On Fri, 9 Aug 2002, Kieren Johnstone wrote:

> Surely if TMR0 overflows at 19.5 KHz, by switching a PWM every time I could
> get 9.7 KHz, every 256 interrupts I could get about 76 Hz; in the original
> post I mentioned 4.9 KHz being the highest note I'd consider..

Kieren,

You misunderstood Olin.

PWM = Pulse Width Modulation, normally means constant frequency and
varying duty-cycle. What Olin said is that the constant frequency for what
you proposed is 76 Hz. But now, you seem to be suggesting that you want to
generate square waves for your tones!

However, let me suggest a slightly different way in which "PWM" can be
generated. Suppose you divide time into equal intervals. At each interval
you generate a high or a low; i.e. a pulse. Over a period of N pulses,
you're average ouput will be:

  avg = # of high's / total # of time slots

So for example, if you had 100 time slots and 10 of these were high
pulses (and 90 low ones) then the average would be 10/100 = 1/10.

With normal PWM, all of the high pulses are grouped together as one pulse.
But from a signal processing point of view, this is not necessary. So for
example to get the value 1/10 you could generate these various pulse
streams:


10 H, 90 L
5 H, 45 L, 5 H, 45 L,
1 h, 9 L, 1 H, 9 L

Or even this would work:
3 H, 20 L, 1 H, 33 L, 5 H, 7L, 1 H, 30 L

In other words, over the 100 pulses you want 10 high ones and 90 low ones.

If you're driving a motor (or some other big thing that can incur large
switching losses), you may want to minimize the switching and so you'd
choose the 10/90/10/90 approach which groups the highs together. If you're
generating audio, you may wish to *maximize* the carry frequency -
preferably beyond the range of human hearing, so that it is easier to
filter. Thus you'd choose the 1/9/1/9 approach.

To maximize the frequency, all you need to do is implement PWM with phase
accumulators. In this case, all you do is repeatedly add your "duty cycle"
to the phase accumulator. If the phase accumulator rolls over, you output
a "1" if not you output a "0".  So for example:


  unsigned char  phase = 0;
  unsigned char  analog = 15;   // i.e. 15 out of 256

  while (1) {

     old_phase = phase;
     phase = phase + analog;

     if(phase < old_phase)
       output = 1;
     else
       output = 0;

   }

Play with this for different values of "analog" and observe how "output"
changes.

Once you grasp it then consider this assembly code:

     movf   analog,w    ;Get the current analog value
     addwf  phase,f     ;Add it to the phase accumulator
                        ; carry get's set if we rollover.
     rlf    output,f    ;Lsb contains the "rollover" info

What's nice about this is that multiple PWM's can be constructed by just
repeating this snippet. The variable "output" is copied to the I/O port at
the last stage. For 4 outputs, the last rlf will look like this:

     rlf    output,w
     andlw  0x0f
     movwf  PORTB

With this scheme, the maximum frequency occurs at your 9.6 kHz for an
analog value of 1/2 and the minimum frequency is 76 Hz for analog value
1/256 or 255/256. I'd be inclined to write an isochronous loop so that the
frequencies are somewhat higher. You'll want to run this through a low
pass filter to knock off the edges.

Now, note that you don't get something for nothing. It still takes time to
achieve the "average" analog value you seek. It also takes time to
generate the desired signal. This scheme may help, but at these
frequencies you won't ever be competing with Yamaha synthesizers!

Scott

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