Microstrip parallelcoupled filters with cascade trisection and quadruplet responses

Abstract—Microstrip parallel-coupled filters with generalized Chebyshev responses are presented. The basic structure of the proposed filter is a conventional parallel-coupled filter of which the physical dimensions can be easily obtained by the well-known analytical method. With the aid of the equivalent circuit corre-sponding to a conventional parallel-coupled filter, the relative insertion phase from source or load to each open end of resonators can be easily obtained by observing the two-port admittance ma-trix. Applying the cross coupling from source or load to a proper nonadjacent resonator, a trisection or a quadruplet coupling scheme can be realized with prescribed transmission zeros. More importantly, the proposed trisection can be designed to have a transmission zero on the lower or upper stopband by just ad-justing the length of the cross-coupling strip. Using the proposed structure, the conventional time-consuming adjusting procedure to obtain initial physical dimensions of filters is no longer required. In this paper, a fourth-order parallel-coupled filter is used as the basic structure to demonstrate various combinations of transmis-sion zeros. Simulated and measured results are well matched. Index Terms—Cascade quadruplet (CQ), cascade trisection (CT), cross coupling, mixed cascaded quadruplet and trisection, parallel-coupled filter, transmission zero. I