sigma delta modulator design.

Hi

I am exploring the use of sigma delta modulators for designing a DAC. I
coded up a first order modulator in verilog with a 1 bit output and it
behaved as expected.

I coded a second order modulator, to improve performance, and it looks to
me that the digital output of the modulator has to be a 2 bit signal.
Anytime I try any saturation to limit the output to a single bit, the
design simply doesn't work.

(This is not too desirable since it requires a 2 bit DAC. A 1 bit DAC is
good for linearity, not a 2 bit one).

My question:

Does a nth order digital sigma delta modulator need to have a n bit
output?

Thanks,
Venkat.

venkatax wrote:

> Hi
> 
> I am exploring the use of sigma delta modulators for designing a DAC. I
> coded up a first order modulator in verilog with a 1 bit output and it
> behaved as expected.
> 
> I coded a second order modulator, to improve performance, and it looks to
> me that the digital output of the modulator has to be a 2 bit signal.
> Anytime I try any saturation to limit the output to a single bit, the
> design simply doesn't work.
> 
> (This is not too desirable since it requires a 2 bit DAC. A 1 bit DAC is
> good for linearity, not a 2 bit one).
> 
> My question:
> 
> Does a nth order digital sigma delta modulator need to have a n bit
> output?
> 
> Thanks,
> Venkat.
> 
> 

"venkatax" <venkat@chilsemi.com> writes:

> Hi
>
> I am exploring the use of sigma delta modulators for designing a DAC. I
> coded up a first order modulator in verilog with a 1 bit output and it
> behaved as expected.
>
> I coded a second order modulator, to improve performance, and it looks to
> me that the digital output of the modulator has to be a 2 bit signal.
> Anytime I try any saturation to limit the output to a single bit, the
> design simply doesn't work.
>
> (This is not too desirable since it requires a 2 bit DAC. A 1 bit DAC is
> good for linearity, not a 2 bit one).
>
> My question:
>
> Does a nth order digital sigma delta modulator need to have a n bit
> output?

No. You might want to see a presentation I made on this here:

  http://www.digitalsignallabs.com/presentation.pdf
-- 
Randy Yates                      % "Rollin' and riding and slippin' and
Digital Signal Labs              %  sliding, it's magic."
mailto://yates@ieee.org          %  
http://www.digitalsignallabs.com % 'Living' Thing', *A New World Record*, ELO

"venkatax" <venkat@chilsemi.com> writes:

> I am exploring the use of sigma delta 

And it's "delta sigma."
-- 
Randy Yates                      % "The dreamer, the unwoken fool - 
Digital Signal Labs              %  in dreams, no pain will kiss the brow..."
mailto://yates@ieee.org          %  
http://www.digitalsignallabs.com % 'Eldorado Overture', *Eldorado*, ELO

Hi Randy,

Thanks for sharing your presentation with me. Looking through books and
presentations convince me that a nth order classic sigma delta modulator
must have a NTF of (1-z^-1)^n.

But there is the practical matter of signal widths. Slide 16 of your
presentation shows a 2nd order modulator. Let us say that y[n] is a 1 bit
output.

My question is: if r[n] is m bits wide, what are the widths of:
1. s[n]
2. x[n]
3. input to the 2nd stage integrator.
4. output of the 2nd stage integrator.

I tried saturation to keep signal widths in check, but saturation always
resulted in loss of information.

As for nomenclature, here is a tidbit I got from a ADI publication:

We believe that the name delta-sigma is a departure from precedent. Not
just in the sense of grammar, but also in relation to the hierarchy of
operations.

Consider a block diagram for embodying an analog root-mean-square (finding
the square root of the mean of a squared signal) computer. First the signal
is squared, then it is integrated, and finally it is rooted.
If we were to name the overall function after the causal order of
operations, it would have to be called a "square mean root" function. But
naming in order of the hierarchy of its mathematical operations gives us
the familiar—and undisputed—name, root meansquare.

Consider now a block diagram for taking a difference (delta), and then
integrating it (sigma). Its causal order would give delta-sigma, but in
functional hierarchy it is sigma-delta, since it computes the integral of a
difference. We believe that the latter term is correct and follows
precedent; and we have adopted it as our standard.

Venkat.

"venkatax" <venkat@chilsemi.com> writes:

> Hi Randy,
>
> Thanks for sharing your presentation with me. Looking through books and
> presentations convince me that a nth order classic sigma delta modulator
> must have a NTF of (1-z^-1)^n.
>
> But there is the practical matter of signal widths. Slide 16 of your
> presentation shows a 2nd order modulator. Let us say that y[n] is a 1 bit
> output.
>
> My question is: if r[n] is m bits wide, what are the widths of:
> 1. s[n]
> 2. x[n]
> 3. input to the 2nd stage integrator.
> 4. output of the 2nd stage integrator.
>
> I tried saturation to keep signal widths in check, but saturation always
> resulted in loss of information.

