The impact of nonlinearity on degenerate parametric amplifiers

This work investigates the effects of system nonlinearities on degenerate parametric amplifiers. A simple, Duffing-type nonlinearity is appended to a representative equation of motion for a mechanical or electromechanical parametric amplifier, and classical perturbation methods are used to characterize the resulting effects on the amplifier's frequency response and performance. Ultimately, the work demonstrates that parametric amplification can be realized in nonlinear, dynamic-range limited systems, such as resonant micro-or nanosystems, but at the expense of performance degradation. Additionally, it is shown that nonlinear amplifiers can be operated above their linear instability threshold but that doing so results in bistable amplified responses. (C) 2010 American Institute of Physics. [doi:10.1063/1.3446851]