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MOSFET Transconductance

Relates the change in drain current to the change in gate-source voltage for a MOSFET in saturation.

Written by the Vorzep Team

Semiconductor DevicesMOSFET

MOSFET Transconductance Calculator

gm = 2 ID / (VGS − VT)
Select the variable to solve for, then enter the other three values
gm ID VGS VT
Solve for:
Enter the other three values
S
A
V
V
g_m = 2I_D / (V_GS − V_T)
MOSFET Transconductance

Variables

SymbolQuantityUnit
g_mTransconductance (small-signal gain parameter)mS (mA/V)
I_DDrain current (DC bias in saturation)mA
V_GSGate-to-source voltageV
V_TThreshold voltageV
V_OVOverdrive voltage = V_GS − V_TV

What it means

The transconductance g_m of a MOSFET is defined as the change in drain current per change in gate‑source voltage, g_m = ∂I_D/∂V_GS. In saturation, g_m = 2I_D/(V_GS − V_T). It is a measure of the gain of the transistor when used as an amplifier. A higher g_m means better amplification for a given input voltage. It depends on the bias current and the overdrive voltage. The transconductance is a key parameter in analog circuit design, determining the voltage gain of common‑source and source‑follower stages. Example: For I_D = 10mA and overdrive voltage = 2V, g_m = 2*0.01/2 = 0.01 S (10 mS). If a 0.1V input signal is applied to the gate, the drain current will change by about 1mA, leading to voltage amplification when a load resistor is used.

Worked example

MOSFET Transconductance – Practical Example

Real‑World
Scenario: An NMOS has ID = 2 mA and VOV = 0.5 V. Find the transconductance gm.
ParameterValue
ID2 mA
VOV0.5 V
Formulagm = 2·ID / VOV
1gm = 2 × 2 mA / 0.5 V = 4 / 0.5 = 8 mA/V
Final Design gm = 8 mA/V ✓ Transconductance
Why: Transconductance relates the change in drain current to the change in gate‑source voltage – it is a key gain parameter for MOSFET amplifiers.

Common mistakes

  • Transconductance g_m: Relates drain current change to gate‑source voltage change.
  • Units: Siemens (S) – often mS.
  • Alternative: g_m = √(2·k·I_D).
  • Saturation: Valid only in the saturation region.
  • Frequency dependence: g_m decreases at high frequencies due to parasitic capacitances.

Applications

MOSFET transconductance g_m = 2I_D/(V_GS − V_T) measures the change in drain current for a change in gate voltage. It is a key parameter for amplifier gain, bandwidth, and noise performance. Engineers use it to design high‑gain amplifiers, to set the transconductance of operational amplifiers, and to optimise circuit speed. A higher g_m means better amplification. By adjusting the bias current and overdrive voltage, they can achieve the desired gain. This formula is central to analog IC design and is used in both discrete and integrated circuits.

  • CMOS amplifier gain and bandwidth design
  • Operational amplifier internal stage design
  • Transconductance‑capacitance (gm‑C) filter design
  • Noise and distortion analysis in analog circuits
  • Educational understanding of MOSFET amplification