Stability in Collector-to-Base bias

This is one of the circuit which is used to provide biasing for BJT. Voltage divider bias and fixed bias are other biasing circuits. In collector-to-base circuit, resistor R_B connects collector terminal of BJT to base terminal, the specialty of the circuit .. This resistor provides a negative feedback and it helps to reduce variations in the operating point. 

Circuit diagram:

fig 1

R_B stabilizes Ic against changes either due to variations in temperature or due to replacement of transistor by another one. How it happens?

Let us assume Ic is increasing. 

                                                 What about V_CE ?. It will decrease (Increase in Ic increases voltage drop across Rc. Since  Vcc =Voltage across Rc +Voltage V_CE ,  any increase in voltage drop across Rc will reduce V_CE ).

                                                       What about I_B ?. It also will reduce with  V_{CE .} (Equation for V_CE   is V_CE  = I_BR_B+ V_BE      . As per equation I_B and V_CE   are in direct proportion.)

                                                       Reduction in I_B will in turn reduce Ic. Thus the increment in Ic get cancelled and the circuit obtain stabilization. Note that stabilization is obtained because of the reduction in I_B and it would not happen if R_B is not there. So credit for this negative feedback goes to R_B.

Stability factor for collector-to-base bias.

Take general equation for stability factor. It is given in the post 'Stability factors & Biasing circuits'.         --------(1)

In the above equation only variable is dI_B /dIc. Let us find an equation for it from the above circuit.

From the circuit,


Therefore,        differentiate with respect to Ic.(Vcc and V_BE are constants)

                      substitute this in equation for stability factor S.


                 ---(2)   This is the equation for stability factor for collector-to-base bias.


Please refer the equation for stability factor in case of fixed bias. It is  . ------(3)
Compared to fixed bias, stability factor of collector-to-base bias is less. This ensures better stability for collector-to-base bias.