Question

What are $\alpha$ and $\beta$ parameters for a transistor? Obtain a relation between them.

Answer 1

Alpha$={\alpha }_{dc}$:It is defined as the ratio of collector current to emitter current.

${\alpha }_{dc}=\frac{I_c}{I_E}$ ......$\left(1\right)$

Beta$={\beta }_{dc}$:It is the current gain defined as the ratio of collector current to base current.

${\beta }_{dc}=\frac{I_c}{I_B}$ ......$\left(2\right)$

Relation between ${\alpha }_{dc}$ and ${\beta }_{dc}$:

For a transistor,

$I_B=I_C+I_E$ ........$\left(3\right)$ with $I_C\approx I_E$

Dividing both sides of eqn$\left(3\right)$ by $I_c$ we get

$\frac{I_E}{I_C}=\frac{I_B}{I_C}+1$

$\Rightarrow \frac{1}{{\alpha }_{dc}}=\frac{1}{{\beta }_{dc}}+1$

$\Rightarrow {\alpha }_{dc}=\frac{{\beta }_{dc}}{{\beta }_{dc}+1}$ ........$\left(4\right)$

or ${\beta }_{dc}=\frac{{\alpha }_{dc}}{1-{\alpha }_{dc}}$ .........$\left(5\right)$

Equations $\left(4\right)$ and $\left(5\right)$ give the relation between ${\alpha }_{dc}$ and ${\beta }_{dc}$ of a transistor.