You're working at a company, right? They're paying you for doing this
job, right? If you would like to contract my services, I'd be happy to
provide you the answers to these questions in return. Otherwise I see no
reason to do your job for you for free.

Sorry if that seems harsh, flippant, or otherwise offensive, but there's
just so much free advice/time I'm willing to give, and once your
questions start requiring more time than that, we arrive at this
point. Perhaps others here will be willing to answer your questions for
free. [Vlad - you're rubbing off on me...]
-- 
Randy Yates                      % "Bird, on the wing,
Digital Signal Labs              %   goes floating by
mailto://yates@ieee.org          %   but there's a teardrop in his eye..."
http://www.digitalsignallabs.com % 'One Summer Dream', *Face The Music*, ELO

>Sorry if that seems harsh, flippant, or otherwise offensive, but there's
>just so much free advice/time I'm willing to give, and once your
>questions start requiring more time than that, we arrive at this
>point. Perhaps others here will be willing to answer your questions for
>free. [Vlad - you're rubbing off on me...]

You have a point. My quest should be for knowledge, not a solution. I'll
need to figure out if any university offers a online course that covers
oversampling converters.

Regards,
Venkat.

On Thu, 17 Sep 2009 11:06:04 -0500, venkatax wrote:

> Hi Randy,
> 
> Thanks for sharing your presentation with me. Looking through books and
> presentations convince me that a nth order classic sigma delta modulator
> must have a NTF of (1-z^-1)^n.
> 
> But there is the practical matter of signal widths. Slide 16 of your
> presentation shows a 2nd order modulator. Let us say that y[n] is a 1
> bit output.
> 
> My question is: if r[n] is m bits wide, what are the widths of: 
> 1. s[n]
> 2. x[n]
> 3. input to the 2nd stage integrator. 
> 4. output of the 2nd stage integrator.

Wider than m bits, if you want it to work.
> 
> I tried saturation to keep signal widths in check, but saturation always
> resulted in loss of information.

Just as cutting a string always results in a shorter string, the act of 
fixing a variable to some predetermined value will result in a loss of 
information.

> As for nomenclature, here is a tidbit I got from a ADI publication:
(nomenclature argument snipped)

Why don't you try three things:  One, simulate the system in figure 8 
with really wide data paths, except for r and y.  Only when you get it 
working that way should you consider saturating points in the middle.  
Two, you may find that all unity gains aren't what you want -- what 
happens if you precede one or both integrators with attenuation blocks 
(aside from slower settling)?  Three, get the book that Randy refers to 
and read it, or get a related one and read _that_.

-- 
www.wescottdesign.com

"venkatax" <venkat@chilsemi.com> writes:

>>Sorry if that seems harsh, flippant, or otherwise offensive, but there's
>>just so much free advice/time I'm willing to give, and once your
>>questions start requiring more time than that, we arrive at this
>>point. Perhaps others here will be willing to answer your questions for
>>free. [Vlad - you're rubbing off on me...]
>
> You have a point. My quest should be for knowledge, not a solution. I'll
> need to figure out if any university offers a online course that covers
> oversampling converters.

Venkat, you have a very good attitude. If I get some spare time I'll try
to have a look further. Also Tim has some good suggestions.
-- 
Randy Yates                      % "And all you had to say
Digital Signal Labs              %  was that you were 
mailto://yates@ieee.org          %  gonna stay."
http://www.digitalsignallabs.com % Getting To The Point', *Balance of Power*, ELO

"venkatax" <venkat@chilsemi.com> writes:

>>Sorry if that seems harsh, flippant, or otherwise offensive, but there's
>>just so much free advice/time I'm willing to give, and once your
>>questions start requiring more time than that, we arrive at this
>>point. Perhaps others here will be willing to answer your questions for
>>free. [Vlad - you're rubbing off on me...]
>
> You have a point. My quest should be for knowledge, not a solution. I'll
> need to figure out if any university offers a online course that covers
> oversampling converters.

venkat:

I may have it: when you quantize your output, you get one bit. Are
you feeding that bit back to the input as is? You shouldn't be. Try
feeding it back as +FS-1 / -FS+1, where FS is relative to the input
to the quantizer.
-- 
Randy Yates                      % "Midnight, on the water... 
Digital Signal Labs              %  I saw...  the ocean's daughter." 
mailto://yates@ieee.org          % 'Can't Get It Out Of My Head' 
http://www.digitalsignallabs.com % *El Dorado*, Electric Light Orchestra