A series resonant circuit is tuned to 10 MHz and provides 3-dB bandwidth of 100 kHz. The quality factor Q of the circuit is

Concept:

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

In Hz, this can be written as:

f_r is the resonant frequency of the RLC circuit.

Calculation:

With f_r = 10 MHz and BW = 100 kHz, the quality factor will be:

Q = 100

The selectivity/sharpness of the resonance for an 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, better will be selectivity.
• More the Bandwidth, less is the Quality factor, poor will be the selectivity
• For the above figure, B2 > B1, so Q2 < Q1