Fundamentals of Electric Circuit - Chapter 5: Operational amplifiers

0
   
     O a O b
V V V V
i mA
0
8 8
4,8
10 2 10 2
Fundamentals of Electric Circuits – Viet Son Nguyen - 2011
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3
7
R 1
R 2
R 3
R 4
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Chapter 5: Operational amplifiers
VI. Difference amplifier
-
+
 A difference (differential) amplifier is a device that amplifies the difference
between two inputs but rejects any signals common to the two inputs.
Vb
V0
 
 
         
     
 
R
RR R R R R
V V V V V V
R R R R R RR
R
1
22 3 2 2 2
0 2 1 0 2 1
1 3 4 1 1 13
4
1
1
1
 Note that: Va = Vb (ideal op amp):
  
     
 
a a
a
V V V V R R
V V V
R R R R
1 0 2 2
0 1
1 2 1 1
1
V2
V1
0
0
 Applying KCL at node a gives:
Va
 
  

b b
b
V V V V R
V V
R R R R
2 0 4
2
3 4 3 4
 Applying KCL at node b gives:
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Chapter 5: Operational amplifiers
VI. Difference amplifier
-
+
 Since a difference apmlifier must reject a signal common to the two inputs
Vb
V0
   
R
V V V
R
2
0 2 1
1
 If R2 = R1, and R3 = R4, the difference amplifier becomes a subtractor
V2
V1
0
0
V0 = 0 when V1 = V2
4
3
7
R 1
R 2
R 3
R 4
Va
R R
R R
1 3
2 4
 This properties exists when:
 The op amp circuit is a difference amplifier
 V V V
0 2 1
 Remarks:
 The difference amplifier is also known as the subtractor
 The difference amplifier are used in varios applications (instrumentation
amplifier)
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Chapter 5: Operational amplifiers
VI. Difference amplifier
Ex 5.8: Design an op amp circuit with inputs V1 and V2 such that V0 = -5V1 + 3V2
 Applying the difference amplifier equation:
 Solution 1: Using only one op amp
    
R R
V V V
R R
2 2
0 2 1
1 1
5
 Rewrite:
 
     
 
V V V V V
0 1 2 2 1
3
5 3 5
5
 In the other word:
       
      
   
    
   
R
RR R
V V V V V
R RR R
R R
1
22 2
0 2 1 2 1
1 13 3
4 4
1
1 1
5
5 5
1 1
 
 
       
 
 
 
R
R R
RR
R
3
3 4
43
4
1
1
35
2 1
5
1
 Choose:
   
  
R k R k
R R k
1 2
3 4
10 ; 50
20
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Chapter 5: Operational amplifiers
VI. Difference amplifier
Ex 5.8: Design an op amp circuit with inputs V1 and V2 such that V0 = -5V1 + 3V2
 For the inverter:
 Solution 2: Using > 01 op amp inverting amplifier + 2-inputs inverting summer.
 
a
V V
2
3
 For the summer:   
a
V V V
0 1
5
 Combining 02 op amps: V0 = 3V2 - 5V1
V0
Va
V2
V1
 Selecte the resistor value:  R k1 10 ;
4
3
7
R 1
3R1
5R1
5R1
4
3
7
R 1
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R 1
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4
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R 3
4
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R 2
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Chapter 5: Operational amplifiers
VI. Difference amplifier
Ex 5.9: Find the relationship between V0 and 02 - inputs of an instrumentation
amplifier.
 But:

  a b
a b
V V
i V V V V
R
1 2
4
; ;
 There are not current into A1, and A2, the
current I flows through the 3 registers
  V V i R R
01 02 3 4
(2 )
 Therefore:
V0
VO2
V2
V1
 The relationship between inputs and output of an intrumentation amplifier:


V V
i
R
1 2
4
VO1
0
A2
A1
Vb
Va
A3
0
i
 
 
   
 
R R
V V V
R R
2 3
0 2 1
1 4
2
1
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4
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Chapter 5: Operational amplifiers
VI. Difference amplifier
Ex 5.10: Obtain i0 in the instrumentation amplifier circuit.
8,01V
8V
20kΩ
i020kΩ
40kΩ
10kΩ40kΩ
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Chapter 5: Operational amplifiers
VII. Cascaded op amp circuits
 A cascade connection is a head-to-tail arragement of two or more op amp circuits
such that the output of one is the input of the next.
 Each op amp circuit in the string is called a stage.
 Infinite input resistance.
 Zero output resistance.
 The original input signal is increased by the gain of the individual stage.
A A A A
1 2 3
. .
 Characteristics:
 Op amp circuits can be cascaded without changing their input-output
relationships beacause:
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Chapter 5: Operational amplifiers
VII. Cascaded op amp circuits
Ex. 5.11: Find V0 and i0 in the circuit
 At the output of the second op amp:
 The circuit consists of two non-
inverting amplifiers cascaded
 
   
 
a
R
V mV
R
1
2
1 20 100
20mV
10kΩ
3kΩ
4kΩ
12kΩ
a
b
i0
VO
-
+
 At a point:
 
   
 
