1

Jieh-Tsorng Wu

National Chiao-Tung UniversityDepartment of Electronics Engineering

Introduction to Circuit Theory

Operational Amplifiers

2012-09-14

Circuit Theory; Jieh-Tsorng Wu25. Operational Amplifiers

Outline

1. Operational Amplifiers

2. Ideal Operation Amplifier

3. Inverting Amplifier

4. Noninverting Amplifier

5. Summing Amplifier

6. Difference Amplifier

7. Cascaded Circuits

8. Applications

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Circuit Theory; Jieh-Tsorng Wu

Operational Amplifier (Opamp)

It is an electronic unit that behaves like a voltage-controlled voltage source.

It is an active circuit element designed to perform mathematical operations of addition, subtraction, multiplication, division, differentiation and integration.

35. Operational Amplifiers

Circuit Theory; Jieh-Tsorng Wu

Operational Amplifier

45. Operational Amplifiers

2 1

2 1

1 2

)

Differential Input Voltage

0

(

0

o d

d

v A A v

v v v

i i

v v

3

Circuit Theory; Jieh-Tsorng Wu

Typical Ranges for Oamp Parameters

55. Operational Amplifiers

Parameter Typical range Ideal values

Open-loop gain, A 105 to 108 ∞

Input resistance, Ri 105 to 1013 ∞

Output resistance, Ro 10 to 100 0

Supply voltage, VCC 5 to 24 V

Circuit Theory; Jieh-Tsorng Wu

Opamp Output Range

Opamp is in the linear region if –VCC < vo < +VCC.

The slop in the linear region is the voltage gain A.

The differential input range is –VCC /A < vd < +VCC /A.

65. Operational Amplifiers

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Circuit Theory; Jieh-Tsorng Wu

An Inverting Amplifier Using Opamp

75. Operational Amplifiers

1 1 111

1

5 62 10 2 10 50 Find ?

100k 2M 20k 20k 50

1.9999699

When 2 V, 3.9999398, 20.066667 A 0

s o o o

i

dd

o

s

s o

o o sA R R v v

v v v v v v v Avvv v

v

v

v v v

Circuit Theory; Jieh-Tsorng Wu

Ideal Operational Amplifier

85. Operational Amplifiers

1 2

1 20 0

0i

o

A v v

R

R

i i

5

Circuit Theory; Jieh-Tsorng Wu

Inverting Amplifier

95. Operational Amplifiers

1 11

1 1

0i o o

f i

fRv v v v vv

R R v R

Circuit Theory; Jieh-Tsorng Wu

Inverting Amplifier Example

105. Operational Amplifiers

62 6 V

20k 40ka a o

a b o

v v vv v v

6

Circuit Theory; Jieh-Tsorng Wu

Transresistance Amplifiers

115. Operational Amplifiers

0 os

o

s

vi

Rv

Ri

v1

11 1

1 3 2

3 31

1 2

0 0

1

os s

o

s

v vv vi i

R R R

v R RR

i R R

Circuit Theory; Jieh-Tsorng Wu

Noninverting Amplifier

125. Operational Amplifiers

111

1 1

01 fo

i o if

Rv vvv v v v

R R R

7

Circuit Theory; Jieh-Tsorng Wu

Voltage Follower

Provide high Ri, low Ro, and voltage gain=1.

Useful as a buffer.

135. Operational Amplifiers

Circuit Theory; Jieh-Tsorng Wu

Loading Effect

145. Operational Amplifiers

' in21 1 1 1

o1 in2

o1 in2

'1 1 1 1

If

RAv Av

R R

R R

A v A v

Rin2

Ro1

1'1vA11vA

8

Circuit Theory; Jieh-Tsorng Wu

Noninverting Amplifier Example 2

155. Operational Amplifiers

Circuit Theory; Jieh-Tsorng Wu

Dual-Input Amplifier

165. Operational Amplifiers

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Circuit Theory; Jieh-Tsorng Wu

Summing Amplifier

175. Operational Amplifiers

322 3

2 3 2

11

1 1 3

f f foo

f

Rv vv vv

R R R

R Rv v v

R R RR

Circuit Theory; Jieh-Tsorng Wu

Summing Amplifier Example

185. Operational Amplifiers

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Circuit Theory; Jieh-Tsorng Wu

Difference Amplifier

195. Operational Amplifiers

2 4 2 2 1 2 21 2 2 1

1 3 4 1 1 3 4 1

31 22 1

2 4 1

11

1

If , th n

/

e

/o

o

RR R R R R Rv v v v v

R R R R R R R

RR Rv v

R

R

vR R

Circuit Theory; Jieh-Tsorng Wu

Design Example 1

205. Operational Amplifiers

2 1

1 22 22 1

1 3 4 1

1 22 22 1 3 4

1 1 3 4 3 4

Want 3 5

1

1

1 1 1 55 5 3 5

1 1

o

o

v v v

R RR Rv v v

R R R R

R RR RR R R R

R R R R R R

11

Circuit Theory; Jieh-Tsorng Wu

Design Example 2

215. Operational Amplifiers

2 1 2 13 5 3 5a o a ov v v v v v v v

Circuit Theory; Jieh-Tsorng Wu

Cascaded Amplifier

A cascade connection is a head-to-tail arrangement of two or more circuits such that the output of one is the input of the other.

Be careful not to neglect the loading effect of the following stage.

225. Operational Amplifiers

1 2 31

ovA A A A

v

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Circuit Theory; Jieh-Tsorng Wu

Cascaded Amplifier Example 1

235. Operational Amplifiers

20 mV 100 12k 10k

1 1 350 mV3k 4k

350m 100mi 25

10k 10k 1

mV

A0k

a o a

o b oo

a

v v

v v v

v

v

Circuit Theory; Jieh-Tsorng Wu

Cascaded Amplifier Example 2

245. Operational Amplifiers

1 2 1 2

2 43 2 2 6

3 3a b o a bv v v v v v v v v

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Circuit Theory; Jieh-Tsorng Wu

Digital-to-Analog Converter (DAC)

255. Operational Amplifiers

[S1 S2 S3 S4] Decimal Vo

0000 0 0

0001 1 0.125

0010 2 0.25

0011 3 0.375

0100 4 0.5

0101 5 0.625

0110 6 0.75

0111 7 0.875

1000 8 1.0

1001 9 1.125

1010 10 1.25

1011 11 1.375

1100 12 1.5

1101 13 1.625

1110 14 1.75

1111 15 1.875 ref 1 2 3 48 4 2

8f

o

RV V S S S S

R

Circuit Theory; Jieh-Tsorng Wu

Instrumentation Amplifier

265. Operational Amplifiers

4 4

1 2

1

3 4 3

2

1 2a

a

o

b

b

o

v v v v

v v v vi

R R

v v i R R R

32 2 22 1 4 3 2 1

1 1 1 4

2 1 2o o o

RR R Rv v v R v

R Ri R v

R R

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Circuit Theory; Jieh-Tsorng Wu

Instrumentation Amplifier

275. Operational Amplifiers

Output vo depends on the difference between inputs v1 and v2, not on their common-mode voltage.

Voltage gain is adjusted by RG.

The input impedance is very high and does not vary as the gain is adjusted.

2 1

1 2ov

G

v RA

v v R