Table 2.

Resonant frequency equations and their range for the four different modes of the piezoelectric vibration based on bulk acoustic waves

Parameters	Thickness shear (TS) mode	Thickness extensional (TE) mode	Lateral extensional (LE) mode	Flexural (Flex) mode
Resonant frequency equation	$f_0=\frac{1}{2d}\sqrt{\frac{c}{\rho }}(1)$	$f_0=\frac{1}{2d}\sqrt{\frac{c_{33}}{\rho }}(2)$	$f_0=\frac{1}{2W}\sqrt{\frac{c_{31}}{\rho }}(3)$	$f_0=\frac{1}{2\pi }\sqrt{\frac{k}{m}}(4)$
Range of $f_0$	5–25 MHz (see Table 3)	800–4.8 GHz (see Table 5)	50–160 MHz	0.03–3.3 MHz