Relation between current amplification factor α and γ

Current amplification factor α

• It is defined as the ratio of the output current ( collector current ) and input current (  emitter current ).
• It is ratio of the change in collector current to the change in emitter current at constant collector – base voltage ( V_CB ).

                      α = ∆I_C / ∆I_E……….. ( 1 )

Current amplification factor γ

• It is defined as the ratio of the output current ( emitter current ) and input current (  base current ).
• It is ratio of the change in emitter current to the change in base current.

                      γ = ∆I_E / ∆I_B………….( 2 )

Relation between α and γ

As I_E = I_C + I_B

∆I_E = ∆I_C + ∆I_B

Therefore ∆I_B = ∆I_E – ∆I_C………. ( 3 )

From equation ( 2 ) and ( 3 )

γ = ∆I_E / ∆I_E – ∆I_C

Divide numerator and denominator by ∆I_E

γ = [ ∆I_E / ∆I_E ]  / [ ∆I_E – ∆I_C ] / ∆I_E

   = 1 / ( 1 – α )

γ = 1 / ( 1 – α )

       OR

γ ( 1 – α ) = 1

γ – γα = 1

γ – 1 = γα

α = ( γ – 1 ) / γ

α = ( γ – 1 ) / γ

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