Topic
Parametric oscillator
About: Parametric oscillator is a research topic. Over the lifetime, 5836 publications have been published within this topic receiving 95631 citations. The topic is also known as: Parametric excitation.
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TL;DR: The principle of parametric excitation of an oscillatory system has been known for many years as discussed by the authors, and the capacitance/time graph envisaged in the foregoing is a square wave at twice the resonant frequency of the circuit.
Abstract: THE principle of parametric excitation of an oscillatory system has been known for many years. An electric oscillatory circuit can be excited in this way if the condenser plates are instantaneously pulled apart by a fixed amount whenever the voltage reaches a maximum value, and instantaneously restored to their original positions when the voltage is zero. Under these conditions energy is communicated to the circuit when the plates are pulled apart; but none is extracted when they are restored, and so oscillations can be maintained. The capacitance/time graph envisaged in the foregoing is a square wave at twice the resonant frequency of the circuit; but it can be shown that a sinusoidal variation at twice the resonant frequency may be used. Any method of periodically varying the capacitance may be used, or alternatively the inductance may be varied. Moreover, such a circuit can be used as an amplifier, since, at the fundamental frequency, the excitation mechanism is analogous to negative resistance.
156 citations
Patent•
29 Nov 1983TL;DR: In this paper, an oscillator is formed in a rectangular waveguide with both mechanical and electronic tuning, and the effective electrical spacing between the oscillator device and the varactor diode is approximately an integral number of halv-wavelengths at the operating frequency.
Abstract: An oscillator formed in rectangular waveguide (1) with both mechanical and electronic tuning comprises an oscillator device (4) spaced from a movable short-circuit termination (2) with a varactor diode (5) therebetween, the effective electrical spacing between the oscillator device (4) and the varactor (5) being approximately an integral number of halv-wavelengths at the operating frequency. The varactor (5) extends into the waveguide (1) from one broad wall thereof and engages a transverse member (10) extending between the narrow walls so that only part of the heigth of the waveguide (1) at that region is obscured. This enables the operating frequency and hence the extent of coupling of the varactor (5) to the oscillator cavity, and thus the electronic tuning range, to be varied by adjusting the position of the short-circuit (2). To enable the operating frequency to be mechanically adjusted without greatly influencing the electronic tuning range, an E-plane stub (11) with a movable short-circuit termination (12) may be branched from the waveguide (1) at the same region as the varactor (5).
155 citations
153 citations
TL;DR: In this article, the classical Wien-bridge sinusoidal oscillator was studied, and it was shown that the phase shift between the waveforms of the two state variables and the frequency of oscillation both depend on the fractional order of the capacitors.
Abstract: The classical Wien-bridge sinusoidal oscillator is studied, when both of the capacitors of the oscillator acquire a fractional order. Accordingly, the Wien oscillator is described by a set of fractional-order nonlinear differential equations. It is shown that sinusoidal oscillations are preserved but the phase-shift between the waveforms of the two state variables and the frequency of oscillation both depend on the fractional-order, leading to a significant advantage over the integer-type Wien oscillator. Findings are validated via numerical simulations.
150 citations
TL;DR: In this paper, a global nonlinear distributed-parameter model for a piezoelectric energy harvester under para-metric excitation is developed, and the results show that a one-mode approximation in the Galerkin approach is not sufficient to evaluate the per-formance of the harvesters.
Abstract: A global nonlinear distributed-parameter model for a piezoelectric energy harvester under para- metric excitation is developed. The harvester consists of a unimorph piezoelectric cantilever beam with a tip mass. The derived model accounts for geomet- ric, inertia, piezoelectric, and fluid drag nonlinearities. A reduced-order model is derived by using the Euler- Lagrange principle and Gauss law and implementing a Galerkin discretization. The method of multiple scales is used to obtain analytical expressions for the tip deflection, output voltage, and harvested power near the first principal parametric resonance. The effects of the nonlinear piezoelectric coefficients, the quadratic damping, and the excitation amplitude on the output voltage and harvested electrical power are quantified. The results show that a one-mode approximation in the Galerkin approach is not sufficient to evaluate the per- formance of the harvester. Furthermore, the nonlinear piezoelectric coefficients have an important influence on the harvester's behavior in terms of softening or hardening. Depending on the excitation frequency, it is determined that, for small values of the quadratic damping, there is an overhang associated with a sub- critical pitchfork bifurcation.
150 citations