Question:
Q factor of a tuned amplifier does not depend on:
Q factor of a tuned amplifier does not depend on:
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The \(Q\)-factor of a tuned tank circuit depends entirely on its passive component values (\(R\), \(L\), and \(C\)). It is independent of the active voltage gain parameters of the amplifier system.
Updated On: Jun 23, 2026
- Capacitance
- Gain
- Resistance
- Inductance
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The Correct Option is B
Solution and Explanation
Concept:
The Quality Factor (\(Q\)-factor) of a tuned amplifier measures its resonance sharpness and frequency selectivity. It represents the ratio of stored energy to dissipated energy per cycle within the amplifier's resonant tank circuit. A higher \(Q\)-factor indicates a narrower, more selective passband around the center resonant frequency (\(f_0\)), defined by the relation:
\[
Q = \frac{f_0}{\text{Bandwidth}}
\]
The resonant response is determined by the values of the passive components (resistors, inductors, and capacitors) that make up the tank circuit.
Step 1: Analyzing standard mathematical equations for the Q-factor.
Let us look at the mathematical expressions for standard tuned resonant circuit configurations:
• For a standard series resonant tank circuit, the \(Q\)-factor is calculated using the passive component values as: \[ Q = \frac{\omega_0 L}{R} = \frac{1}{\omega_0 C R} = \frac{1}{R}\sqrt{\frac{L}{C}} \]
• For a standard parallel resonant tank circuit, the operational expression is defined as: \[ Q = \frac{R}{\omega_0 L} = \omega_0 C R = R\sqrt{\frac{C}{L}} \] Where \(\omega_0 = \frac{1}{\sqrt{LC}}\) represents the angular resonant frequency, \(R\) is the internal circuit resistance, \(L\) is the circuit inductance, and \(C\) is the circuit capacitance.
Step 2: Checking the dependency parameters.
Looking closely at both expressions, the value of the \(Q\)-factor depends entirely on the passive component values:
• Circuit resistance (\(R\))
• Circuit inductance (\(L\))
• Circuit capacitance (\(C\)) While the \(Q\)-factor directly alters the overall shape and selectivity of the amplifier's frequency response curve, its value is independent of the active voltage gain parameters of the amplifier system. Therefore, the \(Q\)-factor does not depend on the system gain, which matches Option (B).
Step 1: Analyzing standard mathematical equations for the Q-factor.
Let us look at the mathematical expressions for standard tuned resonant circuit configurations:
• For a standard series resonant tank circuit, the \(Q\)-factor is calculated using the passive component values as: \[ Q = \frac{\omega_0 L}{R} = \frac{1}{\omega_0 C R} = \frac{1}{R}\sqrt{\frac{L}{C}} \]
• For a standard parallel resonant tank circuit, the operational expression is defined as: \[ Q = \frac{R}{\omega_0 L} = \omega_0 C R = R\sqrt{\frac{C}{L}} \] Where \(\omega_0 = \frac{1}{\sqrt{LC}}\) represents the angular resonant frequency, \(R\) is the internal circuit resistance, \(L\) is the circuit inductance, and \(C\) is the circuit capacitance.
Step 2: Checking the dependency parameters.
Looking closely at both expressions, the value of the \(Q\)-factor depends entirely on the passive component values:
• Circuit resistance (\(R\))
• Circuit inductance (\(L\))
• Circuit capacitance (\(C\)) While the \(Q\)-factor directly alters the overall shape and selectivity of the amplifier's frequency response curve, its value is independent of the active voltage gain parameters of the amplifier system. Therefore, the \(Q\)-factor does not depend on the system gain, which matches Option (B).
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