Negative feedback stability: For an amplifier with loop gain Aβ, which value of |Aβ| among the given choices yields the most stable closed-loop operation (largest stability margins)?

Introduction / Context:Stability of feedback amplifiers depends on the loop gain magnitude |Aβ| and loop phase. As the Nyquist/Bode criteria indicate, getting too close to the critical point (|Aβ| = 1 with −180° phase) risks oscillation. This question checks conceptual understanding of how loop-gain magnitude influences robustness.

Given Data / Assumptions:

• Negative feedback is used.
• We compare only the magnitudes |Aβ| at the frequency where phase lag approaches −180°.
• Other factors (phase margin, pole locations) are comparable.

Concept / Approach:

Greater stability margin occurs when the locus stays farther from the critical point. Therefore, for similar phase conditions, a smaller |Aβ| provides larger gain margin and usually better phase margin.

Step-by-Step Solution:

Verification / Alternative check:

Bode plot reasoning: with the unity-gain crossover well below the −180° phase point, phase margin is increased; reducing |Aβ| helps achieve that condition.

Why Other Options Are Wrong:

• 0.95: closer to unity → smaller margins.
• 1.20 and 1.50: loop magnitude > 1 at critical phase → risk of oscillation.
• Exactly 1.00: marginal stability.

Common Pitfalls:

• Assuming larger |Aβ| always improves performance; it improves accuracy but can harm stability if phase margin is limited.

Final Answer:

0.70.