Extension of Surface-Wave Transducer Models to Nonsynchronous Frequencies

Abstract

Absfracf-A useful equivalent circuit model is developed for surface-wave transducers which relates directly to the physics of surface waves and does not rely on the equivalent bulk-wave behavior implied by other circuit models. The surface potential is selected as the cross-variable of the transmission-line part of the model, and the through-variable is defined by means of the characteristic admittance and the power flux. With this model, the response of an alternate phase array is extended to frequencies other than the synchronous frequencies. Furthermore, with the aid of reciprocity, the admittance matrix of an elementary transmissionline section is obtained along with the corresponding equivalent circuit. The versatility of this approach is demonstrated through application of the model to the excitation and detection of surface waves by a twenty-element array. for surfxce-wave transducers. Each of these models is in essencf' an adapt'ation of Rlason's [8, 91 equivalent circuit model for bulk-wa8ve transducers. In developing his model, Mason considered the one-dimensional particlc motion of calast8ic bulk waves. These waves were induced either by series-field excitation or crossed-field cxcitnton. The pnrtick motion associatcd with surf:m waves is not quite as simple hccausc surfacc waves cannot hr described properly by ont4irncnsional particle motion. With surface ~a),~es, particle motion occurs in two- or three-dimensional elliptical trajectories. In addit,ion, t,hcre are complicated clectromc~chanical interactions with thr snrface clectrodcs. Because of t'hc complexity of the equations of particle motion for surface waves [IO, 111, no equivalent circuit, models haw yet been dewloped c,omplctely from first principlcs. Adaptation of the llason modcl to surface waves is justified ~~~orc by analogy than actual analysis, although certa,in parts of the equivalent circuit, such as t8hc intcrclcctrodc~ capacitance, have a rigorow theoretical basis [la]. In dcvrloping an equivalent circuit, researchers are fac:ed wit'h t,wo major problems: off-synchronous behavior must, bo accounted for while at, thc same timc a simplc, yet useful, thrw-port model must be ohtaincd. H. Skeic [l31 approached the problem employing perturbat,ion tmhniqurs; off-syxchrollous results were cstimatcd. The normal mode theory of Auld and Kino [I41 supports SL bssfully developed useful equivalent-circuit models