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Derive the expression of quality factor of series R-L-C circuit at resonance.

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Basic Electrical Engineering Electrical Engineering

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The quality factor is , in general, defined as the ratio of resonant frequency to bandwidth. It is given by

$Q = \frac{f_{r}}{(f_{2} - f_{1})} = \frac{2 π L}{R} (\frac{1}{2 π \sqrt{L C}})$

$Q = \frac{1}{R \sqrt{L C}}$

Thus the quality factor, Q can be improved by decreasing the resistance, R or increasing the ratio of inductance to capacitance L/C.

In a series RLC circuit resonance can be obtained by varying f, that is adjusting the values of L and C. In radio receiver, capacitance is varied to tune different radio station so that resonance is obtained at the desired frequency.

Q is also a measure of the degree of sensitivity of the circuit.

Derive the expression of quality factor of series R-L-C circuit at resonance.

Subjects

Basic Electrical Engineering

Radio Frequency and Microwave Engineering

Analog Communication

Electrical Engineering Management

Power Electronics

Power System I

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