Q factor of a coil is given by

Concept:

The coil is a circuit with Resistance and Inductance connected in series as shown:

The quality factor Q is defined as the ratio of the resonant frequency to the bandwidth.

\(Q=\frac{{{f}_{r}}}{BW}\)

Mathematically, for a coil, the quality factor is given by:

\(Q = \frac{{{\omega _o}L}}{R}=\frac{X_L}{R}\)

The sharpness of the resonance in RLC series resonant circuit is measured by the quality factor and is explained in the figure shown below:

Observations:

• Less the Bandwidth, more the Quality factor.
• More the Bandwidth, less is the Quality factor.
• For the above figure, B2 > B1, so Q2 < Q1