3. operational amplifiers - arraytool · 3/3/2016 · 3. operational amplifiers s. s. dan and s....
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Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
3. Operational Amplifiers
S. S. Dan and S. R. Zinka
Department of Electrical & Electronics EngineeringBITS Pilani, Hyderbad Campus
February 10, 2016
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Outline
1 Ideal Op-Amp
2 Inverting Configuration
3 Non-inverting Configuration
4 Integrators & Differentiators
5 Beauty of Miller’s Theorem ***
6 Summary
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Outline
1 Ideal Op-Amp
2 Inverting Configuration
3 Non-inverting Configuration
4 Integrators & Differentiators
5 Beauty of Miller’s Theorem ***
6 Summary
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Introduction
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Introduction
• An operational amplifier, op-amp, is nothing more than a DC-coupled,high-gain differential amplifier
• The name "operational amplifier" stems from the op-amp’s ability toperform mathematical operations.
• One of the reasons for the popularity of the op amp is its versatility ...one can do almost anything with op amps!
• Op amp is a circuit building block of universal importance
• Early op amps were constructed from discrete components (vacuumtubes and then transistors, and resistors), and their cost wasprohibitively high (tens of dollars)
• IC op amp has characteristics that closely approach the assumed ideal
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Introduction
• An operational amplifier, op-amp, is nothing more than a DC-coupled,high-gain differential amplifier
• The name "operational amplifier" stems from the op-amp’s ability toperform mathematical operations.
• One of the reasons for the popularity of the op amp is its versatility ...one can do almost anything with op amps!
• Op amp is a circuit building block of universal importance
• Early op amps were constructed from discrete components (vacuumtubes and then transistors, and resistors), and their cost wasprohibitively high (tens of dollars)
• IC op amp has characteristics that closely approach the assumed ideal
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Introduction
• An operational amplifier, op-amp, is nothing more than a DC-coupled,high-gain differential amplifier
• The name "operational amplifier" stems from the op-amp’s ability toperform mathematical operations.
• One of the reasons for the popularity of the op amp is its versatility ...one can do almost anything with op amps!
• Op amp is a circuit building block of universal importance
• Early op amps were constructed from discrete components (vacuumtubes and then transistors, and resistors), and their cost wasprohibitively high (tens of dollars)
• IC op amp has characteristics that closely approach the assumed ideal
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Introduction
• An operational amplifier, op-amp, is nothing more than a DC-coupled,high-gain differential amplifier
• The name "operational amplifier" stems from the op-amp’s ability toperform mathematical operations.
• One of the reasons for the popularity of the op amp is its versatility ...one can do almost anything with op amps!
• Op amp is a circuit building block of universal importance
• Early op amps were constructed from discrete components (vacuumtubes and then transistors, and resistors), and their cost wasprohibitively high (tens of dollars)
• IC op amp has characteristics that closely approach the assumed ideal
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Introduction
• An operational amplifier, op-amp, is nothing more than a DC-coupled,high-gain differential amplifier
• The name "operational amplifier" stems from the op-amp’s ability toperform mathematical operations.
• One of the reasons for the popularity of the op amp is its versatility ...one can do almost anything with op amps!
• Op amp is a circuit building block of universal importance
• Early op amps were constructed from discrete components (vacuumtubes and then transistors, and resistors), and their cost wasprohibitively high (tens of dollars)
• IC op amp has characteristics that closely approach the assumed ideal
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Introduction
• An operational amplifier, op-amp, is nothing more than a DC-coupled,high-gain differential amplifier
• The name "operational amplifier" stems from the op-amp’s ability toperform mathematical operations.
• One of the reasons for the popularity of the op amp is its versatility ...one can do almost anything with op amps!
• Op amp is a circuit building block of universal importance
• Early op amps were constructed from discrete components (vacuumtubes and then transistors, and resistors), and their cost wasprohibitively high (tens of dollars)
• IC op amp has characteristics that closely approach the assumed ideal
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Let’s See Internal Circuitry of an Op-Amp
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Let’s See Internal Circuitry of an Op-Amp
Non-invertinginput
3
1 kΩ
1
Offsetnull
50 kΩ
1 kΩ
5
Offsetnull
Invertinginput
2
7VS+
5 kΩ
39 kΩ
50 kΩ 50 Ω
7.5 kΩ
4.5 kΩ
30 pF25 Ω
50 Ω
6
Output
4
VS−
Q1
Q8 Q9Q12 Q13
Q14
Q17
Q20
Q2
Q3 Q4
Q7
Q5Q6
Q10
Q11
Q22
Q15
Q19
Q16
Current mirror Current mirror
Current mirrorDifferential amplifier Classs A gain stage
Output stage
Voltage level shifter
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
A Few Types of Op-Amps
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
A Few Types of Op-Amps
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Ideal Op Amp – Terminals
_
+
1
2
3
_
+
1
2
3
4
5
VCC
VEE
_
+
1
2
3
4
5
VCC
VEE
• Require dc power to operate• No terminal of the op-amp package is physically connected to ground• An op amp may have other terminals for specific purposes
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Ideal Op Amp – Terminals
_
+
1
2
3
_
+
1
2
3
4
5
VCC
VEE
_
+
1
2
3
4
5
VCC
VEE
• Require dc power to operate• No terminal of the op-amp package is physically connected to ground• An op amp may have other terminals for specific purposes
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Ideal Op Amp – Terminals
_
+
1
2
3
_
+
1
2
3
4
5
VCC
VEE
_
+
1
2
3
4
5
VCC
VEE
• Require dc power to operate
• No terminal of the op-amp package is physically connected to ground• An op amp may have other terminals for specific purposes
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Ideal Op Amp – Terminals
_
+
1
2
3
_
+
1
2
3
4
5
VCC
VEE
_
+
1
2
3
4
5
VCC
VEE
• Require dc power to operate• No terminal of the op-amp package is physically connected to ground
• An op amp may have other terminals for specific purposes
