EGR 2201 Unit 7
Operational Amplifiers
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Read Alexander & Sadiku, Chapter 5.
Homework #7 and Lab #7 due next
week.
Quiz next week.
Precisely Producing A Small
Voltage
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
Using the trainer’s power supply
knob, it’s difficult to produce a small
voltage, such as 100 mV.
It’s much easier if you apply 5 V
across a 1-k potentiometer
(variable resistor) and
then adjust the
potentiometer to
produce the desired
voltage.



Connect +5 V to socket 1.
Connect GND to socket 3.
Take the output voltage from socket 2.
The Big Picture
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At this point we’ve covered the
primary techniques for analyzing
circuits that contain resistors and
DC sources.
In coming weeks we’ll add new
components:
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Op amps
Capacitors
Inductors
And we’ll add AC sources.
Operational Amplifier
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An operational amplifier (or op
amp) is a type of active element that
behaves like a voltage-controlled
voltage source.
Op amps were developed in the 1950s
and 1960s.


Originally they were used in analog
computers to perform mathematical
operations such as addition, subtraction,
differentiation, and integration.
Since then, many other uses have been
found for op amps. Today they are one of
the most widely used electronic elements.
The 741 Operational Amplifier
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Thousands of different op amp designs
are commercially available.

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In Multisim’s Component Selector, go to
Group=Analog.
One of the oldest and most widely
used op amps is the 741,
originally designed by
Fairchild Semiconductor.
It is typically packaged
as an 8-pin DIP
(dual inline package),
as shown here.
It’s A Complex Device
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
As shown in this
schematic
diagram, the 741
op amp is a
complex device
containing many
elements
packaged
together as an
Diagram from wikipedia
integrated circuit.
We’re not prepared to
understand in detail how it works, so we’ll
treat it as a “black box” whose input and
output pins follow certain rules.
Pin Diagram and Schematic
Symbol for the 741 Op Amp

Looking at the 741
DIP from above, its
pins are numbered
as shown here.


Use the notch or dot
on the case to orient
yourself.
Here is a schematic
symbol.

Regarding pins 1 and 5,
note that “Balance” and
“Offset Null” mean the
same thing.
It Fits the Breadboard Perfectly


The pin spacing is just
right for the holes on a
breadboard.
You should always place
the op amp so that it
straddles one of the
breadboard’s gaps.
That way, the pins on
one side of the op amp
are not connected to the
pins on the other side.
Powering the 741 Op Amp
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
When using the 741
in a circuit, we must
provide it with
power.
We do this by
connecting a positive
supply voltage
(typically +15 V) to
pin 7 and a negative
supply voltage
(typically −15 V) to
pin 4.
Simplified Schematic Symbol

Circuit diagrams often show
a simpler symbol for the
741 that omits the power
supply pins (pins 4 and 7).


Simplified symbol
But even if pins 4 and 7 are
omitted from the diagram, it’s
always understood they must
be connected for the op amp
to work.
The simpler symbol also
omits the Offset Null pins
(pins 1 and 5).

These are advanced pins that
we will not use and will leave
disconnected.
Complete symbol
Pay Attention to Which Input Is
Which
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The − and + labels inside the
Inverting input
op amp symbol identify the
inverting input and noninverting input, respectively. Non-inverting input
Usually op amps are drawn
Inputs in normal order
with these inputs in the order
shown here.
But sometimes the order is
reversed, as shown here.
Don’t assume that the upper
input is the inverting input.
Non-inverting input
Inverting input
Inputs reversed
A Simple Model of What’s Inside
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
The circuit inside an op amp is complicated,
but for many purposes we can think of it as
shown here.
Note that the output
pin is driven by a
dependent voltage
source whose voltage
equals the difference
between the two input
voltages, multiplied
by a constant A,
which is called the
open-loop voltage gain.
Three Crucial Op-Amp Parameters

