Cascading formulas for identical transducer P-matrices

Formulas are derived for the P-matrix of a cascade of identical acoustic transducers, in terms of the P-matrix of one elementary transducer. The derivation makes no assumptions other than reciprocity and the validity of the P-matrix description. Consequently, the results are valid for a wide range of cases, such as simple SAW gratings or group-type single-phase unidirectional transducers (SPUDT's), where each element is a transducer plus grating. The formulas are used to derive a general relation for the directivity of a SPUDT in terms of the directivity of one period.