Pole Migration in Coupled-Resonator Filters

The narrow-band, coupled-resonator filter is analyzed by giving a vector interpretation to the transfer function. The significant parameters are the natural frequencies of the complete filter and the natural frequencies of the individual resonators. It is shown that insertion loss is related to the migration of the natural frequencies (poles) as the coupling coefficients between resonators are increased from zero. A vector construction is described for the pole migration of three coupled resonators.