Stability Factors in a Transistor | Types and Formulas

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:

$\displaystyle S = \left( \dfrac {\partial I_{C}}{\partial I_{\text{CO}}} \right) \longrightarrow \beta, V_{\text{BE}}$ Constant

$\displaystyle S^{'} = \left( \dfrac {\partial I_{C}}{\partial V_{\text{BE}}} \right) \longrightarrow \beta, I_{\text{CO}}$ Constant

$\displaystyle S^{''} = \left( \dfrac {\partial I_{C}}{\partial \beta} \right) \longrightarrow I_{\text{CO}}, V_{\text{BE}}$ Constant

Ideally, Stability factors should be zero to keep operating point stable and fixed.

Practically, Stability factors should have the value as minimum as possible.

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

$\displaystyle S = \left( \dfrac {\partial I_{C}}{\partial I_{\text {CO}}} \right)$

Rate of change of collector current w.r.t reverse saturation current

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

$\displaystyle 1 = \beta \left (\dfrac {\partial I_{B}}{\partial I_{C}} \right) +\left (1+\beta \right) \dfrac {\partial I_{\text{CO}}}{\partial I_{C}}$

$\displaystyle \dfrac {\partial I_{\text{CO}}}{\partial I_{C}} = \left[ \dfrac {(1 - \beta \left( \dfrac {\partial I_{B}}{\partial I_{C}} \right)}{1+\beta} \right]$

$\displaystyle \Longrightarrow \boxed{S = \dfrac {\partial I_{C}}{\partial I_{\text{CO}}} = \left[ \dfrac {1+\beta}{1 - \beta \left( \dfrac {\partial I_{B}}{\partial I_{C}} \right)} \right]}$