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Ideal Op Amp – Terminals
_
+
1
2
3
_
+
1
2
3
4
5
VCC
VEE
_
+
1
2
3
4
5
VCC
VEE
• Require dc power to operate• No terminal of the op-amp package is physically connected to ground• An op amp may have other terminals for specific purposes
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Ideal Op Amp – Characteristics
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Ideal Op Amp – Characteristics
+
-
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Ideal Op Amp – Characteristics
+
_+
_+v1
v2
A (v2 - v1)+
-
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Ideal Op Amp – Characteristics
Inverting input
Noninverting input
Output
+
_+
_+v1
v2
A (v2 - v1)+
-
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Ideal Op Amp – Characteristics
Inverting input
Noninverting input
Output
+
_+
_+v1i1 = 0
i2 = 0v2
A (v2 - v1)+
-
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Ideal Op Amp – Characteristics
Inverting input
Noninverting input
Output
+
_+
_+v1i1 = 0
i2 = 0v2
A (v2 - v1)+
-
A tends to ∞
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Summary of Ideal Op Amp Characteristics
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Summary of Ideal Op Amp Characteristics
• The op amp responds only to the difference signal, v2 − v1, and henceignores any signal common to both inputs (i.e., ∞ CMRR)
• The ideal op amp is not supposed to draw any input current, i.e., theinput impedance of an ideal op amp is supposed to be infinite
• The output terminal is supposed to act as the output terminal of an idealvoltage source, i.e., the output impedance of an ideal op amp issupposed to be zero
• An important characteristic of op amps is that they are direct-coupled ordc amplifiers, where dc stands for direct-coupled
• Ideal op amps will amplify signals of any frequency with equal gain,and are thus said to have infinite bandwidth
• In almost all applications the op amp will not be used alone in aso-called open-loop configuration
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Summary of Ideal Op Amp Characteristics
• The op amp responds only to the difference signal, v2 − v1, and henceignores any signal common to both inputs (i.e., ∞ CMRR)
• The ideal op amp is not supposed to draw any input current, i.e., theinput impedance of an ideal op amp is supposed to be infinite
• The output terminal is supposed to act as the output terminal of an idealvoltage source, i.e., the output impedance of an ideal op amp issupposed to be zero
• An important characteristic of op amps is that they are direct-coupled ordc amplifiers, where dc stands for direct-coupled
• Ideal op amps will amplify signals of any frequency with equal gain,and are thus said to have infinite bandwidth
• In almost all applications the op amp will not be used alone in aso-called open-loop configuration
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Summary of Ideal Op Amp Characteristics
• The op amp responds only to the difference signal, v2 − v1, and henceignores any signal common to both inputs (i.e., ∞ CMRR)
• The ideal op amp is not supposed to draw any input current, i.e., theinput impedance of an ideal op amp is supposed to be infinite
• The output terminal is supposed to act as the output terminal of an idealvoltage source, i.e., the output impedance of an ideal op amp issupposed to be zero
• An important characteristic of op amps is that they are direct-coupled ordc amplifiers, where dc stands for direct-coupled
• Ideal op amps will amplify signals of any frequency with equal gain,and are thus said to have infinite bandwidth
• In almost all applications the op amp will not be used alone in aso-called open-loop configuration
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Summary of Ideal Op Amp Characteristics
• The op amp responds only to the difference signal, v2 − v1, and henceignores any signal common to both inputs (i.e., ∞ CMRR)
• The ideal op amp is not supposed to draw any input current, i.e., theinput impedance of an ideal op amp is supposed to be infinite
• The output terminal is supposed to act as the output terminal of an idealvoltage source, i.e., the output impedance of an ideal op amp issupposed to be zero
• An important characteristic of op amps is that they are direct-coupled ordc amplifiers, where dc stands for direct-coupled
• Ideal op amps will amplify signals of any frequency with equal gain,and are thus said to have infinite bandwidth
• In almost all applications the op amp will not be used alone in aso-called open-loop configuration
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Summary of Ideal Op Amp Characteristics
• The op amp responds only to the difference signal, v2 − v1, and henceignores any signal common to both inputs (i.e., ∞ CMRR)
• The ideal op amp is not supposed to draw any input current, i.e., theinput impedance of an ideal op amp is supposed to be infinite
• The output terminal is supposed to act as the output terminal of an idealvoltage source, i.e., the output impedance of an ideal op amp issupposed to be zero
• An important characteristic of op amps is that they are direct-coupled ordc amplifiers, where dc stands for direct-coupled
• Ideal op amps will amplify signals of any frequency with equal gain,and are thus said to have infinite bandwidth
• In almost all applications the op amp will not be used alone in aso-called open-loop configuration
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Summary of Ideal Op Amp Characteristics
• The op amp responds only to the difference signal, v2 − v1, and henceignores any signal common to both inputs (i.e., ∞ CMRR)
• The ideal op amp is not supposed to draw any input current, i.e., theinput impedance of an ideal op amp is supposed to be infinite
• The output terminal is supposed to act as the output terminal of an idealvoltage source, i.e., the output impedance of an ideal op amp issupposed to be zero
• An important characteristic of op amps is that they are direct-coupled ordc amplifiers, where dc stands for direct-coupled
• Ideal op amps will amplify signals of any frequency with equal gain,and are thus said to have infinite bandwidth
• In almost all applications the op amp will not be used alone in aso-called open-loop configuration
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Outline
1 Ideal Op-Amp
2 Inverting Configuration
3 Non-inverting Configuration
4 Integrators & Differentiators
5 Beauty of Miller’s Theorem ***
6 Summary
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Inverting Configuration
_
+_+vI
R1
+vO
R2
• As mentioned in the previous section, op amps are not used alone;rather, the op amp is connected to passive components in a feedbackcircuit
• Here we are using negative feedback. Can you guess how?• Why the above configuration is known as the inverting configuration?
