Reduced Integral Equations for Coupled Resonators Related Directly to the Lumped Equivalent Circuit

The coupling coefficient between two resonators is conventionally found from the two resonant frequencies. To find these frequencies in distributed structures, full wave frequency domain eigenvalue analysis is required. This process can be quite lengthy, since it has to be repeated at each design iteration. In addition, 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 using a reduced representation whose order is the number of coupled resonators. This representation comes useful in an iterative design process, where the repeated usage of the reduced representation replaces the lengthy full wave analysis, apart from a preliminary stage involving individual resonators only. The method also predicts the frequency dependence of the coupling coefficients.