It is often useful to define a \"quality factor\" (or \"Q-factor\") for an oscil

Question

It is often useful to define a "quality factor" (or "Q-factor") for an oscillator: Q = 2 pi times Energy stored / Energy dissipated during one period Find an expression for the Q-factor of a series RLC circuit driven at the resonant frequency omega 0 in terms of R, L and C. (Hint: it is simplest to consider the energy stored in the inductor. You might find the table of standard integrals in the Appendix of your text book useful for calculating the energy dissipated in one period.) What does it mean physically if Q

Explanation / Answer

Please ask if you have any doubt.I will help you.

a) In a series RLC circuit the current maximum current

through the circuit occurs at resonance frequency.

I(max) = V/R.

Therefore,

Energy stored = 0.5 L (I(max))2 .

The energy dissipated in the circuit is I2R ,

when integrated over a cycle is kagnet

EdissT = (0.5 (I(max))2R)(2/o) .

Thus when these values are substituted the Q comes out as

Q = oL / R.

b) The Q < 1 ,implies that the circuit is not a good one for filtering.

According to physical reason the Q should be high for good filtering operation.

The circuit when suddenly closed with a wire ,

Starts oscillation with a damping constant because of resistance and finally ends up with 0 energy thereby dissipating all its power through R.

Note : The energy stored can also be calculated in terma of capacitor and the expression for Q would be different.

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