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Inverting Configuration
_
+_+vI
R1
+vO
R2
• As mentioned in the previous section, op amps are not used alone;rather, the op amp is connected to passive components in a feedbackcircuit
• Here we are using negative feedback. Can you guess how?• Why the above configuration is known as the inverting configuration?
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Inverting Configuration
_
+_+vI
R1
+vO
R2
• As mentioned in the previous section, op amps are not used alone;rather, the op amp is connected to passive components in a feedbackcircuit
• Here we are using negative feedback. Can you guess how?• Why the above configuration is known as the inverting configuration?
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Inverting Configuration
_
+_+vI
R1
+vO
R2
• As mentioned in the previous section, op amps are not used alone;rather, the op amp is connected to passive components in a feedbackcircuit
• Here we are using negative feedback. Can you guess how?
• Why the above configuration is known as the inverting configuration?
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Inverting Configuration
_
+_+vI
R1
+vO
R2
• As mentioned in the previous section, op amps are not used alone;rather, the op amp is connected to passive components in a feedbackcircuit
• Here we are using negative feedback. Can you guess how?• Why the above configuration is known as the inverting configuration?
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Closed-Loop Gain
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Closed-Loop Gain
_
+_+vI
R1
+vO
R2
v0 = −R2R1
v1
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Closed-Loop Gain
_
+_+vI
R1
+vO
R2
∞
v0 = −R2R1
v1
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Closed-Loop Gain
_
+_+vI
R1
+vO
R2
?? ∞
v0 = −R2R1
v1
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Closed-Loop Gain
_
+_+vI
R1
+vO
R2
0 0 V ∞
v0 = −R2R1
v1
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Closed-Loop Gain
_
+_+vI
R1
+vO
R2
00 V
?
?∞
v0 = −R2R1
v1
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Closed-Loop Gain
vI/R1
_
+_+vI
R1
+vO
R2
00 V
vI/R1
∞
v0 = −R2R1
v1
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Closed-Loop Gain
vI/R1
_
+_+vI
R1
+vO
R2
00 V
vI/R1
∞
v0 = −R2R1
v1
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Closed-Loop Gain – A Few Observations
• The closed-loop gain is independent of the op-amp gain.
• The fact that the closed-loop gain depends entirely on external passivecomponents (resistors R1 and R2) is very significant. It means that wecan make the closed-loop gain as accurate as we want by selectingpassive components of appropriate accuracy.
• Through applying negative feedback we have obtained a closed-loopgain that is much smaller than A but is stable and predictable. That is,we are trading gain for accuracy.
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Closed-Loop Gain – A Few Observations
• The closed-loop gain is independent of the op-amp gain.
• The fact that the closed-loop gain depends entirely on external passivecomponents (resistors R1 and R2) is very significant. It means that wecan make the closed-loop gain as accurate as we want by selectingpassive components of appropriate accuracy.
• Through applying negative feedback we have obtained a closed-loopgain that is much smaller than A but is stable and predictable. That is,we are trading gain for accuracy.
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Closed-Loop Gain – A Few Observations
• The closed-loop gain is independent of the op-amp gain.
• The fact that the closed-loop gain depends entirely on external passivecomponents (resistors R1 and R2) is very significant. It means that wecan make the closed-loop gain as accurate as we want by selectingpassive components of appropriate accuracy.
• Through applying negative feedback we have obtained a closed-loopgain that is much smaller than A but is stable and predictable. That is,we are trading gain for accuracy.
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Closed-Loop Gain – A Few Observations
• The closed-loop gain is independent of the op-amp gain.
• The fact that the closed-loop gain depends entirely on external passivecomponents (resistors R1 and R2) is very significant. It means that wecan make the closed-loop gain as accurate as we want by selectingpassive components of appropriate accuracy.
• Through applying negative feedback we have obtained a closed-loopgain that is much smaller than A but is stable and predictable. That is,we are trading gain for accuracy.
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Effect of Finite Open-Loop Gain
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Effect of Finite Open-Loop Gain
_
+_+vI
R1
+vO
R2
i1 = i2 =vI + vO/A
R1
vOvI
=−R2/R1
1 + (1 + R2/R1) /A
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Effect of Finite Open-Loop Gain
_
+_+vI
R1
+vO
R2
A
i1 = i2 =vI + vO/A
R1
vOvI
=−R2/R1
1 + (1 + R2/R1) /A
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Effect of Finite Open-Loop Gain
_
+_+vI
R1
+vO
R2
?? A
i1 = i2 =vI + vO/A
R1
vOvI
=−R2/R1
1 + (1 + R2/R1) /A
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Effect of Finite Open-Loop Gain
_
+_+vI
R1
+vO
R2
0 - vO/A A
i1 = i2 =vI + vO/A
R1
vOvI
=−R2/R1
1 + (1 + R2/R1) /A
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Effect of Finite Open-Loop Gain
_
+_+vI
R1
+vO
R2
0
?
