MOSFET Transconductance (gm)
Transconductance gm is the rate at which the drain current changes with respect to the gate-source voltage:
gm = ∂ID / ∂VGS
1. Linear (Triode) Region
Condition:
VDS < VGS − VT
Drain Current:
ID =
μnCox(W/L)
[(VGS − VT)VDS
− VDS2/2]
Taking derivative with respect to VGS:
gm =
μnCox(W/L)VDS
Let:
kn = μnCox(W/L)
Then:
gm = knVDS
In the linear region, transconductance is directly proportional to VDS.
2. Saturation Region
Condition:
VDS ≥ VGS − VT
Drain Current:
ID =
(1/2)kn(VGS − VT)2
Taking derivative with respect to VGS:
gm =
kn(VGS − VT)
Alternative forms:
gm =
2ID / (VGS − VT)
gm =
√(2knID)
Summary
| Region | Drain Current (ID) | Transconductance (gm) |
|---|---|---|
| Linear (Triode) | kn[(VGS−VT)VDS − VDS2/2] | gm = knVDS |
| Saturation | (1/2)kn(VGS−VT)2 | gm = kn(VGS−VT) |
Summary
Linear Region: gm depends on VDS
Saturation Region: gm depends on the overdrive voltage
VOV = VGS − VT