Circuit design based on MEM resonators is usually carried out with the help of electromechanical analogies. Table 3.2 shows a set of such analogies. This way, the well-established CAD tools of conventional RF/microwave circuit design may be exploited. Once the circuit in question meets the electrical response specifications, the analogies enable a path back to the mechanical world where the physical realization of the devices ultimately lies.
A smallsignal electrical equivalent circuit for the clamped-clamped MEM resonator was developed by Bannon . The resonator is modeled by a core RLC, with values given by (3.21) to (3.24), together with transformers that enable the coupling to both the electrical excitation ni and the output force fc.
The transformer parameters are given by where he models the transformation of input device voltage to mechanical motion, and hc models the mechanical impedance transformation achieved by the mechanical coupling to the beam at a location a distance lc from the anchor. Referred to the center of the electrode port, the circuit of Figure 3.36 may be transformed into a series RLC circuit with the following values : Clearly, the quality factor is a function of the dynamic stiffness and, thus, of the polarization voltage VP .