Sigma Deltas

The counter acts like a 1st-order filter. If you use a higher-order filter in the modulator, then you can follow it with a higher-order low-pass. You can also claim that you don't care as much about high-frequency accuracy (this is not a bad claim for audio and some other things). I believe that most commercial S-D converters use 2nd- or 3rd-order modulators and filters.

For a 2nd-order system the theoretical (and no doubt highly optimistic) lower bound for oversampling would be 2^8, or about 12MHz; the same lower bound for a 3rd-order system would be 2^5.333, or 1.8MHz.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Yes...most of the time I have used first order sigma-deltas since they are very easy to setup and you don't have to worry about stability and all that.

How did you get those numbers by the way? The reason I don't want to go to advanced order sigma-deltas is because the data I am sampling is DC. As going to second order SDs would mean that my output would have a low frequency tone. (I am not sure if this is correct, but for some reason, I remember someone telling me this). Would it be okay to use a

2nd or higher order SD for sampling a DC signal?

(Technically I am wrong to call them SD, it should delta-sigma since that's what the inventers Inose and Yasuda called them.)

From the theory that if you have a 2nd-order filter it'll be x^2 as good, and a 3rd-order will be x^3 as good. In practice these are absolute upper bounds, real performance will be much worse -- but the ADI converters seem to approach this.

As far as the issues with tone generation etc., I don't know. If I were going to make a S-D converter I'd have to do a lot of studying, so I just scrutinize data sheets and look for issues.

Yes, well -- I use S-D because that's what seems to be more popular today. You can invent something and call it whatever you like, whatever the majority of folk call it is what its name ends up being.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

It's pretty close: Googlecounts of 111,000 for S-D vs. 86,000 for D-S (with most of the sororities and fraternities eliminated)

Best regards, Spehro Pefhany

--
"it's the network..."                          "The Journey is the reward"
speff@interlog.com             Info for manufacturers: http://www.trexon.com
Embedded software/hardware/analog  Info for designers:  http://www.speff.com

See the book "Digital Signal Processing A Pratical Guide for Engineers and Scientists". Steven W. Smith explains on page 65 why a digital low pass filter and decimator is equivalent to a counter for converting the comparator's output into a 16 bit word. For the example you give yes you would have to wait 65,536 samples fon the first valid output. But there after with a 64 to 1 decimation and a 3 million samples per second input stage sampling rate the A/D output rate would be 46,875 16 bit words per second. Note the digital filter output is a moving average.

One key concept always seems to be missing in the block diagrams for Sigma-Delta A/D converters that use a digital filter and decimator to convert a comparator's one bit output to a m bit word. m is the resolution of the Sigma-Delta A/D converter. That is the zero to one, zero to full scale, output of the comparator is first converted into a zero to full scale word, word size consistent with the resolution of the A/D converter, before the signal is fed to a digital filter. For a 16 bit A/D converter, m = 16, the input to the digital filter will be either be a 16 bit word with every bit equal to zero or every bit equal to 1. Therefor with the comparator operating at a 3 million samples per second sampling rate the input to the digital filter is 3 million

16 bit words per second. Next because the digital filter is a low pass filter its output will be a moving average of its previous inputs with an output rate of 3 million 16 bit words per second. The output of the digital filter is then decimated. A decimation of 64 to 1 will produce an A/D output rate of 46,875 16 bit words per second.

" How is it that you can get the 16 bit digital out with 3 Megasample/s? Is it the digital filter or something else"

You are right if you only have 1 counter. You couldn't use a Sigma Delta A/D converter with audio. But what if you have 65,536 counters and start the first counter counting with the first sample, start the second counter counting with the second sample, start the third counter counting with the third sample and so on until after 65,536 samples you have started all counters. Then after each counter has counted for 65,536 samples read its output and restart it counting. In this configuration you would have to wait for 65536 samples for the first ouput from a Sigma Delta A/D converter. But after the first output the data rate would be 3 million 16 bit words per second for your example. Conceptually this is what the digital filter in a Sigma Delta A/D converter does when it calculates a moving average of a Sima Dela comparator's output. Then when you decimate the digital filter's output by 64 to 1 you would only need 1024 counters and there would be a 64 sample delay between the start of each counter if you implemented in hardware what Sigma Delta manufacturers do in software.