The Q meter is an instrument designed to measure some electrical properties of coils and capacitors.

The principle of the Q meter is based on series resonance –

The voltage drop across the coil or capacitor is Q times the applied voltage (where Q is the ratio of reactance to resistance, XL/R).

If a fixed voltage is applied to the circuit, a voltmeter across the capacitor can be calibrated to read Q directly.

Some of the applications of Q meter are as follows:

1. Impedance measurement using Q meter
2. Characteristic impedance measurement of transmission line using Q meter

Impedance measurement using Q meter:

Unknown impedance can be measured using a Q meter, either by series or shunt substitution method. If the impedance to be measured is small, the former (series substitution) is used and if it is large the latter (shunt substitution) method is used.

In the Q meter method of measurement of Z (impedance), the unknown impedance Zx is determined by individually determining its components RX and LX. The technique utilizes an LC tank of a Q meter. L is externally connected standard coil. Figure (a) shows the method of series substitution while Figure (b) shows the shunt substitution method.

Referring to Figure(a),

• The unknown impedance is shorted or otherwise not connected and the tuned circuit is adjusted for resonance at the oscillator frequency.
• The value of Q and C are noted.

• The unknown impedance is then connected, the capacitor is varied for resonance, and new values Q’ and C’ are noted.

   

$From \ part \ 1, we \ have\ \omega L=1/\omega C ----- (1)$

$From\ part\ 2, we\ have\ \omega L + X_x = 1/ \omega C’ -----(2)$

Subtracting Eq. (1) from Eq. (2), we get

$X-x= \dfrac{1}{\omega C’} -\dfrac{1}{ \omega C} \\[4ex]X-x= \dfrac{1}{ \omega C} \left ( \dfrac {C-C'}{C'} \right )\\[4ex]X-x= \dfrac{1}{ \omega} \left ( \dfrac {C-C'}{CC'} \right)$

Since R’=R + Rx

∴Rx=R'- R where R is the resistance of the auxillary coil.

$\therefore R_x= R’ – R= \dfrac{\omega L}{Q’}-\dfrac{\omega L}{Q}\\[3ex] \ \ \ \ R_x= \omega L \left ( \dfrac {Q-Q'}{QQ'} \right)$

• The unknown impedance ZX can be calculated from the equationZX=RX + j XX
• A positive value of XX indicates inductive reactance and a negative value indicates capacitive reactance.

If ZX is considerably greater than XL, the unknown impedance is shunted across the coil and the capacitor, as shown in Figure (b).

• YX represents the shunt admittance of the unknown impedance. It consists of two shunt elements, conductanceGX and susceptanceBX.
• In this method, YX is disconnected and the capacitor C is tuned to the resonant value.
• At the oscillator frequency, the values of Q and C are noted.
• WithYX connected, the capacitor is tuned again for resonance at the oscillator frequency and the new values Q' and C' are noted.

$Hence \ Y_x = G_x+ jB_{x}$

$and \ B_x=\omega C- \omega C'$

$also\ G_x = \dfrac{1}{ \omega L} \left ( \dfrac {Q-Q'}{QQ'} \right)$

$\therefore Y_x = \dfrac{1}{ \omega L} \left ( \dfrac {Q-Q'}{QQ'} \right) \\[3ex] \ \ \ \ Y_x= j \omega (C-C')$

The accuracy with which the reactance can be determined by the method of substitution is quite high. Error may mainly be because

1. C' cannot be accurately determined since the resonance curve may be flat due to additional resistance and,

2. The stray inductance associated with the tuning capacitor causes errors at VHF.

    

The accuracy with which the resistance component of the unknown impedance is obtained is poor. If the losses in the unknown impedance are too small to introduce any change in the Q, the substitution method is quite satisfactory. The substitution method can also be used for measuring the losses of the coil. It is not satisfactory for measuring the losses of an air-dielectric capacitor, since they are too small to be detected by this method.

Measurement of Characteristic impedance (Z0) of a Transmission line using Q meter:

Figure (c) shows a series substitution method for determining the characteristic impedance of a transmission line and figure (d) shows a shunt or parallel method of substitution for the same purpose.

In Figure (c), the transmission line or cable under test is tuned for series resonance. Since the input impedance is low, the method of series substitution can be used to determine Z0 = R0 +jX0 for the transmission line, as explained above. The reactance/unit length of the line is the total reactance divided by the length L. Series resonance occurs when the line is short-circuited and the line length is an even multiple of a ƛ/4 and when open-circuited an odd multiple of ƛ/4.

Parallel resonance occurs when the line is short-circuited and the length is an odd multiple of ƛ/4, or open-circuited it is an even multiple of ƛ/4. (ƛ=lambda)