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The given circuit We have been asked to find the input impedance of the given circuit (above) I've done the small signal representation of the circuit which is as follows ss representation The question is :the expression to be proved I tried to solve it i'm getting this result : Rin= ( rR2+[(R3//R4//R5)(B+1)R2])÷R2+r

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Just a short hint:

Are you familiar with the MILLER-effect (which drastically reduces the input resistance)? Here we have the opposite effect - BOOTSTRAPPING via C2. This method drastically increases the effective dynamic resistance of R2 because the emitter signal voltage is nearly identical to the base signal and is in phase with the base signal voltage.

Hence, there is only a very little signal current through R2, which is needed, of course, for establishing the necessary DC bias at the base node.

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