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Design >> Analog Design >> Why the transfer funcion of DAC is not contained in NTF of CTDSM
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Message started by moore on Sep 17^th, 2011, 4:37pm

Title: Why the transfer funcion of DAC is not contained in NTF of CTDSM
Post by moore on Sep 17^th, 2011, 4:37pm

Suppose the transfer funciton of DAC is D(s), (e.g. for NRZ D(s)=(1-exp(-sTs))/sTs)
Since D(s) is in the feed back loop, then NTF should be 1/(1+D(s)H(s)), H(s) is the loop filter transfer funciton.
However, in most case we find NTF=1/(1+H(s)), and D(s) is missing!

Can anyone tell me why?

I guess it is like this:

For NRZ:
exp(-sTs) in Taylor series can be 1-sTs+...
Thus D(s) can be simplified as [1-(1-sTs)]/sTs, and finally it turns out to be 1.

Am I correct?

Many thanks!

Title: Re: Why the transfer funcion of DAC is not contained in NTF of CTDSM
Post by loose-electron on Sep 18^th, 2011, 1:34pm

CTDSM?

please define your question in a manner that can be understood -

You are asking about a Noise Transfer Function of a DAC in some sort of system?

Title: Re: Why the transfer funcion of DAC is not contained in NTF of CTDSM
Post by Alexandar on Sep 19^th, 2011, 2:41am

CTDSM = continuous time Delta sigma modulator ;)

I guess the question is why a certain term vanishes in the overall transfer function? Just plain mathematics I guess? ^^

Title: Re: Why the transfer funcion of DAC is not contained in NTF of CTDSM
Post by moore on Sep 19^th, 2011, 5:38am

yes.
Do you know the answer?

Title: Re: Why the transfer funcion of DAC is not contained in NTF of CTDSM
Post by sheldon on Oct 9^th, 2011, 2:37am

Moore,

Sorry, I don't quite follow your logic. However, please consider that
you actually don't directly use the output of a Delta-Sigma DAC. The
output is needs to be filtered, by the anti-aliasing filter. The signal is
within the bandwidth of the anti-aliasing filter and is passed. The noise
is outside the anti-aliasing filter bandwidth and is suppressed.
Understanding Delta-Sigma Data Converters by Schreier &
Temes has a nice discussion of the filter design. Maybe that accounts
for the missing terms in your analysis.

Best Regards,

Sheldon

Title: Re: Why the transfer funcion of DAC is not contained in NTF of CTDSM
Post by Praveen K on Oct 10^th, 2011, 3:03am

Hi moore,

The DAC is assumed be '1' so that its easy to explain the noise shaping of Sigma Delta. But this is done just for introduction and explaining of sigma delta system.

But when it comes to actual implementation of Sigma delta modulator of a particular order and DAC which can be either NRZ or RZ or HRZ(half return to zero) or a combination of these, the DAC transfer function will be taken into account to find the coefficients of the over all system to make it stable.

To answer your question: DAC TF should be included in NTF for sure.

you can refer to this book, one of the best ref for continuous time sigma delta modulators,

Continuous-time delta-sigma modulators for high-speed A/D/ conversion ... By James A. Cherry, W. Martin Snelgrove