Define α & β and derive the relation between (α) &) (β) of transistor.

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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)

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)