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Concept
Antiresonance
Summary
In the physics of coupled oscillators, antiresonance, by analogy with resonance, is a pronounced minimum in the amplitude of an oscillator at a particular frequency, accompanied by a large, abrupt shift in its oscillation phase. Such frequencies are known as the system's antiresonant frequencies, and at these frequencies the oscillation amplitude can drop to almost zero. Antiresonances are caused by destructive interference, for example between an external driving force and interaction with another oscillator.
Antiresonances can occur in all types of coupled oscillator systems, including mechanical, acoustical, electromagnetic, and quantum systems. They have important applications in the characterization of complicated coupled systems.
The term antiresonance is used in electrical engineering for a form of resonance in a single oscillator with similar effects.
RC circuit and RLC circuit
In electrical engineering, antiresonance is the condition for which the reactance vanishes and the impedance of an electrical circuit is very high, approaching infinity.
In an electric circuit consisting of a capacitor and an inductor in parallel, antiresonance occurs when the alternating current line voltage and the resultant current are in phase. Under these conditions the line current is very small because of the high electrical impedance of the parallel circuit at antiresonance. The branch currents are almost equal in magnitude and opposite in phase.
The simplest system in which antiresonance arises is a system of coupled harmonic oscillators, for example pendula or RLC circuits.
Consider two harmonic oscillators coupled together with strength g and with one oscillator driven by an oscillating external force F. The situation is described by the coupled ordinary differential equations
where the ωi represent the resonance frequencies of the two oscillators and the γi their damping rates. Changing variables to the complex parameters:
allows us to write these as first-order equations:
We transform to a frame rotating at the driving frequency
yielding
where we have introduced the detunings Δi = ω − ωi between the drive and the oscillators' resonance frequencies.
Official source
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