Designer’s Guide Community

moore

Junior Member

Offline

Posts: 10

Why the transfer funcion of DAC is not contained in NTF of CTDSM
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!

Back to top

IP Logged

loose-electron Senior Fellow Offline Best Design Tool = Capable Designers Posts: 1638 San Diego California	Re: Why the transfer funcion of DAC is not contained in NTF of CTDSM Reply #1 - 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?
Back to top	Jerry Twomey www.effectiveelectrons.com Read My Electronic Design Column Here Contract IC-PCB-System Design - Analog, Mixed Signal, RF & Medical IP Logged

Lex Senior Member Offline Posts: 201 Eindhoven, Holland	Re: Why the transfer funcion of DAC is not contained in NTF of CTDSM Reply #2 - 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? ^^
Back to top	IP Logged

moore Junior Member Offline Posts: 10	Re: Why the transfer funcion of DAC is not contained in NTF of CTDSM Reply #3 - Sep 19^th, 2011, 5:38am yes. Do you know the answer?
Back to top	IP Logged

sheldon

Community Fellow

Offline

Posts: 751

Re: Why the transfer funcion of DAC is not contained in NTF of CTDSM
Reply #4 - 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

Back to top

IP Logged

Praveen K

Junior Member

Offline

Posts: 25
Bangalore

Re: Why the transfer funcion of DAC is not contained in NTF of CTDSM
Reply #5 - 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

Back to top

IP Logged