Coupled-Resonator Filters With Frequency-Dependent Couplings: Coupling Matrix Synthesis

This letter presents a novel technique for synthesis of coupled-resonator filters with inter-resonator couplings varying linearly with frequency. The values of non-zero elements of the coupling matrix are found by solving a nonlinear least squares problem involving eigenvalues of matrix pencils derived from the coupling matrix and reference zeros and poles of scattering parameters. The proposed method was verified by numerical tests carried out for various coupling schemes including triplets and quadruplets for which the frequency-dependent coupling was found to produce an extra zero.