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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 ...
Low-Q circuits are therefore damped and lossy and high-Q circuits are underdamped and prone to amplitude extremes if driven at the resonant frequency. [a] Q is related to bandwidth; low-Q circuits are wide-band and high-Q circuits are narrow-band. In fact, it happens that Q is the inverse of fractional bandwidth
The damping ratio provides a mathematical means of expressing the level of damping in a system relative to critical damping. For a damped harmonic oscillator with mass m, damping coefficient c, and spring constant k, it can be defined as the ratio of the damping coefficient in the system's differential equation to the critical damping coefficient:
There is no unit designation for transmissibility, although it may sometimes be referred to as the Q factor. The transmissibility is used in calculation of passive hon efficiency. The lesser the transmissibility the better is the damping or the isolation system.
The logarithmic decrement can be obtained e.g. as ln(x 1 /x 3).Logarithmic decrement, , is used to find the damping ratio of an underdamped system in the time domain.. The method of logarithmic decrement becomes less and less precise as the damping ratio increases past about 0.5; it does not apply at all for a damping ratio greater than 1.0 because the system is overdamped.
Zero damping will produce a maximum response. Very high damping produces a very boring SRS: A horizontal line. The level of damping is demonstrated by the "quality factor", Q which can also be thought of transmissibility in sinusoidal vibration case. Relative damping of 5% results in a Q of 10.
The settling time for a second order, underdamped system responding to a step response can be approximated if the damping ratio by = () A general form is T s = − ln ( tolerance fraction × 1 − ζ 2 ) damping ratio × natural freq {\displaystyle T_{s}=-{\frac {\ln({\text{tolerance fraction}}\times {\sqrt {1-\zeta ^{2}}})}{{\text ...
At around 4 kHz, the real-life difference between an amplifier with a moderate (100) damping factor and one with a low (20) damping factor is about 0.37 dB. However, the amplifier with the low damping factor is acting more like a subtle graphic equaliser than is the amplifier with the moderate damping factor, where the peaks and dips in the ...