---
title: "EMOSFET principle, characteristics, ac model"
subject: "Electronics Devices and Circuit"
chapter: 3
key: "semester_3/electronics_devices_and_circuit:emosfet-working-ac-equivalent"
source: https://www.bctengineer.com/q/semester_3/electronics_devices_and_circuit/emosfet-working-ac-equivalent
site: BCT Engineering
---

# EMOSFET principle, characteristics, ac model

Electronics Devices and Circuit · Chapter 3: Field-Effect Transistor

- Asked in: 2068 Baisakh, 7 marks
- Video: [MOSFET - Enhancement Type MOSFET Explained (Construction, Working and Characteristics Explained)](https://www.youtube.com/watch?v=l9LBIy9Ioxo) — ALL ABOUT ELECTRONICS
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/electronics_devices_and_circuit/emosfet-working-ac-equivalent
- Whole chapter: https://www.bctengineer.com/md/semester_3/electronics_devices_and_circuit/chapter-3

## Question

Describe the principle of operation of EMOSFET with the help of IV characteristic curves and algebraic expressions. Also show its ac equivalent circuit model.

## Short answer

An n-channel EMOSFET creates an inversion layer when VGS exceeds threshold Vt. ID is zero below Vt, follows k(VGS−Vt)² in saturation and k[2(VGS−Vt)VDS−VDS²] in triode. AC model: open gate, current source gm·vgs from drain to source, gm=2k(VGSQ−Vt).

## Answer

An enhancement MOSFET (E-MOSFET) has no physical channel when VGS = 0. A channel is created (induced) by the gate voltage, and the drain current flows through that channel.

#### Structure and principle (n-channel)
```text
   S      G       D
   |      |       |
 [n+]--[oxide]--[n+]
 \_____ p-substrate _____/
```

- Two n+ regions (source, drain) are diffused into a p-type substrate. A thin SiO2 layer insulates the metal gate from the substrate.
- With VGS = 0 there are two back-to-back p-n junctions, so ID ≈ 0 (cut-off).
- When VGS is made positive, holes are repelled from beneath the gate and electrons are attracted. At VGS = Vt (threshold voltage) an n-type **inversion layer** forms and joins source to drain.
- A larger VGS gives more electrons, a deeper channel and so more current.
- With VGS > Vt and a small VDS, the channel acts as a resistor. As VDS increases, the channel near the drain narrows. At VDS = VGS − Vt the channel pinches off at the drain end and ID stops increasing.

#### Regions and algebraic expressions
| Region | Condition | Drain current |
|---|---|---|
| Cut-off | VGS < Vt | ID = 0 |
| Triode (ohmic) | VGS > Vt, VDS < VGS − Vt | ID = k [2(VGS − Vt) VDS − VDS²] |
| Saturation | VGS > Vt, VDS ≥ VGS − Vt | ID = k (VGS − Vt)² |

Here k = μn Cox W / (2L) is the device constant, found from data as k = ID(on)/(VGS(on) − Vt)².

#### IV characteristics
```text
 ID ^                          transfer curve
    |   VGS4 ------------      ID
    |   VGS3 ------------       |        /
    |  / VGS2 -----------       |      _/
    | /   VGS1 ----------       |   __/
    +----------------> VDS      +--+-----------> VGS
   (saturation to the right of       Vt
    the VDS = VGS - Vt boundary)
```

- Output curves: ID against VDS for several VGS values. They rise in the triode region and become almost flat (saturation) beyond VDS = VGS − Vt.
- Transfer curve: parabolic ID against VGS, starting at Vt.

#### AC equivalent circuit model
Small-signal parameters at the Q point:

- gm = ∂ID/∂VGS = 2k (VGSQ − Vt)
- ro = 1/(λ ID) (drain resistance, large)

```text
 G o---                     +----------+-----o D
        +                   |          |
       vgs  (open)    gm·vgs (↓)      [ro]
        -                   |          |
 S o------------------------+----------+-----o S
```

The gate-source path is an open circuit (infinite input resistance), and the drain-source path is a voltage-controlled current source gm·vgs (flowing from drain to source) in parallel with ro.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What happens at VGS = Vt in an n-channel E-MOSFET?
   A. An n-type inversion layer forms joining source and drain
   B. The channel is pinched off
   C. The substrate breaks down
   D. The gate conducts
   Answer: A. A positive gate repels holes and attracts electrons, forming an inversion channel at the threshold. (Key point: Channel induction)

2. The channel pinches off at the drain end when:
   A. VDS = VGS - Vt
   B. VDS = Vt
   C. VGS = 0
   D. VDS = 0
   Answer: A. At VDS = VGS - Vt pinch-off occurs and ID saturates as k(VGS-Vt)^2. (Key point: Saturation condition)

3. Which equation holds in the triode region?
   A. ID = k(VGS-Vt)^2
   B. ID = k[2(VGS-Vt)VDS - VDS^2]
   C. ID = 0
   D. ID = IDSS
   Answer: B. Triode (VDS < VGS - Vt) uses the k[2(VGS-Vt)VDS - VDS^2] form. (Key point: Region equations)

4. The ac model of the E-MOSFET consists of:
   A. Open gate-source, current source gm vgs in parallel with ro
   B. A resistor rπ at the gate
   C. A voltage source at the drain
   D. A diode
   Answer: A. The gate draws no current (open), and the drain path is gm*vgs in parallel with ro. (Key point: AC model)

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