of Microprocessors

DIGITAL-TO-ANALOG AND ANALOG-TO-DIGITAL CONVERTERS 263
UNKNOWN
10.0 r~~;~rE DAC VOLTAGE
7.5 / TRIAL 2 / 4
5.0i-----'~+--t------___f'=='1.---i"-------
UJ 2.5 6 7 8
~ ol--....J-----=----------------_
§: _ 2.5 TRIAL I
-5.0
-7.5
-10.0
TIME
TIME
Fig. 7-30. Successive approximation search method
DAC with a range of -10 V to + 10 V in the ADC system. The first trial is
used to determine the polarity of the unknown voltage. The DAC is set to 0
V output and the comparator is read after sufficient delay for settling. In this
case, the comparator output would be high, indicating that the unknown is
higher than the trial, which is indeed the case. The next trial value should be
+ 5 V. This time the comparator output would be low, indicating that the
trial was too high.
At this point it is known that the unknown is somewhere between 0 V
and +5 V. The rule is that the next trial value should always be set midway
in the range that the unknown is known to occupy. The result of the trial
will be a new range, half the size of the previous one, that is also known to
surround the unknown. Proceeding, the next trial would be midway between
oand +5, namely +2.5. The sequence would continue: low, try 3 .75; high,
try 3.125; low, try 3.437; high, try 3.281; high, etc. Note that after only
seven trials the unknown has been pinned down to within 30 mY, better
than 0.15% of full-scale accuracy. Eventually the voltage range surrounding
the unknown becomes as small as the step size of the DAC used to generate
the trial voltages, and the conversion is declared to be complete. The last
trial value is the converted result.
Now if the reader is observant he may have noted that the trial values
are nice round numbers-in the binary sense. Assuming the use of an 8-bit
offset binary DAC, the sequence of trials expressed in binary would be:
10000000 (0), 11000000 (5), 10100000 (2.5), 10 110000 (3.75), 10101000
(3.125), 10101100 (3.437), 10101010 (3.281), etc.
It turns out that computation of the next trial value is really no computation
at all. It is simply a bit manipulation that any microprocessor is quite
adept at. If the binary input to the DAC is treated as a register, the manipulation
is as follows: