Relation between current amplification factor α and β

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 β

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

                      β = ∆I_C / ∆I_B………….( 2 )

Relation between α and β

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 )

β = ∆I_C / ∆I_E – ∆I_C

Divide numerator and denominator by ∆I_E

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

   = α / ( 1 – α )

β = α / ( 1 – α )

      OR

β ( 1 – α ) = α

β – βα = α

β = α + βα

β = ( 1 + β ) α

α = β / ( 1 + β )

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