Table 8.

Description of several classic transduction mechanisms applied to coupled BAW MEMS resonators.

Transduction Methods	Capacitive Actuation and Sensing	Piezoresistive Sensing	Piezoelectric Actuation and Sensing
Actuation force (F)	$F\approx \left(\frac{1}{2}{V}_{\mathrm{d}}^2+2\left|V_{\mathrm{ac}}\right|V_{\mathrm{d}}\right)\frac{\mathrm{d}C}{\mathrm{d}x}$ [76]	Not applicable yet	$F=\frac{e_{33}{A}_3{V}_{ac}}{h}- \mathrm{Longitudinal}$ $F=\frac{e_{31}{A}_1{V}_{ac}}{h}$- Transverse [92]
Sensed motional current (imot)	$i_{\mathrm{mot}}=V_{\mathrm{d}}\frac{\partial C}{\partial x}\frac{\partial x}{\partial t}$ [76]	$i_{\mathrm{mot}}\approx \frac{V_{\mathrm{d}}}{R}\left(\frac{\Delta R_{\mathrm{r}}}{R_{\mathrm{r}}}\right)$ [95]	$\left|i_{\mathrm{mot}}\right|=\left|\omega \cdot e_{33}{A}_3{S}_3\right| \mathrm{Longitudinal}$ $\left|i_{\mathrm{mot}}\right|=\left|\omega \cdot e_{31}{A}_3{S}_1\right|$ Transverse [92]
Cons	Parasitic capacitance; Nonlinearity; complex circuit design; thin film damping; limitation in liquids [96]	Temperature dependency; high power consumption with using high DC voltages; noisy	Processing difficulty in piezoelectric materials; not possible static measurement
Pros	Low power consumption; good noise performance; easy to fabricate	Simple setup; inherent shielding; applicable to liquids [97]	Eliminating frequency drifts caused by DC voltage variations due to no DC voltages needed here [13]; Applicable to liquids [98,99,100,101]