An analytical approach of extracting coupling matrix and unloaded Q of A bandpass filter

This paper presents an analytic approach of coupling matrix (CM) extraction for computer aided tuning of general Chebyshev narrow bandpass filters. This approach is based on an accurate extraction of complex poles of Y parameters. As a side product, unloaded Q for each resonator can also be extracted. Rational polynomials for Y parameters are reconstructed by legitimately determining their denominator and numerators separately. In order to ensure a correct mapping of a physical filter to its coupled resonator circuit model, an approach for determining the phase loading is proposed. The proposed technique can be effectively used in practical tuning of a high order filter with cross couplings.