A parallel resonant RLC circuit is shown in Figure 1.
The input admittance of a parallel R-L-C circuit is given by,
By definition, at resonant frequnecy inductive and capacitive susceptances are equal in magnitude and opposite in phase. Therefore they cancel each other.
Quality factor(Q) of a parallel R-L-C circuit at resonance is
So the Q-factor at resonance is
From Eq-(1), Eq-(2) and Eq-(4),
At resonant frequency , which is real and minimum.
The input impedance of parallel RLC circuit value deceases by at half power frequencies .
From Eq-(6) the condition for is and for is
The bandwidth of the circuit is . Using Eq-(7) and Eq-(8), bandwidth is given as . The resonant frequency is geometric mean of upper and lower 3dB frequencies, .
Quality factor is
For small deviations in frequency from resonant frequency , , input impedance is given by,
or when the deviations are very small compared to , input impedance is approximated as
From the above equation, at resonant frequency, the input impedance is R and is maximum at that frequency. Below it is inductive and above it is capacitive.