Quality factor tuning of micromechanical resonators via electrical dissipation

Sensitive capacitive transduction of micromechanical resonators can contribute significant electrical dissipation, which degrades the quality factor of the eigenmodes. We theoretically and experimentally demonstrate a scheme for isolating the electrical damping of a mechanical resonator due to Ohmic dissipation in the readout amplifier. The quality factor suppression arising from the amplifier is strongly dependent on the amplifier feedback resistance and parasitic capacitance. By studying the thermomechanical displacement noise spectrum of a doubly clamped micromechanical beam, we confirm that electrical dissipation tunes the actual, not effective, quality factor. Electrical dissipation is an important consideration in the design of sensitive capacitive displacement transducers, which are a key component in resonant sensors and oscillators.