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start at Ic'= Ic1+Ic2 Ib'=Ib1 Ic1=B1*Ib' Ie1=Ib2=Ib'(B1+1)=Ib'B1 + Ib'

Ic' = Ib'*B1 + Ic2

Ic2= B2(Ib'B1+Ib')

Ic' = Ib'B1 + Ib'B1B2 + Ib'B2

divide by Ib'

Ic'/Ib'= current gain =B'=B1+B2+B1B2

note: calculations without resistance

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Q: How to calculate the current gain in darlington pair?
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