ECE 2100

Circuit Analysis

Lesson 16

Chapter 5:

Operational Amplifiers 1

Daniel M. Litynski, Ph.D.

http://homepages.wmich.edu/~dlitynsk/

2

Circuit Theorems - Chapter 4

4.1 Motivation

4.2 Linearity Property

4.3 Superposition

4.4 Source Transformation

4.5 Thevenin’s Theorem

4.6 Norton’s Theorem

4.7 Maximum Power Transfer

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

4.7 Maximum Power Transfer (1)

L

ThTHL

R

VPRR

4

2

max

If the entire circuit is replaced by its

Thevenin equivalent except for the

load, the power delivered to the load is:

The power transfer profile with different RL

For maximum power dissipated in

RL, Pmax, for a given RTH,

and VTH,

L

LTh

ThL R

RR

VRiP

2

2

9

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.

2

4

1 V+

(a)

1

3vx

+

i

v0+ vx

9 V+ io

1 +

VTh

+

3vx

2

+ vx 4

(b)

Fig. a

=> To determine RTH

Fig. b

=> To determine VTH

*Refer to in-class illustration, textbook, RL = 4.22 , Pm = 2.901W

4.7 Maximum Power Transfer (2)

20

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.

21

EE2100Circuit Analysis

Chapter 5

Operational Amplifier

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

22

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

23

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 elementdesigned to perform mathematical operations of addition, subtraction, multiplication, division, differentiation and integration.

24

5.1 What is an Op Amp (2)

A typical op amp: (a) pin configuration, (b) circuit symbol

25

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)

26

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

5.1 What is an Op Amp (4)

Typical ranges for op amp parameters

27

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

28

5.2 Ideal Op Amp (2)Example 1:

Determine the value of io.

*Refer to in-class illustration, textbook Ans: 0.65mA