An analysis of overtone modes in monolithic crystal filters

A previous treatment of overtone modes in trapped energy resonators is extended to the case of two pole monolithic crystal filters. The asymptotic dispersion relations for the fundamental and odd overtone coupled thickness-shear and thickness-twist waves near cutoff along with the simple approximate edge conditions at junctions, which were employed in the earlier treatment of resonators, are applied in the analysis of two-pole monolithic crystal filters. Both thickness-shear and thickness-twist coupling directions are considered. The influence of piezoelectric stiffening, electrode mass loading and electrical shorting is included in the analysis. A lumped parameter representation of the admittance matrix for the two-port device is obtained. Numerical results are presented for a few geometrical configurations.