Mumbai University > Electronics Engineering > Sem3 > Electronic Instruments and Measurements

Marks: 10M

Year: Dec 2014

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 LorC 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

$$V=IR \\ SoQ=\frac{X_L}{R}=\frac{IX_L}{R}=\frac{V_C}{V}$$

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.

Atresonance,

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