Single element excitation and detection of (micro-)mechanical resonators

The authors describe a single-element approach for the excitation and detection of the vibrational motion of (micro-)mechanical resonators. An equivalent electrical one-port network is derived for an electrostatically and a piezoelectrically driven resonator. In this way, the effect of the mechanical resonator is transformed into the electrical domain and can easily be accounted for in a circuit simulation. A detection circuit, based on an (on-chip) bridged design, is proposed as a way to compensate for the parasitic parallel load of the one-port. A criterion is given for the accepted level of unbalance of the bridge if a minimal phase shift of 90 degrees in the transfer characteristic around resonance is required.<>