An analytical theory for the scattering of surface acoustic waves by a single electrode in a periodic array on a piezoelectric substrate

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Abstract
An analytical theory is presented that leads to the scatter matrix of a sngle electrode for an acoustic surface wave propagating through a periodic array of electrodes on an anisotropic piezoelectric substrate. The scatter matrix elements are obtained analytically as functions of frequency and metallization ratio, considering only the electrical loading by the electrodes; mechanical loading effects are neglected. The results may be used directly in the broad band analysis of surface acoustic wave reflectors and multistrip couplers. Previous works have provided these parameters numerically for electrically shorted and open arrays at stop band frequencies (frequencies where the array period is an integer number of half wavelengths). This work extends the analysis in three ways: (a) the analysis is valid for all frequencies, (b) the external electrical load connected to the electrodes is included as a parameter, and (c) the scatter matrix elements are determined analytically instead of numerically.