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Design >> Mixed-Signal Design >> Phase Noise of Δ-Σ modulators
https://designers-guide.org/forum/YaBB.pl?num=1276575200

Message started by Mayank on Jun 14^th, 2010, 9:13pm

Title: Phase Noise of Δ-Σ modulators
Post by Mayank on Jun 14^th, 2010, 9:13pm

I have read many papers on ΔΣ modulator design & they depict phase noise plots for 2nd, 3rd & 4th order modulation.
How do they obtain those phase noise plots for ΔΣ modulators ?
Solely through MATLAB models or from SPICE simulation ??

Title: Re: Phase Noise of Δ-Σ modulators
Post by ipyd on Jun 15^th, 2010, 5:52am

Hi Mayank,

I've never done it before. But, I guess, they save all simulation SPICE results and then plot it using MATLAB code.
I know it's not related, but you may go to : http://cmosedu.com/cmos2/MSD_Matlab/MSD_MATLAB.htm
as reference..

Sorry, i can not help you much.
--ipyd

Title: Re: Phase Noise of Δ-Σ modulators
Post by pancho_hideboo on Jun 15^th, 2010, 6:13am

Mayank wrote on Jun 14^th, 2010, 9:13pm:

How do they obtain those phase noise plots for ΔΣ modulators ?
Solely through MATLAB models or from SPICE simulation ??

If your main interest is a noise shaping characteristics of ΔΣ modulator, use Signal Flow Model Simulator such as
Mathworks Simulink
Agilent Ptolemy
Agilent SystemVue

Or use Event-Driven Simulators such as
Cadence NCSim
Synopsys VCS

If your interest is a characteristics of whole ΔΣ Fractional-N synthesizer including VCO,
use Berkeley Design Automation AFS Transient Noise Analysis.

See the followings.
http://www.designers-guide.org/Forum/YaBB.pl?num=1238242506
http://www.designers-guide.org/Forum/YaBB.pl?num=1259714206/2#2

Title: Re: Phase Noise of Δ-Σ modulators
Post by Mayank on Jun 16^th, 2010, 3:21am

I want to obtain Output Spectrum of a first order Δ-Σ modulator with & without dither.

If you can refer to the following paper availabe on ieeexplore ---

Reduced complexity 1-bit high order digital delta-sigma modulator for low voltage fractional-N synthesis applications
By -- B. Bornoosh, A. Afzali-Kusha, R. Dehghani, M. Mehrara, S.M. Atarodi & M. Nourani

I am trying to obtain the plot (from the paper ) that i am attaching with this post.
How do i get this ?
If someone can help pls.

Title: Re: Phase Noise of Δ-Σ modulators
Post by sheldon on Jun 16^th, 2010, 5:34am

Mayank,

Does page 45 provide the measurement you are looking for?

http://www.designers-guide.org/Analysis/PLLnoise+jitter.pdf

Best Regards,

Sheldon

Title: Re: Phase Noise of Δ-Σ modulators
Post by pancho_hideboo on Jun 16^th, 2010, 5:46am

Mayank wrote on Jun 16^th, 2010, 3:21am:

I am trying to obtain the plot (from the paper) that i am attaching with this post.
How do i get this ?

If your interest is a post processing of data, see the followings.
http://www.designers-guide.org/Forum/YaBB.pl?num=1213204643
http://www.designers-guide.org/Forum/YaBB.pl?num=1245144421

Title: Re: Phase Noise of Δ-Σ modulators
Post by sheldon on Jun 16^th, 2010, 6:17am

Title: Re: Phase Noise of Δ-Σ modulators
Post by sheldon on Jun 16^th, 2010, 6:18am

Sorry,

See page 44.

Best Regards,

Sheldon

Title: Re: Phase Noise of Δ-Σ modulators
Post by pancho_hideboo on Jun 16^th, 2010, 6:55am

Quote:

One should not simply apply an FFT to the output signal of the VCO/FDN to determine L(Δf) for the PLL.
The result would be quite inaccurate because the FFT samples the waveform at evenly spaced points,
and so misses the jitter of the transitions.
Instead, L(Δf) can be measured with Spectre’s Fourier Analyzer,
which uses a unique algorithm that does accurately resolve the jitter [16].
However, it is slow if many frequencies are needed and so is not well suited to this application.

This is no more than an advertisement of Fourier Integral Calculation in Cadence Spectre.
And it is not proper in general.

If sampling time step is enough small, we can never miss jitter.

