Lecture 34: Electronic Circuits 1 - Large Signal and Small Signal Models of MOS Devices

Introduction

• Instructor: Bass Audra Savvy
• Focus: Continuing development of large signal and small signal models for MOS devices in circuit analysis.

Recap of Lecture 33

• Key Concept: Incrementing the gate-source voltage (Vgs) by Delta V results in an increment of drain current (Id) by Gm * Delta V, where Gm is the transconductance.
• Simplified circuit representation removes the battery to focus on variations caused by input signals.

Small Signal Model vs. Large Signal Model

• Small Signal Model: Only considers variations (changes) in signals (voltages, currents) caused by input signals.
• Large Signal Model: Represents the full characteristics of the MOS device, including the bias conditions.
• **Key Relationships:
  • Large Signal Model:
    • Id = (1/2) * μ_n * Cox * (W/L) * (Vgs - Vth)^2 (including channel length modulation)
  • Small Signal Model:
    • ΔId = Gm * ΔVgs
    • Often expressed as Id = Gm * V1 (small signal voltage representation)

Circuit Analysis Approach

1. Bias Calculation: Use the large signal model to determine bias conditions.
2. Signal Analysis: Apply small signal variations and analyze the effects using the small signal model.
3. Constant Sources:
   • Voltage sources: In small signal analysis, constant voltage sources become short circuits (zero voltage).
   • Current sources: Constant current sources become open circuits (zero current).

Example Circuit Analysis

• Example circuit includes a microphone, batteries, and MOS devices.
• Constructing the small signal model:
  • Microphone as a small AC voltage source.
  • Batteries replaced by short circuits.
  • MOS devices represented with their small signal models.

Channel Length Modulation

• Discussion on how channel length modulation affects small signal models.
• Incrementing Vds (drain-source voltage) impacts Id (drain current).
• Procedure for constructing small signal models:
  1. Apply bias voltages to the device.
  2. Increment one voltage at a time and measure changes in current.
  3. Model the changes using proper circuit elements (current sources, resistors).

Constructing the Small Signal Model for MOSFET

• Initial Increment: Incrementing Vgs leads to changes in Id due to Gm.
• Second Increment: Incrementing Vds leads to changes in Id due to channel length modulation.
• Final small signal model captures both Gm and output resistance (Ro).

P-MOS Device

• Introduction to P-MOS devices:
  • Structure: P-type substrate, N+ regions for source and drain.
  • Operation: Gate must be negative with respect to source, and drain must be more negative than the source.
• Large Signal Model:
  • Similar to N-MOS but involves negative voltages.
  • Id = - (1/2) * μ_p * Cox * (W/L) * (Vgs - Vth)^2 (including channel length modulation).

Small Signal Model for P-MOS

• Model is identical to N-MOS model:
  • Small signal parameters are the same; only the orientation of the device changes.
• Importance of understanding both N-MOS and P-MOS devices in CMOS technology.

Example Summary

• Small signal model includes microphone as a small signal voltage source and simplifies complex circuits by identifying equivalent voltages and currents.
• Encouragement to simplify circuits before applying detailed analysis.

Conclusion

• Reminder to practice and internalize the small signal and large signal models for both N-MOS and P-MOS devices.