Idealized analysis of SAW longitudinally coupled resonator filters

A surface acoustic wave (SAW) longitudinally coupled resonator (LCR) filter consists of either two or three interdigital transducers located between two strongly reflecting gratings. The behavior of this structure is, in general, very complex because the transducers are of the single-electrode type, which gives strong electrode reflections. It is shown here that, for the filter passband, a number of realistic assumptions can be used to derive a very simple set of approximate relations for the device Y-matrix. The simplifications involve reciprocity, symmetry, and power conservation. The theory also uses the necessary fact that each grating, combined with its adjacent transducer, must have high directivity so that application of a voltage results in wave generation primarily toward the center of the device. For a three-transducer device, it is shown using symmetry that the central transducer behaves as if it were transparent, despite having strong electrode reflections. Hence, the device behaves as a single resonant cavity. The simple Y-matrix formulae are shown to agree very well with accurate results obtained by a coupling-of-modes (COM) analysis for both types of device. They also lead to simple formulae for the electrical loading required to obtain a flat, low-loss filter response. Equivalent circuits also are discussed.