Transistor Transconductance

gm = Ic / VT

Quick answer

This calculator solves gm = Ic / VT for Transconductance. With Collector Current 20 mA, Thermal Voltage 0.6 V, the result is 33.33 mS. It solves in 3 directions, so you can enter the values you have and get the one you need.

Calculator

Transconductance (mS)
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Formula

gm = Ic / VT

Description

Transconductance measures how strongly a transistor’s output current responds to its input voltage. For a bipolar transistor it equals the collector current divided by the thermal voltage, so it is set purely by bias current. It is the core gain parameter of a stage: voltage gain equals gm times the load resistance, and it sets the bandwidth and noise of the amplifier.

Variables

  • gm — Transconductance (S = A/V)
  • Ic — Collector bias current (A)
  • VT — Thermal voltage (≈25–26 mV)

Practical Notes

At 1 mA, gm ≈ 38 mS. Unlike a FET, a BJT’s gm is set by current alone, giving very predictable gain. Voltage gain Av = −gm·RC.

Symbols and units

Symbol Meaning Default unit Accepted units
gm Transconductance mS µS, mS, S
Ic Collector Current mA pA, nA, µA, mA, A, kA
Vt Thermal Voltage mV pV, nV, µV, mV, V, kV

Step by step

  1. 1. What you know: Collector Current 20 mA, Thermal Voltage 0.6 V
  2. 2. The relation: gm = Ic / VT
  3. 3. Substitute: Ic = 20 mA, Vt = 0.6 V
  4. 4. Result: Transconductance = 33.33 mS

Related quantities from the same inputs

  • P = V × I = 12 mW

Worked examples

Minimum range

Given: Collector Current 100 µA, Thermal Voltage 10 mV

Result: Transconductance = 10 mS

Low range

Given: Collector Current 1 mA, Thermal Voltage 100 mV

Result: Transconductance = 10 mS

Typical

Given: Collector Current 20 mA, Thermal Voltage 0.6 V

Result: Transconductance = 33.33 mS

High range

Given: Collector Current 0.5 A, Thermal Voltage 0.9 V

Result: Transconductance = 0.5556 S

Maximum range

Given: Collector Current 5 A, Thermal Voltage 9 V

Result: Transconductance = 0.5556 S

Solving for each variable

Solve for Transconductance

Collector Current 100 µA, Thermal Voltage 10 mV → 10 mS

Solve for Collector Current

Transconductance 100 µS, Thermal Voltage 10 mV → 1 µA

Solve for Thermal Voltage

Transconductance 100 µS, Collector Current 100 µA → 1 V

How Transconductance changes with Collector Current

Collector Current (input) Transconductance (result)
2 mA 3.333 mS
5 mA 8.333 mS
10 mA 16.67 mS
15 mA 25 mS
20 mA 33.33 mS
30 mA 50 mS
40 mA 66.67 mS
80 mA 133.3 mS
140 mA 0.2333 S
0.2 A 0.3333 S

The same result in other units

Unit Value
µS 33330
mS 33.33
S 0.03333

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Frequently asked questions

How do you calculate Transistor Transconductance?

Use gm = Ic / VT. With Collector Current 20 mA, Thermal Voltage 0.6 V, Transconductance works out to 33.33 mS.

How do you calculate transistor thermal voltage vt?

Rearrange for Transconductance: with Collector Current 1 mA, Thermal Voltage 100 mV, Transconductance is 10 mS.

What is the formula for Transistor Transconductance?

The formula is gm = Ic / VT. Transconductance measures how strongly a transistor’s output current responds to its input voltage.

How do you find Collector Current when you know the other values?

Rearrange for Collector Current: with Transconductance 100 µS, Thermal Voltage 10 mV, Collector Current is 1 µA.

How do you find Thermal Voltage when you know the other values?

Rearrange for Thermal Voltage: with Transconductance 100 µS, Collector Current 100 µA, Thermal Voltage is 1 V.

What units does Transistor Transconductance use?

Transconductance is shown in µS, mS, S. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

Related Concepts

All Discrete Amplifiers formulas →
Thermal Voltage Small-Signal Emitter Resistance Transistor Transconductance Diode Dynamic Resistance Common-Emitter Voltage Gain BJT Alpha–Beta Relationship Darlington Pair Current Gain Emitter-Follower Input Impedance

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