Signal Paths from Analog to Digital

Introduction
Designers of analog electronic control systems have continually faced the following obstacles in arriving at
a satisfactory design:
1. Instability and drift due to temperature variations.
2. Dynamic range of signals and nonlinearity when pressing the limits of the range.
3. Inaccuracies of computation when using analog quantities.
4. Adequate signal frequency range.
Today’s designers, however, have a significant alternative offered to them by the advances in integrated
circuit technology, especially low-power analog and digital circuits. The alternative new design technique
for analog systems is to sense the analog signal, convert it to digital signals, use the speed and accuracy of
digital circuits to do the computations, and convert the resultant digital output back to analog signals.
The new design technique requires that the electronic system designer interface between two distinct design
worlds. First, between analog and digital systems, and second, between the external human world and the
internal electronics world. Various functions are required to make the interface. First, from the human world
to the electronics world and back again and, in a similar fashion, from the analog systems to digital systems
and back again. Analog and Digital Circuits for Control System Applications identifies the electronic functions
needed, and describes how electronic circuits are designed and applied to implement the functions,
and gives examples of the use of the functions in systems.

A Refresher
Since the book deals with the electronic functions and circuits that interface or couple analog-to-digital
circuits and systems, or vice versa, a short review is provided so it is clearly understood what analog means
and what digital means.
Analog
Analog quantities vary continuously, and analog systems represent the analog information using electrical
signals that vary smoothly and continuously over a range. A good example of an analog system is the recording
thermometer shown in Figure 1-1. The actual equipment is shown in Figure 1-1a. An ink pen records the

temperature in degrees Fahrenheit (ºF)
and plots it continuously against time on
a special graph paper attached to a drum
as the drum rotates. The record of the
temperature changes is shown in Figure
1-1b. Note that the temperature changes
smoothly and continuously. There are no
abrupt steps or breaks in the data.
Another example is the automobile fuel
gauge system shown in Figure 1-2. The
electrical circuit consists of a potentiometer,
basically a resistor connected
across a car battery from the positive
terminal to the negative terminal, which
is grounded. The resistor has a variable
tap that is rotated by a float riding on the
surface of the liquid inside the gas tank.
A voltmeter reads the voltage from the variable tap to the negative side of the battery (ground). The voltmeter
indicates the information about the amount of fuel in the gas tank. It represents the fuel level in the tank.
The greater the fuel level in the tank the greater the voltage reading on the voltmeter. The voltage is said to
be an analog of the fuel level. An analog
of the fuel level is said to be a copy of the
fuel level in another form—it is analogous
to the original fuel level. The voltage (fuel
level) changes smoothly and continuously
so the system is an analog system, but is
also an analog system because the system
output voltage is a copy of the actual output
parameter (fuel level) in another form.
Digital
Digital quantities vary in discrete levels.
In most cases, the discrete levels are just
two values—ON and OFF. Digital systems
carry information using combinations of
ON-OFF electrical signals that are usually
in the form of codes that represent the
information. The telegraph system is an
example of a digital system.
The system shown in Figure 1-3 is a
simplified version of the original telegraph
system, but it will demonstrate the principle
and help to define a digital system.
The electrical circuit (Figure 1-3a) is a
battery with a switch in the line at one end
and a light bulb at the other. The person

at the switch position is remotely located from the person at the light bulb. The information is transmitted
from the person at the switch position to the person at the light bulb by coding the information to be sent
using the International Morse telegraph code.
Morse code uses short pulses (dots) and long pulses (dashes) of current to form the code for letters or
numbers as shown in Figure 1-3b. As shown in Figure 1-3c, combining the codes of dots and dashes for
the letters and numbers into words sends the information. The sender keeps the same shorter time interval
between letters but a longer time interval between words. This allows the receiver to identify that the code
sent is a character in a word or the end of a word itself. The T is one dash (one long current pulse). The H is
four short dots (four short current pulses). The R is a dot-dash-dot. And the two Es are a dot each. The two
states are ON and OFF—current or no current. The person at the light bulb position identifies the code by
watching the glow of the light bulb. In the original telegraph, this person listened to a buzzer or “sounder”
to identify the code.
Coded patterns of changes from one state to another as time passes carry the information. At any instant of
time the signal is either one of two levels. The variations in the signal are always between set discrete levels,
but, in addition, a very important component of digital systems is the timing of signals. In many cases, digital
signals, either at discrete levels, or changing between discrete levels, must occur precisely at the proper
time or the digital system will not work. Timing is maintained in digital systems by circuits called system
clocks. This is what identifies a digital signal and the information being processed in a digital system.
Binary
The two levels—ON and OFF—are most commonly identified
as 1(one) and zero (0) in modern binary digital systems, and
the 1 and 0 are called binary digits or bits for short. Since the
system is binary (two levels), the maximum code combinations
2n depends on the number of bits, n, used to represent the
information. For example, if numbers were the only quantities
represented, then the codes would look like Figure 1-4, when
using a 4-bit code to represent 16 quantities. To represent larger
quantities more bits are added. For example, a 16-bit code can
represent 65,536 quantities. The first bit at the right edge of the
code is called the least significant bit (LSB). The left-most bit
is called the most significant bit (MSB).
Binary Numerical Quantities
Our normal numbering system is a decimal system. Figure 1-5
is a summary showing the characteristics of a decimal and a binary
numbering system. Note that each system in Figure 1-5 has
specific digit positions with specific assigned values to each position. Only eight digits are shown for each
system in Figure 1-5. Note that in each system, the LSB is either 100 in the decimal system or 20 in the binary
system. Each of these has a value of one since any number to the zero power is equal to one. The following
examples will help to solidify the characteristics of the two systems and the conversion between them.