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Basic Electric Circuits

Introduction To Operational Amplifiers

Lesson 8

Basic Electric Circuits

Operational Amplifiers

One might ask, why are operational amplifiers

included in Basic Electric Circuits?

The operational amplifier has become so cheap in

price (often less than 1.00 per unit) and it can

be used in so many applications, we present an

introductory study early-on in electric circuits.

1

Basic Electric Circuits

Operational Amplifiers

What is an operational amplifier? This

particular form of amplifier had the name

Operational attached to it many years ago.

As early as 1952, Philbrick Operational

Amplifiers (marketed by George A. Philbrick)

were constructed with vacuum tubes and were used

in analog computers. Even as late as 1965,

vacuum tube operational amplifiers were still in

use and cost in the range of 75.

Some reports say that Loebe Julie actually

developed the operational amplifier circuitry.

2

Basic Electric Circuits

Operational Amplifiers

The Philbrick Operational Amplifier.

From Operational Amplifier, by Tony van Roon

http//www.uoguelph.ca/antoon/gadgets/741/741.htm

l

Basic Electric Circuits

Operational Amplifiers

My belief is that operational was used as a

descriptor early-on because this form of

amplifier can perform operations of

- adding signals

- subtracting signals

- integrating signals,

The applications of operational amplifiers (

shortened to op amp ) have grown beyond those

listed above.

3

Basic Electric Circuits

Operational Amplifiers

At this level of study we will be concerned with

how to use the op amp as a device. The internal

configuration (design) is beyond basic circuit

theory and will be studied in later

electronic courses. The complexity is

illustrated in the following circuit.

4

Basic Electric Circuits

Operational Amplifiers

The op amp is built using VLSI techniques. The

circuit diagram of an LM 741 from National

Semiconductor is shown below.

V

Vin(-)

Vo

Vin()

V-

Figure 8.1 Internal circuitry of LM741.

5

Taken from National Semiconductor data sheet as

shown on the web.

Basic Electric Circuits

Operational Amplifiers

Fortunately, we do not have to sweat a circuit

with 22 transistors and twelve resistors in order

to use the op amp

The circuit in the previous slide is usually

encapsulated into a dual in-line pack (DIP). For

a single LM741, the pin connections for the chip

are shown below.

Taken from National Semiconductor data sheet as

shown on the web.

6

Figure 8.2 Pin connection, LM741.

Basic Electric Circuits

Operational Amplifiers

The basic op amp with supply voltage included is

shown in the diagram below.

Figure 8.3 Basic op am diagram with supply

voltage.

7

Basic Electric Circuits

Operational Amplifiers

In most cases only the two inputs and the output

are shown for the op amp. However, one should

keep in mind that supply voltage is required, and

a ground. The basic op am without a ground is

shown below.

Figure 8.4 Outer op am diagram.

8

Basic Electric Circuits

Operational Amplifiers

A model of the op amp, with respect to the

symbol, is shown below.

Figure 8.5 Op Amp Model.

9

Basic Electric Circuits

Operational Amplifiers

The previous model is usually shown as follows

Figure 8.6 Working circuit diagram of op amp.

10

Basic Electric Circuits

Operational Amplifiers

Application As an application of the previous

model, consider the following configuration.

Find Vo as a function of Vin and the resistors

R1 and R2.

11

Figure 8.7 Op amp functional circuit.

Basic Electric Circuits

Operational Amplifiers

In terms of the circuit model we have the

following

Figure 8.8 Total op amp schematic for voltage

gain configuration.

12

Basic Electric Circuits

Operational Amplifiers

Circuit values are

R1 10 k? R2 40 k? A 100,000 Ri

1 meg ?

13

Basic Electric Circuits

Operational Amplifiers

We can write the following equations for nodes a

and b.

Eq 8.1

Eq 8.2

14

Basic Electric Circuits

Operational Amplifiers

Equation 8.1 simplifies to

Eq 8.3

Equation 8.2 simplifies to

Eq 8.4

15

Basic Electric Circuits

Operational Amplifiers

From Equations 8.3 and 8.4 we find

Eq 8.5

This is an expected answer.

