# how to understand sigma-delta adc in time domain?

Started by November 11, 2008
```I'm trying to think of a way to understand sigma-delta ADCs in time
domain.

Up to my understanding, two key technology of sigma-delta ADCs are
oversampling and noise shaping. In frequency domain, oversampling evenly
spreads the square(delta)/12 quantization noise between 0 and samping
frequency fs. Then with the help of decimation filter, we can remove the
noise out of baseband fB. So, the remaining noise is just 1/OSR of the
quantization noise. This understanding works well in freqency domain. But I
cannot relate this to time domain understanding. Why averaging more 1s and
-1s means pushing noise to higher frequency...I think maybe when the
samples are denser,the digital output are more similar to the original

Also, for noise shaping, I can just simply think the negative feedback
forces the output to equal the input...

Can anybody here give me some advice on time domain understanding of

Thank you very much~

```
```On Nov 11, 7:42&#2013266080;pm, "lxx.helen" <lxx.he...@gmail.com> wrote:
> I'm trying to think of a way to understand sigma-delta ADCs in time
> domain.
>
> Up to my understanding, two key technology of sigma-delta ADCs are
> oversampling and noise shaping. In frequency domain, oversampling evenly
> spreads the square(delta)/12 quantization noise between 0 and samping
> frequency fs. Then with the help of decimation filter, we can remove the
> noise out of baseband fB. So, the remaining noise is just 1/OSR of the
> quantization noise. This understanding works well in freqency domain. But I
> cannot relate this to time domain understanding. Why averaging more 1s and
> -1s means pushing noise to higher frequency...I think maybe when the
> samples are denser,the digital output are more similar to the original
>
> Also, for noise shaping, I can just simply think the negative feedback
> forces the output to equal the input...
>
> Can anybody here give me some advice on time domain understanding of
>
> Thank you very much~

I have extensive slide presentations on this topic, which I will be
happy to share.

