Q. What are the Current relations in common emitter configuration?

In a CB configuration Ie is the input current and Ic is the output current. These currents are relayed through the equations given below

I_e=I_c+I_b

I_c=II_e+I_cb0

In CE configuration, Ib becomes the input current and the Ic is the output current. We are interested in knowing how the output Ic is related with the input current Ib. That is, we should find a relation such as

I_c = f(I_b)

To obtain the relation, we simply substitute the expression  of  Ie  from the equations given earlier,so that

I_c = ID_c(I_c+I_b) + I_cbo

or

(1-I_dc)I_c=I_dcI_b+I_cbo

or

I_c = (I_dc/(1-I_dc))I_b+(1/(1-Id_c))I_cbo

In thjis equation,Ic is given in terms of Ib. The equations can be simplified somewhat by defining

? I_dc/(1-I_dc)

and

I_ceo=I_cbo/(1-I_dc)

thus equation becomes

Ic=?_dcIb+I_ceo