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switched capacitor integrator noise simulation results (Read 7540 times)
alireza
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Re: switched capacitor integrator noise simulation results
Reply #45 - Feb 19th, 2010, 8:49pm
 
pancho_hideboo wrote on Feb 19th, 2010, 1:57am:
alireza wrote on Feb 18th, 2010, 9:26pm:
However, I cannot accept that 2kT/C which is a well-known estimate for the input-referred noise of a switched-capacitor integrator "ignores" noise folding!
Otherwise, design methodology used for design of SC delta-sigma modulators (and other SC filters) would all be in question!
I am quite sure that 2kT/C estimate does take noise folding into account. (Noise folding is the basic principle of noise analysis for SC circuits.)
I can't understand what you want to claim.

The reason why I mentioned this was that I believe the 2kT/C estimate for the total input-referred noise power is very true, and includes everything physical which happens in the real world. (i.e. measurement.) Therefore, this value should be treated as a reference for the total discrete-time input-referred noise power. (In fact, 2kT/C noise power is caused by the switches noise, i.e. when the opamp noise is negligible compared to switches. In the literature, there are also derivations of the total noise power when the opamp noise is dominant.) For the discussion here, we are only analysing/simulating switches noise.

Based on what you mentioned the rise in the spectrum of the input-referred noise in pnoise (sources) sim is due to the fact that output noise spectrum is folded, but the gain transfer function only considers zero side band. Therefore, the input spectrum has the effects of noise folding uncancelled. Folded noise only manifests itself at high frequencies, since the integrator gain is low. However, when we look at the system as a discrete-time system folding should not be taken into account, as in discrete-time domain there is no freq. component beyond fs/2.
So, the discrete-time input-referred noise power should be calculated based on the low-frequency portion of the psd obtained from spectre multiplied by fs/2, where the effect of folding is negligible due to high integrator gain.
This way the simulated DT input-referred noise power is almost exactly 2kT/C, and matches very well with the theory. Otherwise, if someone only integrates the input psd obtained from pnoise (sources) from 0 to fs/2, the result is 10-20dB (depending on opamp parameters, etc) larger than the 2kT/C value which is not acceptable.

Regards.


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« Last Edit: Feb 19th, 2010, 10:58pm by alireza »  
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pancho_hideboo
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Re: switched capacitor integrator noise simulation results
Reply #46 - Feb 20th, 2010, 7:18am
 
alireza wrote on Feb 19th, 2010, 8:49pm:
Otherwise, if someone only integrates the input psd obtained from pnoise (sources) from 0 to fs/2, the result is 10-20dB (depending on opamp parameters, etc) larger than the 2kT/C value which is not acceptable.
I think still you can't understand equivalent input noise correctly.
And still you can not evaluate ENBW as maximum frequency for integration.

Simply consider single noise observation point for multiple noise inputs.
Here multiple noise inputs mean actual noise sources inside circuits and folding noises of each actual noise sources.

Then consider meaning of equivalent input noise for one defined input.

There are two switches which generate noise in SC integrator at least.
Contribution to output from these noises are correlated in time domain.
Again see http://www.designers-guide.org/Forum/YaBB.pl?num=1258339986/27#27

[Note] Output noise and input noise are both k*T/C for simple continuous time RC LPF, although input noise PSD is perfectly flat until infinite frequency.
In this case there is only one noise source and there is no folding noise.

alireza wrote on Feb 19th, 2010, 8:49pm:
The reason why I mentioned this was that I believe the 2kT/C estimate for the total input-referred noise power is very true, and includes everything physical which happens in the real world. (i.e. measurement.)
No. It seems you don't have experience of actual measurement.

Output noise and output noise PSD are both absolutely physical observables.
But both input noise and input noise PSD are not.

alireza wrote on Feb 19th, 2010, 8:49pm:
However, when we look at the system as a discrete-time system folding should not be taken into account, as in discrete-time domain there is no freq. component beyond fs/2.
Your interpretation is very wrong.

I think Discrete-time system which you mean is an ideal impulse sampling system whose transfer function described by H(z=ejωTs).
Even by an ideal impulse sampling, noise folding effects are included naturally.

See last comments in http://www.designers-guide.org/Forum/YaBB.pl?num=1258339986/23#23

I think you are misunderstanding my answer in the following.
http://www.designers-guide.org/Forum/YaBB.pl?num=1260505047/1#1

Any gain given by PAC is not H(z=ejωTs).


