---
title: "Ebers-Moll model"
subject: "Electronics Devices and Circuit"
chapter: 2
key: "semester_3/electronics_devices_and_circuit:ebers-moll-model"
source: https://www.bctengineer.com/q/semester_3/electronics_devices_and_circuit/ebers-moll-model
site: BCT Engineering
---

# Ebers-Moll model

Electronics Devices and Circuit · Chapter 2: The Bipolar Junction Transistor

- Asked in: 2082 Shrawan, 4 marks; 2079 Baisakh, 5 marks; 2078 Kartik, 3 marks; 2075 Chaitra, 4 marks; 2070 Chaitra, 4 marks (asked 5 times)
- Video: [Electronic Devices: BJT - Ebers Moll Model](https://www.youtube.com/watch?v=nnmN-eba8EQ) — techgurukula
- 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/ebers-moll-model
- Whole chapter: https://www.bctengineer.com/md/semester_3/electronics_devices_and_circuit/chapter-2

## Question

Explain Ebers-Moll model with necessary figure and mathematical expressions.

## Short answer

The Ebers-Moll model represents the BJT as two back-to-back diodes with coupled current sources. Terminal currents: IE = −IF + αR IR, IC = αF IF − IR, where IF = IES(e^VBE/VT − 1), IR = ICS(e^VBC/VT − 1), with αF IES = αR ICS = IS.

## Answer

The **Ebers-Moll (EM) model** is a large-signal model valid in all regions of operation (active, saturation, cut-off). It treats the BJT as two back-to-back diodes coupled by current sources, because each junction injects carriers that are collected by the other.

#### Equivalent circuit (injection version)
```text
  C o---+-----------+
        |           |
       ( ) αF·IF   DC | IR
        |           |
  B o---+-----------+
        |           |
       ( ) αR·IR   DE | IF
        |           |
  E o---+-----------+
```
- DE: base-emitter diode carrying IF; DC: base-collector diode carrying IR.
- A fraction αF of the emitter diode current IF reaches the collector (forward operation), and a fraction αR of IR reaches the emitter (reverse operation).

#### Equations
Diode currents:
```text
IF = IES [exp(VBE/VT) - 1]
IR = ICS [exp(VBC/VT) - 1]
```
Terminal currents:
```text
IE = -IF + αR IR
IC =  αF IF - IR
IB = -(IE + IC) = (1 - αF) IF + (1 - αR) IR
```
(with IE and IC taken as flowing into the transistor)

Reciprocity relation: αF IES = αR ICS = IS.

Written in terms of IS, the commonly used form is:
```text
IC = IS [exp(VBE/VT) - exp(VBC/VT)] - (IS/βR)[exp(VBC/VT) - 1]
```

#### Operating regions
- **Active:** BE forward, BC reverse: IC ≈ αF IF ≈ IS exp(VBE/VT).
- **Cut-off:** both junctions reverse biased: only small leakage currents flow.
- **Saturation:** both junctions forward biased: IC is reduced and VCE(sat) is about 0.2 V.
- **Reverse active:** BE reverse, BC forward, with βR much smaller than βF.

Typical values: αF = 0.98 to 0.998, αR = 0.02 to 0.5.

## Check yourself

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

1. For which operating regions is the Ebers-Moll model valid?
   A. Active only
   B. All regions: active, saturation, cut-off
   C. Saturation only
   D. Cut-off only
   Answer: B. It is a large-signal model for all regions. (Key point: Model validity)

2. How does the model represent the BJT?
   A. An op-amp
   B. Two capacitors
   C. A single resistor
   D. Two back-to-back diodes coupled by current sources
   Answer: D. Each junction injects carriers into the other, giving the coupled sources alpha_F I_F and alpha_R I_R. (Key point: Structure)

3. What is the expression for IC?
   A. IC = alpha_R IR - IF
   B. IC = IF - alpha_F IR
   C. IC = IF + IR
   D. IC = alpha_F IF - IR
   Answer: D. IC = alpha_F IF - IR (directed into the transistor). (Key point: Terminal currents)

4. Which relation holds?
   A. alpha_F + alpha_R = 1
   B. alpha_F = alpha_R
   C. IES = ICS
   D. alpha_F IES = alpha_R ICS = IS
   Answer: D. The reciprocity relation ties the diode saturation currents to IS. (Key point: Reciprocity)

## Related in Electronics Devices and Circuit

- [Ebers-Moll model and ac T-model of BJT](https://www.bctengineer.com/question.md?key=semester_3%2Felectronics_devices_and_circuit%3Aebers-moll-t-model) — Electronics Devices and Circuit, chapter 2, asked 2×
- [Ebers-Moll terminal currents; BJT configuration applications](https://www.bctengineer.com/question.md?key=semester_3%2Felectronics_devices_and_circuit%3Aebers-moll-terminal-currents-applications) — Electronics Devices and Circuit, chapter 2

## Related in other subjects

- [Static vs dynamic mathematical model](https://www.bctengineer.com/question.md?key=semester_8%2Fsimulation_and_modeling%3Astatic-vs-dynamic-math-model) — Simulation and Modeling, chapter 2, asked 3×
- [Dynamic mathematical model with example](https://www.bctengineer.com/question.md?key=semester_8%2Fsimulation_and_modeling%3Adynamic-mathematical-model) — Simulation and Modeling, chapter 2, asked 2×
- [Static mathematical model with example](https://www.bctengineer.com/question.md?key=semester_8%2Fsimulation_and_modeling%3Astatic-mathematical-model) — Simulation and Modeling, chapter 2