Approximate analysis of SAW longitudinally-coupled resonator (LCR) filters

The LCR filter, also known as a dual-mode SAW (DMS) filter, is well established as a technique for realising bandpass filters with very low insertion loss and good stop-band suppression. Typically, this device has a three-transducer structure G-T-T-T-G (where T=transducer and G=grating), with the outer transducers connected together. Usually all the transducers are the single-electrode type, strongly affected by electrode reflections, and this complicates the device behaviour. This paper presents a simplified approximate analysis making use of reciprocity and power conservation. It is shown that, when shorted, the central transducer behaves as a component that causes dispersion of the waves but does not reflect them. In consequence, the device behaves like a simple resonant cavity, but with cavity length dependent on frequency. From this point of view, a 2-pole device is a single cavity with two resonant modes, not a pair of cavities coupled together. For the filter passband, simple relations are obtained for the device Y-parameters in terms of the P-matrices of the SAW components, and the frequency response is readily calculated. The approximate analysis is verified by comparison with an accurate analysis using the COM method. The implications of the approximate analysis for device design are discussed.