Stability of Feedback (3): Problem-Solving

Stability of Feedback (3): Problem-Solving

by Vincent Chang

Formal & Physical Sciences Control & Robotics TJFElectronics engineeringTJFMAutomatic control engineering
🎙 Vincent Chang 👥 2K 📅 November 19, 2020 ⏱ 10 min 👁 129 📄 tutorial 🧭 2026-08-17
Available in: English (current) Français

Keywords

stabilityfeedbackloop gainphase margincritical beta

Summary

This lecture, part of a series on feedback stability, focuses on solving a specific problem to determine the maximum allowable feedback factor (beta) for a three-pole amplifier to remain stable. The instructor, Vincent Chang, begins by reviewing the conditions for instability: the presence of feedback and frequency-dependent behavior in the open-loop gain or feedback network. He emphasizes the importance of the loop gain’s magnitude and phase, particularly at the frequency where the phase reaches -180 degrees (F_pi). Two equivalent stability criteria are presented: one based on the magnitude at F_pi (must be less than 1 for stability) and another based on the phase at the unity-gain frequency (must be less than 180 degrees). The problem involves a resistive feedback network (constant beta) and an open-loop gain with three poles, two of which are at 10^4 rad/s, and a DC gain of 10^6 (120 dB). The solution involves deriving the phase expression, finding the frequency where the phase is -180 degrees, and then calculating the loop gain magnitude at that frequency to solve for the critical beta. The result is a critical beta of 0.02, meaning the feedback factor must be less than this value to avoid oscillation. The instructor concludes by noting that if phase or gain margin requirements are added, the allowable beta becomes even smaller.

217 words

Critical Evaluation

Value of the Information & Strength of the Argument

The video provides a valuable worked example that bridges theory and practice, demonstrating how to apply the stability criteria to a realistic amplifier model. The argumentation is logical and step-by-step, with clear explanations of each mathematical manipulation. The instructor effectively reinforces the key concepts from previous lectures and shows how to use them in problem-solving. The value lies in the practical application of stability analysis, which is essential for circuit designers. The argumentation is solid, though it could benefit from a more formal derivation and discussion of assumptions.

Scientific Rigor, Source Quality, Title Accuracy

The scientific rigor is adequate for an educational tutorial. The instructor correctly applies standard control theory concepts (Bode plots, phase margin) and the math is accurate. However, no external sources are cited, and the presentation is informal, with occasional verbal fillers. The title accurately reflects the content, which is a problem-solving session on feedback stability. The video is part of a structured course, and the instructor’s credentials (Ph.D. in EE, 30 years of teaching) lend credibility. The lack of citations is a minor weakness, but the content is based on well-established principles.

195 words

Title / Content Match

The title accurately reflects the content, which focuses on solving a stability problem for a feedback amplifier.

Quality & Reliability

7/10

The content is a clear, step-by-step tutorial on feedback stability analysis, based on established control theory. The instructor demonstrates a systematic approach to solving a specific problem, but the video lacks explicit citations to sources or references, and the presentation is somewhat informal.

Key Moments

Markers derived by PSI from the transcript: the creator did not define chapters.

Contribution & Novelties

This video provides a clear, worked example of stability analysis for a feedback amplifier, which is a common but non-trivial problem in analog circuit design. The instructor’s step-by-step approach helps demystify the process and reinforces the theoretical concepts. The novelty lies in the pedagogical presentation, not in new research findings.

Pour aller plus loin :

  • Bode plot — Essential tool for frequency response analysis.
  • Phase margin — Key stability metric discussed in the video.
  • Control theory — Broader context for feedback systems.

82 words

Radar Profile

The radar profile shows a balanced performance across all dimensions, with slightly higher scores in technical level and information quality, reflecting the video's focus on a specific technical problem. The lower score in information quantity is due to the short duration and narrow scope.

Reliability 7/10