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The resonance effect of the LC circuit has many important applications in signal processing and communications systems. The most common application of tank circuits is tuning radio transmitters and receivers. For example, when tuning a radio to a particular station, the LC circuits are set at resonance for that particular carrier frequency.
Increase of amplitude as damping decreases and frequency approaches resonant frequency of a driven damped simple harmonic oscillator. [1] [2]Resonance is a phenomenon that occurs when an object or system is subjected to an external force or vibration that matches its natural frequency.
The Q factor is a parameter that describes the resonance behavior of an underdamped harmonic oscillator (resonator). Sinusoidally driven resonators having higher Q factors resonate with greater amplitudes (at the resonant frequency) but have a smaller range of frequencies around that frequency for which they resonate; the range of frequencies for which the oscillator resonates is called the ...
To cause resonance, the phase of a sinusoidal wave after a round trip must be equal to the initial phase so the waves self-reinforce. The condition for resonance in a resonator is that the round trip distance, , is equal to an integer number of wavelengths of the wave:
All diagonal elements in a tuned filter are equal to zero because a susceptance vanishes at the resonant frequency. Important merit of the matrix M {\displaystyle \mathbf {M} } is the fact that it allows to directly compute the frequency response of the equivalent network having the inductively coupled resonant circuits,.
If is cubic, these are then the three-wave terms; if quartic, these are the four-wave terms, and so on. Canonical transformations can be repeated to obtain higher-order terms, as long as the lower-order resonant interactions are not damaged, and one skillfully avoids the small divisor problem , [ 5 ] which occurs when there are near-resonances.