When we use this
simple model of
an op amp,
three crucial
parameters are:
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
The input resistance Ri (Bigger is better.)
The output resistance Ro (Smaller is better.)
The open-loop gain A (Bigger is better.)
Typical Real Values and Ideal
Values
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Table 5.1 shows typical values of these
parameters for real op amps.
For simplicity, we will usually assume the
values given in the “Ideal” column.
Too Much of a Good Thing?
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Having an extremely high (or infinite)
voltage gain may seem like a good thing
for an amplifier—and it is!
But in practical circuits, we generally
want a much smaller voltage gain—
maybe 20 or 50.
Therefore we usually connect other
elements to the op amp. The purpose
of these other elements is to reduce the
circuit’s overall gain.
Negative Feedback
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In general, negative feedback means
connecting a circuit’s output back to its
input in such a way that the output
voltage is reduced.
In the case of an op amp, negative
feedback means connecting the op
amp’s output directly or indirectly to its
inverting input.
(For positive feedback, which we
won’t use, you would connected the
output to the non-inverting input.)
Examples of Negative Feedback
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
In almost all of the op-amp circuits you’ll see
in this course, the op amp’s output is fed back
to its inverting input.
A few examples:
Examples of Negative Feedback
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For each of these circuits, the op amp’s voltage
gain is (ideally) infinite, but the overall voltage
gain of the entire circuit—op amp plus other
elements—is much less, because of the
negative feedback.
Let’s see how to compute the overall voltage
gain.
The Two “Golden Rules” of Op
Amps
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
To analyze circuits like the ones on the
previous slide, we’ll rely on two simple
properties of an ideal op amp with
negative feedback:
1. The current into each input terminal
is zero.
2. The voltage across the input
terminals is zero.
Horowitz and Hill, in their classic book
The Art of Electronics, call these the
“golden rules” of op amps.
Golden Rule #1
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
The current into each input terminal is
zero:
𝑖1 = 0
and
𝑖2 = 0
This property follows from the op amp’s
infinite input resistance.
Golden Rule #2
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
The voltage across the input terminals is
zero:
𝑣1 = 𝑣2
or
𝑣𝑑 = 0
This property follows from the negative
feedback and the ideal op amp’s infinite
voltage gain.
Five Standard Op-Amp
Configurations

Op amps are often combined with other
elements to form one of the following five
standard configurations:
1.
2.
3.
4.
5.

Inverting Amplifier
Non-inverting Amplifier
Voltage Follower
Summing Amplifier
Difference Amplifier
You can use the two golden rules to
analyze any of these circuits. But you’ll
save time if you learn to recognize these
standard configurations and remember
their equations.
Standard Op-Amp Configuration
#1

Op amps are very often combined with
other elements to form one of the
following five standard configurations:
1. Inverting Amplifier
2.
3.
4.
5.
Non-inverting Amplifier
Voltage Follower
Summing Amplifier
Difference Amplifier
Inverting Amplifier


When connected as
shown here, the
op amp and two
resistors form an
inverting amplifier.
Using the Golden
Rules along with
KCL and Ohm’s law,
we can show that
𝑅𝑓
𝑣𝑜 = − 𝑣𝑖
𝑅1
Inverting Amplifier Drawn Another
Way

In the chapter summary
on page 200, the
inverting amplifier is
drawn as shown below,
using “bubble” symbols
for vi and vo.


It’s understood that vi and
vo are measured relative to
the reference node.
Unfortunately, the two
drawings use different
labels for the feedback
resistor. (Rf versus R2)
Standard Op-Amp Configuration
#2

Op amps are very often combined with
other elements to form one of the
following five standard configurations:
1.
Inverting Amplifier
2.
Non-inverting Amplifier
3.
4.
5.
Voltage Follower
Summing Amplifier
Difference Amplifier
Non-Inverting Amplifier


When connected as
shown here, the
op amp and two
resistors form a
non-inverting
amplifier.
Using the Golden
Rules along with
KCL and Ohm’s law,
we can show that
𝑅𝑓
𝑣𝑜 = (1 + )𝑣𝑖
𝑅1
Non-Inverting Amplifier Drawn
Another Way

In the chapter summary
on page 200, the noninverting amplifier is
drawn as shown below,
using “bubble” symbols
for vi and vo.


It’s understood that vi and
vo are measured relative to
the reference node.
Unfortunately, the two
drawings use different
labels for the feedback
resistor. (Rf versus R2)
Standard Op-Amp Configuration
#3

Op amps are very often combined with
other elements to form one of the
following five standard configurations:
2.
Inverting Amplifier
Non-inverting Amplifier
3.
Voltage Follower
1.
4.
5.
Summing Amplifier
Difference Amplifier
A Special Case of a Non-Inverting
Amplifier
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
Suppose that in a non-inverting
amplifier we let Rf = 0 and R1 = ∞.
𝑅𝑓
Since 𝑣𝑜 = (1 + )𝑣𝑖 for a non-inverting
𝑅1
amplifier, we can easily see that this
will give us
𝑣𝑜 = 𝑣𝑖

This special case is quite common and
has its own name….
Voltage Follower
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
When connected as
shown here, the
op amp forms a
voltage follower.
As we saw on the
previous slide,
𝑣𝑜 = 𝑣𝑖
Voltage Follower Drawn Another
Way

In the chapter summary
on page 200, the
voltage follower is
drawn as shown below,
using “bubble” symbols
for vi and vo.

It’s understood that vi and
vo are measured relative to
the reference node.
Saturation
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
Before looking at the next op-amp
configuration, we note that an op
amp’s output voltage can never go
outside the range of the supply
voltages connected to the op
amp’s power pins.
In the case of the 741
op amp, this means
the voltage at pin 6
can never be greater
than the voltage at
pin 7 or less than the
voltage at pin 4.
Saturation: Example
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Example: For the
inverting amplifier
shown,
𝑣𝑜 = −2.5 𝑣𝑖
But suppose the op amp’s power pins
are connected to +15 V and −15 V. If
we set vi equal to 10 V, vo will saturate
at about −15 V, even though according
to our formula it should be −25 V.
Standard Op-Amp Configuration
#4

Op amps are very often combined with
other elements to form one of the
following five standard configurations:
3.
Inverting Amplifier
Non-inverting Amplifier
Voltage Follower
4.
Summing Amplifier
5.
Difference Amplifier
1.
2.
Summing Amplifier

When connected as
shown here, the op
amp and resistors
form a summing
amplifier.


The one shown here
sums three input
voltages, but this can
be extended to any number of input voltages.)
Using the Golden Rules along with KCL and
Ohm’s law, we can show that
𝑅𝑓
𝑅𝑓
𝑅𝑓
𝑣𝑜 = −( 𝑣1 + 𝑣2 + 𝑣3 )
𝑅1
𝑅2
𝑅3
Summing Amplifier Drawn Another
Way

This time the book’s
original drawing uses
“bubble” symbols, but
elsewhere the summing
amplifier is sometimes
drawn as shown below,
without bubbles.
A Special Case of a Summing
Amplifier

We can think of the inverting amplifier (which
we studied earlier) as a special case of a
summing amplifier in which there is just one
input voltage instead of two or more.
Summing Amplifier
Inverting Amplifier
𝑅𝑓
𝑣𝑜 = − 𝑣𝑖
𝑅1
𝑅𝑓
𝑅𝑓
𝑅𝑓
𝑣𝑜 = −( 𝑣1 + 𝑣2 + 𝑣3 )
𝑅1
𝑅2
𝑅3
Standard Op-Amp Configuration
#5

Op amps are very often combined with
other elements to form one of the
following five standard configurations:
4.
Inverting Amplifier
Non-inverting Amplifier
Voltage Follower
Summing Amplifier
5.
Difference Amplifier
1.
2.
3.
Difference Amplifier


When connected as
shown here, the
op amp and four
resistors form a
difference
amplifier.
Using the Golden
Rules along with
KCL and Ohm’s law,
we can show that
𝑅2
𝑣𝑜 =
(𝑣2 −𝑣1 )
𝑅1
Difference Amplifier Drawn
Another Way

In the chapter summary
on page 200, the
difference amplifier is
drawn as shown below,
using “bubble” symbols
for vi and vo.

It’s understood that v1, v2,
and vo are measured
relative to the reference
node.
Table 5.3 (on page 200)
Cascaded Op-Amp Circuits

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A cascade connection is a head-to-tail
arrangement of two or more circuits such
that one circuit’s output is the next circuit’s
input.
Example: In this
cascaded op-amp
circuit, the first stage
is a voltage follower,
and the second
stage is a
non-inverting
amplifier.