Q - factor - Engineering Notes

Q - factor:

• 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 like self inductance, self capacitance and resistance. 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 Q times of the applied voltage to 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 direct connection of Q meter is shown in the below figure.

 

Q - meter circuit diagram

• A wide range of 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, Rsh usually of the order of 0.02 ohm. So it introduces almost no resistance into the oscillatory circuit and represents a voltage across the low value shunt resistance Rsh, V is measured by a thermo - couple meter and the voltage across the capacitor, Vc is measured by an electronic voltmeter.
• For carrying the measurement, the unknown coil is connected to the test terminals of the instrument, and the circuit is turned 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 Rsh are obtained and Q - factor of the coil is determined as follows:
• By definition Q factor of the coil  is given by, Q = XL / R
• And when the circuit is under resonance condition XL = XC then Q = XC / R = Q. Vin where Q is known as magnification factor. Q = VC / Vin
• This relation is used to calibrate the volt scale of capacitor voltmeter into Q scale.
• This Q factor is called the circuit Q because this measurement includes distributed capacitance of coil, shunt resistor Rsh. So, the calculated Q - factor of the coil will be somewhat less than the actual Q - factor.
• There are two more connections of Q meter namely series connection and shunt connection as given below.

Series connection of Q - factor:

In this method the unknown test impedance is connected in series with the reference coil. This method is employed for measurement of low test impedance i.e, low value resistors, small coils and large capacitors.

At resonance, 

w.L = 1 / w.C1 and  Q1 = w.L / R = 1 / w.C1.R

Xs = (C1 - C2) / w.C1.C2

Rs = (Q1.C1 - Q2.C2) / w.C1.C2.Q1.Q2

Qx = Xs / Rs = (C1 - C2). Q1.Q2 / ( Q1.C1 - Q2.C2)

Series connection of Q factor

Parallel Connection of Q - factor : 

In this connection the unknown test impedance is connected in parallel to the tuning capacitor. This method is employed for measurement of high impedance i.e, high value resistors, certain inductors and small capacitors.

1 / RP = w.C1 / Q2 = 1 / R.Q1

XP = 1 / w(C2 - C1)

Qx = RP / XP = (C1 - C2). Q1. Q2 / (Q1.C1 - Q2.C2)

Parallel connection of Q factor

The main error in the measurement of Q is due to distributed or stray capacitance of the circuitary. To check for this, the Q is measured at two frequencies f1 and 2f1. It should be same if not,

Cd = (C1 - C1.C2) / 3