?- vO/A A
i1 = i2 =vI + vO/A
R1
vOvI
=−R2/R1
1 + (1 + R2/R1) /A
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Effect of Finite Open-Loop Gain
_
+_+vI
R1
+vO
R2
0
?
?- vO/A A
i1 = i2 =vI + vO/A
R1
vOvI
=−R2/R1
1 + (1 + R2/R1) /A
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Effect of Finite Open-Loop Gain
_
+_+vI
R1
+vO
R2
0
?
?- vO/A A
i1 = i2 =vI + vO/A
R1
vOvI
=−R2/R1
1 + (1 + R2/R1) /A
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Effect of A on Input and Output Resistances
_
+_+vI
R1
+vO
R2
0
?
?- vO/A A
Ri =vII1
=vIR1
vI + vO/A=
R1
1 +(
vOvI
)/A
< R1 (1)
Ro = 0 (2)
To make Ri high we should select a high value for R1. However, if the requiredgain is also high, then R2 could become impractically large. We may concludethat the inverting configuration suffers from a low input resistance.
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Effect of A on Input and Output Resistances
_
+_+vI
R1
+vO
R2
0
?
?- vO/A A
Ri =vII1
=vIR1
vI + vO/A=
R1
1 +(
vOvI
)/A
< R1 (1)
Ro = 0 (2)
To make Ri high we should select a high value for R1. However, if the requiredgain is also high, then R2 could become impractically large. We may concludethat the inverting configuration suffers from a low input resistance.
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Effect of A on Input and Output Resistances
_
+_+vI
R1
+vO
R2
0
?
?- vO/A A
Ri =vII1
=vIR1
vI + vO/A=
R1
1 +(
vOvI
)/A
< R1 (1)
Ro = 0 (2)
To make Ri high we should select a high value for R1. However, if the requiredgain is also high, then R2 could become impractically large. We may concludethat the inverting configuration suffers from a low input resistance.
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Effect of A on Input and Output Resistances
_
+_+vI
R1
+vO
R2
0
?
?- vO/A A
Ri =vII1
=vIR1
vI + vO/A=
R1
1 +(
vOvI
)/A
< R1 (1)
Ro = 0 (2)
To make Ri high we should select a high value for R1. However, if the requiredgain is also high, then R2 could become impractically large. We may concludethat the inverting configuration suffers from a low input resistance.
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Effect of A on Input and Output Resistances
_
+_+vI
R1
+vO
R2
0
?
?- vO/A A
Ri =vII1
=vIR1
vI + vO/A=
R1
1 +(
vOvI
)/A
< R1 (1)
Ro = 0 (2)
To make Ri high we should select a high value for R1. However, if the requiredgain is also high, then R2 could become impractically large. We may concludethat the inverting configuration suffers from a low input resistance.
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Now, let’s see two applications of op-amp inverting configuration ...
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
1st Application – The Weighted Summer
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
1st Application – The Weighted Summer
_
++vO
Rf
R1
R2
Rn
v1
vn
v2
itot =v1R1
+v2R2
+ · · ·+ vn
Rn
vO = −(
v1R1
+v2R2
+ · · ·+ vn
Rn
)Rf = −
(Rf
R1v1 +
Rf
R2v2 + · · ·+
Rf
Rnvn
)
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
1st Application – The Weighted Summer
_
++vO
Rf
00 V
R1
R2
Rn
v1
vn
v2
itot =v1R1
+v2R2
+ · · ·+ vn
Rn
vO = −(
v1R1
+v2R2
+ · · ·+ vn
Rn
)Rf = −
(Rf
R1v1 +
Rf
R2v2 + · · ·+
Rf
Rnvn
)
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
1st Application – The Weighted Summer
_
++vO
Rf
00 V
R1
R2
Rn
?
v1
vn
v2
itot =v1R1
+v2R2
+ · · ·+ vn
Rn
vO = −(
v1R1
+v2R2
+ · · ·+ vn
Rn
)Rf = −
(Rf
R1v1 +
Rf
R2v2 + · · ·+
Rf
Rnvn
)
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
1st Application – The Weighted Summer
_
++vO
Rf
00 V
R1i1
R2i2
Rnin
?
v1
vn
v2
itot =v1R1
+v2R2
+ · · ·+ vn
Rn
vO = −(
v1R1
+v2R2
+ · · ·+ vn
Rn
)Rf = −
(Rf
R1v1 +
Rf
R2v2 + · · ·+
Rf
Rnvn
)
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
1st Application – The Weighted Summer
_
++vO
Rf
00 V
R1i1
R2i2
Rnin
?
v1
vn
v2
itot =v1R1
+v2R2
+ · · ·+ vn
Rn
vO = −(
v1R1
+v2R2
+ · · ·+ vn
Rn
)Rf = −
(Rf
R1v1 +
Rf
R2v2 + · · ·+
Rf
Rnvn
)
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
1st Application – The Weighted Summer
_
++vO
Rf
00 V
R1i1
R2i2
Rnin
?
v1
vn
v2
itot =v1R1
+v2R2
+ · · ·+ vn
Rn
vO = −(
v1R1
+v2R2
+ · · ·+ vn
Rn
)Rf = −
(Rf
R1v1 +
Rf
R2v2 + · · ·+
Rf
Rnvn
)
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
2nd Application – Generalized Weighted Summer
_
+
vO
Ra
R1
R2
Rn
v1
vn
v2
_
+
Rc
Rb
Rn+1
Rm
vn+1
vm
vO =Ra
R1
Rc
Rbv1 + · · ·+
Ra
Rn
Rc
Rbvn−
Rc
Rn+1vn+1 −
Rc
Rn+2vn+2 − · · · −
Rc
Rmvm
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
2nd Application – Generalized Weighted Summer
_
+
vO
Ra
R1
R2
Rn
v1
vn
v2
_
+
Rc
Rb
Rn+1
Rm
vn+1
vm
vO =Ra
R1
Rc
Rbv1 + · · ·+
Ra
Rn
Rc
Rbvn−
Rc
Rn+1vn+1 −
Rc
Rn+2vn+2 − · · · −
Rc
Rmvm
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
2nd Application – Generalized Weighted Summer
_
+
vO
Ra
R1
R2
Rn
v1
vn
v2
_
+
Rc
Rb
Rn+1
Rm
vn+1
vm
vO =Ra
R1
Rc
Rbv1 + · · ·+
Ra
Rn
Rc
Rbvn−
Rc
Rn+1vn+1 −
Rc
Rn+2vn+2 − · · · −
Rc
Rmvm
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Outline
1 Ideal Op-Amp
2 Inverting Configuration
3 Non-inverting Configuration
4 Integrators & Differentiators
5 Beauty of Miller’s Theorem ***
6 Summary
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Non-inverting Configuration
_
+
_+vI
R1
+vO
R2
• As mentioned in the previous sections, op amps are not used alone;rather, the op amp is connected to passive components in a feedbackcircuit
• Here also we are using negative feedback. Can you guess how?• Why the above configuration is known as the non-inverting
configuration?
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Non-inverting Configuration
_
+
_+vI
R1
+vO
R2
• As mentioned in the previous sections, op amps are not used alone;rather, the op amp is connected to passive components in a feedbackcircuit
• Here also we are using negative feedback. Can you guess how?• Why the above configuration is known as the non-inverting
configuration?
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Non-inverting Configuration
_
+
_+vI
R1
+vO
R2
• As mentioned in the previous sections, op amps are not used alone;rather, the op amp is connected to passive components in a feedbackcircuit
• Here also we are using negative feedback. Can you guess how?• Why the above configuration is known as the non-inverting
configuration?
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Non-inverting Configuration
_
+
_+vI
R1
+vO
R2
• As mentioned in the previous sections, op amps are not used alone;rather, the op amp is connected to passive components in a feedbackcircuit
• Here also we are using negative feedback. Can you guess how?
• Why the above configuration is known as the non-invertingconfiguration?
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Non-inverting Configuration
_
+
_+vI
R1
+vO
R2
• As mentioned in the previous sections, op amps are not used alone;rather, the op amp is connected to passive components in a feedbackcircuit
• Here also we are using negative feedback. Can you guess how?• Why the above configuration is known as the non-inverting
configuration?
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Closed-Loop Gain
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Closed-Loop Gain
_
+
_+vI
R1
+vO
R2
i1 = i2 =vIR1
vO = vI +vIR1
R2 = vI
(1 +
R2R1
)
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Closed-Loop Gain
_
+
_+vI
R1
+vO
R2
??
i1 = i2 =vIR1
vO = vI +vIR1
R2 = vI
(1 +
R2R1
)
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Closed-Loop Gain
_
+
_+vI
R1
+vO
R2
0vI
i1 = i2 =vIR1
vO = vI +vIR1
R2 = vI
(1 +
R2R1
)
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Closed-Loop Gain
_
+
_+vI
R1
+vO
R2
0vI
?
?
i1 = i2 =vIR1
vO = vI +vIR1
R2 = vI
(1 +
R2R1
)
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Closed-Loop Gain
_
+
_+vI
R1
+vO
R2
vI/R1
vI/R1
0vI
i1 = i2 =vIR1
vO = vI +vIR1
R2 = vI
(1 +
R2R1
)
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Closed-Loop Gain
_
+
_+vI
R1
+vO
R2
vI/R1
vI/R1
0vI
i1 = i2 =vIR1
vO = vI +vIR1
R2 = vI
(1 +
R2R1
)
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Closed-Loop Gain
_
+
_+vI
R1
+vO
R2
vI/R1
vI/R1
0vI
i1 = i2 =vIR1
vO = vI +vIR1
R2 = vI
(1 +
R2R1
)
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Effect of Finite Open-Loop Gain
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Effect of Finite Open-Loop Gain
_
+
_+vI
R1
+vO
R2
i1 = i2 =vI − vO/A
R1
vOvI
=1 + R2/R1
1 + (1 + R2/R1) /A
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Effect of Finite Open-Loop Gain
_
+
_+vI
R1
+vO
R2
? A?
i1 = i2 =vI − vO/A
R1
vOvI
=1 + R2/R1
1 + (1 + R2/R1) /A
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Effect of Finite Open-Loop Gain
_
+
_+vI
R1
+vO
R2
0 AvI - vO/A
i1 = i2 =vI − vO/A
R1
vOvI
=1 + R2/R1
1 + (1 + R2/R1) /A
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Effect of Finite Open-Loop Gain
_
+
_+vI
R1
+vO
R2
0 AvI - vO/A
?
i1 = i2 =vI − vO/A
R1
vOvI
=1 + R2/R1
1 + (1 + R2/R1) /A
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Effect of Finite Open-Loop Gain
_
+
_+vI
R1
+vO
R2
0 AvI - vO/A
?
i1 = i2 =vI − vO/A
R1
vOvI
=1 + R2/R1
1 + (1 + R2/R1) /A
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Effect of A on Input and Output Resistances
_
+
_+vI
R1
+vO
R2
0 AvI - vO/A
?
