Q. Derive the equations of the self bias circuit?

A circuit which is used to establish a stable operating point is the self biasing configuration. The circuit is shown in Fig

The physical reason for an improvement in stability with the circuit is the following:

If Ic increases or tends to increase because Ico has risen as a result of the elevated temperature, the current in Re increases. As a result of the voltage drop across Re the base current is decreased. Hence Ic will increase less than it would have, had there been no self biasing resistor Re.

Kirchoffs voltage law around the collector circuit yields

-V_cc + I_c (R_e+R_e) + I_e.R_e+ V_ce = 0

Kirchoffs voltage law around the base circuit is

V = I_e.R_e+V_be+(I_b+I_c)R_e.

Hence in the active region the collector current is given by

I_c=bI_b+(1+b)I_co.