One-Port SAW Resonators Using Natural SPUDT Substrates

We discuss the design of one-port surface acoustic wave (SAW) resonators using substrates with a partial or total degree of directivity, that is, the natural single-phase unidirectional transducer (N-SPUDT) effect. A general design method gives a resonance when all three frequencies (the required resonance frequency and the Bragg frequencies) are different. A second method has been derived from the resonance condition for a symmetrical substrate. Two further methods incorporate lambda/4 gaps. The capacitance ratio is presented as a function of the phase of the electrode reflection coefficient. The simulations use data for the N-SPUDT orientation of lanthanide. The reflection coefficient for Al electrodes has been calculated from finite element modeling (FEM) analysis. The approximate perturbation theory is found to agree well for small film thickness (h/lambda < 2%). The phase of the reflection coefficient is typically 150deg, not quite the ideal value of 180deg. Measurements on resonators using Al and Cu films are presented.