One wish to deliver to the resistor , what is the value of in if the small signal gain is ?
Consider the thermal voltage to be
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By the hybrid pi model we can get that the small signal gain of this circuit is V i V o = R 1 + g m 1 R 1 = 0 . 8 by rearanging this we get g m = 0 . 5 S . Since the thermal voltage is U T = 2 6 m V , it follows that I C = g m ⋅ U T = 1 3 m A , since β > > 1 , I C ≈ I E . Now consider the case where V o = 0 V , all of the current in I E is going thrugh I 1 , so I E = I 1 = 1 3 m A , since this current don't change, I E = 1 3 m A