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Measurements >> Phase Noise and Jitter Measurements >> Phase Noise or L?
https://designers-guide.org/forum/YaBB.pl?num=1036525104

Message started by Ken Kundert on Nov 5^th, 2002, 11:38am

Title: Phase Noise or L?
Post by Ken Kundert on Nov 5^th, 2002, 11:38am

When running SpectreRF's PNoise analysis within Artist, the environment provides a "Phase Noise" button as part of its direct-plot capability. The label on this button is misleading, which has caused a substantial amount of user confusion.

It is important to know that when you press this button you are actually plotting the normalized voltage noise, or L, and not the phase noise (this is why the result has units of dBc). This function was added when we added support for oscillators. Oscillator designers use L as a way of characterizing the phase noise of their oscillators. This works because for oscillators the phase noise dominates, especially close to the carrier, and so they need not distinguish between phase noise and voltage noise. Furthermore, in oscillators the values of L and S_phi (the phase noise) are actually the same in most cases, which adds to the confusion.

However, problems arise when engineers who are not designing oscillators use the phase noise direct plot function thinking that this function is decomposing the total noise into amplitude and phase noise components and plotting only the phase noise. It is not doing that. Rather it is plotting L = S_v(df)/V₁², where S_v is the power spectral density of the voltage at an offset frequency of df and V₁ is the amplitude of the fundamental. Thus, it is plotting the noise power normalized to the power of the fundamental.

Title: Re: Phase Noise or L?
Post by Eugene on Nov 5^th, 2002, 4:24pm

Hi Ken,
I'm afraid I'm confused now. You say that for oscillators, L and Sphi are the same values. However, In your papers you show L = Sphi/2. Furthermore, if I followed your math correctly,the L in your papers is Sv(df) divided by the *power* of the fundamental (referenced to one ohm), not the square of the amplitude. One thing is for sure: in modeling RF components there are more factors of two than one can shake a stick at and it is hard to keep them straight.
-Eugene

Title: Re: Phase Noise or L?
Post by Ken Kundert on Nov 5^th, 2002, 8:46pm

Whoops! I spoke too hastily.

Your right, L is S_v(df) divided by the power of the fundamental, and so L = S_v(df)/(2V₁²)
.
With L and S_phi, we can both claim to be right. L = S_phi when using double-sided (complex exponential) Fourier representation, and L = S_phi/2 when using a single-sided (trigonometric) Fourier representation.

Good eye, and thanks for keeping me honest.

-Ken

Title: Re: Phase Noise or L?
Post by Eugene on Nov 18^th, 2002, 1:53pm

My work has forced me to revisit this issue again and I am still not I have it straight. Are you sure about the double (single) sided Fourier series explanation? It seems your paper uses the double sideband representation, yet you have

L = (1/2)*Sphi.

Title: Re: Phase Noise or L?
Post by Ken Kundert on Nov 18^th, 2002, 2:08pm

No, I am not convinced I have it right yet either. Let me look into this and get back to you.

Title: Re: Phase Noise or L?
Post by Eugene on Nov 18^th, 2002, 3:21pm

While you're at it, it would be great if you could confirm that in your paper, "a" is the double sided density driving the Wiener process and Sphi is a double sided density centered about zero Hz. Thanks.

Title: Re: Phase Noise or L?
Post by Eugene on Nov 19^th, 2002, 5:48pm

Ken,
I found a fairly concise explanation of Sphi and L in Egan's book:

William F. Egan, "Phase-Lock Basics", John Wiley & Sons, Inc. 1998. ISBN 0-471-24261-6, pages 304-310.

Egan gives a simple example showing that L = Sphi/2 where L is a single-sided, single-sideband, passband PSD shifted down to baseband and Sphi is a single-sided baseband PSD.

However, as I read Demir's May 2000 Circuits and Systems paper ( at least the part I can follow),

L(fm) ~ 10log10(a*(fc/fm)^2), which differs from your expression by 3dB but perhaps you define L differently.

Now all I need to do is figure out why my code still produces a 3dB error but that is something I must deal with myself.

Title: Re: Phase Noise or L?
Post by Eugene on Nov 19^th, 2002, 9:25pm

The strange thing is that while the noisy voltage domain VCO model produces the correct passband, single-sideband, single-sided PSD, the phase-domain "equivalent" produces a single-sided baseband PSD that is shy 3dB.

Title: Re: Phase Noise or L?
Post by Eugene on Nov 20^th, 2002, 10:22pm

Ken,
I believe I discovered why the phase domain model seemed to give 3dB less phase noise. I believe the Analog Artist's waveform calculator's PSD function is 3dB off. I checked a simple sinusoid as well as a filtered noise signal. In both cases, the variance of the signal as computed from the time domain waveform was twice the area under the PSD function.

That makes my voltage domain model 3dB high but I think that is probably just uncertainty in eye-ballling the value because the PSD was fairly jagged.

Title: Re: Phase Noise or L?
Post by Ken Kundert on Nov 21^st, 2002, 1:44pm

Have you done anything to compenstate for the noise bandwidth of the window function. For a Hanning window that noise bandwidth is 1.5 bins, which could neatly explain a 3dB difference.

-Ken

Title: Re: Phase Noise or L?
Post by Eugene on Nov 21^st, 2002, 3:03pm

On the simple test case of white noise filtered by an RC circuit, I compared results using a Hanning window and a rectangular window. The two PSD's were nearly identical and both were 3dB in error. Should the factor of 1.5 also apply to the rectangular window?

