Output Stages - 1 -

One wish to deliver 0.5 W 0.5 W to the resistor R 1 R_1 , what is the value of I 1 I_1 in m A mA if the small signal gain is 0.8 v v 0.8 {v \over v} ?

Consider the thermal voltage to be 26 m V 26 mV

Tip: β > > 1 \beta >> 1


The answer is 13.

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1 solution

João Areias
Jun 27, 2018

By the hybrid pi model we can get that the small signal gain of this circuit is V o V i = R 1 R 1 + 1 g m = 0.8 \frac{V_o}{V_i} = \frac{R1}{R1 + {1\over gm}} = 0.8 by rearanging this we get g m = 0.5 S gm = 0.5 S . Since the thermal voltage is U T = 26 m V U_T = 26mV , it follows that I C = g m U T = 13 m A I_C = gm \cdot U_T = 13mA , since β > > 1 \beta >> 1 , I C I E I_C \approx I_E . Now consider the case where V o = 0 V V_o = 0V , all of the current in I E I_E is going thrugh I 1 I1 , so I E = I 1 = 13 m A I_E = I1 = 13mA , since this current don't change, I E = 13 m A I_E = 13mA

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