Metal-Oxide-Semiconductor Field-Effect Transistor (N-Channel)

Symbol

Saturation Region

Conditions:

\begin{matrix} V_{G S} > V_{t} \\ V_{D S} > V_{G S} - V_{t} \end{matrix}

Equations:

I_{D S} = \frac{1}{2} k_{n} V_{O V}^{2} = \frac{1}{2} k_{n} (V_{G S} - V_{t})^{2}

Where:

\begin{matrix} V_{t} = threshold voltage \\ V_{O V} = V_{G S} - V_{t} \\ k_{n} = μ_{n} C_{o x} \frac{W}{L} \end{matrix}

Triode Region

Conditions:

\begin{matrix} V_{G S} > V_{t} \\ V_{D S} < V_{G S} - V_{t} \end{matrix}

Equations:

\begin{matrix} \begin{aligned} I_{D S} & = k_{n} (V_{O V} - \frac{1}{2} V_{D S}) V_{D S} \\ = k_{n} ((V_{G S} - V_{t}) V_{D S} - \frac{1}{2} V_{D S}^{2}) \end{aligned} \end{matrix}

Where:

\begin{matrix} V_{t} = threshold voltage \\ V_{O V} = V_{G S} - V_{t} \\ k_{n} = μ_{n} C_{o x} \frac{W}{L} \end{matrix}

Large Signal Model

NMOS Large Signal

Small Signal Model

$\pi$ -model

NMOS Small Signal Pi

T-model

NMOS Small Signal T

Metal-Oxide-Semiconductor Field-Effect Transistor (P-Channel)

Symbol

Saturation Region

Conditions:

\begin{matrix} V_{S G} > | V_{t p} | \\ V_{S D} > V_{S G} - | V_{t p} | \end{matrix}

Equations:

I_{D S} = \frac{1}{2} k_{n} (V_{S G} - V_{t p})^{2}

Where:

\begin{matrix} V_{t p} = threshold voltage \\ k_{n} = μ_{n} C_{o x} \frac{W}{L} \end{matrix}

Triode Region

Conditions:

\begin{matrix} V_{S G} > V_{t p} \\ V_{S D} < V_{S G} - V_{t p} \end{matrix}

Equations:

I_{D S} = k_{n} ((V_{S G} - V_{t p}) V_{S D} - \frac{1}{2} V_{S D}^{2})

Where:

\begin{matrix} V_{t p} = threshold voltage \\ k_{n} = μ_{n} C_{o x} \frac{W}{L} \end{matrix}

Large Signal Model

PMOS Large Signal