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Design >> Analog Design >> 1/f3 noise.
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Message started by judean on Feb 22^nd, 2006, 8:57pm

Title: 1/f3 noise.
Post by judean on Feb 22^nd, 2006, 8:57pm

Hi,
I know about the 1/f noise in oscillator.But this diagram shows the presence of 1/f4,1/f3 and 1/f2 apart from 1/f.
What is the reason of the presence of the 1/f4..1/f2 values in the phase noise diagram.How can it be avoided or reduced in our design work.

Title: Re: 1/f3 noise.
Post by vivkr on Feb 23^rd, 2006, 1:47am

Hi,

I am not an oscillator expert, but don't you think that the increase in the slope as you get closer and closer
to the resonance frequency is due to the very fact that the oscillator transfer function shoots to Infinity at this
frequency (or a very large value for a real oscillator).

How would you measure the phase noise at such close frequency offsets reliably? In fact, if you went even closer,
I bet you might even see steeper slopes on your dB curve.

I would say that you ought to look at the noise contained in a certain bandwidth at a certain offset from the resonance
frequency. For instance, at 1 uHz from the resonance, you may see a huge figure for your curve, but then you are unlikely
to notice this in your application unless you let your oscillator run for an incredibly long interval and measure all the noise
in this long period.

I would recommend that you read the papers by Hajimiri and Lee or some other good reference.

By the way, where do you have this figure from?

Regards
Vivek

Title: Re: 1/f3 noise.
Post by judean on Feb 23^rd, 2006, 3:02am

Hi Vivek,
Thanks a lot for the answer.I will try to come back after reading the papers.
This was a question I was asked,and i found it on the net.
Regards
V

Title: Re: 1/f3 noise.
Post by Ken Kundert on Feb 23^rd, 2006, 4:53pm

Oscillators, by their very nature, amplify any noise by 1/Δf². This effect is described in www.designers-guide.org/Analysis/rf-sim.pdf (see equation (7)). Thus, white noise from within the oscillator creates noise with a slope of Δf^-2 at the output. Flicker noise produces noise with a slope of Δf^-3. If the oscillator is followed by a noisy buffer, you would also see white noise (slope of Δf⁰) and perhaps flicker noise (Δf^-1) at the output.

I have no idea where noise with a slope of Δf^-4 comes from, and I have never seen results that exhibited it.

-Ken

Title: Re: 1/f3 noise.
Post by David Lee on Mar 11^th, 2006, 3:08am

You will find 1/f^4 (random walk FM noise or jitter) in ultra high precision clocks, such as quartz and cesium (atomic) clocks, which also exhibit 1/f^3 (flicker FM noise), and 1/f^2 (white FM noise). If you are really really curious and wish to learn more, check out this fascinating, introductory note: "The Science of Timekeeping," by David W. Allan, Neil Ashby, and Clifford C. Hodge, HP Application Note 1289, and classic technical references therein. For example, download at http://www.allanstime.com/Publications/DWA/Science_Timekeeping/

Title: Re: 1/f3 noise.
Post by Ken Kundert on Mar 12^th, 2006, 2:07pm

This is another example of a document were the author states the presence of "Random Walk FM" noise, but gives no explanation of what causes the noise. I don't doubt that it exists, I just cannot image what is causing it, and so I don't know what situations where one might need to worry about it.

-Ken

Title: Re: 1/f3 noise.
Post by David Lee on Mar 15^th, 2006, 10:46pm

For an oscillator to exhibit 1/f^4 phase noise, the oscillator's natural (free-running) frequency needs to be a random walk process, which has increasing variance. Basically, the natural frequency is wandering significantly over time. In a quartz oscillator, the natural frequency is determined by a mechanical vibrating reference, that is known to be sensitive to long-term dimensional changes and mechanical stress caused by the oscillator's environment. Ref. 36 in "The Science of Timekeeping" and others often cite environmental factors such as mechanical shock, vibration and temperature as the cause for 1/f^4 noise. Let's suppose the oscillator's environment (such as temperature) is regulated by another oscillator over a longer time scale. This will cause the natural frequency to drift in a random walk fashion, thus giving rise to 1/f^4 noise. