Alciatore D.G., Histand M.B. Introduction to Mechatronics and Measurement Systems
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161
CHAPTER
5
Analog Signal Processing
Using Operational
Amplifiers
T
his chapter presents operational amplifier circuits that are important for
interfacing analog components in a mechatronic system. ■
INPUT SIGNAL
CONDITIONING
AND INTERFACING
- discrete circuits
amplifiers
- filters
- A/D, D/D
OUTPUT SIGNAL
CONDITIONING
AND INTERFACING
- D/A, D/D
- PWM
- power transistors
power op amps
GRAPHICAL
DISPLAYS
- LEDs
- digital displays
- LCD
- CRT
SENSORS
- switches
- potentiometer
- photoelectrics
- digital encoder
- strain gage
- thermocouple
- accelerometer
- MEMs
ACTUATORS
- solenoids, voice coils
- DC motors
- stepper motors
- servo motors
- hydraulics, pneumatics
MECHANICAL SYSTEM
- system model - dynamic response
DIGITAL CONTROL
ARCHITECTURES
- logic circuits
- microcontroller
- SBC
- PLC
- sequencing and timing
- logic and arithmetic
- control algorithms
- communication
amplifiers
CHAPTER OBJECTIVES
After you read, discuss, study, and apply ideas in this chapter, you will:
1. Understand the input/output characteristics of a linear amplifier
2. Understand how to use the model of an ideal operational amplifier in circuit
analysis
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162 CHAPTER 5 Analog Signal Processing Using Operational Amplifiers
3. Know how to design op amp circuits
4. Be able to design an inverting amplifier, noninverting amplifier, summer,
difference amplifier, instrumentation amplifier, integrator, differentiator,
and sample and hold amplifier
5. Understand the characteristics and limitations of a “real” operational amplifier
5.1 INTRODUCTION
Since electrical circuits occur in virtually all mechatronic and measurement systems,
it is essential that engineers develop a basic understanding of the acquisition and
processing of electrical signals. Usually these signals come from transducers, which
convert physical quantities (e.g., temperature, strain, displacement, flow rate) into
currents or voltages, usually the latter. The transducer output is usually described as
an analog signal, which is continuous and time varying.
Often the signals from transducers are not in the form we would like them to be.
They may
■ Be too small, usually in the millivolt range
■ Be too “noisy,” usually due to electromagnetic interference
■ Contain the wrong information, sometimes due to poor transducer design or
installation
■ Have a DC offset, usually due to the transducer and instrumentation design
Many of these problems can be remedied, and the desired signal information
extracted through appropriate analog signal processing. The simplest and most com-
mon form of signal processing is amplification, where the magnitude of the voltage
signal is increased. Other forms include signal inversion, differentiation, integration,
addition, subtraction, and comparison.
Analog signals are very different from digital signals, which are discrete, using
only a finite number of states or values. Since computers and microprocessors require
digital signals, any application involving computer measurement or control requires
analog-to-digital conversion. This chapter covers the basic elements of analog sig-
nal processing including the design and analysis of signal processing circuits. The
operational amplifier is an integrated circuit used as a building block in many of
these circuits. Chapter 6 focuses on digital circuits, and Chapter 8 deals with con-
verting analog signals into a format that can be processed by digital devices such as
computers.
5.2 AMPLIFIERS
People have spent their lives studying and writing about amplifiers, so we cannot
expect to do justice to the subject in a few pages. However, we will look at the
salient features of amplifiers and determine how we may design one using integrated
circuits.
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Figure 5.1 Amplifier model.
amplifier
V
in
V
ou
t
+
–
+
–
I
in
I
out
5.2 Amplifiers 163
Ideally, an amplifier increases the amplitude of a signal without affecting the
phase relationships of different components of the signal. When choosing or design-
ing an amplifier, we must consider size, cost, power consumption, input impedance,
output impedance, gain, and bandwidth. Physical size depends on the components
used to construct the amplifier. Prior to the 1960s, vacuum tube amplifiers were
common, but they were heavy power consumers with significant heat dissipation.
Portable units were large and heavy and required frequent battery replacement.
Since its advent, solid state technology, where charge carriers move through a solid
semiconductor material, has replaced the vacuum tube technology, where bulky
tubes enclosed a gas at low pressure through which electrons flowed. Today, solid
state transistors and integrated circuits have dramatically changed amplifier design,
resulting in small, cool-running amplifiers. They consume little power and are easily
made portable using rechargeable batteries.
Generally, we model an amplifier as a two-port device, with an input and output
voltage referenced to ground, as illustrated in Figure 5.1 . The voltage gain A
v
of an
amplifier defines the factor by which the voltage is changed:
V
out
A
v
V
in
(5.1)
Normally we want an amplifier to exhibit amplitude linearity, where the gain is
constant for all frequencies. However, amplifiers may be designed to intentionally
amplify only certain frequencies, resulting in a filtering effect. In such cases, the out-
put characteristics are governed by the amplifier’s bandwidth and associated cutoff
frequencies.
The input impedance of an amplifier, Z
in
, is defined as the ratio of the input volt-
age and current:
Z
in
V
in
I
in
(5.2)
Most amplifiers are designed to have a large input impedance so very little current is
drawn from the input.
The output impedance is a measure of how much the output voltage drops with
output current:
Z
out
Δ
V
out
I
in
(5.3)
where the voltage drop
Δ
V
out
is measured relative to the output voltage with no cur-
rent. Most amplifiers are designed to have a very small output impedance so the
output voltage will not change much as the output current changes.
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Figure 5.2 Op amp terminology and schematic representation.
–
+
inverting input
terminal
noninverting input terminal
output terminal
V
–
V
+
V
out
∞
164 CHAPTER 5 Analog Signal Processing Using Operational Amplifiers
See Section 2.4 for more information related to input and output impedance.
The input impedance of an amplifier is analogous to that of a voltmeter, and the out-
put impedance is analogous to that of a voltage source.
5.3 OPERATIONAL AMPLIFIERS
The operational amplifier, or op amp, is a low-cost and versatile integrated circuit
consisting of many internal transistors, resistors, and capacitors manufactured into
a single chip of silicon. It can be combined with external discrete components to
create a wide variety of signal processing circuits. The op amp is the basic building
block for
■ Amplifiers
■ Integrators
■ Summers
■ Differentiators
■ Comparators
■ A/D and D/A converters
■ Active filters
■ Sample and hold amplifiers
We present most of these applications in subsequent sections. The op amp derives its
name from its ability to perform so many different operations.
5.4 IDEAL MODEL FOR THE OPERATIONAL
AMPLIFIER
Figure 5.2 shows the schematic symbol and terminal nomenclature for an ideal op
amp. It is a differential input, single output amplifier that is assumed to have infinite
gain. The two inputs are called the inverting input, labeled with a minus sign, and
the noninverting input, labeled with a plus sign. The symbol is sometimes used
in the schematic to denote the infinite gain and the assumption that it is an ideal
op amp. The voltages are all referenced to a common ground. The op amp is an
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Figure 5.3 Op amp feedback.
feedback loop
V
–
V
+
V
ou
t
–
+
∞
Figure 5.4 Op amp equivalent circuit.
+
V
–
V
+
I
+
= 0
I
–
= 0
I
out
–
+
V
out
V
ou
t
5.4 Ideal Model for the Operational Amplifier 165
active device requiring connection to an external power supply, usually plus and
minus 15 V. The external supply is not normally shown on circuit schematics. Since
the op amp is an active device, output voltages and currents can be larger than the
signals applied to the inverting and noninverting terminals.
As illustrated in Figure 5.3 , an op amp circuit usually includes feedback from
the output to the negative (inverting) input. This so-called closed loop configuration
results in stabilization of the amplifier and control of the gain. When feedback is
absent in an op amp circuit, the op amp is said to have an open loop configuration.
