Coupling parameters for a side-coupled ring resonator and a microstrip line

A ring resonator side coupled to a microstrip line shows two close but distinct resonance peaks. These are identified as due to even-mode (magnetic field) and odd-mode (electric field) coupling. Equivalent circuit models for both cases have been proposed and coupling parameters are calculated using piecewise, coupled-line approximations. The calculated coupling coefficients for the two cases are compared with the experimentally-measured coupling coefficients and show very good agreement with the models used.