of Microprocessors

DIGITAL TONE GENERATION TECHNIQUES 419
LOOP CLC
CLEAR CARRY FLAG
2
ADC
STA
NOP
NOP
NOP
NOP
B
DAC
ADD B TO ACCUMULATOR
WRITE ACCUMULATOR TO DAC
WAIT 16 CLOCKS FOR A
TOTAL LOOP TIME OF
25 f.LSEC WHICH GIVES
A 40-ks/s SAMPLE RATE
NOP
JMP
JMP
*+3
LOOP REPEAT
Assuming that the A register was initially 0 and that B contains 1, the
sequence of numbers that would be sent to the DAC would be 1, 2, 3,
4, ... 125, 126, 127. Now, assuming twos-complement arithmetic, the next
addition would try to produce 128, which, of course, overflows the 6502's 8­
bit accumulator, producing instead a result of -128. The sequence would
continue -127, -126, ... , - 2, -1, 0, 1, etc., and a full sawtooth cycle
has been completed. The overflow from + 127 to - 128 is simply the
sawtooth flyback.
In a typical 6502, this loop would execute in 25 f.Lsec, giving a sample
rate of 40 ks/s. Since 256 times around the loop are required for a single
sawtooth cycle, the sawtooth frequency will be 40 ks/s/256 = 156.25 Hz,
essentially D-sharp below middle C. Now, what if B has the value 2 in it?
Register A, starting at zero would be 0, 2, 4, ... , 124, 126, -128,
-126, ... , - 2, 0, 2, etc. It would take only 128 iterations for a complete
cycle, so the tone frequency would be 312.5 Hz, precisely twice what it was.
Other frequencies can be had by setting B to other values. Thus, continuing
the analog sawtooth analogy, the content of B represents the current into the
integrator, although it will be called the increment in the discussion to follow.
Improving Frequency Resolution
Obviously, only a very limited number of frequencies is available with
this basic loop. Another way to change the sawtooth frequency is to change
the loop time and thus the sample rate, perhaps by changing the number of
NOP instructions. However, this would violate the holy dogma of direct
computer synthesis, which decrees that the sample rate shall remain constant
throughout the system.
Actually, the numbers in the accumulator and B should be considered
as /ractions between - 1 and + 1. Thus, the accumulator starts at 0,
increments in units of 1/128 to 127/128, overflows to -128/128, continues to
0, and repeats. B can hold values of 1/128, 2/128, 3/128, etc. The sawtooth
ftequency is given by F = 40,000[/2, where I is the ftaction stored in B, the
40,000 is the sample rate, and the 2 is because the sawtooth traverses a range
of 2 units; from - 1 to + 1. In order to get finer frequency resolution, it is
simply necessary to specify the increment with more ptecision.
3
4
2
2
2
2
2
3
-.2
25