Operational Amplifiers
Instructor: Chia-Ming TsaiElectronics Engineering
National Chiao Tung UniversityHsinchu, Taiwan, R.O.C.
Contents• Introduction
• Operational Amplifiers (OP AMPs)
• Ideal OP AMP
• Inverting AMP
• Noninverting AMP
• Summing AMP
• Difference AMP
• Cascaded OP AMP Circuits
• Applications
Introduction
• The op amp is a basic building block for performing mathematical operations such as summation, amplification, integration, and differentiation
• The concept of virtual short between the differential inputs of the op amp is extremely important for circuit analysis
OP AMPs
• Complex circuit networks consisting of transistors, resistors, capacitors, and diodes
Cont’d
12
12
210 (KCL)
vvAAvv
vvv
iiiii
do
d
Equivalent circuit of an op amp
+
_
Cont’dParameter Typical
rangeIdeal value
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
Slope = A
Example
? Find
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102
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R
A
short virtualare inputs alDifferenti
0 V 20
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2, & 1 nodeat KCL Applying
1
v
v
v
s
o
Ideal OP AMP• Infinite open-loop voltage gain: A • Infinite input resistance: Ri
• Zero output resistance: Ro 0
• v1 = v2 (virtual short) assumed for analysis
Inverting AMP
The equivalent circuit
f
oi
R
vv
R
vvii
1
1
121
1, nodeat KCL Applying
if
o vR
Rv
vv
1
21
0
amp, op idealan For
(feedback resistor)
Example: I-to-V Converters
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2
3
1
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R
R
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Noninverting AMP
f
o
R
vv
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1
1
121
1
0
, nodeat KCL Applying
if
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vR
Rv
vvv
1
21
1
amp, op idealan For
Voltage Follower• Conditions: Rf = 0 or R1 = or both
• Unity gain: Av = 1
• Useful as a buffer amp due to its very high Ri and very low Ro
Summing AMP
3
3
2
2
1
1321
, nodeat KCL Applying
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v
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3
32
21
1
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Difference AMP
43
2
21
1
, nodeat KCL Applying
, nodeat KCL Applying
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vv
b
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a
bb
oaa
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2
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11
22
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1
2
, If
1
1
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vR
Rv
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ba
Cascaded OP AMP Circuits
321
and 0
amps, op idealFor
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RR oi
Applications: DAC[V1 V2 V3 V4] 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
MSB: most significant bitLSB: least significant bit
Digital-to-Analog Converter (DAC)
Applications:Instrumentation Amplifier (IA)
Gv
vo
R
RA
vvAv
21
12
Cont’d• Characteristics of IA
– Voltage gain adjustable by RG
– Very high Ri and very low Ro
– The differential voltage is amplified and the common-mode voltage is rejected