I don't care at all whatever interpretation or understanding you take.
So take any interpretation or understanding which you think most preferable.
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« Last Edit: Feb 21st, 2010, 6:45am by pancho_hideboo »  
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alireza
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Re: switched capacitor integrator noise simulation results
Reply #47 - Feb 21st, 2010, 10:18pm
 
pancho_hideboo wrote on Feb 20th, 2010, 7:18am:
alireza wrote on Feb 19th, 2010, 8:49pm:
Otherwise, if someone only integrates the input psd obtained from pnoise (sources) from 0 to fs/2, the result is 10-20dB (depending on opamp parameters, etc) larger than the 2kT/C value which is not acceptable.
I think still you can't understand equivalent input noise correctly.
And still you can not evaluate ENBW as maximum frequency for integration.


The fact that you are suggesting to use ENBW, implies that the input noise to the system should be "white", Otherwise it makes no sense to use ENBW for a colored input noise! In this case, the input noise spectrum from spectre is NOT white! How do you use ENBW for it?


pancho_hideboo wrote on Feb 20th, 2010, 7:18am:
There are two switches which generate noise in SC integrator at least. Contribution to output from these noises are correlated in time domain.Again see url]http://www.designers-guide.org/Forum/YaBB.pl?num=1258339986/27#27[/url]
.

So far you have provided different theoretical reasons for the rise in the input noise spectrum, and one was correlation between the noise sources. But this does not make sense. In a SC integrator there are 4 switches and their noise sources are all uncorrelated. I have confirmed this statement with simulations. In simulations the noise of the switches was enabled one at a time, and still the same colored spectrum can be observed for the input-referred noise. In fact, it is only the switch noise of the integration phase which causes the colored psd. The psd due to sampling phase switch is white!
Please see the attached plot. This plot has been obtained using pnoise (sources) simulation, but the result is plotted up to fs/2. Because the singular points at fs harmonics, do not allow the rise near fs/2 be observed. Given that with only one noise source this phenomenon still happens proves that this explanation is wrong!


alireza wrote on Feb 19th, 2010, 8:49pm:
The reason why I mentioned this was that I believe the 2kT/C estimate for the total input-referred noise power is very true, and includes everything physical which happens in the real world. (i.e. measurement.)
pancho_hideboo wrote on Feb 20th, 2010, 7:18am:
No. It seems you don't have experience of actual measurement.
Output noise and output noise PSD are both absolutely physical observables.
But both input noise and input noise PSD are not.


I am not sure if you are familiar with design of delta-sigma modulators. In DS Mods, there is the concept of STF (Signal Transfer Function). In many DS Mods STF=1; meaning that when you measure the output SNR you have effectively measured the input SNR, hence the input noise.
BUT I prefer not to be so picky about details, and look at the main problem instead. what I meant in my previous post was that 2kT/C is correct, accurate and the simulation is accurate only if it can match to it. (I can provide references, if there is any doubt in accurateness of this statement.) Given this, and the fact that with the rise in the input psd, simulation results is 10-20dB higher than reality, how would you justify the simulation result? IF you think the integration bandwidth is not fs/2 then what is it? I think if you can help me in answering this question, the problem is solved easier. This has been my question since post #1!

1) pancho_hideboo wrote on Dec 11th, 2009, 4:14am:
While H(z=ejωTs) considers only zero sideband.


2) pancho_hideboo wrote on Feb 20th, 2010, 7:18am:
Any gain given by PAC is not H(z=ejωTs).

What do you mean it is not H(z)? Aren't 1) and 2) in contradiction?
The gain of the output zero-side band/ input zero side band IS EXACTLY H(z). I have again confirmed this by plotting the PAC gain, importing it to MATLAB and comparing with |H(z)| given by MATLAB.








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« Last Edit: Feb 22nd, 2010, 8:42pm by alireza »  

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pancho_hideboo
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Re: switched capacitor integrator noise simulation results
Reply #48 - Feb 22nd, 2010, 12:21am
 
I think you can't uderstand differences between ideal circuit assuming ideal impulse sampling and actual circuits.

Actual SC integrator is no more than continuous time domain circuits if seeing from Cadence Spectre.
This is true even if you don't use Sample&Hold circuit for output.
Also this is true for any SPICE type simulator including Cadence Spectre.

And this is true for real physical actions of SC integrator.

alireza wrote on Feb 21st, 2010, 10:18pm:
The fact that you are suggesting to use ENBW, implies that the input noise to the system should be "white"
Not correct.

alireza wrote on Feb 21st, 2010, 10:18pm:
Otherwise it makes no sense to use ENBW for a colored input noise!
Not correct.

Only output noise [Vrms2] and gain are real observable.
But both input noise [Vrms2] and input noise PSD [Vrms2/Hz] are not.

Approximately, input noise[Vrms2] is "output noise"/gain(freq=0)2 for LPF application.
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« Last Edit: Feb 22nd, 2010, 2:22pm by Ken Kundert »  
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