Overview

• FETs are voltage-controlled semiconductor devices
• Terminals: Source (S), Gate (G), Drain (D), Body (B); in most circuits, the body is tied to the source
• The electric field from the gate voltage controls the current between drain and source

Types of FETs

• MOSFETs (Metal-Oxide Semiconductor FETs)
  • Most widely used.
  • PMOS: used in early designs.
  • NMOS: higher performance due to electron mobility.
  • CMOS: combines NMOS and PMOS for low power; dominant in digital circuits.
• JFETs (Junction FETs)
  • Used in analog circuits, op-amps, and RF designs.
  • Always depletion-mode.

MOSFETs

Characteristics

• Voltage-controlled, unipolar device.
• N-channel: electrons are carriers. P-channel: holes are carriers.
• Gate current ≈ 0 ($i_G = 0$).
• Body current ≈ 0 ($i_B = 0$).

Modes of Operation

1. Cutoff Region $v_{GS} \le V_{TN}$ ⇒ $i_D = 0$

2. Triode (Linear) Region $v_{GS} - V_{TN} > 0$ and $v_{GS} - V_{TN} > v_{DS}$ ⇒ $i_D = K_n[(v_{GS} - V_{TN})v_{DS} - \tfrac{v_{DS}^2}{2}]$

3. Saturation Region $v_{GS} - V_{TN} > 0$ and $v_{DS} > v_{GS} - V_{TN}$ ⇒ $i_D = \tfrac{K_n}{2}(v_{GS} - V_{TN})^2(1 + \lambda v_{DS})$

Where: $K_n = K_n' \tfrac{W}{L}$, $K_n' = \mu_n C_{ox}'$

Equivalent Circuit

Channel-Length Modulation

• When $v_{DS} > v_{DSAT}$, channel shortens by $\Delta L$.
• Current slightly increases instead of saturating. $i_D = \tfrac{K_n'}{2}\tfrac{W}{L}(v_{GS} - V_{TN})^2(1 + \lambda v_{DS})$
• $\lambda$ (channel length modulation parameter): $0 \le \lambda \le 0.2 \text{ V}^{-1}$
  • Usually $\lambda \approx 0$, so it is negligible

Transconductance ($g_m$)

• Defines how $i_D$ changes with $v_{GS}$:

• In triode region: $g_m = K_n v_{DS} = \frac{i_D}{v_{GS} - V_{TN} - \tfrac{v_{DS}}{2}}$
• In saturation region: $g_m = K_n (v_{GS} - V_{TN}) = \frac{2i_D}{v_{GS} - V_{TN}}$
• Larger $g_m$ → higher amplifier gain.
• $g_m$ is approximately twice as large in saturation as in triode.

Enhancement vs. Depletion MOSFETs

PMOS Transistors

• Built in n-type substrate with p-type source and drain.
• Requires $v_{GS} < V_{TP}$ (where $V_{TP} < 0$) for conduction.
• Follows similar I–V relationships as NMOS but with reversed polarities.

MOSFET as a Switch

• Off-state: $v_{GS} = 0$ → open circuit (cutoff region).
• On-state: $v_{GS} > V_{TN}$ → low $R_{DS}$ (triode region).
• Used in digital logic gates, such as CMOS inverters.

Biasing MOSFETs

Purpose

• To set a stable Q-point $(I_D, V_{DS}, V_{GS})$ for desired operation region.
• Bias defines the DC condition; signal varies around it. $v_{GS} = V_{GS} + v_{gs}$, $i_D = I_D + i_d$

Common Biasing Methods

Bias Equation: $V_{DD} = I_D R_D + V_{DS}$

Example: Q-point Verification

• Assume saturation: check if $V_{DS} > V_{GS} - V_{TN}$. If true, assumption correct.

• For channel-length modulation: $i_D = \tfrac{K_n}{2}(V_{GS} - V_{TN})^2(1 + \lambda V_{DS})$

Biasing Summary

JFETs

Structure and Operation

• Depletion-mode device only.
• Current controlled by gate–source voltage ($v_{GS}$) through the channel.
• Terminals: Gate (G), Source (S), Drain (D).
• High input impedance, low noise.

I–V Relationships

For n-channel JFET:

• Cutoff: $v_{GS} \le V_P$ ⇒ $i_D = 0$

• Triode region: $i_D = \tfrac{2I_{DSS}}{V_P^2}\left[(v_{GS} - V_P)v_{DS} - \tfrac{v_{DS}^2}{2}\right]$

• Saturation region (Pinch-off): $i_D = I_{DSS}\left(1 - \tfrac{v_{GS}}{V_P}\right)^2(1 + \lambda v_{DS})$

where

• $V_P$: pinch-off voltage
• $I_{DSS}$: drain current at $v_{GS} = 0$

Equivalent Circuit

• Same as MOSFET, but the dependent current source value is $i_{DSS} \left(\frac{V_{OD}}{V_{p}}\right)$ in pinch-off, where $V_{OD} \equiv V_{GS} - V_{p}$

Comparison: MOSFET vs. JFET

Key Equations Summary

• Triode Region: $i_D = K_n[(v_{GS} - V_{TN})v_{DS} - \tfrac{v_{DS}^2}{2}]$

• Saturation Region: $i_D = \tfrac{K_n}{2}(v_{GS} - V_{TN})^2(1 + \lambda v_{DS})$

• Transconductance: $g_m = \tfrac{2i_D}{v_{GS} - V_{TN}}$

• Bias Line: $V_{DD} = I_D R_D + V_{DS}$

References

• Course slides, chapter 4: Field-Effect Transistors
• Course slides, chapter 5: Bipolar Junction Transistors