Bipolar Junction Transistors (NPN)

Symbol

NPN BJT Symbol

Active Mode

Conditions:

V_{C} > V_{B} > V_{E}

Equations:

\begin{matrix} V_{B E} = 0.7 V \\ I_{C} = I_{S} e^{\frac{V_{B E}}{V_{T}}} \\ I_{B} = \frac{1}{β} I_{S} e^{\frac{V_{B E}}{V_{T}}} \\ I_{E} = I_{C} + I_{B} \\ I_{C} = β I_{B} \\ I_{E} = \frac{I_{C}}{α} \\ α = \frac{β}{β + 1} \end{matrix}

Saturations Mode

Conditions:

\begin{matrix} V_{E} < V_{B} \\ V_{C} < V_{B} \\ \frac{I_{C}}{I_{B}} < β \end{matrix}

Equations:

\begin{matrix} V_{B E} = 0.7 V \\ V_{C E s a t} = 0.2 V \end{matrix}

Large Signal Model

NPN BJT Large Signal

NPN BJT Large Signal

Small Signal Model

$\pi$ -model

BJT Small Signal Pi

BJT Small Signal Pi

\begin{matrix} g_{m} = \frac{I_{C}}{V_{T}} \\ r_{π} = \frac{V_{T}}{I_{B}} = \frac{β}{g_{m}} \\ r_{o} = \frac{V_{A}}{I_{C}} \end{matrix}

T-model

BJT Symbol

\begin{matrix} g_{m} = \frac{I_{C}}{V_{T}} \\ r_{e} = \frac{V_{T}}{I_{E}} = \frac{α}{g_{m}} \\ r_{o} = \frac{V_{A}}{I_{C}} \end{matrix}

Bipolar Junction Transistors (PNP)

Symbol

BJT Symbol

Active Mode

Conditions:

V_{E} > V_{B} > V_{C}

Equations:

\begin{matrix} V_{E B} = 0.7 V \\ I_{C} = I_{S} e^{\frac{V_{E B}}{V_{T}}} \\ I_{B} = \frac{1}{β} I_{S} e^{\frac{V_{E B}}{V_{T}}} \\ I_{C} = I_{E} + I_{B} \\ I_{C} = β I_{B} \\ I_{E} = \frac{I_{C}}{α} \\ α = \frac{β}{β + 1} \end{matrix}

Saturations Mode (PNP)

Conditions:

\begin{matrix} V_{B} < V_{E} \\ V_{B} < V_{E} \\ \frac{I_{C}}{I_{B}} < β \end{matrix}

Equations:

\begin{matrix} V_{E B} = 0.7 V \\ V_{C E s a t} = 0.2 V \end{matrix}

Large Signal Model

BJT Symbol

BJT Symbol