Compressed integral equations for coupled resonators

Lumped coupled resonators circuits are widely used as prototype circuits for microwave band pass filters design. The relation between the lumped coupling coefficients and the coupling between the distributed resonators is commonly defined using a two coupled resonators model and its two resonant frequencies. In cases with multiple resonators, this method is applied to each pair of resonators separately. In this work, a method is presented for extracting the complete coupling matrix for any number of resonators. The method does not require full wave analysis at each design iteration, except for a preliminary analysis of individual resonators. Rather than evaluating resonant frequencies, a reduced Galerkin formulation is developed for the solution of the integral equations, with an order that is reduced to the number of coupled resonators. In this way, a fast and physically transparent design procedure is afforded. The method also predicts the frequency dependence of the coupling coefficients.