Answered: Figure P12.14 200 k2 10 ka 120 k2 150…

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

The op amps as shown are ideal (a) What are the voltage gain, input resistance, and output resistance of the overall amplifier? (b) If the input
voltage υ_I = 1 mV, what are the voltages at each of the eight nodes in the amplifier circuit?

Figure P12.14
200 k2
10 ka
120 k2
150 k2
12 k2
200 k2
20 k2

Expert Solution

Step 1

To determine the voltage gain, input resistance, and output resistance is determined by,

The other two op-amp is cascaded in series. The first, has the voltage gain,

$\begin{array}{rcl} A_{v 1} & = & 1 + \frac{150}{120} \\ = & 1 + 12.5 \\ = & 13.5 \end{array}$

Now, the voltage gain of the 2^nd op-amp,

$A_{v 2} = 1 + \frac{200}{10} A_{v 2} = 21$

Step 2

Now, the voltage gain of the 3rd op-amp,

$A_{v 3} = 1 + \frac{200}{20} A_{v 3} = 1 + 10 A_{V 3} = 11$

As all the op-amp is in cascaded connection therefore, the overall gain will given by the product of the individual gain.

$A = A_{V 1} A_{V 2} A_{V 3} A = 11 \times 21 \times 13.5 A = 3118.5$

Step 3

The input resistance of the overall amplifier is given by,

$v_{i} = 120 i_{i} R_{i} = 120 k o h m$

therefore, the output resistance will be determined by,

$\begin{array}{rcl} R_{o u t} & = & \frac{200 \times 20}{220} \\ = & 18.18 o h m \end{array}$

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