Title: Re: Phase Noise of Δ-Σ modulators
Post by sheldon on Jun 16^th, 2010, 7:14am

Pancho,

Actually it is not, read the next page, page 45, and will see that an
alternate approach is recommended. By saving the periods you can
apply the PSD. BTW, the problem is not the simulator time steps, it
is the resolution of the FFT. The number of FFT samples required to
capture the jitter is extremely high so it is not an efficient tool for
this problem.

Best Regards,

Sheldon

Title: Re: Phase Noise of Δ-Σ modulators
Post by pancho_hideboo on Jun 16^th, 2010, 7:19am

sheldon wrote on Jun 16^th, 2010, 7:14am:

Actually it is not

Very not correct.

sheldon wrote on Jun 16^th, 2010, 7:14am:

read the next page, page 45, and will see that an alternate approach is recommended.
By saving the periods you can apply the PSD.

Again you are wrong. You are very missing point and don't understand point.

You refered L(Δf) in your append : http://www.designers-guide.org/Forum/YaBB.pl?num=1276575200/6#6
On the other hand, this is an evaluation of Sφ(Δf) based on well-known Spectrum Estimation Technique which is useful for getting small frequency resolution with small number of samples.
Here evenly spaced time step samples can be used.
http://www.designers-guide.org/Forum/YaBB.pl?num=1242749411

Statements which you refered regarding evaluation of L(Δf) are similar to old day's claim regarding advantage of Shooting Newton of Cadence Spectre compared to HB analysis.

Small frequency resolution requires very long capturing time.
On the other hand, we have to make time step very small so we can not miss jitter.

So if time steps are evenly spaced even for period where jitters are not included,
it is not efficient regarding total time points.
This is a claim of Fourier Integral Calculation in Cadence Spectre.

sheldon wrote on Jun 16^th, 2010, 7:14am:

The number of FFT samples required to capture the jitter is extremely high
so it is not an efficient tool for this problem.

But FFT of evenly spaced time step sampling data is used in actual instruments.
And it is very practical and useful level.

I can set RBW(Resolution Band Width) 1Hz in my Real Time Spectrum Analyzer based on FFT with practical sweep time.

Title: Re: Phase Noise of Δ-Σ modulators
Post by Mayank on Jun 16^th, 2010, 9:19pm

Guys Guys Guys,

We digress.....

I am not interested in Post-Processing of waveforms. I am well aware how to do that either in MATLAB or in Cadence ADE or wotever.

I wanted to know how to setup a Test-Bench around my Δ-Σ modulator model in MATLAB to obtain this output spectrum plot. can this be done in MATLAB ?

Is this waveform the output of a Fractional PLL in which SDM is applied because SDM just produces output Division factors.
How do i obtain a FFT of a signal from that ??
Which signal is this plot indicative of ?

@ Sheldon : I am aware of this concept that Cadence quotes in its ANs.

& Pancho is right. Page 45 is referring to Sphi, not Lphi calculation.

But pls. address my queries above. We will discuss the FFT funda on a simulator forum later.

Title: Re: Phase Noise of Δ-Σ modulators
Post by pancho_hideboo on Jun 17^th, 2010, 1:41am

Mayank wrote on Jun 16^th, 2010, 9:19pm:

@ Sheldon : I am aware of this concept that Cadence quotes in its ANs.
& Pancho is right. Page 45 is referring to Sphi, not Lphi calculation

No, you don't understand my append correctly.

This is no more than an advertisement of Fourier Integral Calculation in Cadence Spectre.
And it is not proper in general.
If sampling time step is enough small, we can never miss jitter.

Mayank wrote on Jun 16^th, 2010, 9:19pm:

I wanted to know how to setup a Test-Bench around my Δ-Σ modulator model in MATLAB to obtain this output spectrum plot.
can this be done in MATLAB ?

I use Mathworks Simulink, although it is possible by using Mathworks MATLAB.

Mayank wrote on Jun 16^th, 2010, 9:19pm:

Is this waveform the output of a Fractional PLL in which SDM is applied because SDM just produces output Division factors.

Yes.
See Figure-3 of http://www.designers-guide.org/Forum/YaBB.pl?num=1213204643/4#4
But DSM is modeled by MATLAB not Simulink here.

I recommd you use Simulink not MATLAB.

Title: Re: Phase Noise of Δ-Σ modulators
Post by Mayank on Jun 17^th, 2010, 3:03am

Quote:

This is no more than an advertisement of Fourier Integral Calculation in Cadence Spectre.
And it is not proper in general.
If sampling time step is enough small, we can never miss jitter.

