Formula & Calculator
MOSFET Saturation Current
Models the drain current of a MOSFET operating in the saturation region.
Interpretation
MOSFET saturation current: I_D = ½k(V_GS − V_T)², valid when V_DS > V_GS − V_T.
The current depends on the square of the gate‑source overdrive voltage.
Example: k=2mA/V², V_GS=5V, V_T=1V → I_D = 0.5 × 2 × (5−1)² = 1 × 16 = 16mA.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| I_D | Drain current (in saturation region) | mA |
| k | Transconductance parameter (μₙ·Cₒₓ·W/L) | mA/V² |
| V_GS | Gate-to-source voltage | V |
| V_T | Threshold voltage | V |
| V_OV | Overdrive voltage = V_GS − V_T | V |
What it means
In the saturation region (V_DS > V_GS − V_T), the drain current of an n‑channel MOSFET is given by I_D = ½ k (V_GS − V_T)², where k = μ_n·C_ox·(W/L) is the transconductance parameter. This equation shows that the current depends on the square of the overdrive voltage (V_GS − V_T) and is independent of V_DS (ideally). Saturation is the region of operation for amplifiers, where the MOSFET acts as a voltage‑controlled current source. The transconductance g_m = 2I_D/(V_GS − V_T). This equation is used to design analog circuits, such as amplifiers and current mirrors. Example: With k=2mA/V², V_GS=5V, and V_T=1V, the overdrive is 4V. I_D = 0.5 * 2 * 4² = 1 * 16 = 16 mA. This is the drain current in saturation.
Worked example
MOSFET Saturation Current – Practical Example
Real‑World| Parameter | Value |
|---|---|
| k | 0.5 mA/V² |
| VT | 1 V |
| VGS | 3 V |
| Formula | ID = ½·k·(VGS − VT)² |
Common mistakes
- Parameter k: The transconductance parameter – depends on device geometry and process.
- Threshold voltage V_T: The gate voltage at which the channel starts to conduct.
- Overdrive: V_GS − V_T – must be positive for saturation.
- Condition: V_DS ≥ V_GS − V_T – otherwise in the linear region.
- Units: I_D in amperes.
Applications
MOSFET saturation current is I_D = ½k(V_GS − V_T)², valid in the saturation region. This square‑law equation is used to design analog circuits, such as amplifiers and current mirrors. Engineers use it to set bias currents, to design transconductance amplifiers, and to estimate gain. The overdrive voltage (V_GS − V_T) determines the drain current, making the MOSFET a voltage‑controlled current source. Understanding this formula is essential for CMOS analog design, where matched transistors and current sources are used. This equation is also the basis for many sensor and switch applications.
- Design of amplifiers, current mirrors, and differential pairs
- Bias circuit design for analog ICs
- Transconductance and gain calculations
- Voltage references and current sources
- Educational foundation of MOSFET operation
Frequently Asked Questions
For a MOSFET in saturation, the drain current is I_D = ½·k·(V_GS − V_T)², where k = µ₀C₀ₓ(W/L) and V_T is the threshold voltage. This is the square-law region.
Transconductance is the change in drain current per change in gate-source voltage: g_m = ∂I_D/∂V_GS = 2I_D/(V_GS − V_T) = √(2k I_D). It is a key small‑signal parameter for amplifier gain.
Transconductance is in siemens (S) or mhos. It is the ratio of current change (A) to voltage change (V).
g_m is proportional to √I_D (since I_D ∝ (V_GS−V_T)²). Increasing the bias current increases g_m, which improves gain.
g_m = √(2µ₀C₀ₓ (W/L) I_D). A larger W/L increases g_m for the same current, improving gain.
Common errors: 1) Using the formula for linear region (it applies only in saturation), 2) Forgetting that g_m depends on process parameters, 3) Using the formula without the factor of 2, 4) Confusing g_m with the output conductance g_ds, 5) Not accounting for body effect.
Used in: common‑source amplifier gain calculations, op‑amp design, RF circuits, current mirrors, and gain‑bandwidth product optimization.
Channel length modulation adds a factor (1 + λ V_DS) to the current, resulting in a finite output resistance. The modified equation is I_D = ½k (V_GS−V_T)² (1+λ V_DS).
For p-channel, the voltages are negative relative to source. The formula uses |V_GS| and |V_T| with appropriate signs. The transconductance is similar but with hole mobility instead of electron mobility.