What is the formula for MOSFET Drain Current (Saturation)?

The MOSFET Drain Current (Saturation) formula is Id = K × (Vgs − Vth)² (K = ½·µ·Cox·W/L), where Id—Drain current (A); K—Conduction parameter ½µCox(W/L) (A/V²); Vgs—Gate-source voltage (V); Vth—Threshold voltage (V).

MOSFET Drain Current (Saturation)

Q: How do you calculate MOSFET Drain Current (Saturation)?

Use the formula Id = K × (Vgs − Vth)² (K = ½·µ·Cox·W/L). In saturation an enhancement MOSFET’s drain current follows a square law in the gate overdrive (Vgs minus threshold). Enter the values you know in the calculator above and it solves for the remaining variable.

Id = K · (Vgs − Vth)²

Calculator

Drain Current

Conduction Parameter

Gate-Source Voltage

Threshold Voltage

Result

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Formula

Id = K × (Vgs − Vth)² (K = ½·µ·Cox·W/L)

Description

In saturation an enhancement MOSFET’s drain current follows a square law in the gate overdrive (Vgs minus threshold). The conduction parameter K bundles the carrier mobility, oxide capacitance, and the width-to-length ratio of the channel. This is the design equation for biasing MOSFET amplifier and current-source stages and for sizing switches.

Variables

Id — Drain current (A)
K — Conduction parameter ½µCox(W/L) (A/V²)
Vgs — Gate-source voltage (V)
Vth — Threshold voltage (V)

Practical Notes

Valid only above threshold and in saturation (Vds > Vgs − Vth). Transconductance gm = 2·K·(Vgs − Vth) = 2·√(K·Id), so gm grows with bias current—unlike a BJT’s linear gm.

Related Concepts

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