MOSFET Small-Signal Model (2): Output Resistance & Body Transconductance

MOSFET Small-Signal Model (2): Output Resistance & Body Transconductance

by Vincent Chang

Formal & Physical Sciences Engineering & Technology TJFElectronics engineeringTJFDElectronic devices and materials
🎙 Vincent Chang 👥 2K 📅 February 10, 2021 ⏱ 19 min 👁 731 📄 tutorial 🧭 2026-08-17
Available in: English (current) Français

Keywords

MOSFETsmall-signal modeloutput resistancebody transconductancechannel length modulation

Summary

This lecture, part of a series on MOSFET small-signal models, extends the first-order model to include second-order effects: channel length modulation and body effect. The instructor, Vincent Chang, begins by reviewing the first-order model (transconductance gm) and then introduces channel length modulation, which causes the drain current to increase with drain-source voltage in saturation. This leads to the definition of output resistance r0, derived as the partial derivative of drain current with respect to drain-source voltage, yielding r0 = VA/ID (or 1/(λID)). The second part of the lecture addresses the body effect, where the threshold voltage depends on the source-body voltage. This gives rise to a body transconductance gmb, which quantifies the influence of the body voltage on the drain current. The derivation uses the chain rule and introduces a parameter χ (chi) that relates gmb to gm, with typical values of 0.1-0.3. The lecture concludes with a summary of the extended small-signal model including gm, r0, and gmb.

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Critical Evaluation

Value of the Information & Strength of the Argument

The video provides a clear and structured explanation of the second-order MOSFET small-signal model. The instructor uses a step-by-step approach, starting from the large-signal equations and deriving the small-signal parameters through partial derivatives. The argumentation is solid, with each step logically following from the previous one. The use of intuitive explanations, such as the ‘front door’ and ‘back door’ analogy for the gate and body, helps in understanding the concept of transconductance. The derivation of output resistance and body transconductance is mathematically rigorous and consistent with standard textbooks. The instructor also emphasizes the physical meaning behind the equations, which adds value to the learning experience.

Scientific Rigor, Source Quality, Title Accuracy

The scientific rigor is high, as the content aligns with established semiconductor physics. The instructor does not cite specific sources, but the material is standard in microelectronics education. The title accurately reflects the content, which is focused on the two second-order effects. The video is a tutorial, and the instructor’s credentials lend credibility to the presentation. However, the lack of references to external sources or textbooks may be a minor limitation for those seeking further reading.

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Title / Content Match

The title accurately reflects the content, which focuses on the second-order small-signal model of MOSFETs, specifically output resistance and body transconductance.

Quality & Reliability

8/10

The instructor has a Ph.D. in Electrical Engineering and 30 years of teaching experience. The content is technically accurate and follows standard textbook derivations. However, the video lacks citations to specific sources, and the presentation is somewhat informal with verbal fillers.

Key Moments

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

Contribution & Novelties

The video provides a clear and systematic derivation of the second-order MOSFET small-signal model, specifically focusing on output resistance and body transconductance. It bridges the gap between first-order and higher-order models, making it a valuable resource for students and engineers. The use of intuitive analogies and step-by-step derivations enhances understanding.

Pour aller plus loin :

114 words

Radar Profile

The radar profile shows high scores in quality of information, technical level, and reliability, with a slightly lower score in quantity of information due to the focused scope. This indicates a technically rigorous and reliable tutorial, though it may not cover a broad range of topics.

Reliability 8/10