Pancho, could you please explain this point in detail.
THAT If the sampling time is small enough, even though different than transition points, how can we not miss jitter in FFT ??
It would be helpful, coz i think this point is going unexplained & misunderstood through past few posts.

Quote:

See Figure-3 of http://www.designers-guide.org/Forum/YaBB.pl?num=1213204643/4#4
But DSM is modeled by MATLAB not Simulink here.

This was helpful.

Quote:

I recommd you use Simulink not MATLAB.

Roger that.

--
Mayank

Title: Re: Phase Noise of Δ-Σ modulators
Post by pancho_hideboo on Jun 17^th, 2010, 3:09am

Mayank wrote on Jun 17^th, 2010, 3:03am:

THAT If the sampling time is small enough, even though different than transition points, how can we not miss jitter in FFT ??

In general, we know time resolution of generated jitters.
So if we use fixed time step solver in signal flow model simulator,
we have to set analysis time step lesser than time resolution of jitter.
In this case, FFT of many points are invoked.

Mathworks Simulink have both continuous and fixed time step solvers.
If you use continuous time solver in Mathworks Simulink,
you can use Mathworks MATLAB function to evaluate spectrum for data in "Workspace".

Mayank wrote on Jun 17^th, 2010, 3:03am:

Quote:

See Figure-3 of http://www.designers-guide.org/Forum/YaBB.pl?num=1213204643/4#4
But DSM is modeled by MATLAB not Simulink here.

This was helpful.

This is not DSM for Fractional-N Synthesizer.

I can't find proper example of typical 3-cascaded-MASH-DSM for Fractional-N Synthesizer now.

Title: Re: Phase Noise of Δ-Σ modulators
Post by Mayank on Jun 17^th, 2010, 4:14am

Quote:

we have to set analysis time step lesser than time resolution of jitter.

What do you mean by resolution of Jitter ??

Quote:

This is not SDM for Fractional-N Synthesizer.

I can't find proper example of typical 3-cascaded-MASH-SDM for Fractional-N Synthesizer.
Posted by: Mayank

yeah, it's a band-Pass SDM, probably for some ADC application.

Title: Re: Phase Noise of Δ-Σ modulators
Post by pancho_hideboo on Jun 17^th, 2010, 4:17am

Mayank wrote on Jun 17^th, 2010, 4:14am:

Quote:

we have to set analysis time step lesser than time resolution of jitter.

What do you mean by resolution of Jitter ??

If you use jitter generator model for fixed time step simulator, answer is self-evident.
If you use jitter generator for continous time simulator without sepecifying lowest time resolution, we can't know time resolution.

Title: Re: Phase Noise of Δ-Σ modulators
Post by sheldon on Jun 17^th, 2010, 5:21am

Mayank,

You might find this paper interesting, it deals with some of the issues
with writing PLL models for discrete time simulators.

http://www.cppsim.com/Publications/JNL/perrott_dtc02.pdf

You might also want to look at cppsim while it is not MATLAB, you find
it interesting. It is fast, has libraries to support PLL simulation, high
level tools for PLL design, and some useful tutorial examples.

Best Regards,

Sheldon

Title: Re: Phase Noise of Δ-Σ modulators
Post by Mayank on Jun 17^th, 2010, 5:50am

@ Pancho :

Quote:

Now, i got what you meant by jitter resolution. Thanks.
Will get myself acquainted with the Schrier toolbox.

@ Sheldon :
Thanks for the link. I have worked on cppsim & sue models. The paper explains decently the PLL modelling. But cppsim is mainly for phase domain modelling of PLL. I was more interested in SDM Design. Thanks anyways.

Title: Re: Phase Noise of Δ-Σ modulators
Post by Ken Kundert on Jun 17^th, 2010, 4:59pm

Pancho,
Your comments about the simulator are only part of the issue. The Fourier transform itself samples the waveforms on a fixed interval. Assuming that the signal is a square wave, any jitter that occurs between the sample points is unobservable by the Fourier transform. Hence, Sheldon's original comment is correct.

-Ken

Title: Re: Phase Noise of Δ-Σ modulators
Post by pancho_hideboo on Jun 17^th, 2010, 8:14pm

Ken Kundert wrote on Jun 17^th, 2010, 4:59pm:

The Fourier transform itself samples the waveforms on a fixed interval.

Right if we use conventional FFT.

Ken Kundert wrote on Jun 17^th, 2010, 4:59pm:

Assuming that the signal is a square wave, any jitter that occurs between the sample points is unobservable by the Fourier transform.
Hence, Sheldon's original comment is correct.

