Relations for Analysis and Design of Surface-Wave Resonators

Analysis and design relations are presented for elec- trical resonators formed from an interdigital transducer on a piezo- electric substrate, with arrays of many metal reflecting elements on both sides of the transducer to create surface-wave resonance. The "image" point of view is used for analyzing the arrays. Simple expressions are obtained for predicting the stop-band width of an array, the stop-band attenuation of an array, and the apparent point of reflection from the array, in terms of r = ZJZ, the ratio of the surface-wave impedance in the metalized regions to that in the unmetalized regions. The attenuation relation also provides a con- venient means for measuring r. Simple means are presented for including the array dissipation loss in the calculation of its input impedance, and such loss is found to be major significance. Equivalent circuits are presented for surface-wave resonators, along with equations for the reactance or susceptance slope param- eters and resonance Q's at the frequencies of series and parallel resonance. Several experimental resonators were fabricated, and the measured results agree well with the theory. Our experimental results show that for an array of metal reflecting strips if the outer ends of the strips are shorted together r 1.