Question

A Q-meter works on the principle of:

• A. Mutual Induction
• B. Series Resonance
• C. Parallel Resonance
• D. Piezoelectric effect

Hint:

At series resonance, the voltage across the capacitor is \( Q \) times the input voltage: \( V_C = Q \cdot V_{\text{in}} \).
This voltage magnification effect is what makes direct \( Q \) measurements possible.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks to identify the fundamental operating principle of a Q-meter.
A Q-meter is an instrument designed to measure the Quality Factor (\( Q \)) of an inductor, as well as characteristics like self-capacitance, inductance, and dissipation factor of RF components.

Step 2: Key Formula or Approach:
The Q-meter is built using a series RLC circuit.
At the resonant frequency (\( f_0 \)), the inductive reactance (\( X_L \)) is equal to the capacitive reactance (\( X_C \)):
\[ X_L = X_C \implies \omega_0 L = \frac{1}{\omega_0 C} \] The total impedance of the circuit is purely resistive and is equal to the coil's internal resistance \( R \).
The voltage across the capacitor (\( V_C \)) at resonance is given by:
\[ V_C = I \cdot X_C = \left(\frac{V}{R}\right) \cdot X_C = V \cdot \left(\frac{X_C}{R}\right) = Q \cdot V \]

Step 3: Detailed Explanation:
The detailed operation of the Q-meter is explained below:

• Series Resonance Condition:
- A known, low-amplitude RF voltage \( V \) is injected into the series RLC circuit through a very low shunt resistance.
- The variable capacitor \( C \) of the Q-meter is tuned until the circuit reaches series resonance, which is indicated by the maximum voltage across the capacitor.

• Voltage Magnification:
- At resonance, the voltage across the capacitor (\( V_C \)) is magnified by a factor equal to the Quality Factor of the coil (\( Q \)):
\[ Q = \frac{V_C}{V} \] - Since the input voltage \( V \) is maintained at a constant, calibrated level, a high-impedance electronic voltmeter connected across the capacitor can be calibrated directly to read the \( Q \) value of the coil.

Step 4: Final Answer:
The operating principle of a Q-meter is based on the phenomenon of Series Resonance.