# [SOLVED]Simplified BJT model question (sedra smith)

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#### peterpops

##### Junior Member level 3
Hello!

Another question regarding a problem in Microelectronic circuits 5th ed by Sedra Smith (exercise 1.20)

Please see the attached image. Everything except the green arrow and label is in the original figure Problem:
Find the input resistance between terminals B and G in the circuit shown in the attached image. The voltage vx is a test voltage with the input resistance Rin defined as Rin = vx / ix

My approach
ix = ib

the currents sum in the point above E in the figure is
ix + βix - ie = 0

EQ 1: ix = ie / (1 + β)

ie = ve / Re

ve = vx * (Re / (Re + rπ))

ie = vx / (Re + rπ)

inserted into EQ 1

ix = (vx / (Re + rπ)) / (1 + β) = vx / ((Re + rπ)*(1 + β))

And finally

Rin = vx/ix = (Re + rπ)*(1 + β)

However

Answer by the book is Rin = rπ + (β + 1)Re

So I have one "βrπ" to much.. what's wrong with my calculations??

The equation Ve=... is not correct. This equation assumes that Ve is determined by Vx only - and you forgot the current source.

The equation Ve=... is not correct. This equation assumes that Ve is determined by Vx only - and you forgot the current source.

Ahh okay, but how do I incorporate that into the Ve-equation? I've been looking around at different methods (DC network analysis methods) but I can't get anyone to work. Could you point me in the right direction?

The circuit diagram in post#1 is a LINEAR small-signal circuit. Therefore, you can apply the superposition method.
Its one of the fundamental laws which is used to calculate the voltage-current distribution in a circuit with more than one sources.

The circuit diagram in post#1 is a LINEAR small-signal circuit. Therefore, you can apply the superposition method.
Its one of the fundamental laws which is used to calculate the voltage-current distribution in a circuit with more than one sources.

Thanks! I tried a some of the other methods without success but the superposition worked! Thanks!

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