Parametric feedback oscillators

A parametric feedback oscillator includes a resonator which has at least one transduction element and at least one electromechanical resonating element. The resonator is configured to accept as input a parametric excitation signal at a frequency 2[omega]0 and to provide a resonating output signal at a frequency [omega]0. A cascaded feedback path in any electrically coupled cascade order includes at least one non-linear element, at least one phase shifter electrically, and at least one amplifier. The cascade feedback path is configured to receive as input the resonating output signal at a frequency [omega]0 and configured to provide as output a feedback path signal as the parametric excitation signal at a frequency 2[omega]0 to the resonator.; A parametric feedback oscillator output terminal is configured to provide the resonating output signal at the frequency [omega]0 as an output signal. A method of causing a parametric feedback oscillation is also described.