Sunday 7 September 2014

Stability factors & Biasing circuits

Stability factors seems to be  heavy???. Make a trip along with fundamentals of BJT- plz click here - BJT - first glimpse

Stability factors & Biasing circuits: 

An idea about biasing and stabilization will help in the study of Stability factors -plz check the following paragraph.

Things to be ensured before wiring an amplifier:

Before setting up an amplifier circuit, operating point should be fixed at an appropriate position on the load line - preferably at the center of the load line. This can be done with the help of a biasing circuit. It is also to be ensured that the operating point does not shift due to changes in temperature or due to variations in transistor parameters(see explanation below) - in other words operating point should be stable.
The maintenance of the operating point stable is known as stabilization.

##  We have, Ic = β IB + (1+β)Ico . Since Ico and β are vary with temperature, Ic also varies with temperature - it will change operating point.  Variations in transistor parameters such as β and VBE (These variations occurs when one transistor in a circuit is replaced with another of the same type)  also will affect position of the operating point. ##    
Next we discuss about Stability factor.

Stability factor (S) is defined as the rate of change of collector current(Ic) with respect to the reverse saturation current(Ico), keeping β and VBE  constant.

{\rm{S = }}\frac{{dIc}}{{dIco}}  at constant β and VBE .                 ------(1)                                                                                        

What is desirable for S - a large value or a small value?     Smaller  S indicates higher stability. ( S high means variations in Ic is large with change in Ico - it will vary operating point).

Now we are going to derive an equation for S. For that lets take this equation below,  

Ic = \beta {\rm I}{\rm B} + (1 + \beta ){\rm I}{\rm{co}}        ----(1)
Differentiate this equation with respect to 'Ic', consider β as a constant(see definition of S).

\frac{d}{{dIc}}Ic = \frac{d}{{dIc}}\left( {\beta {\rm I}{\rm B} + (1 + \beta ){\rm I}{\rm{co}}} \right)     -------(2)

1 = \beta \frac{{dIB}}{{dIc}} + (1 + \beta )\frac{{dIco}}{{dIc}}

1 = \beta \frac{{dIB}}{{dIc}} + \frac{{(1 + \beta )}}{S}

From this, write equation for Stability factor, S

\therefore S = \frac{{(1 + \beta )}}{{1 - \beta \frac{{dIB}}{{dIc}}}}         ----(3)

One more

A second Stability factor, Sv can be defined by considering variations in Ic with respect to VBE .  Here Ico and β are considered as constants.
  Sv = \frac{{dIc}}{{dVBE}}            at constant Ico and β      ------(4)

One more  ..

A third Stability factor, Sβ   is defined for expressing variations in Ic with respect to β. It is the rate of change of Ic with respect to  β.    S\beta = \frac{{dIc}}{{d\beta }}at constant Ico and VBE ------(5)
          
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