05 operational amplifiers - national chiao tung university · 3 circuit theory; jieh-tsorng wu...
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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
9
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
10
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