# Stability Factors

$\displaystyle \Rightarrow$ Stability factor indicates the degree of change in operating due to variation in temperature. There are three variables which are temperature dependent. We can define three stability factors :

$\displaystyle S = \frac {\partial I_{C}}{\partial I_{CO}} \rightarrow \beta, V_{BE}$  Constant

$\displaystyle S^{'} = \frac {\partial I_{C}}{\partial V_{BE}} \rightarrow \beta, I_{CO}$  Constant

$\displaystyle S^{''} = \frac {\partial I_{C}}{\partial \beta} \rightarrow I_{CO}, V_{BE}$  Constant

$\displaystyle \Rightarrow$ Ideally, Stability factors should be zero to keep operating point stable and fixed.

$\displaystyle \Rightarrow$Practically, Stability factors should have the value as minimum as possible.

$\displaystyle \Rightarrow$ Effect of change in $\displaystyle I_{CO}$, is more dominant over the change in $\displaystyle \beta$ and $\displaystyle V_{BE}$. Hence $\displaystyle S$ is calculated here.

$\displaystyle S = \frac {\partial I_{C}}{\partial I_{CO}}$

$\displaystyle \Rightarrow$ Rate of change of collector current w.r.t reverse saturation current

$\displaystyle I_{C} = \beta I_{B} + (1+\beta) I_{CO}$

$\displaystyle 1 = \beta \biggl (\frac {\partial I_{B}}{\partial I_{C}} \biggr ) +\biggl (1+\beta \biggr ) \frac {\partial I_{CO}}{\partial I_{C}}$

$\displaystyle \Rightarrow \frac {\partial I_{CO}}{\partial I_{C}} = \biggl [ \frac {(1 - \beta \frac {\partial I_{B}}{\partial I_{C}}}{1+\beta} \biggr ]$

$\displaystyle \Rightarrow S = \frac {\partial I_{C}}{\partial I_{CO}} = \biggl [ \frac {1+\beta}{1 - \beta \frac {\partial I_{B}}{\partial I_{C}}} \biggr ]$