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 ] 


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