Page 861 - Mechanical Engineers' Handbook (Volume 2)

852 Mechatronics

6 ANALOG-TO-DIGITAL CONVERSION
The world we live in is analog. To interface digital computers to an analog mechanical
system, an A/D conversion process is required. Converting from an analog signal to a digital
number is a two-step process that involves (1) quantization and (2) coding. The process of
quantization is where the range of the analog signal is broken down into a discrete number
of bins. In coding, the bin ‘‘location’’ of the analog signal is converted into a digital number
that can be understood by the computer. There are literally hundreds of A/D converter types.
Several definitions are required to discuss A/D converters:

Resolution n refers to the number of bits used to digitally approximate the analog value
of the input.
Number of possible states N 2 .
n
Analog quantization size Q is a measure of the analog change that can be resolved
(minimum error):
V V
Q max min
N

6.1 Four-Bit A/D Converter
To understand the terms explained above, the example in Fig. 38 will be used. In the example,
a tachometer is used to measure the speed of an electric motor. The tachometer produces a
voltage between 12 and 12 V that is linearly proportional to the speed of the motor. The
analog voltage output of the motor will be read with a 4-bit A/D converter. Therefore, the
4
A/D converter has a resolution of 4 bits and can have 16 (2 ) possible states (0000–1111
or 0–15). The analog quantization size will be 1.5 V [(12 ( 12))/16]. This means, for
example, that all voltages between 10.5 and 12 V will be represented by the encoded digital
number 1111.

7 DIGITAL-TO-ANALOG (D/A) CONVERTER

A D/A converter has many of the same issues as an A/D converter. The resolution is given
in the number of bits used to create the output analog voltage. For example, a 4-bit D/A

Digital output 12 V

1111
1110 1.5 V
1101

Tachometer analog
voltage input
0000
-12 V
Figure 38 Analog-to-digital conversion.