Direct synthesis of general Chebyshev bandpass filters with a frequency variant complex load

This paper presents a direct approach to the synthesis of a general Chebyshev coupled resonator filter with a frequency variant complex load. The new approach is based on the power wave renormalization of admittance parameters of a matched filter with a complex load to unitary load. When the port reference is changed from a complex load to a real load, a set of new expressions of admittance parameters can be obtained for the same filter. By introducing a piece of dispersive transmission line to the original matched filter, the poles of the original admittance parameters are retained, which greatly facilitates the extraction of the new admittance parameters, and consequently the synthesis of the coupling matrix. The approach is applicable to the synthesis of an optimal channel filter of a diplexer and a multiplexer, where the load presented at a port of the filter is a frequency variant complex load in a wide frequency range.