On the unlimited gain of a nonlinear parametric amplifier

• Nonlinear parametric amplifier response is studied within and beyond resonance.
• The system response amplitude can be large at arbitrarily small external excitation.
• Very large amplifier gain can be achieved in a broad range of system parameters.
• Very meaningful parametric amplification can be realized in nonlinear systems.

The present paper is concerned with analysis of the response of a nonlinear parametric amplifier in a broad range of system parameters, particularly beyond resonance. Such analysis is of particular interest for micro- and nanosystems, since many small-scale parametric amplifiers exhibit a distinctly nonlinear behavior when amplitude of their response is sufficiently large. The modified method of direct separation of motions is employed to study the considered system. As the result it is obtained that steady-state amplitude of the nonlinear parametric amplifier response can reach large values in the case of arbitrarily small amplitude of external excitation, so that the amplifier gain tends to infinity. Very large amplifier gain can be achieved in a broad range of system parameters, in particular when the amplitude of parametric excitation is comparatively small. The obtained results clearly demonstrate that very meaningful parametric amplification can be realized in resonant systems driven within a nonlinear response regime, and that nonlinear parametric amplifier possesses certain advantages over linear one.