Question

what is Quality factor?

Answer 1

Q (Quality factor) is times the ratio of the total energy stored divided by the energy lost in a single cycle or equivalently the ratio of the stored energy to the energy dissipated over one radian of the oscillation. It is a dimensionless parameter that compares the time constant for decay of an oscillating physical system's amplitude to its oscillation period. Equivalently, it compares the frequency at which a system oscillates to the rate at which it dissipates its energy.

The width (bandwidth) of the resonance is given by:

For mechanical systems:

For a single damped mass-spring system, the Q factor represents the effect of simplified viscous damping or drag, where the damping force or drag force is proportional to velocity. The formula for the Q factor is:

$$Q = \frac {\sqrt {M k}}{D}$$

where $M$ is the mass, $k$ is the spring constant, and $D$ is the damping coefficient, defined by the equation $F_{\text{damping}} = Dv$ , where $v$ is the velocity.