An Analytical Approach to Computer-Aided Diagnosis and Tuning of Lossy Microwave Coupled Resonator Filters

This paper presents a novel analytical approach to extracting of the coupling matrix of a narrow band general Chebyshev bandpass filter with losses. The approach is very useful for computer aided tuning of a microwave bandpass filter. The concept of phase loading is revealed for the first time in the community of computer aided tuning. The analytical approach consists of three elements: 1) a theoretic formula that leads to a practical scheme for determining the phase loading; 2) a theoretic formula for de-embedding the section of unknown transmission lines at the two ports of a filter; and 3) a theory for determining the unloaded Q of a filter if the loss for each resonator is nearly the same. To make the approach easy to use, some practical techniques for reconstructing rational functions of Y-parameters from a set of filter response are also provided in the paper. The proposed diagnosis approach is applicable to a general coupled resonator filter with losses and therefore can be effectively used in computer aided tuning of high order filters with cross couplings.