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In article <1992Apr14.074317.18517@slab.slip.uiuc.edu> dat33228@uxa.cso.uiuc.edu writes:
]The master clock pulse for the Pulse Width Modulation portion of one of the  
]Carver CD players runs at 33MHz.  If you consider that you are feeding a value  
]to the initial stage of this converter every 1/44.1K seconds, then you would be  
]left with 33M/44.1K different possible widths that a pulse could take on.
]
]33,000,000 pulses/sec
]--------------------- = 748.29... pulses / sample
]  44.1 samples/sec
]
]WHOA!  That's only 748 different pulse widths!  How in the heck do you get that  
]to convert into an analog value that can take on 65536 different voltage  
]levels?  Or, for that matter, how did you get a 16 bit value to shrink down  
]into those 748 possible widths, that would then get translated to an analog  
]signal that rivals direct A/D?  I understand the concept of reducing error by  
]converting pulse width to analog voltage levels, but not with these numbers!

That's not how it works. Consider what happens if you output constant
width pulses (square waves) and just vary the number of ones and zeros.
Feed it into an integrator (perhaps just an RC circuit).
All ones gives you an upward ramp. All zeroes gives you a downward ramp.
In between gives you.... in-between. Thus, what you are doing is matching
the slope of the audio signal, not the instantaneous amplitude (although
the effect is the same). There are several techniques for doing this
(which basically have different integrator configurations). They
all go under the general heading of "delta modulation."

You can make a delta-modulation A/D with the following trivial
circuit:

                 +---+
              +--| R |---+
   Audio In   |  +---+   |
     +-----+  | |\       |              +--------------> Digital Output
   --|  R  |--*-|+\      |   +------+   |
     +-----+    |   \    |   |      |   |  +---+       
                |    +---*---| D  Q |---*--| R |----+--------+
                |   /   CLK  |      |      +---+    |        |
          +-----|-/     ------>     |             ------     |
          |     |/           |      |             ------     |
          |   Op Amp         +------+               |        |
          |                                        Gnd       |
          |                                                  |
          +--------------------------------------------------+

To convert the digital bit stram back to audio, just feed it into
an R/C network with the same values as in the A/D shown above.

If you use a comparator, you don't need the feedback resistor shown
on the op-amp. Furthermore, with the op-amp you may have to provide
some level shifting circuitry into the Flip-Flop, whereas a comparator
will provide the right levels.

This circuit provides simple delta mode. There are other kinds (Delta-Sigma
is what is used for high precision audio). One neat thing about delta
mode is that the precision depends only on the 1/0 balance of the
comparator and (in this case) the flip flop. Thus it is much easier
to make high precision delta mode A/D's than it is to make them using
successive approximation.

This circuit will NOT encode DC levels - only AC signals!

Finally, the following is an exercise for the reader: Make two of
these widgets, digitize two signals, and feed the resulting bit stream
into an exclusive-OR gate. Take the output of the XOR into an RC circuit.

What do you get?
]
]Or am I missing something here?

Yep.


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