, is described to determine the characteristic function based on bandpass prototype. The values of circuit elements are synthesized by equating the admittance parameters obtained from the circuit analysis and filter characteristic function. Synthesis of 7-pole and 4-pole filters with 60% and 54% relative bandwidths respectively are given as examples.