Third-order intermodulation distortion in capacitively-driven CC-beam micromechanical resonators

The mechanism behind third order intermodulation distortion (IM/sub 3/) in capacitively driven clamped-clamped beam micromechanical ("CC-beam /spl mu/mechanical") resonators is shown to arise mainly from nonlinear interactions between applied off-resonance electrical signals and the mechanical displacements they induce. Analytical formulations for the third-order input intercept point (IIP/sub 3/) are then presented, first with simplifications that allow a closed form expression, then with additional complexities to account for second-order effects, such as beam bending due to an applied dc-bias voltage. Using this analytical formulation, predicted voltage IIP/sub 3/\´s of 1.8 V and 6.5 V for 9.2 MHz and 17.4 MHz /spl mu/mechanical resonators, respectively, closely match measured values of 1.8 V and 6.3 V. Extensive data on the dependence of IIP/sub 3/ on dc-bias voltage, resonator Q, and resonator center frequency, are also included to lend further insight into the trade-offs involved when designing for a specific linearity requirement.