Admittance calculations for non-reflective SAW transducers

This paper concerns SAW transducers using regular electrodes with negligible electrode reflections, for example the common types with 3 or 4 electrodes per period. Assuming power conservation and no diffraction, the conductance of such transducers is easily and accurately obtained using quasi-static theory. For apodised transducers it is usual to envisage the transducer as a limited number of unapodised sub-transducers (`channels´) connected electrically in parallel, and this is inconvenient and involves an undesirable approximation. In contrast, the frequency response and capacitance calculations are simple linear sums, without the need to channelise. It is shown here that the conductance analysis can be rearranged such that channelisation becomes unnecessary. This gives a sum in which each term corresponds to the current induced in one electrode by the wave launched at another. The large number of such terms is substantially reduced by grouping together those with the same delay. This gives a result without approximation and which is simple to calculate. The Hilbert transform, needed for the acoustic susceptance, is obtained using a simple algebraic transformation of the conductance This avoids the usual numerical Hilbert transform, another source of error. The method can be straight-forwardly adapted to allow for propagation loss