Semiconductor Electronics Part 2

Current gain in common base,
α=‌

∆IC

∆IE

Current gain in common emitter,
β=‌

∆IC

∆IB

Here, ∆lC= change in collector current,
∆IE= change in emitter current
  and ∆IB= change in base current.
We know that,
∆lE=∆IB+∆IC
Divide by the ∆Ic on both sides, we get
‌

∆IE

∆IC

=‌

∆IB

∆IC

+‌

∆IC

∆IC

⇒‌‌‌

1

α

=‌

1

β

+1⇒‌

1

α

=‌

β+1

β

⇒‌‌α=‌

β

β+1