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# Discussion Groups | Comp.DSP | how to caculate the ripple of sigma-delta conveter

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# how to caculate the ripple of sigma-delta conveter - clarkkevin - 2006-03-03 04:22:00

```Hello,

Let's consider  a Sigma-Delta analog to digital converter following
by decimation filters.
Do the passband ripples of the decimation filter play a significant
role in not to degrade the precision afforded by the Sigma Delta  ?
I have been said that if a Sigma Delta converter hold a precision of
n
bits, the passband ripple of the folowing decimation filter must be
inferior to -20*log10(1-2^(-n)) in order to preserve the performances.

clarkkevin```

# Re: how to caculate the ripple of sigma-delta conveter - Al Clark - 2006-03-03 09:44:00

```"clarkkevin" <z...@gmail.com> wrote in

> Hello,
>
>    Let's consider  a Sigma-Delta analog to digital converter following
> by decimation filters.
>   Do the passband ripples of the decimation filter play a significant
> role in not to degrade the precision afforded by the Sigma Delta  ?
>   I have been said that if a Sigma Delta converter hold a precision of
> n
> bits, the passband ripple of the folowing decimation filter must be
> inferior to -20*log10(1-2^(-n)) in order to preserve the performances.
>
>
>
>
> clarkkevin
>
>

I don't think so. There are of course, many things that are going to
affect the accuracy of the measurement. For example, the voltage
reference is likely to be far less accurate than required for perfect N
bit accuracy. The input amplifier gain is another factor. All of these
parameters are going to scale the conversion by a constant factor. In
principle, you could even calibrate this factors out.

The transfer function of the decimation filter is going to be multiplied
with the incoming spectrum. You might say that you are measuring the
composite of the two. If you had .1dB of ripple and a perfect N bit
converter, you input would be known to N bits + .1dB ripple. At fullscale
the ripple would be 10 x larger than at -20dB from fullscale.

In many measurement situations, the range is much more important from a
logarithmic point of view. The fact that almost all converters are linear
doesn't change this. For example, if I was measuring sound pressure, it
makes more sense to consider the level in dB(re20uPa), that is dB(SPL)
than in absolute Pa (pressure). A 1dB change might be meaningful whether
the level is 60dB or 80dB, The sound pressure variation is 10 times
greater for the 80dB case.

--
Al Clark
Danville Signal Processing, Inc.
--------------------------------------------------------------------
Purveyors of Fine DSP Hardware and other Cool Stuff
Available at http://www.danvillesignal.com```

# Re: how to caculate the ripple of sigma-delta conveter - clarkkevin - 2006-03-03 21:19:00

```Hi Al Clark
I sincerely thank you for your support.After what you said I
still don't know how to define the ripple,for example if I have a N bit
converter the input number is 2^N-1,when my converter ripple is less
than 20log(2^N-1) the number will overflow.Of course when I see this
thing happen I can take it don't happen.but I believe it will bring
noise.because with a definately frequency all the input number is
multiply with the ripple but the large number.
please tell me when I have a 16 bit 5M nyquist frequency sigma
delta converter. how much ripple of this converter it must be.how to
caculate it.Dose the modulator infect the ripple calculation.```

# Re: how to caculate the ripple of sigma-delta conveter - Al Clark - 2006-03-04 10:56:00

```"clarkkevin" <z...@gmail.com> wrote in news:1141438798.316346.8410

> Hi Al Clark
>       I sincerely thank you for your support.After what you said I
> still don't know how to define the ripple,for example if I have a N bit
> converter the input number is 2^N-1,when my converter ripple is less
> than 20log(2^N-1) the number will overflow.Of course when I see this
> thing happen I can take it don't happen.but I believe it will bring
> noise.because with a definately frequency all the input number is
> multiply with the ripple but the large number.
>       please tell me when I have a 16 bit 5M nyquist frequency sigma
> delta converter. how much ripple of this converter it must be.how to
> caculate it.Dose the modulator infect the ripple calculation.
>
>

I'm sorry, I not sure I understand your question or confusion. I'm also not
sure where you are going to get a 5M sigma delta converter (at least the 5M
is the passband)

--
Al Clark
Danville Signal Processing, Inc.
--------------------------------------------------------------------
Purveyors of Fine DSP Hardware and other Cool Stuff
Available at http://www.danvillesignal.com```