of Microprocessors

262 MUSICAL ApPLICATIONS OF MICROPROCESSORS
until the comparator switches from high to low, indicating that the unknown
input voltage has just been crossed. Of course, this is not likely to be
any faster than the voltage-to-time methods described earlier. However, if
the unknown voltage has not changed much since the last reading, the search
could be started at the last value rather than zero.
A refinement of the linear search is the tracking ADC. In operation, the
comparator output is constantly monitored. If the comparator output is
high, the DAC output is increased one step. If it is low, the DAC is backed
off one step. The result is that the DAC always contains the digital equivalent
of the input voltage within one step, provided the unknown voltage
changes slowly. The inherent one-step oscillation around the correct value
may be suppressed by use of a window comparator, which has an "equals"
output as well as a greater-than and less-than output. If the equals window is
set to be a little over one step wide, the oscillation is stopped. A window
comparator is simply two ordinary comparators with different reference
voltages-the difference being the window width.
The control circuit for a tracking ADC is exceptionally simple, just a
high-frequency oscillator and an up--down counter. The comparator output is
connected to the direction control input of the counter and the clock makes
the counter count in the indicated direction. The clock period must be longer
than the settling time of the DAC. Usually in a microcomputer system, the
clock can be a microprocessor clock phase chosen such that the counter never
changes when it might be read by the microprocessor. As long as the rate of
input voltage change does not exceed the counting speed, the tracking ADC
has a "zero" conversion time. The slew rate limitation can be very real,
however. For example, a 12-bit tracking ADC with I-MHz clock would
require over 4 msec to slew from one end of the range to the other. Ifused for
direct digitizing of audio, such a converter could not handle full-scale sine
waves higher than 77 Hz without serious errors.
Successive Approximation Search
The most efficient search algorithm and the one used by all high-speed
ADCs is termed successive approximation. The same algorithm is called a binary
search by computer scientists. It works by progressively narrowing in on the
unknown voltage level by testing a series of carefully chosen "trial" voltages
and looking at the comparator output for a high-low indication. (This same
problem is the basis of a popular computer game in which the computer
"thinks" of a random number and responds to the player's guesses with a "too
high" or "too low" verdict.) It is easily proven that no more efficient search
algorithm exists when only a high-low comparison decision is available for
each trial.
Referring to Fig. 7-30, it is easy to see how the algorithm works. The
example is one of homing in on an unknown voltage of + 3.253 V using a