MOSFET regions of operation

A MOSFET sits in one of three regions depending on its terminal voltages. Each region has its own note; this one ties them together.

Region	Condition	Behaviour
Cut-off	$V_{GS}<V_t$	No channel, $i_D=0$. Device off.
Triode	$V_{GS}>V_t$ and $V_{DS}<V_{OV}$	Channel formed end-to-end. Gate-controlled resistor.
Saturation	$V_{GS}>V_t$ and $V_{DS}\ge V_{OV}$	Channel pinched at drain. Voltage-controlled current source, used for amplification.

Here $V_t$ is the Threshold voltage and $V_{OV}=V_{GS}-V_t$ the Overdrive voltage.

How to identify the region

Two questions, in order:

1. Is $V_{GS}>V_t$? If no, cut-off, done, $i_D=0$. If yes, a channel exists; continue.
2. Is $V_{DS}\ge V_{OV}$? If yes, the channel is pinched off at the drain (Channel pinch-off) and you’re in saturation. Use the MOSFET square-law $i_D=\frac{1}{2}{k}_n{V}_{OV}^2$. If no, the channel is still continuous and you’re in triode, so use $i_D=k_n[V_{OV}{V}_{DS}-V_{DS}^2/2]$.

Same idea drives the DC-analysis recipe: in MOSFET DC analysis you assume saturation, solve, then check whether $V_{DS}\ge V_{OV}$ actually holds; if it doesn’t, redo in triode.

$i_D$ vs $v_{DS}$ for one $V_{GS}$: triode below $V_{OV}$, saturation above.

Regions of the enhancement n-MOSFET: cut-off, triode, saturation.

The p-MOSFET: same three regions, via magnitudes

A p-MOSFET has the same three regions, but all the controlling voltages ($V_{GS}$, $V_{DS}$, $V_t$) are negative. Rather than juggle signs, work in magnitudes:

• Cut-off: $|V_{GS}|<|V_{tp}|$.
• Triode: $|V_{GS}|>|V_{tp}|$ and $|V_{DS}|<|V_{OV}|$.
• Saturation: $|V_{GS}|>|V_{tp}|$ and $|V_{DS}|\ge |V_{OV}|$.

with $V_{tp}<0$ the p-MOSFET threshold and $|V_{OV}|=|V_{GS}|-|V_{tp}|$. The physics mirrors the n-MOSFET: holes instead of electrons, n-substrate instead of p, and a negative gate voltage to turn it on.

p-MOSFET regions: same three, inverted polarities ($V_{GS},V_{DS},V_t$ negative).