BJT Widlar Current Source (3): Output Resistance

BJT Widlar Current Source (3): Output Resistance

by Vincent Chang

Formal & Physical Sciences Engineering & Technology TJFElectronics engineeringTJFCElectronics: circuits and components
🎙 Vincent Chang 👥 2K 📅 November 4, 2020 ⏱ 16 min 👁 2K 📄 tutorial 🧭 2026-08-17
Available in: English (current) Français

Keywords

Widlar current sourceoutput resistanceBJTsmall-signal modelhybrid-pi model

Summary

This lecture video, part of a series on analog integrated circuit design, focuses on the output resistance of the BJT Widlar current source. The instructor begins by contrasting the basic current mirror with the Widlar mirror, highlighting the addition of emitter resistance. He emphasizes the need for AC analysis even for a DC current source, explaining that real current sources are not ideal and their output resistance is a measure of their quality. The core of the lecture is a detailed derivation of the output resistance using the hybrid-pi small-signal model, showing that the intuitive answer (ro + re) is incorrect because it neglects the effects of r_pi and the voltage-controlled current source. The derived expression shows that the output resistance is significantly enhanced, typically by a factor of thousands, due to the feedback introduced by the emitter resistance. The instructor then presents simulation results, demonstrating the output characteristic and highlighting key takeaways: the minimum voltage for proper operation, the suitability for low-current IC design, and the need to reconcile simulation with hand analysis. The lecture concludes with homework assignments to reinforce the concepts.

184 words

Critical Evaluation

Value of the Information & Strength of the Argument

The video provides high educational value by thoroughly explaining the derivation of the output resistance, correcting common misconceptions, and reinforcing the importance of small-signal analysis. The argumentation is solid, as the instructor systematically builds from the circuit schematic to the small-signal model, applies circuit laws, and arrives at a precise expression. He also validates the theory with simulation results, which strengthens the credibility of the explanation. The step-by-step approach makes the content accessible to students with a background in electronics.

Scientific Rigor, Source Quality, Title Accuracy

The scientific rigor is high: the derivation is mathematically sound and the simulation results are consistent with the theoretical analysis. The instructor does not cite external sources, but the content is based on established textbook material in analog IC design. The title accurately reflects the content, and the video is well-structured with clear learning objectives. The instructor’s credentials (Ph.D. in Electrical Engineering, 30 years of teaching experience) add to the reliability of the content.

169 words

Title / Content Match

The title accurately reflects the content, which focuses on the output resistance of the BJT Widlar current source.

Quality & Reliability

8/10

The video is a lecture by an experienced professor (30 years in semiconductor education) and provides a rigorous derivation of the output resistance of the Widlar current source, including the small-signal model and simulation results. The content is technically accurate and well-structured, though it lacks citations to external sources.

Key Moments

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

Contribution & Novelties

The video provides a clear and detailed derivation of the output resistance of the Widlar current source, correcting a common intuitive mistake and highlighting the significant enhancement due to the emitter resistance. It bridges theory with simulation, offering practical insights for IC design.

Pour aller plus loin :

  • Widlar current source — Wikipedia article providing background and context.
  • Hybrid-pi model — Wikipedia article on the small-signal model used in the derivation.
  • Early effect — Wikipedia article explaining the Early voltage, which is key to the output resistance.

87 words

Radar Profile

The radar profile shows high scores across all dimensions, indicating a well-balanced and reliable educational video. The strong technical depth and clear explanation make it a valuable resource for students and engineers.

Reliability 8/10