This configuration results in considerable instability due to the very high gain, and
it is seldom used. The utility of feedback will become evident in the examples pre-
sented in the following sections.
Figure 5.4 illustrates an ideal model that can aid in analyzing circuits contain-
ing op amps. This model is based on the following assumptions that describe an
ideal op amp:
1 . It has infinite impedance at both inputs; hence, no current is drawn from the
input circuits. Therefore,
I
+
I
−
0==
(5.4)
2 . It has infinite gain. As a consequence, the difference between the input voltages
must be 0; otherwise, the output would be infinite. This is denoted in Figure 5.4
by the shorting of the two inputs. Therefore,
V
+
= V
−
(5.5)
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Figure 5.5 741 op amp pin-out.
5
6
7
8
4
2
3
4
6
5
7
81
–
+
–15 V
+15 V
V
out
x
x
top view
x
166 CHAPTER 5 Analog Signal Processing Using Operational Amplifiers
Even though we indicate a short between the two inputs, we assume no current
may flow through this short.
3 . It has zero output impedance. Therefore, the output voltage does not depend on
the output current.
Note that V
out
, V
, and V
are all referenced to a common ground. Also, for stable
linear behavior, there must be feedback between the output and the inverting input.
These assumptions and the model may appear illogical and confusing, but they
provide a close approximation to the behavior of a real op amp when used in a cir-
cuit that includes negative feedback. With the aid of this ideal model, we need only
Kirchhoff’s laws and Ohm’s law to completely analyze op amp circuits.
Actual op amps are usually packaged in an eight-pin dual in-line package (DIP)
integrated circuit (IC), sometimes called a chip. The designation for a general purpose
op amp produced by many IC manufacturers is 741. It is illustrated in Figure 5.5 with
its pin configuration (pin-out). As with all ICs, one end of the chip is marked with an
indentation or spot, and the pins are numbered counterclockwise (looking at the top of
the IC) and consecutively starting with 1 at the left side of the marked end. For a 741
series op amp, pin 2 is the inverting input, pin 3 is the noninverting input, pins 4 and 7
are for the external power supply, and pin 6 is the op amp output. Pins 1, 5, and 8 are
not normally used, and no connections are required. Figure 5.6 illustrates the internal
design of a 741 IC available from National Semiconductor. Note that the circuits are
composed of transistors, resistors, and capacitors that are easily manufactured on a
single silicon chip. The most valuable details for the user are the input and output
parts of the circuit having characteristics that affect externally connected components.
The manufacture of integrated circuits is very involved, requiring extremely
expensive equipment. Video Demo 5.1 shows various common packages in which
ICs are made available, and Video Demos 5.2 through 5.4 describe and illustrate
all of the steps of the manufacturing process. Fortunately, due to high production
volume of components used in consumer and industrial applications, the economy of
scale prevails, and ICs can be sold at very affordable prices.
Many different op amp designs are available from IC manufacturers. The input
impedances, bandwidth, and power ratings can vary significantly. Also, some require
only a single-output (unipolar) power supply. Although the 741 is widely used,
another common op amp is the TL071 manufactured by Texas Instruments. Its pin
Video Demo
5.1Integrated
circuits
5.2Integrated
circuit manu-
facturing process
stages
5.3Chip
manufacturing
process
5.4How a CPU
is made
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Figure 5.6 741 internal design. (Courtesy of National Semiconductor,
Santa Clara, CA)
5.5 Inverting Amplifier 167
configuration is identical to the 741, but because it has FET inputs, it has a larger
input impedance and a wider bandwidth.
IC manufacturers provide complete information on their devices in documents
called data sheets. Internet Links 5.1 and 5.2 point to the complete data sheets for
both the 741 and TL071. If you don’t have much experience looking at these data
sheets, they can be very overwhelming. However, they contain all the information
you would ever need to use the devices. Useful information includes the device pin-
out (e.g., see Figure 5.5 ), input and output current and voltage specifications, voltage
source requirements, and impedances. Section 5.14 at the end of this chapter pro-
vides some guidance on specific things to look for in an op data sheet.