Fortunately, we are not required to do elaborate

circuit analysis, as above, to find the

relationship between the output and input of an

op amp. Simplifying the analysis is our next

consideration.

16

Basic Electric Circuits

Operational Amplifiers

For most all operational amplifiers, Ri is 1

meg ? or larger and Ro is around 50 ? or less.

The open-loop gain, A, is greater than 100,000.

Ideal Op Amp

The following assumptions are made for the ideal

op amp.

17

Basic Electric Circuits

Ideal Op Amp

Figure 8.9 Ideal op amp.

- i1 i2 0 Due to infinite input resistance.
- Vi is negligibly small V1 V2.

18

Basic Electric Circuits

Ideal Op Amp

Find Vo in terms of Vin for the following

configuration.

19

Figure 8.10 Gain amplifier op amp set-up.

Basic Electric Circuits

Ideal Op Amp

Writing a nodal equation at (a) gives

Eq 8.6

20

Basic Electric Circuits

Ideal Op Amp

Eq 8.7

With Vi 0 we have

With R2 4 k? and R1 1 k?, we have

Earlier we got

21

Basic Electric Circuits

Ideal Op Amp

When Vi 0 in Eq 8.7 and we apply the Laplace

Transform

Eq 8.8

In fact, we can replace R2 with Zfb(s) and R1

with Z1(s) and we have the important expression

Eq 8.9

22

Basic Electric Circuits

Ideal Op Amp

At this point in circuits we are not able to

appreciate the utility of Eq 8.9. We will

revisit this at a later point in circuits but for

now we point out that judicious selections of

Zfb(s) and Zin(s) leads to important applications

in

- Analog Filters

- Analog Compensators in Control Systems

- Application in Communications

23

Basic Electric Circuits

Ideal Op Amp

Example 8.1 Consider the op amp configuration

below.

Assume Vin 5 V

Figure 8.11 Circuit for Example 8.1.

24

Basic Electric Circuits

Operational Amplifiers

Example 8.1 cont.

At node a we can write

Eq 8.10

From which V0 -51 V

25

Basic Electric Circuits

Operational Amplifiers

Example 8.2 Summing Amplifier. Given the

following

Figure 8.12 Circuit for Example 8.2.

Eq 8.11

26

Basic Electric Circuits

Operational Amplifiers

Example 8.2 Summing Amplifier. continued

Equation 8.11 can be expressed as

Eq 8.12

If R1 R2 Rfb then,

Eq. 8.13

Therefore, we can add signals with an op amp.

27

Basic Electric Circuits

Operational Amplifiers

Example 8.3 Isolation or Voltage Follower.

Applications arise in which we wish to connect

one circuit to another without the first circuit

loading the second. This requires that we

connect to a block that has infinite

input impedance and zero output impedance. An

operational amplifier does a good job of

approximating this. Consider the following

Figure 8.13 Illustrating Isolation.

28

Basic Electric Circuits

Operational Amplifiers

Example 8.3 Isolation or Voltage Follower.

continued

Figure 8.14 Circuit isolation with an op amp.

It is easy to see that V0 Vin

29

Basic Electric Circuits

Operational Amplifiers

Example 8.4 Isolation with gain.

Figure 8.15 Circuit for Example 8.4

Writing a nodal equation at point a and

simplifying gives

30

Basic Electric Circuits

Operational Amplifiers

Example 8.5 The noninverting op amp.

Consider the following

Figure 8.16 Noninverting op am configuration.

31

Basic Electric Circuits

Operational Amplifiers

Example 8.5 The noninverting op amp. Continued

Writing a node equation at a gives

Remember this

32

Basic Electric Circuits

Operational Amplifiers

Example 8.6 Noninverting Input.

Find V0 for the following op amp configuration.

Figure 8.17 Op amp circuit for example 8.6.

33

Basic Electric Circuits

Operational Amplifiers

Example 8.6 Noninverting Input.

The voltage at Vx is found to be 3 V.

Writing a node equation at a gives

or

34

CIRCUITS

End of Lesson 8

Operational Amplifiers

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