Ri → ∞
Ro = 0
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Effect of A on Input and Output Resistances
_
+
_+vI
R1
+vO
R2
0 AvI - vO/A
?
Ri → ∞
Ro = 0
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Effect of A on Input and Output Resistances
_
+
_+vI
R1
+vO
R2
0 AvI - vO/A
?
Ri → ∞
Ro = 0
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Effect of A on Input and Output Resistances
_
+
_+vI
R1
+vO
R2
0 AvI - vO/A
?
Ri → ∞
Ro = 0
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Now, let’s see an application of op-amp non-inverting configuration ...
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
An Application—The Voltage Follower
_
+
_+vI
+vO
++
vO
+
vI vI
• The property of high input impedance is a very desirable feature of thenon-inverting configuration
• Also known as unity-gain amplifier
• The circuit is said to have 100% negative feedback
• Since the non-inverting configuration has a gain greater than or equal tounity, depending on the choice of gain, some prefer to call it “a followerwith gain”
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
An Application—The Voltage Follower
_
+
_+vI
+vO
++
vO
+
vI vI
• The property of high input impedance is a very desirable feature of thenon-inverting configuration
• Also known as unity-gain amplifier
• The circuit is said to have 100% negative feedback
• Since the non-inverting configuration has a gain greater than or equal tounity, depending on the choice of gain, some prefer to call it “a followerwith gain”
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
An Application—The Voltage Follower
_
+
_+vI
+vO
++
vO
+
vI vI
• The property of high input impedance is a very desirable feature of thenon-inverting configuration
• Also known as unity-gain amplifier
• The circuit is said to have 100% negative feedback
• Since the non-inverting configuration has a gain greater than or equal tounity, depending on the choice of gain, some prefer to call it “a followerwith gain”
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
An Application—The Voltage Follower
_
+
_+vI
+vO
++
vO
+
vI vI
• The property of high input impedance is a very desirable feature of thenon-inverting configuration
• Also known as unity-gain amplifier
• The circuit is said to have 100% negative feedback
• Since the non-inverting configuration has a gain greater than or equal tounity, depending on the choice of gain, some prefer to call it “a followerwith gain”
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
An Application—The Voltage Follower
_
+
_+vI
+vO
++
vO
+
vI vI
• The property of high input impedance is a very desirable feature of thenon-inverting configuration
• Also known as unity-gain amplifier
• The circuit is said to have 100% negative feedback
• Since the non-inverting configuration has a gain greater than or equal tounity, depending on the choice of gain, some prefer to call it “a followerwith gain”
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
An Application—The Voltage Follower
_
+
_+vI
+vO
++
vO
+
vI vI
• The property of high input impedance is a very desirable feature of thenon-inverting configuration
• Also known as unity-gain amplifier
• The circuit is said to have 100% negative feedback
• Since the non-inverting configuration has a gain greater than or equal tounity, depending on the choice of gain, some prefer to call it “a followerwith gain”
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Outline
1 Ideal Op-Amp
2 Inverting Configuration
3 Non-inverting Configuration
4 Integrators & Differentiators
5 Beauty of Miller’s Theorem ***
6 Summary
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Inverting Configuration with General Impedances
_
+_+vI
Z1
+vO
Z2
vOvI
= −Z2Z1
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Inverting Configuration with General Impedances
_
+_+vI
Z1
+vO
Z2
vOvI
= −Z2Z1
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Inverting Configuration with General Impedances
_
+_+vI
Z1
+vO
Z2
vOvI
= −Z2Z1
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Op-Amp Integrator
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Op-Amp Integrator
_
+_+vI
R
+vO
C
vO = − 1C
∫ t
−∞
(vIR
)dt =
1RC
∫ 0
−∞vIdt− 1
RC
∫ t
0vIdt = −VC −
1RC
∫ t
0vIdt
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Op-Amp Integrator
_
+_+vI
R
+vO
C
?
?
vO = − 1C
∫ t
−∞
(vIR
)dt =
1RC
∫ 0
−∞vIdt− 1
RC
∫ t
0vIdt = −VC −
1RC
∫ t
0vIdt
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Op-Amp Integrator
_
+_+vI
R
+vO
C
0
0 V
vO = − 1C
∫ t
−∞
(vIR
)dt =
1RC
∫ 0
−∞vIdt− 1
RC
∫ t
0vIdt = −VC −
1RC
∫ t
0vIdt
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Op-Amp Integrator
_
+_+vI
R
+vO
C
0
0 V
?
