Q-meter:

The Q-factor for a series L–C–R circuit is the voltage magnification at resonance, i.e.

\(Q-factor = \frac{voltage\ across\ capacitor}{supply\ voltage}\)

\(=\frac{V_C}{V}\)

The simplified circuit of a Q-meter, used for measuring Q-factor. Current from a variable frequency oscillator flowing through a very low resistance r develops a variable frequency voltage, \(V_r\), which is applied to a series L–R–C circuit. The frequency is then varied until resonance causes voltage \(V_c\) to reach a maximum value. At resonance \(V_r\) and \(V_c\) are noted. Then

\(Q-factor=\frac{V_c}{V_r} = \frac{V_c}{I_r}\)

In a practical Q-meter, \(V_r\) is maintained constant and the electronic voltmeter can be calibrated to indicate the Q-factor directly. If a variable capacitor C is used and the oscillator is set to a given frequency, then C can be adjusted to give resonance. In this way inductance L may be calculated using

\(f_r= \frac{1}{2\pi\sqrt{LC}}\)

Since \(Q= \frac{2\pi fL }{R}\),

then R may be calculated

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