#### peterpops

##### Junior Member level 3

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 v

_{x}is a test voltage with the input resistance R

_{in}defined as R

_{in}= v

_{x}/ i

_{x}

**My approach**

i

_{x}= i

_{b}

the currents sum in the point above E in the figure is

i

_{x}+ βi

_{x}- i

_{e}= 0

EQ 1: i

_{x}= i

_{e}/ (1 + β)

i

_{e}= v

_{e}/ R

_{e}

v

_{e}= v

_{x}* (R

_{e}/ (R

_{e}+ r

_{π}))

i

_{e}= v

_{x}/ (R

_{e}+ r

_{π})

inserted into EQ 1

i

_{x}= (v

_{x}/ (R

_{e}+ r

_{π})) / (1 + β) = v

_{x}/ ((R

_{e}+ r

_{π})*(1 + β))

And finally

R

_{in}= v

_{x}/i

_{x}= (R

_{e}+ r

_{π})*(1 + β)

However

**Answer by the book is R**

_{in}= r_{π}+ (β + 1)R_{e}So I have one "βr

_{π}" to much.. what's wrong with my calculations??