α : The ratio of output collector current IC to input emitter current IE in the CB configuration is called current gain alpha (α).
β : The ratio of output collector current IC to the input base current IB in the CE configuration is called current gain beta (β) .
Relationship between α and β:
We know, IE = IB + IC
Dividing the above equation on both sides by
IC, IE/IC = IB/IC + 1
Since IC/IE = α and IC/IB = β
So, IE/IC = 1/ α and IB/IC = 1/β
Therefore, 1/ α =( 1/β) + 1
hence 1/ α = (1+β )/ β
Therefore, α = β /(1+β)