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Chapter 4. Operational amplifiers

2014. 9. 24.

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2Contents

1. Introduction

2. Op-Amp Models

3. Fundamental Op-Amp Circuits

4. Comparators

5. Application Examples

6. Design Examples

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3Why operational amplifiers ?

1. Originally, the op-amp was designed to perform mathematical operations such as addition, subtraction, differentiation, and integration.

2. By adding simple networks to the op-amp, we can create these “building blocks” as well as voltage scaling, current-to-voltage conversion, and myriad more complex applications.

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42. Op-amp model

0,0, ARR OiIdeal op-amp :

ini

0,0 inini

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5Example

001

ARR

RA

RR

R

V

V

LO

L

Thi

i

S

O

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6Example : unity gain buffer

inOiSS VARRRIV 0)(

inOO VAIRV 0

iin IRV

1)()( 0

0

0

0

iOiS

iO

inOiS

inO

S

O

IRARRRI

IRAIR

VARRRI

VAIR

V

V

SO VV

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7Example 4.2Let us determine the gain of the basic inverting op-amp configuration shown in the figure using both the non-ideal and ideal op-amp models

0

0

2

10

2

11

1

1

o

eo

o

i

S

R

A

R

RRR

1

2

22221

120

11111111

/

R

R

RA

RRRRRRR

RR

ooi

S

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Ideal model

1

221, R

RIRIR

S

ooS

Virtual short

][0 V

I

I

• Step 1. Use the ideal op-amp model: Ao = ∞, Ri = ∞, Ro = 0.i+= i-=0, v+= v-

• Step 2. Apply nodal analysis to the resulting circuit.• Step 3. Solve nodal equations to express the output voltage in terms of the

op-amp input signals.

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Let us now determine the gain of the basic non-inverting op-amp configuration shown in the figure.

Example 4.3

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Consider the op-amp circuit shown in the figure. Let us determine an expression for the output voltage.

Example 4.5

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11Example 4.6

The circuit shown in the figure is a precision differential voltage-gain device. It is used to provide a single-ended input for an analog-to-digital converter. We wish to derive an expression for the output of the circuit in terms of the two inputs.

0

0

2

212

1

2

21

1

1

2

1

RRR

RRR

G

a

G

ao

Go R

R

R

R 2

1

221

21)(

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12Example 4.7

xV

43010

10 oox

VVkk

kV

1V

04

2

01010

021121

121

VVVVVVV

k

VV

k

VV

x

x

21 48 VVVo

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134.4 Comparators

(a) A zero-crossing detector and (b) the corresponding input/output waveforms.

(a) An ideal comparator and (b) its transfer curve.

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14Application example 4.11An instrumentation amplifier of the form shown in Fig. 4.26 has been suggested. Thisamplifier should have high-input resistance, achieve a voltage gain Vo/(V1-V2) of 10, em-ploy the MAX4240 op-amp listed in Table 4.1, and operate from two 1.5 V AA cell batter-ies in series. Let us analyze this circuit, select the resistor values, and explore the validity of this configuration.

2xV

1V

2V

yxoA

ox

A

xy

VVVR

VV

R

VV

22R

VV

R

VV

R

VV yx 21

2

2

1

1

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)(),( 212

2211

1 VVR

RVVVV

R

RVV yx

)(1 2121 VV

R

RRVVVV xyxo

22

12

21

11 1,1 V

R

RV

R

RVV

R

RV

R

RV yx

)(102

1 211

21

RRR

R

VV

Vo

RR 5.41

kRkRex 450,100) 1

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