Exact closed-form expressions for piezoelectric velocity shift, piezoelectric reflectivity, transduction coefficient, and capacitance in the case of IDT with complex unit cell

Original, exact closed-form expressions for the coupling-of-modes (COM) equation parameters and capacitance in the case of IDT with arbitrarily complex unit cell are reported. These results are based placed exact analytic solution of the electrostatic problem for an arbitrary periodic electrode system in an arbitrary external electric field. The piezoelectric velocity shift and the piezoelectric reflectivity per period are calculated as the Fourier transforms of the unit cell charge distribution generated by the electric field of a SAW incident on the cell. The transduction coefficient per period is calculated as the Fourier transform of the unit cell charge distribution generated by the potential difference between adjacent cells. All COM parameters are calculated as functions of frequency. Several structures with different unit cells are considered and compared