Q factor

The quality factor Q, and goodness, circuit quality, sharpness of resonance, resonant circuit quality, or pole quality Q- factor called, is a measure of the damping of a vibrating system (eg a resonant circuit ) in electrical engineering. This is called the case of weakly damped oscillating systems of systems of high quality, since the quality factor of the reciprocal of the loss factor d ( damping):

Definition and calculation

Describes the quality factor, the extent to which energy can be stored in a vibratory system with respect to the converted energy loss:

Special case: a quality factor of 0.5 (or an attenuation of 2) corresponds in physics to the aperiodic limiting case where there are no more vibration.

Alternatively, the quality factor Q is calculated as the resonance frequency f0 (also referred to as center frequency ) based on the bandwidth B:

Here, the bandwidth results for:

With the upper limit frequency f2 and the lower limit frequency f1.

In view of the level as a function of the frequency, the bandwidth is defined as the frequency range of the boundaries of the voltage level has changed by the linear factor with respect to the extreme value; logarithmically equivalent to about -3 dB.

As can be seen from the above equations, corresponding to a large quality factor Q of a small range B and vice versa.

The quality factor alone does not describe the steepness of a filter, because this includes necessarily the maximum level of boost or cut with the bandwidth. Namely, when - at constant quality factor - the level is greatly increased, a greater slope of the filter appears to the left and right of the resonance frequency as if the gain is increased only slightly.

Quality in electrical engineering

The quality of an oscillatory system can be calculated as the ratio between oscillating reactive power PBlind ( at resonance frequency) and effective power Peff:

Knowledge of the complex AC circuit analysis are required for these calculations.

Series

For a series circuit of a resistor R with a coil of the inductor L and a capacitor C, the following applies:

Using the complex angular frequency of the current I and

For this system is given by the above relation a quality of:

Parallel connection

In analogy to results for a parallel connection of coil, capacitor and resistor to the complex voltage U:

Examples

The following table lists several orders of magnitude of figures of merit for various oscillating systems are given.