The Q, quality factor, of a resonant circuit is a measure of the goodness
or quality of a resonant circuit. A higher value for this figure of merit
correspondes to a more narrow bandwith, which is desirable in many
applications. More formally, Q is the ration of power stored to power dissipated
in the circuit reactance and resistance.
Series Resonance
The resonance of a series RLC circuit occurs when the
inductive and capacitive reactances are equal in magnitude but cancel each
other because they are 180 degrees apart in phase. The sharp minimum in
impedance which occurs is useful in tuning applications. The sharpness of the
minimum depends on the value of R and is characterized by the "Q" of
the circuit.
The frequency response of the circuits current
magnitude above, relates to the “sharpness” of the resonance in a series
resonance circuit. The sharpness of the peak is measured quantitatively and is
called the Quality factor, Q of the circuit. The quality factor relates the
maximum or peak energy stored in the circuit (the reactance) to the energy
dissipated (the resistance) during each cycle of oscillation meaning that it is
a ratio of resonant frequency to bandwidth and the higher the circuit Q, the smaller the bandwidth.
Parallel
Resonance
The Q-factor of a parallel resonance circuit is the
inverse of the expression for the Q-factor of the series circuit. Also in
series resonance circuits the Q-factor gives the voltage magnification of the
circuit, whereas in a parallel circuit it gives the current magnification.
The selectivity or Q-factor for a
parallel resonance circuit is generally defined as the ratio of the circulating
branch currents to the supply current and is given as:
The Q-factor of a parallel resonance circuit is the inverse
of the expression for the Q-factor of the series circuit. Also in series
resonance circuits the Q-factor gives the voltage magnification of the circuit,
whereas in a parallel circuit it gives the current magnification
Resonant circuits are used to respond selectively to signals
of a given frequency while discriminating against signals of different
frequencies. If the response of the circuit is more narrowly peaked around the
chosen frequency, we say that the circuit has higher selectivity. A quality
factor Q, is a measure of that selectivity, and we speak of a circuit having a high
Q if it is more narrowly selective.
An example of the application of resonant circuits is the
selection of AM radio stations by the radio receiver. The selectivity of the
tuning must be high enough to discriminate strongly against stations above and
below in carrier frequency, but not so high as to discriminate against the
"sidebands" created by the imposition of the signal by amplitude
modulation.
Consider a circuit where R, L and C are all in parallel. The
lower the parallel resistance, the more effect it will have in damping the
circuit and thus the lower the Q.