?
vO = − 1C
∫ t
−∞
(vIR
)dt =
1RC
∫ 0
−∞vIdt− 1
RC
∫ t
0vIdt = −VC −
1RC
∫ t
0vIdt
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Op-Amp Integrator
_
+_+vI
R
+vO
C
0
0 V
vI/R
vI/R
vO = − 1C
∫ t
−∞
(vIR
)dt =
1RC
∫ 0
−∞vIdt− 1
RC
∫ t
0vIdt = −VC −
1RC
∫ t
0vIdt
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Op-Amp Integrator
_
+_+vI
R
+vO
C
0
0 V
vI/R
vI/R
vO =
− 1C
∫ t
−∞
(vIR
)dt =
1RC
∫ 0
−∞vIdt− 1
RC
∫ t
0vIdt = −VC −
1RC
∫ t
0vIdt
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Op-Amp Integrator
_
+_+vI
R
+vO
C
0
0 V
vI/R
vI/R
vO = − 1C
∫ t
−∞
(vIR
)dt =
1RC
∫ 0
−∞vIdt− 1
RC
∫ t
0vIdt = −VC −
1RC
∫ t
0vIdt
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Op-Amp Integrator
_
+_+vI
R
+vO
C
0
0 V
vI/R
vI/R
vO = − 1C
∫ t
−∞
(vIR
)dt =
1RC
∫ 0
−∞vIdt− 1
RC
∫ t
0vIdt =
−VC −1
RC
∫ t
0vIdt
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Op-Amp Integrator
_
+_+vI
R
+vO
C
0
0 V
vI/R
vI/R
vO = − 1C
∫ t
−∞
(vIR
)dt =
1RC
∫ 0
−∞vIdt− 1
RC
∫ t
0vIdt = −VC −
1RC
∫ t
0vIdt
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Op-Amp Integrator in Frequency Domain
_
+_+vI
R
+vO
C
(dB)
CR
(log scale)
VoVi
1ω
6 dB/octave-
vOvI
= −Z2Z1
= −1/jωCR
= − 1jωRC
=1
ωRC∠90
We can observe that
at ω = 0, the above circuit is operating with an open
loop.
So, it is clear that the integrator circuit will suffer deleterious effects from thepresence of the op-amp input dc offset voltage.
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Op-Amp Integrator in Frequency Domain
_
+_+vI
R
+vO
C
(dB)
CR
(log scale)
VoVi
1ω
6 dB/octave-
vOvI
= −Z2Z1
= −1/jωCR
= − 1jωRC
=1
ωRC∠90
We can observe that
at ω = 0, the above circuit is operating with an open
loop.
So, it is clear that the integrator circuit will suffer deleterious effects from thepresence of the op-amp input dc offset voltage.
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Op-Amp Integrator in Frequency Domain
_
+_+vI
R
+vO
C
(dB)
CR
(log scale)
VoVi
1ω
6 dB/octave-
vOvI
= −Z2Z1
= −1/jωCR
= − 1jωRC
=1
ωRC∠90
We can observe that at ω = 0, the above circuit is operating with an open
loop.
So, it is clear that the integrator circuit will suffer deleterious effects from thepresence of the op-amp input dc offset voltage.
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Op-Amp Integrator in Frequency Domain
_
+_+vI
R
+vO
C
(dB)
CR
(log scale)
VoVi
1ω
6 dB/octave-
vOvI
= −Z2Z1
= −1/jωCR
= − 1jωRC
=1
ωRC∠90
We can observe that at ω = 0, the above circuit is operating with an open
loop.
So, it is clear that the integrator circuit will suffer deleterious effects from thepresence of the op-amp input dc offset voltage.
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Op-Amp Integrator in Frequency Domain
_
+_+vI
R
+vO
C
(dB)
CR
(log scale)
VoVi
1ω
6 dB/octave-
vOvI
= −Z2Z1
= −1/jωCR
= − 1jωRC
=1
ωRC∠90
We can observe that at ω = 0, the above circuit is operating with an open
loop.
So, it is clear that the integrator circuit will suffer deleterious effects from thepresence of the op-amp input dc offset voltage.
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Miller Integrator
C
R
RF
vO (t)vI (t) +
_
+ _
+
vOvI
= −Z2Z1
= −
(RF
1+jωRFC
)R
= − RF/R1 + jωRFC
So, dc problem of the integrator circuit can be alleviated by connecting aresistor RF across the integrator capacitor C.
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Miller Integrator
C
R
RF
vO (t)vI (t) +
_
+ _
+
vOvI
= −Z2Z1
= −
(RF
1+jωRFC
)R
= − RF/R1 + jωRFC
So, dc problem of the integrator circuit can be alleviated by connecting aresistor RF across the integrator capacitor C.
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Miller Integrator
C
R
RF
vO (t)vI (t) +
_
+ _
+
vOvI
= −Z2Z1
= −
(RF
1+jωRFC
)R
= − RF/R1 + jωRFC
So, dc problem of the integrator circuit can be alleviated by connecting aresistor RF across the integrator capacitor C.
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Miller Integrator
C
R
RF
vO (t)vI (t) +
_
+ _
+
vOvI
= −Z2Z1
= −
(RF
1+jωRFC
)R
= − RF/R1 + jωRFC
So, dc problem of the integrator circuit can be alleviated by connecting aresistor RF across the integrator capacitor C.
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Op-Amp Differentiator
C
R
vI (t) vO(t)
i
i
0
0 V
_
+_
+
_
+
vO = −iR = −CdvIdt× R = −RC
dvIdt
vOvI
= −Z2Z1
= − R1/jωRC
= −jωRC = ωRC∠− 90
Differentiator circuits behaves like noise magnifiers and also sufferer fromstability problems. So, they are generally avoided in practice.
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Op-Amp Differentiator
C
R
vI (t) vO(t)
i
i
0
0 V
_
+_
+
_
+
vO = −iR = −CdvIdt× R = −RC
dvIdt
vOvI
= −Z2Z1
= − R1/jωRC
= −jωRC = ωRC∠− 90
Differentiator circuits behaves like noise magnifiers and also sufferer fromstability problems. So, they are generally avoided in practice.
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Op-Amp Differentiator
C
R
vI (t) vO(t)
i
i
0
0 V
_
+_
+
_
+
vO = −iR = −CdvIdt× R = −RC
dvIdt
vOvI
= −Z2Z1
= − R1/jωRC
= −jωRC = ωRC∠− 90
Differentiator circuits behaves like noise magnifiers and also sufferer fromstability problems. So, they are generally avoided in practice.
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Op-Amp Differentiator
C
R
vI (t) vO(t)
i
i
0
0 V
_
+_
+
_
+
vO = −iR = −CdvIdt× R = −RC
dvIdt
vOvI
= −Z2Z1
= − R1/jωRC
= −jωRC = ωRC∠− 90
Differentiator circuits behaves like noise magnifiers and also sufferer fromstability problems. So, they are generally avoided in practice.
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Op-Amp Differentiator
C
R
vI (t) vO(t)
i
i
0
0 V
_
+_
+
_
+
vO = −iR = −CdvIdt× R = −RC
dvIdt
vOvI
= −Z2Z1
= − R1/jωRC
= −jωRC = ωRC∠− 90
Differentiator circuits behaves like noise magnifiers and also sufferer fromstability problems. So, they are generally avoided in practice.
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Outline
1 Ideal Op-Amp
2 Inverting Configuration
3 Non-inverting Configuration
4 Integrators & Differentiators
5 Beauty of Miller’s Theorem ***
6 Summary
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Inverting Configuration
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Inverting Configuration
_
+_+v1
R1
+v2
R2
A
+vi
+
-AviR2/(1+A)
R1
_+v1+v2
R2/(1+A-1)
+vi
+
vo
+
-Avi
R2
R1
_+v1+v2
v2v1
= − AR2R1 (1 + A) + R2
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Non-inverting Configuration (Wrong!)
_
+
_+v1
R1
+v2
R2
A
+vi
+
-AviR2/(1+A)
R1
+v2
R2/(1+A-1)
+vi
+
vo
+
-Avi
R2
R1
v1
+v2
v1
v2v1
=AR2
R1 (1 + A) + R2
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Miller’s Theorem
+
V2= KV1
1 2Z II
+
V2= KV1Z1 Z2
1 2I2= II1= I
+
V1
+
V1
Z1 = Z/ (1− K)
Z2 = Z/(1− 1/K)
Miller’s theorem needs a common ground (or reference voltage) on bothsides ...
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Miller’s Theorem
+
V2= KV1
1 2Z II
+
V2= KV1Z1 Z2
1 2I2= II1= I
+
V1
+
V1
Z1 = Z/ (1− K)
Z2 = Z/(1− 1/K)
Miller’s theorem needs a common ground (or reference voltage) on bothsides ...
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Miller’s Theorem
+
V2= KV1
1 2Z II
+
V2= KV1Z1 Z2
1 2I2= II1= I
+
V1
+
V1
Z1 = Z/ (1− K)
Z2 = Z/(1− 1/K)
Miller’s theorem needs a common ground (or reference voltage) on bothsides ...
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Outline
1 Ideal Op-Amp
2 Inverting Configuration
3 Non-inverting Configuration
4 Integrators & Differentiators
5 Beauty of Miller’s Theorem ***
6 Summary
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
Summary of Ideal Op Amp Characteristics
• The op amp responds only to the difference signal, v2 − v1, and henceignores any signal common to both inputs (i.e., ∞ CMRR)
• The ideal op amp is not supposed to draw any input current, i.e., theinput impedance of an ideal op amp is supposed to be infinite
• The output terminal is supposed to act as the output terminal of an idealvoltage source, i.e., the output impedance of an ideal op amp issupposed to be zero
• An important characteristic of op amps is that they are direct-coupled ordc amplifiers, where dc stands for direct-coupled
• Ideal op amps will amplify signals of any frequency with equal gain,and are thus said to have infinite bandwidth
• In almost all applications the op amp will not be used alone in aso-called open-loop configuration
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Inverting Configuration
_
+_+vI
R1
+vO
R2
vOvI
=−R2/R1
1 + (1 + R2/R1) /A
Ri =R1
1 +(
vOvI
)/A
Ro = 0
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Non-inverting Configuration
_
+
_+vI
R1
+vO
R2
vOvI
=1 + R2/R1
1 + (1 + R2/R1) /A
Ri → ∞
Ro = 0
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Op-Amp Integrator
_
+_+vI
R
+vO
C
(dB)
CR
(log scale)
VoVi
1ω
6 dB/octave-
vOvI
= −Z2Z1
= −1/jωCR
= − 1jωRC
=1
ωRC∠90
We can observe that at ω = 0, the above circuit is operating with an open
loop.
So, it is clear that the integrator circuit will suffer deleterious effects from thepresence of the op-amp input dc offset voltage.
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Miller Integrator
C
R
RF
vO (t)vI (t) +
_
+ _
+
vOvI
= −Z2Z1
= −
(RF
1+jωRFC
)R
= − RF/R1 + jωRFC
So,the dc problem of the integrator circuit can be alleviated by connecting aresistor RF across the integrator capacitor C.
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Ideal Op-Amp Inverting Configuration Non-inverting Configuration Integrators & Differentiators Beauty of Miller’s Theorem *** Summary
The Op-Amp Differentiator
C
R
vI (t) vO(t)
i
i
0
0 V
_
+_
+
_
+
vO = −iR = −CdvIdt× R = −RC
dvIdt
vOvI
= −Z2Z1
= − R1/jωRC
= −jωRC = ωRC∠− 90
Differentiator circuits behaves like noise magnifiers and also sufferer fromstability problems. So, they are generally avoided in practice.
3. Operational Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus