The Q factor

We have come across Q before when discussing image quality. Q is also used to
describe resonance quality.

Filters are formed by the cascading of a number of resonant elements. Resonant elements
are formed by the interaction of inductance, capacitance, and resistance. The figure
of merit or quality of the resonant circuit (that is, its sharpness of resonance) is
indicated by the Q factor. The higher the ratio of the reactance at resonance to the series
resistance, the higher the Q and the sharper the resonance. In a parallel circuit Q =
XL/rS. In practice a capacitor is less lossy (more ideal) than the inductor, thus it is the
resistive component of the inductor that determines the Q.
Another way to envisage Q is a consideration of the energy in a resonant circuit. If
the L and C components were ideal, then the energy would circulate ad infinitum.
In practice, energy is lost in the series resistance, and so the energy dies away. Taking
energy from the circuit will also produce the same effect. This is referred to as damping
or loading the circuit. The Q of a circuit fed from and loaded by a finite impedance
is referred to as the loaded Q. Filters may be considered as a number
of cascaded resonant sections. The consideration of losses, loading, and Q apply
equally to multiple sections as a single section. 317