Title: Re: Phase Noise or L?
Post by Eugene on Nov 21^st, 2002, 3:09pm

But to answer your question specifically, I did not apply any correction factors for the window function. Is that necessary with the psd function?

Title: Re: Phase Noise or L?
Post by Ken Kundert on Nov 21^st, 2002, 5:08pm

The factor of 1.5 compensates for the equivlant noise bandwidth of the bins, which is dependent on the window function. So for a rectantular window, the factor would not be 1.5, but I don't believe it will be 1 either. I am currently unable to find my copy of Harris, nor can I find it on the web, so I cannot tell you what it should be though.

You can look the number up yourself by finding a copy of
F. Harris. On the use of windows for harmonic analysis with the discrete Fourier transform. Proceedings of the IEEE, vol. 66, no. 1, January 1978.

Title: Re: Phase Noise or L?
Post by Eugene on Nov 21^st, 2002, 10:41pm

Thanks for the lead Ken. I'll check it out.

Title: Re: Phase Noise or L?
Post by Ken Kundert on Apr 1^st, 2003, 5:00pm

Eugene,
There were several places in my phase noise and jitter papers where I was not careful in distinguishing single-sided and double-sided transforms. As a result, there were several factor-of-two errors. I believe I have identified and corrected all of them in the latest versions of the papers, which I uploaded today. Please let me know if you see any further issues.

Thanks,
-Ken

Title: Re: Phase Noise or L?
Post by Eugene on Apr 3^rd, 2003, 7:24pm

I looked over the new papers. It looks like we agree now. Thanks.

Title: Re: Phase Noise or L?
Post by McCorquodale on Jul 10^th, 2003, 2:51pm

Speaking of conversions, I have a simple observation. In the paper, "Predicting the Phase Noise and Jitter of
PLL-Based Frequency Synthesizers," page 30, section 10.1, I am confused by the relationship between the PSD and the autocorrelation function. Specifically, they do not appear to be related correctly, unless I am overlooking something.

The PSD and the autocorrelation function should be Fourier transform pairs. Thus, by integrating the autocorrelation function in tau (i.e. t1 - t2), one should obtain the DSB PSD. Thus, integrating equation (64) in tau would yield "c." However, the SSB PSD given in equation (63) is "2c." Considering that this is an SSB PSD, I would assume it should be c/2, thus giving a DSB PSD of "c" as is obtained by integration.

Or, similarly, the equations would be as follows:

(63) Sn(f) = c

(64) Rn(t1 - t2) = 2c delta(t1 - t2)

Where (63) is an SSB PSD. I find this to be of significace because it changes the phase noise to period jitter conversion expressions using (73) and (77) by a factor of 2. I also have a copy of an earlier version of this article where these particular expressions are different by a factor of 2.

Any help is appreciated.

Thanks,

Michael

Title: Re: Phase Noise or L?
Post by YDJ on Jul 20^th, 2003, 11:55pm

Hi Ken,

Following the post about "Phase Noise or L?" , I am using Cadence 4.4.6 version to perform PSS/pnoise simulation on the PFD/CP with reference frequency 2.5MHz and 20 max sideband. When I press the "phase noise " button in the direc-plot function, is it showing the curve of a normalized current noise, or L?
Is it normalized with respect to the charge pump current? How come I get the result with unit is dBc/Hz not dBc?

As you said that the current noise at output of the CP is change with the current switch turn on time. How come this "phase noise" is not change with CP current pulse time ( I have simulated) ?

Is this normalized current noise (dBc/Hz) or the total current noise (A/sqrt Hz) of CP affect the PLL output phase noise more? and How to reduce the normailed current noise (dBc/Hz) in the design stage?

I've read thru some articles, they are talking about the 1HZ noise floor in PFD/CP. Is that any relationship between the normalized phase noise with this 1Hz noise floor?

Thanks for your help.

Title: Re: Phase Noise or L?
Post by August West on Jul 21^st, 2003, 10:21am

YDJ,
The normalized current noise and L are the same thing. L is the noise density normalized to the total noise, that is why the units are dBc/Hz rather than dBc. In other words, L(f) is the noise power in a 1 Hz bandwidth centered at f relative to the total power in the signal. Before converting to decibels, the units are (W/Hz)/(W), after converting to decibels the units become dBc/Hz.

I'm afraid I do not understand the rest of your questions. Could you rephrase them?

-August

Title: Re: Phase Noise or L?
Post by Jitter Man on Dec 21^st, 2003, 11:03am

McCorquodale wrote on Jul 10^th, 2003, 2:51pm:

The single- and double-sided PSDs are related as follows (found in a footnote on page 13),
S_DS(0) = S_SS(0)
S_DS(f) = S_SS(f)/2 for f != 0
As such, the double-sided equivalent to (63) is
S_n(f) = c,
which is the transform of (64). Thus, the equations given in the paper appear to be correct (or at least consistent).

[glb]Jitter Man[/glb]

Title: Re: Phase Noise or L?
Post by Eugene on Feb 28^th, 2004, 2:51pm

Egan's book gives a pretty clear explanation of the relationship between L and S with a simple FM example.

William Egan, "Phase-Lock Basics". John Wiley and Sons.
pages 304-310