Tuneable, non-degenerated, nonlinear, parametrically-excited amplifier

The proposed parametric amplifier scheme can be tuned to amplify a wide range of input frequencies by altering the parametric excitation with no need to physically modify the oscillator. Parametric amplifiers had been studied extensively, although most of the work focused on amplifiers that are parametrically excited at a frequency twice the amplifier's natural frequency. These amplifiers are confined to amplifying predetermined frequencies. The proposed parametric amplifier's bandwidth is indeed tuneable to nearly any input frequency, not bound to be an integer multiple of a natural frequency. In order to tune the stiffness and induce a variable frequency parametric excitation, a digitally controlled electromechanical element must be incorporated in the realization. We introduce a novel parametric amplifier with nonlinearity, Duffing type hardening, that bounds the otherwise unlimited amplitude. Moreover, we present a multi degree of freedom system in which a utilization of the proposed method enables the projection of low frequency vector forces on any eigenvector and corresponding natural frequency of the system, and thus to transform external excitations to a frequency band where signal levels are considerably higher. Using the method of multiple scales, analytical expressions for the responses have been retrieved and verified numerically. Parametric studies of the amplifiers' gain, sensitivities and spatial projection of the excitation on the system eigenvectors were carried out analytically. The results demonstrate the advantage of the proposed approach over existing schemes. Practical applications envisaged for the proposed method will be outlined.