Basic Electric Circuits

1
Basic Electric Circuits
Introduction To Operational Amplifiers
Lesson 8
2
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
3
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
4
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
5
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
6
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
7
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(-)
Vin()
Vo
V-
5
Taken from National Semiconductor data sheet as
shown on the web.
Figure 8.1 Internal circuitry of LM741.
8
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.
9
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
10
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
11
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
12
Basic Electric Circuits
Operational Amplifiers
The previous model is usually shown as follows
Figure 8.6 Working circuit diagram of op amp.
10
13
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.
14
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
15
Basic Electric Circuits
Operational Amplifiers
Circuit values are
R1 10 k? R2 40 k? Ro 50
? A 100,000 Ri 1 meg ?
13
16
Basic Electric Circuits
Operational Amplifiers
We can write the following equations for nodes a
and b.
Eq 8.1
Eq 8.2
14
17
Basic Electric Circuits
Operational Amplifiers
Equation 8.1 simplifies to
Eq 8.3
Equation 8.2 simplifies to
Eq 8.4
15
18
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
19
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
20
Basic Electric Circuits
Ideal Op Amp
Figure 8.9 Ideal op amp.

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

18
21
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.
22
Basic Electric Circuits
Ideal Op Amp
Writing a nodal equation at (a) gives
Eq 8.6
20
23
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
24
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
25
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
26
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
27
Basic Electric Circuits
Operational Amplifiers
Example 8.1 cont.
At node a we can write
Eq 8.10
From which V0 -51 V (op amp will
saturate)
25
28
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
29
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
30
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
31
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
32
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
33
Basic Electric Circuits
Operational Amplifiers
Example 8.5 The noninverting op amp.
Consider the following
Figure 8.16 Noninverting op am configuration.
31
34
Basic Electric Circuits
Operational Amplifiers
Example 8.5 The noninverting op amp. Continued
Writing a node equation at a gives
Remember this
32
35
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
36
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
37
CIRCUITS
End of Lesson 8
Operational Amplifiers