---
title: "Transconductance gm of BJT"
subject: "Electronics Devices and Circuit"
chapter: 2
key: "semester_3/electronics_devices_and_circuit:bjt-transconductance-gm"
source: https://www.bctengineer.com/q/semester_3/electronics_devices_and_circuit/bjt-transconductance-gm
site: BCT Engineering
---

# Transconductance gm of BJT

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

- Asked in: 2074 Ashwin, 1+3 marks; 2069 Chaitra, 2+4 marks (asked 2 times)
- Video: [How to calculate the transconductance of BJT](https://www.youtube.com/watch?v=Kc2oG_LZZc8) — Signals Systems
- 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/bjt-transconductance-gm
- Whole chapter: https://www.bctengineer.com/md/semester_3/electronics_devices_and_circuit/chapter-2

## Question

Define transconductance (gm). Derive gm for BJT.

## Short answer

gm is ratio of change in collector current to change in VBE: gm = ∂iC/∂vBE. From iC = IS exp(vBE/VT), gm = IC/VT. At room temperature (VT = 25 mV), gm = 40 IC (e.g., 40 mA/V for IC = 1 mA).

## Answer

**Transconductance (gm)** is the ratio of the change in output (collector) current to the small change in input voltage (VBE) that causes it, at a fixed VCE. It measures how effectively the input voltage controls the output current: gm = ∂iC/∂vBE (units: A/V or S, mA/V).

#### Derivation for BJT
In the active region the collector current is
```text
iC = IS exp(vBE / VT)
```
Let vBE = VBE + vbe, where VBE is the dc bias and vbe the small signal:
```text
iC = IS exp(VBE/VT) · exp(vbe/VT) = IC exp(vbe/VT)
```
For vbe ≪ VT (about < 10 mV), exp(x) ≈ 1 + x:
```text
iC = IC (1 + vbe/VT) = IC + (IC/VT) vbe
```
The signal part is ic = (IC/VT) vbe, so
```text
gm = ic/vbe = ∂iC/∂vBE |at Q = IC / VT
```
Or by differentiation: gm = d/dvBE [IS exp(vBE/VT)] = iC/VT = IC/VT.

#### Remarks
- At room temperature VT = 25 mV, so gm = 40 IC; for IC = 1 mA, gm = 40 mA/V.
- gm is proportional to the dc collector current only (independent of the transistor's size).
- Related quantities: rπ = β/gm and re = α/gm ≈ 1/gm.
- Voltage gain of CE stage: Av = -gm RC.

## Check yourself

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

1. What is gm?
   A. VBE/IC
   B. IC/IB
   C. dIB/dVBE
   D. dIC/dVBE at fixed VCE
   Answer: D. Transconductance is the output current change per input voltage change. (Key point: Definition)

2. What is gm of a BJT?
   A. IC x VT
   B. VT/IC
   C. beta/VT
   D. IC/VT
   Answer: D. Differentiating IS exp(vBE/VT) gives IC/VT. (Key point: Result)

3. What is gm at IC = 1 mA, VT = 25 mV?
   A. 4 mA/V
   B. 400 mA/V
   C. 40 mA/V
   D. 25 mA/V
   Answer: C. gm = 1/25 mV = 40 mA/V. (Key point: Numbers)

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