You are also wrong.
That is no more than an advertisement of Fourier Integral Calculation in Cadence Spectre.

If we use fixed time step solver in signal flow model simulator and set analysis time step lesser than time resolution of jitter,
we can never miss jitter in FFT.

http://www.designers-guide.org/Forum/YaBB.pl?num=1276575200/14#14

Title: Re: Phase Noise of Δ-Σ modulators
Post by Mayank on Jun 17^th, 2010, 8:59pm

Quote:

If we use fixed time step solver in signal flow model simulator and set analysis time step lesser than time resolution of jitter,
we can never miss jitter in FFT.

Suppose, if the accuracy of discrete time simulator is 1ps,
& we upsample the waveform, be it square or sine, at less than 1ps,
then i dont think we are missing anything.
Since for taking FFT, we are sampling at rate higher than the accuracy of the simulator. I think that's what Pancho meant by
Quote:

we have to set analysis time step lesser than time resolution of jitter.

Then i agree with what Pancho said.

But, obviously this method requires unnecessary upsampling at such high frequency in the Post-Processing Phase generating large no. of timepoints.

If Ken says, Spectre employs a better algo taking only transition timepoints into consideration, then it's worth it.

Speaking alongwith the on-going but digressed discussion,

Ken, if you say, taking a FFT directly over VCO/FDN to determine phase noise is incorrect, then while doing transient noise simulations on PLLs, when we take DFT of the output clock to obtain phase noise PSD, IS THAT INCORRECT TOO ??

--
Mayank.

Title: Re: Phase Noise of Δ-Σ modulators
Post by Ken Kundert on Jun 18^th, 2010, 9:07am

If you are using a fixed-time step simulator, you have already greatly limited your ability to represent jitter unless you convert the jitter to a real quantity that is passed on each transition. This is the idea behind Michael Perrott's CppSim and the matlab scrip I used in my PLL jitter paper.

Furthermore, if you are using a fixed-time step simulator there is no need to up-sample as no new information is gained. It is best to synchronize the sample rate of the Fourier Transform with the time step of the simulator.

-Ken

Title: Re: Phase Noise of Δ-Σ modulators
Post by Ken Kundert on Jun 18^th, 2010, 4:09pm

Mayank,
I never mentioned Spectre or its algorithms. Nor did I say that using a FFT to determine phase noise was incorrect. Rather I am just reiterating the point that Sheldon made, that FFTs sample the waveform and so have limited ability to resolve jitter. I believe Sheldon made an important point, and I believe that point was being lost.

-Ken

Title: Re: Phase Noise of Δ-Σ modulators
Post by sheldon on Jun 18^th, 2010, 5:43pm

Mayank,

Please see the following reference, the Fourier Integral is available
in MATLAB.

http://www.mathworks.se/access/helpdesk/help/toolbox/symbolic/fourier.html

Try it and see how if works your application.

Best Regards,

Sheldon

Title: Re: Phase Noise of Δ-Σ modulators
Post by Mayank on Jun 24^th, 2010, 10:23pm

Quote:

Got your point. :)

Quote:

Furthermore, if you are using a fixed-time step simulator there is no need to up-sample as no new information is gained. It is best to synchronize the sample rate of the Fourier Transform with the time step of the simulator.

Right, but i do it just to increase the span of FFT for better viewing.

Title: Re: Phase Noise of Δ-Σ modulators
Post by pancho_hideboo on Jun 26^th, 2010, 10:27pm

Consider actual instruments for evaluation of jitter characteristics.

They are based on fixed time step sampling even if edge trigger is used with not only Real-Time-Sampling but also Equivalent-Time-Sampling technique.

You know that they are very practical level, if you have experiences of actual measurements.

Title: Re: Phase Noise of Δ-Σ modulators
Post by hyy95 on Jul 1^st, 2010, 1:16am

In the realworld measurements, lots of averaging is done to bring down the noise floor.
In simulation, if the FFT points is not large enough or if you can't do tons of averaging, the quantize noise itself will kill the result.

Title: Re: Phase Noise of Δ-Σ modulators
Post by pancho_hideboo on Jul 1^st, 2010, 4:21am

hyy95 wrote on Jul 1^st, 2010, 1:16am:

You are misunderstanding.

The main reason why many period sets are required is to capture many jitters and to increase frequency resolution for low frequency, since it is no more than monte carlo trials.

Of course, you can decrease floor level of noise, if you utilize frame averaging of spectrums for short time.