Operational Amplifiers
Basic Theory
&
Use in Analog Signal Processing
By
Muhammad Bilal
PhD Candidate
Department of Computer Engineering, LUMS
Operational Amplifiers – Brief History
• Appeared around 1947 (vacuum tube age)
• Combination of High Gain & Negative Feedback
• Miniaturization after invention of BJT
• Integrated Circuit Operational Amplifier
– Robert Widlar at Fairchild Semiconductor Corps
(1968)
– Industry standard, the 741
Operational Amplifiers as Analog Computers
• Operational Amplifier
– Addition
– Subtraction
– Multiplication by a constant (Gain)
– Integration
– Differentiation
• MONIAC
Operational Amplifiers
Op-Amps
Schematic
Block Diagram
Analysis Model (Ideal OpAmp)
• Differential Input
– Input Resistance almost infinity
– Output Resistance (Ro) almost zero
– Gain (A) almost infinity
OpAmp Configurations
• Inverting Amplifier
OpAmp Configurations-- Inverting Amplifier
Vin  V p  Vn
Vout  AVin ( A  )
(V p  0)  Vout  A(Vn )
• No current can flow through
Vp,Vn terminals
iR1
Vin  Vn
R1
Vout
Vin 
A
R1
Vout
Vin

iR 2

Vn  Vout
R2

 Vout
 Vout
A
R2

R2

R1
OpAmp Configurations-- Inverting Amplifier
Lessons from Inverting Amp. configuration
• Gain is set via external components
– Stable gain due to ratio of resistors
• Effects of extremely high gain
– Virtual short circuit (Vp = Vn)
– Negative Feedback compensates for the
internal high gain of OpAmp
OpAmp Configurations– Non-Inverting Amplifier
Gain = 1 + R2 / R1
OpAmp Configurations– Voltage Follower
Due to negative feedback,
virtual short will occur,
forcing Vn to be equal to Vp
which is in turn equal to Vs.
Thus Vout = Vs and hence
the name voltage follower.
OpAmp Configurations-- Inverting Amplifier
• Generic
• Gain = - Z2 / Z1
1
Z Capacitor 
j C
Z Inductor  jL
Z Re sistor  R
  2f
OpAmp Configurations-- Integrator
Vout ( j )
j

Vin ( j ) RC
Frequency Response of "Integrator"
10
9
8
Magnitude
7
6
5
4
3
2
1
0
0
10
20
30
40
50
60
Frequency
70
80
90
100
OpAmp Configurations-- Integrator
• Time Domain Analysis
OpAmp Configurations-- Differentiator
Vout ( j )
  jRC
Vin ( j )
Frequency Response of "Differentiator"
10
9
8
Magnitude
7
6
5
4
3
2
1
0
0
10
20
30
40
50
60
Frequency
70
80
90
100
OpAmp Configurations-- Differentiator
• Time Domain Analysis
OpAmp Configurations-- Filters
• Integrator
– First Order Low Pass Filter
– Extremely high gain at low frequencies
• Only used within a closed loop
• Differentiator
– First Order High Pass Filter
OpAmp Circuits– Frequency Counter
• A ‘Differentiator’ followed by ‘Peak
Detector’
OpAmp Circuits– Summer
Vout = -(Vs2 + Vs1)
(R1=R2=R3)
OpAmp Circuits– Summer
OpAmp Circuits– Difference Amplifier
Vout = Vs2 – Vs1
(R1=R2=R3=R4)
OpAmp Circuits– Current Amplifiers
•
•
•
•
V to V
V to I
I to V
I to I
OpAmp Circuits– Filters
• First Order Filters
– Integrator (Low Pass)
– Differentiator (High Pass)
– Superposition (Band Pass)
OpAmp Circuits– Filters
•First Order Low Pass Filter
Vout ( j )
R2
1

Vin ( j )
R1 1  jR2C
OpAmp Circuits– Filters
•Second Order Low Pass Filter
OpAmp Non-linear Circuits
• Voltage Comparators
• Schmitt Trigger
– Variable Threshold
OpAmp Non-linear Circuits
• Superdiode
– Another manifestation of ‘virtual short’ due to
negative feedback
OpAmp Non-linear Circuits
• Signal Generators
– Multivibrator
• Square wave to Triangular
wave conversion
– Integrator
OpAmp—Solution of Differential Equations
•
•
•
•
Real time
Precise
Applicable to any order
Constant Coefficient DE’s only
OpAmp—Solution of Differential Equations
• First Order Constant Coefficient DE
dx
a  bx  f (t )
dt
OpAmp—Solution of Differential Equations
• First Order Constant Coefficient DE
• R-C circuit simulation
dx
a  bx  f (t )
dt
b
 t
a
x(t )  Ae
OpAmp—Solution of Differential Equations
• Second Order Constant Coefficient DE
• R-L-C circuit simulation
d 2x
dx
a 2  b  cx  f (t )
dt
dt
x(t )  e at ( A cos(t )  B sin(t ))
OpAmp—Solution of Differential Equations
• Second Order DE simulation
– Hardware Simulation of R-L-C circuit without
actual use of Inductor
– Implementation of precise mathematical
relationships given by DE’s
Analog Signal Processing
• Pros
–
–
–
–
Inherently Analog World
Precision
Simplicity
Intuitive Designs vs ‘Programming’
• Cons
–
–
–
–
Non-linearity
Rigidity
Noise Floor
Temperature dependence
Practical OpAmps Limitations
• Gain-Bandwidth Product
• Common Mode Rejection
• Slew Rate
Open Loop OpAmp Characteristics
Device
LM741C
LF351
OP-07
LH0003
AD549K
Technology
BJT
BiFET
BJT
Hybrid
BJT
BiFET
AOL(typ)
200 k
100 k
400 k
40 k
100 k
Rin
2 M
1012 
8 M
100 k
1013  || 1 pF
Ro
50 
30 
60 
50 
~100 
Slew Rate
0.5 V/s
13 V/s
0.3 V/s
70 V/s
3 V/s
CMRR
90 dB
100 dB
110 dB
90 dB
90 dB
References
• Design with Operational Amplifiers and Analog Integrated
Circuits,Sergio Franco, 3rd Edition.
• Basic Engineering Circuit Analysis, David Irwin, 8th Edition.
• Electronic Devices and Circuit Theory, Robert Boylsted, 9th Edition.