Library / Circuits, electronics and noise / ELN-23
Circuits, electronics and noise
MOSFET transconductance from overdrive voltage
Small-signal transconductance of a square-law MOSFET in saturation, from its quiescent drain current and overdrive voltage Vov = Vgs − Vth.
- Ref
- ELN-23
- Rev
- v1
- Field
- Circuits, electronics and noise
- Result
- gm [S]
For a square-law MOSFET in saturation, gm = dId/dVgs = k Vov. Using Id = ½k Vov² to remove k gives gm = 2Id/Vov. For a given current, a lower overdrive voltage gives a higher transconductance (a wider, more efficient transistor) at the price of less voltage headroom and lower speed. This holds locally with the drain voltage fixed.
Small-signal transconductance of a square-law MOSFET in saturation, from its quiescent drain current and overdrive voltage Vov = Vgs − Vth. It holds locally with the drain voltage fixed.
Calculator
- Equivalent k, 2Id/Vov²0.002 A/V²
- Transconductance efficiency, gm/Id1 1/V
- Intrinsic source resistance, 1/gm250 Ω
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- At 0.004 A and an overdrive of 2 V the transconductance is 0.004 S, which is 1 per volt of current gm/Id.
- Halving the overdrive to 1 V at the same current doubles gm to 0.008 S.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (S) | Local step | Change in result |
|---|---|---|---|---|---|---|
| ID Quiescent drain current | 1e-5 to 0.1 A | 1e-5 | 0.1 | 0.09999 | +10% | +10 % |
| Vov Overdrive voltage | 0.1 to 5 V | 0.0016 | 0.08 | 0.0784 | +10% | −9.09 % |
Sweep of Overdrive voltage
| Overdrive voltage (V) | Transconductance (S) |
|---|---|
| 0.1 | 0.08 |
| 0.7125 | 0.01123 |
| 1.325 | 0.006038 |
| 1.938 | 0.004129 |
| 2.55 | 0.003137 |
| 3.163 | 0.00253 |
| 3.775 | 0.002119 |
| 4.388 | 0.001823 |
| 5 | 0.0016 |
Sweep one variable
Variables and how each one contributes
Transconductance
What the equation gives you. Everything else feeds it.
Quiescent drain current
The quiescent drain current, in A. Raises gm in direct proportion. Raising it by 10 % (to 0.0044) moves the result by +10 %, from 0.004 to 0.0044 S.
Overdrive voltage
The overdrive voltage Vgs − Vth, in V. A larger overdrive lowers gm at the same current, in inverse proportion. Raising it by 10 % (to 2.2) moves the result by −9.09 %, from 0.004 to 0.003636 S.
Worked example with the values above
- Double the current: 2Id = 0.008 A.
- Divide by the overdrive: 0.008 / 2.
- gm = 0.004 S.
Assumptions and limits
- A long-channel NMOS device in strong inversion and the square-law model.
- Triode and saturation formulas used only in their stated regions, and body effect ignored.
Common mistakes
- Using the triode formula when Vds is above Vgs − Vth, or the saturation formula when it is below.
- Forgetting that k here has no factor of one half in the triode formula.
- Applying the saturation gm formula to a device in weak inversion or velocity saturation.
Statistics and uncertainty
Real transistors depart from the square-law model, especially at short channel lengths, where velocity saturation changes the current dependence. The threshold voltage varies from part to part, so results with small overdrive are very sensitive to it.
Where it is used
- Bias and gain estimates for MOSFET amplifiers, switches and current sources.
- Quick checks of simulation results by hand.
Maths you need
- MOSFET regions: cut-off, triode and saturation
- Overdrive voltage: Vov = Vgs − Vth
- Small-signal model: gm and ro at a bias point