Fourth-Order Microstrip Band-Pass Filter with Mixed Cross-Coupling

In this paper, we provide the solution of the direct and inverse problems for a fourth-order band-pass filter (BPF) in which the cross-coupling between extreme resonators K-14 is mixed. The solution of the direct problem allows determining the transmission zeros (attenuation poles) of the filter using specified coupling coefficients. In the inverse problem, transmission zeros, from which the coupling coefficients of the filter are determined, are set. The solutions are based on conductivity matrix [(Y) over tilde] of the BPF and its minor M-41, as well as a special form of representation of the mixed cross-coupling coefficient in this matrix. All possible options for the placement of the transmission zeros of the considered filter are established. A sample of an experimental microstrip filter, as well as its measured and simulated frequency characteristics corresponding to its two different states, is presented.