#### Question

What are α and β parameters for a transistor? Obtain a relation between them.

#### Solution

Alpha (α_{dc}): It is defined as the ratio of collector current to emitter current.

`alpha_(dc)="I"_c/"I"_E` -----------------(Equation 1)

Beta (βdc): It is the current gain defined as the ratio of collector current to the base current.

`beta_(dc)="I"_c/"I"_B` --------------------(Equation 2)

Relation between α_{dc} and β_{dc}:

For a transistor,

I_{E} = I_{B} + I_{C} (with I_{c} ≅ I_{E}) -----------(Equation 3)

Divinding both the side of eqn.(3) with I_{c} ,we get :

`"I"_E/"I"_c="I"_B/"I"_C+1`

`1/alpha_(dc)=1/beta_(dc)+1`

`alpha_(dc)=beta_(dc)/(1+beta_(dc))` -----------------------(Equation 4)

Or, `beta_(dc)=alpha_(dc)/(1-alpha_(dc))` ----------------------(Equation 5)

Equations (4) and (5) give the relation between α_{dc} and β_{dc} of a transistor.