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200 CHAPTER EIGHT
It should have at least 12 bits. The calculation is 60 db/5 db/bit 12 bits. More infor-
mation on the S/N ratio can be found at http://searchnetworking.techtarget.com/
sDefinition/0,,sid7_gci213018,00.html.

A/D Dithering

A/D converters are not perfect. They convert analog signals into digital representations
of the original signal. If the original signal is a very smoothly changing signal, then the
digitization of the signal can add significant noise to the signal. This comes into play
in at least two situations:

Sometimes the A/D itself will have difficulty stepping over major bit boundaries.
Suppose, for example, we’re using a 16-bit A/D and that the signal steps over the
boundary from 7FFFH to 8000H. The number 7FFFH is in hexadecimal (base 16)
notation explained at the following URLs:
www.whatis.techtarget.com/definition/0,,sid9_gci212247,00.html
www.hostingworks.com/support/dict.phtml?foldoc=hexadecimal.
Many bits are changing at the same time, and the A/D may have trouble keeping
the same accuracy it might have with simply stepping from 7FFEH to 7FFFH.
Quantization error also creeps in. No matter what, the A/D can only represent the
input signal to the accuracy given by the number of bits in the A/D. In a smoothly
changing input signal, these effects can become noticeable. This effect is most
often seen in graphic images; the human eye is very efficient at picking out error
patterns in smoothly changing pictures.
To counteract these effects, a random signal is added to the input signal. This dither-
ing of the input signal is generally sufficient to blur the deleterious effects mentioned
earlier. Dithering can be added in many ways:
Analog noise We can simply put a noise source at the input of the A/D. The mag-
nitude of the noise source should be just about the size of the quantization noise.
If the range of the A/D is 10 volts, and it’s a 10-bit A/D, then a single bit change
in the A/D digital output covers 10V/2 10 mv. Adding a 10 mv noise source
10
to the analog input stage would create the type of dithering needed. Using a noise
source larger than 10 mv would also work, at the expense of lower resolution.
Random shifting One way to get around A/D imperfections is to dynamically
(and randomly) shift the range of the A/D. A random voltage can be added to the
input of the A/D and later be subtracted digitally from the A/D output. All the con-