Parametric oscillator

A parametric oscillator is a driven harmonic oscillator in which the oscillations are driven by varying some parameter of the system at some frequency, typically different from the natural frequency of the oscillator. A simple example of a parametric oscillator is a child pumping a playground swing by periodically standing and squatting to increase the size of the swing's oscillations. The child's motions vary the moment of inertia of the swing as a pendulum. The 'pump' motions of the child must be at twice the frequency of the swing's oscillations. Examples of parameters that may be varied are the oscillator's resonance frequency ω {displaystyle omega } and damping β {displaystyle eta } . A parametric oscillator is a driven harmonic oscillator in which the oscillations are driven by varying some parameter of the system at some frequency, typically different from the natural frequency of the oscillator. A simple example of a parametric oscillator is a child pumping a playground swing by periodically standing and squatting to increase the size of the swing's oscillations. The child's motions vary the moment of inertia of the swing as a pendulum. The 'pump' motions of the child must be at twice the frequency of the swing's oscillations. Examples of parameters that may be varied are the oscillator's resonance frequency ω {displaystyle omega } and damping β {displaystyle eta } . Parametric oscillators are used in several areas of physics. The classical varactor parametric oscillator consists of a semiconductor varactor diode connected to a resonant circuit or cavity resonator. It is driven by varying the diode's capacitance by applying a varying bias voltage. The circuit that varies the diode's capacitance is called the 'pump' or 'driver'. In microwave electronics, waveguide/YAG-based parametric oscillators operate in the same fashion. Another important example is the optical parametric oscillator, which converts an input laser light wave into two output waves of lower frequency ( ω s , ω i {displaystyle omega _{s},omega _{i}} ). When operated at pump levels below oscillation, the parametric oscillator can amplify a signal, becoming a parametric amplifier (paramp). Varactor parametric amplifiers have been developed as low-noise amplifiers in the radio and microwave frequency range. The advantage of a parametric amplifier is that it has much lower noise than an ordinary amplifier based on a gain device like a transistor or vacuum tube. This is because in the parametric amplifier a reactance is varied instead of a (noise-producing) resistance. They have been used in very low noise radio receivers in radio telescopes and spacecraft communication antennas.