Design Of Cross-coupled Filters

Modern microwave communication systems require high-performance filters having low insertion loss and high selectivity together with linear phase in its passband. Cross-coupled filters are able to accomplish these specifications by introducing the prescribed transmission zeros.Due to their good performances, cross-coupled filters are widely used in practice.This paper is mainly devoted to general coupling matrix synthesis methods for generalized Chebyshev filtering functions and the realization technology in practical microwave circuits. Firstly, two methods for the direct synthesis of the coupling matrix are described, the first for the N×N matrix and the second for the N+2 matrix. Based on the relationship between zeros and poles of the characteristic function, a novel method is presented to determine the general Chebyshev filter degree and transmission zeros. Secondly, a different synthesis approach based on using optimization is presented to find the coupling matrix of a prescribed topology. Thirdly, we discuss the methods of similarity transformations with which to realize the cross-coupled filter topologies,including cul-de-sac, CT, CQ and so on. Moreover, the full-wave EM simulation is used to find the relationship between the desired parameters and the physical structure of the filters. Finally, filter examples are employed to illustrate the procedure and the validity of the proposed method.