Electrostatics of Apodized Saw Transducers

Interdigital transducers (IDT) of surface acoustic waves (SAWs) comprise large numbers of metal strips placed on the substrate of piezoelectric crystal with help of microelectronic technology. Their main purpose is to distribute the electric field delivered to the transducer bus-bars over the substrate surface in specific manner determining the transducer frequency response in the generated SAWs. In typical cases of uniform transducers, all strips have equal length, but in many SAW filters, there are apodized IDTs, with strips of different lengths. Practically, strips extend an entire acoustic channel aperture width to avoid perturbation of the SAW propagation conditions, and the apodization is obtained by making a narrow gap in a strip with its two parts connected to different transducer bus-bars. The electrostatics of such planar system is analyzed below, using the BIS expansion method applicable to periodic strips on anisotropic dielectric media -the fundamental analysis for spectral theory of IDTs.