```
```On Nov 11, 9:30&#2013266080;pm, Robert Adams <robert.ad...@analog.com> wrote:
> On Nov 11, 7:42&#2013266080;pm, "lxx.helen" <lxx.he...@gmail.com> wrote:
>
>
>
> > I'm trying to think of a way to understand sigma-delta ADCs in time
> > domain.
>
> > Up to my understanding, two key technology of sigma-delta ADCs are
> > oversampling and noise shaping. In frequency domain, oversampling evenly
> > spreads the square(delta)/12 quantization noise between 0 and samping
> > frequency fs. Then with the help of decimation filter, we can remove the
> > noise out of baseband fB. So, the remaining noise is just 1/OSR of the
> > quantization noise. This understanding works well in freqency domain. But I
> > cannot relate this to time domain understanding. Why averaging more 1s and
> > -1s means pushing noise to higher frequency...I think maybe when the
> > samples are denser,the digital output are more similar to the original
> > analog input. This seems reasonable, but &#2013266080;too simple or general...
>
> > Also, for noise shaping, I can just simply think the negative feedback
> > forces the output to equal the input...
>
> > Can anybody here give me some advice on time domain understanding of
>
> > Thank you very much~
>
> I have extensive slide presentations on this topic, which I will be
> happy to share.
>

i wouldn't sneeze at an offer like that coming from this person.

hey Bob, if this is already conveniently zipped or otherwize
encapsulated, wanna send send me some of it?

r b-j
```
```robert bristow-johnson wrote:
>> On Nov 11, 7:42 pm, "lxx.helen" <lxx.he...@gmail.com> wrote:
>>
>>
>>
>>> I'm trying to think of a way to understand sigma-delta ADCs in time
>>> domain.
>>> Up to my understanding, two key technology of sigma-delta ADCs are
>>> oversampling and noise shaping. In frequency domain, oversampling evenly
>>> spreads the square(delta)/12 quantization noise between 0 and samping
>>> frequency fs. Then with the help of decimation filter, we can remove the
>>> noise out of baseband fB. So, the remaining noise is just 1/OSR of the
>>> quantization noise. This understanding works well in freqency domain. But I
>>> cannot relate this to time domain understanding. Why averaging more 1s and
>>> -1s means pushing noise to higher frequency...I think maybe when the
>>> samples are denser,the digital output are more similar to the original
>>> Also, for noise shaping, I can just simply think the negative feedback
>>> forces the output to equal the input...
>>> Can anybody here give me some advice on time domain understanding of
>>> Thank you very much~
>> I have extensive slide presentations on this topic, which I will be
>> happy to share.
>>
>
> i wouldn't sneeze at an offer like that coming from this person.
>
> hey Bob, if this is already conveniently zipped or otherwize
> encapsulated, wanna send send me some of it?

If it's no trouble, may I see it too?

Jerry
--
Engineering is the art of making what you want from things you can get.
&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
```
```lxx.helen@gmail.com

Thank you very very much~

>On Nov 11, 7:42=A0pm, "lxx.helen" <lxx.he...@gmail.com> wrote:
>> I'm trying to think of a way to understand sigma-delta ADCs in time
>> domain.
>>
>> Up to my understanding, two key technology of sigma-delta ADCs are
>> oversampling and noise shaping. In frequency domain, oversampling
evenly
>> spreads the square(delta)/12 quantization noise between 0 and samping
>> frequency fs. Then with the help of decimation filter, we can remove
the
>> noise out of baseband fB. So, the remaining noise is just 1/OSR of the
>> quantization noise. This understanding works well in freqency domain.
But=
> I
>> cannot relate this to time domain understanding. Why averaging more 1s
an=
>d
>> -1s means pushing noise to higher frequency...I think maybe when the
>> samples are denser,the digital output are more similar to the original
>>
>> Also, for noise shaping, I can just simply think the negative feedback
>> forces the output to equal the input...
>>
>> Can anybody here give me some advice on time domain understanding of
>>
>> Thank you very much~
>
>I have extensive slide presentations on this topic, which I will be
>happy to share.
>
>
>
```
```On Nov 11, 10:00&#2013266080;pm, Jerry Avins <j...@ieee.org> wrote:
> robert bristow-johnson wrote:
> >> On Nov 11, 7:42 pm, "lxx.helen" <lxx.he...@gmail.com> wrote:
>
> >>> I'm trying to think of a way to understand sigma-delta ADCs in time
> >>> domain.
> >>> Up to my understanding, two key technology of sigma-delta ADCs are
> >>> oversampling and noise shaping. In frequency domain, oversampling evenly
> >>> spreads the square(delta)/12 quantization noise between 0 and samping
> >>> frequency fs. Then with the help of decimation filter, we can remove the
> >>> noise out of baseband fB. So, the remaining noise is just 1/OSR of the
> >>> quantization noise. This understanding works well in freqency domain. But I
> >>> cannot relate this to time domain understanding. Why averaging more 1s and
> >>> -1s means pushing noise to higher frequency...I think maybe when the
> >>> samples are denser,the digital output are more similar to the original
> >>> analog input. This seems reasonable, but &#2013266080;too simple or general...
> >>> Also, for noise shaping, I can just simply think the negative feedback
> >>> forces the output to equal the input...
> >>> Can anybody here give me some advice on time domain understanding of
> >>> Thank you very much~
> >> I have extensive slide presentations on this topic, which I will be
> >> happy to share.
>
> > i wouldn't sneeze at an offer like that coming from this person.
>
> > hey Bob, if this is already conveniently zipped or otherwize
> > encapsulated, wanna send send me some of it?
>
> If it's no trouble, may I see it too?
>
> Jerry
> --
> Engineering is the art of making what you want from things you can get.
> &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;- Hide quoted text -
>
> - Show quoted text -

Bob
```
```On Tue, 11 Nov 2008 18:42:20 -0600, lxx.helen wrote:

> I'm trying to think of a way to understand sigma-delta ADCs in time
> domain.
>
> Up to my understanding, two key technology of sigma-delta ADCs are
> oversampling and noise shaping. In frequency domain, oversampling evenly
> spreads the square(delta)/12 quantization noise between 0 and samping
> frequency fs. Then with the help of decimation filter, we can remove the
> noise out of baseband fB. So, the remaining noise is just 1/OSR of the
> quantization noise. This understanding works well in freqency domain.
> But I cannot relate this to time domain understanding. Why averaging
> more 1s and -1s means pushing noise to higher frequency...I think maybe
> when the samples are denser,the digital output are more similar to the
> general...
>
> Also, for noise shaping, I can just simply think the negative feedback
> forces the output to equal the input...
>
> Can anybody here give me some advice on time domain understanding of
>
> Thank you very much~

While you're waiting for Robert's slides, here's something to ponder:

You have it a bit wrong; the front end of a delta-sigma modulator is
designed to shape the noise more or less during the sampling process, so
you can't really separate the sampling from the noise shaping.

What it does is to take the output of a 1-bit DAC that follows the train
of 1's and 0's that come out of the comparator, and uses that as feedback
to a loop that contains an integrator.  Since an integrator has higher
gain the lower the frequency gets, the noise _must_ be reduced at these
lower frequencies.

IIRC the article that I wrote on sigma-delta techniques covers the time-
domain aspect of this -- see http://www.wescottdesign.com/articles/