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Inverter phase noise calculation (Read 15605 times)
rfmems
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Inverter phase noise calculation
Apr 10th, 2008, 5:30am
 
In a lot of literatures, the inverter phase noise is calculated as

(1) calculate the timing jitter rms using voltage noise rms and slew rate
(2) assume the integrated phase noise is evenly distributed in the Nyquist bandwidth.

I read a lot of times saying it is because the folding back because of sampling. But I just can not physically picture it.
does not a time domain sampling generate replicas in frequency domain? Why can we ignore thess replicas and say that all the noise is evenly distributed in the Nyquist band?

Probablly it is a stupid question, but surprisingly, a lot of people knows this rule and use it often, but don't know why.

Thanks a lot.
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rfmems
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Re: Inverter phase noise calculation
Reply #1 - Apr 10th, 2008, 2:49pm
 
In Ken's "predict phase noise and jitter in PLL", for the frequency divider, when calculating the jitter, the integration is also from 0 to fout/2.
I think it is the same case as inverter, is there any reason why it is assumed that the noise bandwidth is fout/2?
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Frank Wiedmann
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Re: Inverter phase noise calculation
Reply #2 - Apr 10th, 2008, 11:49pm
 
See http://www.designers-guide.org/Analysis/sc-filters.pdf , especially section 2.2 and figure 3.
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rfmems
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Re: Inverter phase noise calculation
Reply #3 - Apr 11th, 2008, 8:16am
 
Sampled RC filtered white noise in the spetrum have aliasing replicas all over the spectrum.

It is true that integration from 0 to fout/2 gives KT/C which is the total power of the unsampled white noise

According to Wiener-Khinchine theorem,

var(phi(t))=SSB phase noise spectrum integration from 0 to infinity. Here I believe the phase noise spectrum should be the sampled white noise spectrum.

Now why we can drop all the spectrum beyond fout/2 when calculating jitter?

Or in another word, why can we integrate unsampled white noise for the jitter (phase error) of a sampled system?




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Re: Inverter phase noise calculation
Reply #4 - Apr 11th, 2008, 8:40am
 
When inputing noise into a linear time periodic varying (LTPV) system,
becuase of frequency translation, the output noise at f has contribution from input
noise at f+n*PSSfund, (-infinity<n<+infinity).
This is noise folding. It is physical.

When sampling the above output noise from LTPV at t0+n*T,(T=1/PSSfund, 0<=t0<T, -infinity<n<+infinity).  
and do PSD for it, the PSD repeats every PSSfund.
This is aliasing. It is not physical.

See http://www.designers-guide.org/Forum/YaBB.pl?num=1059089369/1#1
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rfmems
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Re: Inverter phase noise calculation
Reply #5 - Apr 11th, 2008, 9:23am
 
Yes, I agree it is unphysical.

But let's think about a more physical way, sample and hold, then you have a sinc function on the spectrum which can attenuate the high order replicas.

Even in this case, I do not see why spectrum beyond fout/2 should be dropped. Is there an explaination to that?


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pancho_hideboo
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Re: Inverter phase noise calculation
Reply #6 - Apr 11th, 2008, 9:27am
 
Quote:
Yes, I agree it is unphysical.
But let's think about a more physical way, sample and hold, then you have a sinc function on the spectrum which can attenuate the high order replicas.

You are completely misunderstanding sampling process of tdnoise in SpectreRF.
I think you are assuming sampling process along time axis with finite width sampling aperture.
Sampling period is 1/fout. So sampling is done at t0+n*T,(T=1/fout, 0<=t0<T, -infinity<n<+infinity).  
I think you are assuming small sampling period divided 1/fout period.


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« Last Edit: Apr 11th, 2008, 11:33pm by pancho_hideboo »  
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rfmems
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Re: Inverter phase noise calculation
Reply #7 - Apr 11th, 2008, 9:36am
 
I am not concerned by tdnoise in spectre.

What I was trying to do is inverter phase noise analysis, in literature I found the approach, assume white noise

from transistor only has effect on phase noise at zero-crossing. Then this is like a sampled white noise effect the phase noise.

