Equivalent circuit for the microstrip ring resonator suitable for broadband materials characterisation

A simple equivalent circuit of the edge coupled microstrip ring resonator is developed based on both circuit and electromagnetic theory. The new model extends the work done by previous authors by including the effects of radiation loss, the coupling gap and the feed network as well as extending the frequency range by including higher-order modes. The model accurately predicts the resonant frequencies of the ring including the effects of dispersion and thick conductors. The equivalent circuit allows measurement of the resonance frequencies and the Q factors to be made independently of the coupling gap dimensions, which traditionally have been difficult to accurately model. A method of determining radiation loss is also presented, which has often been incorrectly neglected in the past. Experimental results support the accuracy of the equations and measurements on alumina rings that demonstrate a frequency accuracy of better than 1% over 12 resonant modes in the frequency range 3-33 GHz.