Shameless Plug

Embedded Systems Programming Magazine has sunk to a new low -- they made _my_ article their cover story in the July issue.
Tee hee.
http://www.embedded.com/showArticle.jhtml?articleID "101730
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Tim Wescott
Wescott Design Services
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In a shameless crosspost on sci.electronics.design, sci.engr.control

Congratulations, and my condolences to ESP. :)
Scanning over the article, it looks good, I've been aware of the techniques you describe for a while, but it's always good to see another article on it and some more ideas on how to use it.

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On Sat, 03 Jul 2004 22:59:56 -0700, the renowned Tim Wescott

Good show.
Best regards, Spehro Pefhany
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Congratulations. It's a good article.
Michael
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Tim Wescott wrote:

Nicely done- I was anxious to see a analytical expression of some sort for the actual distribution of the noise energy as a function of the quantizer resolution and the integrator time constant so that this can be bounded from the start rather than through simulation. Your system reminded of exactly of an analog circuit for very high resolution analog voltage to duty cycle conversion using a single chip oa-vref-comparator combination where the oa integrates the error difference between the Vin and an output of the comparator switching between Vref and gnd.
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Fred Bloggs wrote:

Some software engineers can be remarkably averse to that sort of thing -- editors too.
It doesn't seem to make much difference for a 1st-order system, and analytical expressions for such a nonlinear system are hard to come by. I was going to include 2nd-order sigma-deltas in there, but I was not at all satisfied with my own understanding of them so I'm leaving those bits out until I know what the f*** I'm talking about.

It sounds like you were just using a 1st-order analog sigma-delta. The sigma-delta modulator itself is what is used in those itty bitty 24-bit ADC converters that you can get for instrumentation, they're just preceded by a 2nd- or 3rd-order loop filter, and succeeded by _lots_ of digital filtering before the answer gets chunked out to a microprocessor.
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Tim Wescott
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On Sat, 03 Jul 2004 22:59:56 -0700, Tim Wescott

Nice one, Tim. Today ESP., tomorrow, Time. ;->
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On Sat, 03 Jul 2004 22:59:56 -0700, Tim Wescott

Hey Tim,
Neat! Congratulations.
[-Rick-]
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On Sat, 03 Jul 2004 22:59:56 -0700, Tim Wescott

Nice.
Hey, what about taking the extra LSBs and using them to index into a lookup table full of duty-cycle "waveform" bitmaps? Then you could approximate higher-order delta-sigmas without actually having to do a bunch of integrations.
Like 0001001000101010 = duty cycle pattern for 5/16 of a DAC lsb
1011010110110011 = 10/16
or something.
John
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