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Transcript of Operational Amplifiers Basic Theory & Use in Analog Signal Processing By Muhammad Bilal PhD...
Operational AmplifiersBasic Theory
& Use in Analog Signal Processing
By
Muhammad BilalPhD 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
Analysis Model (Ideal OpAmp)
• Differential Input– Input Resistance almost infinity– Output Resistance (Ro) almost zero– Gain (A) almost infinity
OpAmp Configurations-- Inverting Amplifier
)()0(
)(
noutp
inout
npin
VAVV
AAVV
VVV
• No current can flow through Vp,Vn terminals
1
2
21
21
21
R
R
V
V
R
VA
V
RA
VV
R
VV
R
VV
ii
in
out
outoutout
in
outnnin
RR
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– 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
f
RZ
LjZ
CjZ
sistor
Inductor
Capacitor
2
1
Re
OpAmp Configurations-- Integrator
RC
j
jV
jV
in
out
)(
)(
0 10 20 30 40 50 60 70 80 90 1000
1
2
3
4
5
6
7
8
9
10Frequency Response of "Integrator"
Frequency
Mag
nitu
de
OpAmp Configurations-- Differentiator
RCjjV
jV
in
out
)(
)(
0 10 20 30 40 50 60 70 80 90 1000
1
2
3
4
5
6
7
8
9
10Frequency Response of "Differentiator"
Frequency
Mag
nitu
de
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– Filters
• First Order Filters
– Integrator (Low Pass)
– Differentiator (High Pass)
– Superposition (Band Pass)
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• R-C circuit simulation
ta
b
Aetx
tfbxdt
dxa
)(
)(
OpAmp—Solution of Differential Equations
• Second Order Constant Coefficient DE• R-L-C circuit simulation
))sin()cos(()(
)(2
2
tBtAetx
tfcxdt
dxb
dt
xda
at
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
Open Loop OpAmp Characteristics
Device LM741C LF351 OP-07 LH0003 AD549K
Technology BJT BiFET BJTHybrid
BJTBiFET
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.