Question Bank MCQ • 2 Marks Section 8: Electronics Operational Amplifiers & Analog Circuits

QB_PH_SEC8_007: Operational Amplifiers & Analog Circuits

Question Statement

According to the Barkhausen criterion for sustained oscillations in a feedback oscillator with open-loop gain $A$ and feedback factor $eta$, the loop gain magnitude and phase shift must satisfy
(A) $|A\beta| = 1$ and net phase shift around the loop is $0^\circ$ or an integer multiple of $360^\circ$
(B) $|A\beta| < 1$ and phase shift is $180^\circ$
(C) $|A\beta| \gg 1$ and phase shift is $90^\circ$
(D) $|A\beta| = 0$ and phase shift is arbitrary
Correct Answer
A
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Step-by-Step Derivation & Verification: 1. **Closed-Loop Transfer Function**: $A_f = \frac{A}{1 - A\beta}$. 2. **Condition for Non-Zero Output with Zero Input**: The denominator must vanish: $1 - A\beta = 0 \implies A\beta = 1$ 3. **Decomposition into Magnitude and Phase**: - $|A\beta| = 1$ - $\angle(A\beta) = 2\pi n \quad (n = 0, 1, 2, \dots)$ 4. **Conclusion**: Magnitude equals 1 and phase is $0^\circ$ or $360^\circ$. Option (A) is correct.
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