Then integrate from 0 to fout/2 to have the integrated phase noise (phase error).

Again, the question is why fout/2? That is contridict to Wiener Khinchine, am I right?
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pancho_hideboo
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Re: Inverter phase noise calculation
Reply #8 - Apr 11th, 2008, 9:58am
 
rfmems wrote on Apr 11th, 2008, 9:36am:
I am not concerned by tdnoise in spectre.
What I was trying to do is inverter phase noise analysis, in literature I found the approach, assume white noise
from transistor only has effect on phase noise at zero-crossing. Then this is like a sampled white noise effect the phase noise.
Then integrate from 0 to fout/2 to have the integrated phase noise (phase error).
Again, the question is why fout/2? That is contridict to Wiener Khinchine, am I right?

Sampling is not along time axis. Sampling period is 1/fout. It is not small sampling period divided 1/fout period.
Again sampling is done at t0+n*T,(T=1/fout, 0<=t0<T, -infinity<n<+infinity).  
You have to study and understand cyclo stationary process.
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« Last Edit: Apr 11th, 2008, 11:35pm by pancho_hideboo »  
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rfmems
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Re: Inverter phase noise calculation
Reply #9 - Apr 12th, 2008, 4:10am
 
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rfmems
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Re: Inverter phase noise calculation
Reply #10 - Apr 12th, 2008, 4:17am
 
Above is a piece of cyclostationary operation.

I agree this is not physical because of the impulse function, more realistic is to do sample and hold.

But I still can not see the fout/2 as a upper limiter of integration. As in the last equation all the replicas are summed up.

Maybe I am wrong, but please let me know where, thanks!
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Re: Inverter phase noise calculation
Reply #11 - Apr 12th, 2008, 4:32am
 
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Re: Inverter phase noise calculation
Reply #12 - Apr 13th, 2008, 7:29am
 
From the calculations above, we can see that the integrated phase noise should actually integrate time-average phase noise for all the frequencies.

When you caluclate timing jitter from phase noise, this is right to sample the time-average noise and integrate that to fout/2.

What concerns me is, in "Phase noise analysis of digital frequency divider", they calculated phase noise from timing jitter by simply dividing the integrated phase noise by 2(fout/2).

I think what they calculated is then strobed phase noise which is not physical as Pancho said.

However, people keep doing very often. I think this is at least not rigorous. And I don't see a reason it can be done in that way.

Maybe I have missed some points here, please let me know if you have some hints, thanks a lot.

Also thanks a lot for the suggestions, Frank and Pancho

Cheers
chenyan
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pancho_hideboo
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Re: Inverter phase noise calculation
Reply #13 - Apr 13th, 2008, 7:43am
 
rfmems wrote on Apr 13th, 2008, 7:29am:
From the calculations above, we can see that the integrated phase noise should actually integrate time-average phase noise for all the frequencies.
This is your misunderstanding point. If signal is averaged over time, you can not get jitter information.

rfmems wrote on Apr 12th, 2008, 4:17am:
I agree this is not physical because of the impulse function, more realistic is to do sample and hold.
rfmems wrote on Apr 13th, 2008, 7:29am:
However, people keep doing very often. I think this is at least not rigorous. And I don't see a reason it can be done in that way.

I can't understand why you think it is not rigorous.

Assume an operation of sampling oscilloscope(digitizing oscilloscope) which shows jitter statistics.
Here an average calculation is done over frames not times. So there is no time window which causes Sinc spectrum such as Sample & Hold you are thinking.

PSD=PSD(time, freq).
For specific time=t0 in 0<=t0<T=1/fout, PSD(t0, freq) is calculated by frame average power not time average power.
Here time=t0 is just one point, it has no width.
Again(4 times), sampling is done at t0+n*T,(T=1/fout, 0<=t0<T, -infinity<n<+infinity).  

Even though Vout(time=t0) is captured by S/H which has finite width time window,
we can compensate S/H characteristics in frame average(Ensemble Average) calculation.

So it is rigorous.
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« Last Edit: Apr 13th, 2008, 11:18pm by pancho_hideboo »  
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