Stability in Feedback Amplifiers Explained | Loop Gain, Nyquist, Phase Margin & Compensation

Laplace Transform series (Parts 1–7): https://www.youtube.com/playlist?list=PLcbqD8G19W4AQ9Yq7AwUwszcjwYjCS-yv If you’re missing the math foundation behind transfer functions and frequency response, start here. This lecture explains stability in feedback amplifiers from a circuit designer’s perspective. We connect loop gain, Nyquist stability, phase margin, and frequency compensation to real analog design problems such as oscillation, bandwidth extension, and robust amplifier behavior across process and temperature variations. The goal is to develop physical intuition for why feedback systems become unstable and how practical analog circuits are stabilized in real silicon implementations. 0:00 Why Stability Is a Physical Problem (Not Just Math) 2:53 Closed-Loop Form and the Meaning of Loop Gain 4:01 The −1 Condition: When Feedback Reinforces Errors 6:15 Nyquist Intuition and the Encirclement Test 8:01 Pole Count Intuition: 1-Pole, 2-Pole, 3-Pole Systems 12:49 Gain Margin vs Phase Margin (What They Measure) 16:46 Practical Workflow: Overlay 1/β on Open-Loop Bode 23:32 Compensation Strategies and Trade-offs This lecture explains stability in feedback amplifiers from first principles, exactly the way practicing analog designers think about it. We begin by defining what stability actually means in a feedback system and why instability is a real design risk in high-gain amplifiers. Using the concept of loop gain, we show how instability arises when feedback reinforces internal signals rather than regulating them. The lecture then develops the key analytical tools used in analog design: • Physical interpretation of the condition L(jω) = −1 • Nyquist stability criterion and its geometric meaning • Why single-pole and two-pole amplifiers are unconditionally stable • Why three-pole systems become conditionally stable • Gain margin and phase margin using Bode plots • Relationship between phase margin and closed-loop peaking • Practical Bode-based stability analysis used in real design flows • Why and how frequency compensation is applied in multi-pole amplifiers Throughout the lecture, emphasis is placed on engineering intuition, not just mathematical rules. Real-world examples are used to explain why circuits that look stable in simulation can oscillate on the bench, and how designers ensure robust stability across process, voltage, and temperature variations. This lecture is suitable for: • Senior undergraduate students in electronics or electrical engineering • Early graduate students studying analog or mixed-signal design • Practicing engineers who want a clear, intuitive understanding of feedback stability Topics covered: Stability, feedback amplifiers, loop gain, Nyquist plot, Bode plot, gain margin, phase margin, root locus intuition, frequency compensation, analog circuit design fundamentals.