Page 336 - Mechatronics with Experiments

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n - bit u(t)
0 n - 1
1
D/A
1 1
0 0 t
CPU

1 n - 1 y(t)
0
A/D
1 1
0 0
t

Quantized signal

3
2
1
0
2.0
2.32 Unquantized signal
-1
-2

-3
-4

FIGURE 5.56: Resolution and range of A/D and D/A converters.

Quantization is the result of the fact that the A/D, D/A, and also the CPU are finite word
and finite resolution devices (Figure 5.56). Let us consider that we are sampling a signal
in the 0 to 7 V DC range. Assume that we have a 3-bit A/D converter. The A/D converter
can represent only 0, 1, 2, 3, 4, 5, 6, 7 VDC signals exactly. If the analog signal was 4.6 V,
it can be represented as either 4 or 5 by the A/D conversion. If the truncation method is
used in the quantization, it will be converted to 4. If the round-off method is used, it will be
converted to 5. The maximum value of the quantization error is the resolution of the A/D
or D/A converter.
For instance, an 8-bit A/D converter can represent 256 different states. If an analog
sensor with a signal range of 0 to 10 VDC is connected to it, the smallest change the A/D
can detect in the signal is 10/255 VDC. Any change in the signal less than 10/255 VDC
will not be detected by the computer. Similiarly, if the A/D converter is 12-bit, the smallest
change detectable in the signal is equal to the signal range divided by 2 12 − 1 = 4095. This
is called the resolution of the A/D converter. If it is 16-bit A/D converter, its resolution is
one part in 2 16 − 1 = 65 535.
The D/A converter converts the digital numbers into analog signals. This is also
referred to as the signal reconstruction stage. Discrete values of control action are presented