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

Abstract

The mechanism behind third order intermodulation distortion (IM 3 ) in capacitively driven clamped-clamped beam micromechanical ("CC-beam µmechanical") 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 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 3 's of 1.8V and 6.5V for 9.2 MHz and 17.4 MHz µmechanical resonators, respectively, closely match measured values of 1.8V and 6.3V.Extensive data on the dependence of IIP 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.