5.5 INVERTING AMPLIFIER
An inverting amplifier is constructed by connecting two external resistors to an op
amp as shown in Figure 5.7 . As the name implies, this circuit inverts and amplifies
the input voltage. Note that the resistor R
F
forms the feedback loop. This feedback
loop always goes from the output to the inverting input of the op amp, implying
negative feedback.
We now use Kirchhoff’s laws and Ohm’s law to analyze this circuit. First, we
replace the op amp with its ideal model shown within the dashed box in Figure 5.8 .
Internet Lin
k
5.1A741 op
amp data sheet
5.25.2 TL071
FET input op amp
data sheet
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Figure 5.7 Inverting amplifier.
R
+
V
in
R
F
V
ou
t
–
+
Figure 5.8 Equivalent circuit for an inverting amplifier.
–
+
R
C
+
+
V
ou
t
i
out
V
out
V
in
i
in
R
F
ideal model
168 CHAPTER 5 Analog Signal Processing Using Operational Amplifiers
Applying Kirchhoff’s current law at node C and utilizing assumption 1, that no cur-
rent can flow into the inputs of the op amp,
i
in
= −i
out
(5.6)
Also, because the two inputs are assumed to be shorted in the ideal model, C is effec-
tively at ground potential:
V
C
= 0
(5.7)
Because the voltage across resistor R is V
in
V
C
V
in
, from Ohm’s law,
V
in
= i
in
R
(5.8)
and because the voltage across resistor R
F
is V
out
V
C
V
out
,
V
out
= i
out
R
F
(5.9)
Substituting Equation 5.6 into Equation 5.9 gives
V
out
= − i
in
R
F
(5.10)
Dividing Equation 5.10 by Equation 5.8 yields the input/output relationship:
V
out
V
in
--------
R
F
R
------
–=
(5.11)
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Figure 5.9 Illustration of inversion.
V
in
t
V
out
t
5.6 Noninverting Amplifier 169
Therefore, the voltage gain of the amplifier is determined simply by the external
resistors R
F
and R, and it is always negative. The reason this circuit is called an
inverting amplifier is that it reverses the polarity of the input signal. This results in a
phase shift of 180 for periodic signals. For example, if the square wave V
in
shown in
Figure 5.9 is connected to an inverting amplifier with a gain of 2, the output V
out
is
inverted and amplified, resulting in a larger amplitude signal 180 out of phase with
the input.
■ CLASS DISCUSSION ITEM 5.1
Kitchen Sink in an Op Amp Circuit
Consider the following op amp circuit:
R
+
kitchen
sink
R
F
V
in
V
ou
t
–
+
What is the effect of the kitchen sink at the noninverting input of the op amp?
5.6 NONINVERTING AMPLIFIER
The schematic of a noninverting amplifier is shown in Figure 5.10 . As the name
implies, this circuit amplifies the input voltage without inverting the signal. Again,
we can apply Kirchhoff’s laws and Ohm’s law to determine the voltage gain of
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Figure 5.10 Noninverting amplifier.
+
R
F
R
V
ou
t
V
in
–
+
Figure 5.11 Equivalent circuit for a noninverting amplifier.
–
+
C
+
+
R
i
in
i
out
R
F
V
out
V
in
V
ou
t
170 CHAPTER 5 Analog Signal Processing Using Operational Amplifiers
this amplifier. As before, we replace the op amp with the ideal model shown in the
dashed box in Figure 5.11 .
The voltage at node C is V
in
because the inverting and noninverting inputs are at
the same voltage. Therefore, applying Ohm’s law to resistor R,
i
in
V
in
–
R
----------=
(5.12)
and applying it to resistor R
F
,
i
out
V
out
V
in
–
R
F
---------------------=
(5.13)
Solving Equation 5.13 for V
out
gives
V
out
i
out
R
F
V
in
+=
(5.14)
Applying KCL at node C gives
i
in
i
out
–=
(5.15)
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