Analytic sensitivity calculations of poles and zeros of general Chebyshev filtering functions for microwave coupled resonators

A methodology for calculating the sensitivity of filtering poles and reflection zeros in coupled resonator structures is presented. Rather than finding the sensitivity of the S-parameters across a given frequency spectrum, the proposed method allows for calculating the sensitivity of each pole and zero with respect to coupling coefficient variations. This provides a better insight into the effects of fabrication tolerance on the filtering response and could lend itself to a more systematic approach to tuning. A detailed numeric example is provided for an asymmetric fourth-order Chebyshev filter.