A few days ago someone asked about increasing the resolution of an A/D by
dithering.
Several excellent responses came, but I wonder if the original questioner
got the
bottom line of what it does.

Dithering increases the resolution by a strictly mathematical procedure,
and, as one
responder answered, can extend any A/D's resolution to arbitrary lengths --
there are
dozens of scientific papers describing the theory in detail, and all the
detail has
to do with making the extra resolution meaningful.

All math is based upon assumptions, and this is no exception.  The first
assumption is
that your A/D, whether 1 bit or 20, is really that accurate.  If you resolve
30 bits,
but they are all in error by 22 bits, you haven't really gained a lot.  The
PIC's A/D
is specified to 8 bits, and when I asked a Microchip application engineer if
I could
dither it to 9 bits, he said their testing was actually to 1/2 LSB accuracy.
9 bits
is unambiguously worthwhile.

One of the responders gave a good explanation of using averaging to increase
resolution;
I'll only add that a trivial example shows what it's all about:

(2+3)/2=2.5.

We've gained a digit by averaging two readings of different value. This is
why dithering
is needed -- as one pointed out, the average of a single value, however many
times
taken, is exactly that value.  Dithering guarantees different values on
different
readings.

I have to disagree with one responder's statement that a triangle wave is
optimum,
though.  This is true only if you know for sure that your sampling is not some
fractional harmonic of the triangle.  Random, zero-centered noise is a much more
effective way to dither.  Gaussian noise is ideal, but you have to be sure
you don't
find that your noise is dominated by, for example, fluorescent lamps, whose
interference is neither Gaussian, nor even symmetric (the only thing that
saves sine
or triangle waves for consideration).

Once your dithering has met the statistical requirements (zero-centered,
larger than
the base resolution, uncorrelated with your sampling), the only limitation on
extending the resolution of your adc is the accuracy of its base resolution.
Many
people have built good, accurate, finely resolved data acquisition systems
with an
accurate reference, a single comparator, a noise diode, and an amplifier to
get the
dithering noise up to the right levels.

It works great! :-)

john perry
jperry@norfolk.infi.net