Answered: 10 k2 10 k2 10 k2 V1 10 ka 10 ka 10 k2…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Question

Write an expression for the output voltage
in terms of the input voltage for the circuit
. Diode D is formed from a
diode-connected transistor, and all three transistors are identical

10 k2
10 k2
10 k2
V1
10 ka
10 ka
10 k2
Figure P12.110

Expert Solution

Step 1

Given:

Th diode is connected to form the diode connected transistor. The transistor being used are identical.

The diagram is shown below as,

Step 2

Hence,

from the figure the first amplifier will have the output voltage $V_{01}$ as follows,

$\frac{V_{1}}{10 K o h m s} = I_{5} e^{(- \frac{V_{o 1}}{V_{T}})} O n r e a r r a n g i n g t h e e q u a t i o n a s, V_{o 1} = - V_{T} \ln (\frac{V_{1}}{10^{4} I_{5}})$

Similarly the output voltage from the second amplifier V_{02 is given as,}

_{$V_{o 2} = - V_{T} \ln (\frac{V_{21}}{10^{4} I_{5}})$}

Step 3

The output voltage V₀₃is determined for the third amplifier is given by the formula as,

$V_{o 3} = - (V_{01} + V_{02}) The values are substituted as, V_{o 3} = V_{T} [\ln (\frac{V_{1}}{10^{4} I_{5}}) + \ln (\frac{V_{2}}{10^{4} I_{5}})] Hence, the value becomes, V_{o 3} = V_{T} \ln (\frac{V_{1} V_{2}}{10^{8} {I_{8}}^{2}})$

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