The quality factor or Q-factor of a resonant circuit is a measure of the “goodness” or quality of a resonant circuit. A higher value for this figure of merit corresponds to a narrower bandwidth, which is desirable in many applications. More formally, Q is the ratio of power stored to power dissipated in the circuit reactance and resistance

A practical application of “Q” is that voltage across L or C in a series resonant circuit is Q times total applied voltage. In a parallel resonant circuit, current through L or C is Q times the total applied current.

The Q-meter is an instrument designed for the measurement of Q-factor of the coil as well as for the measurement of electrical properties of coils and capacitors.

This instrument operates on the principle of series resonance i.e. at resonate condition of an AC series circuit voltage across the capacitor is equal to the applied voltage times of Q of the circuit. If the voltage applied across the circuit is kept constant, then voltmeter connected across the capacitor can be calibrated to indicate Q directly.

Circuit diagram of a Q-meter is shown is figure. A wide-range oscillator with frequency range from 50 kHz to 50 MHz is used as a power supply to the circuit.

The output of the oscillator is shorted by a low-value resistance, $R_{sh}$ usually of the order of 0.02 ohm. So it introduces almost no resistance into the oscillatory circuit and represents a voltage source with a very small or of almost negligible internal resistance.

The voltage across the low-value shunt resistance $R_{sh}$, V is measured by a thermo-couple meter and the voltage across the capacitor, $V_c$ is measured by an electronic voltmeter.

For carrying out the measurement, the unknown coil is connected to the test terminals of the instrument, and the circuit is tuned to resonance either by varying the frequency of the oscillator or by varying the resonating capacitor C.

Readings of voltages across capacitor C and shunt resistance $R_{sh}$ are obtained and Q-factor of the coil is determined as follows:

By definition Q-factor of the coil,

$Q=\frac{X_L}R$

And when the circuit is under resonance condition

${X_L}={X_C}$

And the voltage applied to the circuit

V=IR

So $Q=X_L/R=(IX_L)/R=V_C/V$

This Q-factor is called the circuit Q because this measurement includes the losses of the resonating capacitor, voltmeter and the shunt resistor $R_{sh}$. So, the actual Q-factor of the coil will be somewhat greater than the calculated Q-factor. This difference is usually very small and maybe neglected, except when the resistance of the coil under test is relatively small in comparison to the shunt resistance $R_{sh}$.

The inductance of the coil can also be computed from the known values of frequency f and resonating capacitor C as follows.

At resonance,

**$X_L=X_C$ OR $2πFL=\frac{1}2 πFC$ OR $L=\frac{1}{(2πF)^2} $**

**Sources of errors in Q-meter** –

At high frequencies, the electronic voltmeter may suffer from losses due to the transit time effect. The effect of shunt resistance is to introduce an additional resistance in the tank circuit, which can balance the meter, but only for certain period of time.

Distributed capacitance of self-capacitance of the measuring circuit may cause stray capacitances to enter the meter, which can affect the meter by modifying the actual Q and the inductance of the coil. It is the most significant source of error