Third order intermodulation distortion in capacitive-gap transduced micromechanical filters

The third-order intermodulation distortion in properly terminated high-order bridged clamped-clamped beam (CC-beam) channel-select micromechanical filters has been measured for the first time and found to be appreciably higher than seen on unterminated stand-alone CC-beams. In particular, a three-resonator bridged 8-MHz filter with 140nm gaps posts a measured IIP₃ of 25dBm and 36dBm for two-tone offsets of 200kHz and 400kHz, respectively, which are much larger than the -11.7dBm for a stand-alone 9.2MHz CC-beam with 200kHz two-tone offset. For the case where the required minimum signal-to-noise ratio is 10dB, the IIP₃ of 36dBm translates to an impressive spurious-free dynamic range of 102.3dB. The result matches well the prediction of a new model for non-linearity that incorporates not only parallel-plate capacitor nonlinearity, but also the influence of the filter structure, where Q-loading by the termination reduces the degree of out-of-channel tone suppression, but also reduces the amplitude of resonator motion, which then improves the IIP₃. The full model incorporates these phenomena, plus dependencies on dc-bias, gap spacing, and electrode area.