O a
R
V V mV
R
3
4
1 350
 The current i0 flows through the 10kΩ resistor


    b aV VO b
V V
i i A
R
3
0 0 3
3
(350 100).10
25
10.10
Fundamentals of Electric Circuits – Viet Son Nguyen - 2011
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Chapter 5: Operational amplifiers
VII. Cascaded op amp circuits
Ex. 5.12: Find V0
 The circuit consists of two inverters A and B and a summer C.
10kΩ
2kΩ
5kΩ
15kΩ
a
b
VO
   
a
R
V V V
R
2
1
1
3
6kΩ
8kΩ
4kΩ
V2=2V
V1=1V
A
B
C
   
b
R
V V V
R
4
2
3
4
 These become the inputs to the summer:
   
           
  
O a b
R R
V V V V
R R
7 7
5 6
2
2.( 3) ( 4) 8.333
3
Fundamentals of Electric Circuits – Viet Son Nguyen - 2011
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R 2
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4
3
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Chapter 5: Operational amplifiers
VII. Cascaded op amp circuits
Ex. 5.13: Find V0 if V1 = 2V, V2 = 1,5V
20kΩ
10kΩ
VO
60kΩ
30kΩ50kΩ
V2
V1
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Chapter 5: Operational amplifiers
VIII. Applications
 Op amp has numerous pratical applications:
 Inverters, summers, integrators, differentiators, subtractors, logarithmic
amplifiers
 Instrumentation amplifiers, calibration circuits
 DAC, voltage-to-curent converters, current-to-voltage converters
 Analog computers,
 Filters, clippers, rectifier, regulators, level shifters
 Comparators, gyrators, oscillators
 
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Chapter 5: Operational amplifiers
VIII.1. DAC – Digital-to-Analog Converter
 The digital-to-analog converter (DAC) transforms digital signals into analog form.
A four-bit DAC
 A DAC can be realized by using the binary
weighted ladder:
 The bits are weights according to the
magnitude of their place value.
 Their weights decrease value of Rf/Rn
each lesser bit has half the weight of the next
higher.
    
f f f f
O
R R R R
V V V V V
R R R R
1 2 3 4
1 2 3 4
R 4R 3R 2
4
3
7
R f
R 1
VO
V2V1 V3 V4
LSBMSB
Binary weighted ladder type
 V1,  V4 can assume only two voltage levels (0, 1) (binary code)  DAC
provides a single output that is proportional to the inputs.
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Chapter 5: Operational amplifiers
VIII.1. DAC – Digital-to-Analog Converter
Ex 5.14: Obtain the analog output for binary inputs [0000], [0001], [0010],  [1111].
    
    
f f f f
O
R R R R
V V V V V
R R R R
V V V V V
1 2 3 4
1 2 3 4
0 1 2 3 4
0,5 0,25 0,125
R 4R 3R 2
4
3
7
R f
R 1
VO
V2V1 V3 V4
LSBMSB
10kΩ
10K 20K 40K 80K
Inputs [B] Value [D] -V0
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
1111 15 1.875
 Each bit has a value of 0.125V  cannot represent a
voltage between 1V 1.125V (DAC resolution).
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Chapter 5: Operational amplifiers
VIII.2. Intrumentation amplifier (IA)
 Typical applications of IAs include isolation amplifiers, thermocouple amplifiers,
and data acquisition systems.
 From the Ex 5.9, we have:
R
4
3
7
4
3
7
R
4
3
7
R
R
R
R
2
3
1
Inverted input
Gain set
Gain set
Non-inverted input
Output
V0
V2
V1
RG
 
 
   
 G
R
V V V
R
0 2 1
2
1
 Recall that:
 The IA amplifies small differential signal voltages
superimposed on larger common-mode voltages.
 Since the common-mode voltages are equal, they
cancel each other.
Schematic diagram
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Chapter 5: Operational amplifiers
VIII.2. Intrumentation amplifier (IA)
 The IAs have three major characteristics:
 The voltage gain is adjusted by one externer resistor RG
 The input impedance of both inputs is very high and does not vary as the
gain is adjusted.
 The output VO depends on the difference between the inputs V1 and V2, not
on the voltage common to them (common-mode voltage).
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Chapter 5: Operational amplifiers
VIII.2. Intrumentation amplifier (IA)
Ex: A precision Intrumentation amplifier
Product highlight:
 Input noise is less than 4 nV/√Hz at 1 kHz.
 Pin programmable gains of 1, 100, 200, 500 and
1000 provided on the chip. Using a single
external resistor for other gains.
 The offset voltage, offset voltage drift, gain
accuracy and gain temperature coefficients are
guaranteed for all pretrimmed gains.
 Provides totally independent input and output
offset for high precision applications.
 A sense terminal is provided to enable the user
to minimize the errors induced through long
leads. A reference terminal is also provided to
permit level shifting at the output.
Price (100 - 499) Price (1000)
$4.82 $4.09
Datasheet:
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Chapter 5: Operational amplifiers
VIII.2. Intrumentation amplifier (IA)
Ex: LT167 – Single resistor gain, programmable, precision intrumentation amplifier
Price (1 - 99) Price (1000)
$6.45 $5.55 Datasheet: