ECE 2100
Circuit Analysis
Lesson 16
Chapter 5:
Operational Amplifiers 1
Daniel M. Litynski, Ph.D.
http://homepages.wmich.edu/~dlitynsk/
Circuit Theorems - Chapter 4
4.1
4.2
4.3
4.4
4.5
4.6
4.7
Motivation
Linearity Property
Superposition
Source Transformation
Thevenin’s Theorem
Norton’s Theorem
Maximum Power Transfer
2
ECE 2100
Circuit Analysis
Lesson 15
Chapter 4: Circuit Theorems
Norton’s Theorem
Maximum Power Transfer
Wheatstone Bridge
Operational Amplifiers
(Review and continue the following)
4.7 Maximum Power Transfer (1)
If the entire circuit is replaced by its
Thevenin equivalent except for the
load, the power delivered to the load is:
P
i 2 RL
2
VTh
RTh
RL
RL
For maximum power dissipated in
RL, Pmax, for a given RTH,
and VTH,
2
RL
RTH
Pmax
VTh
4 RL
The power transfer profile with different RL
4
4.7 Maximum Power Transfer (2)
Example 8
Determine the value of RL that will draw
the maximum power from
the rest of the circuit shown below.
Calculate the maximum power.
+
vx
4
v0
+
i
2
vx
4
Fig. a
2
1
1
+
1V
+
9V
io
+
=> To determine RTH
Fig. b
+
3vx
+
VTh
3vx
=> To determine VTH
(a)
(b)
*Refer to in-class illustration, textbook, RL = 4.22 , Pm = 2.901W
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ECE 2100
Circuit Analysis
Chapter 1-4
Basic Concepts
Basic Laws
Methods of Analysis
Circuit Theorems
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
20
EE2100
Circuit Analysis
Chapter 5
Operational Amplifier
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
21
Operational Amplifier - Chapter 5
5.1 What is an Op Amp?
5.2 Ideal Op Amp
5.3 Configuration of Op Amp
5.4 Cascaded Op Amp
5.5 Application
– Digital-to Analog Converter
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5.1 What is an Op Amp (1)
• 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.
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5.1 What is an Op Amp (2)
A typical op amp: (a) pin configuration, (b) circuit symbol
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5.1 What is an Op Amp (3)
The equivalent circuit
Of the non-ideal op amp
Op Amp output:
vo as a function of
Vd
vd = v2 – v1; vo = Avd = A(v2 –v1)
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5.1 What is an Op Amp (4)
Typical ranges for op amp parameters
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
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5.2 Ideal Op Amp (1)
An ideal op amp has the following characteristics:
1. Infinite open-loop gain, A ≈ ∞
2. Infinite input resistance, Ri ≈ ∞
3. Zero output resistance, Ro ≈ 0
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5.2 Ideal Op Amp (2)
Example 1:
Determine the value of io.
*Refer to in-class illustration, textbook
Ans: 0.65mA
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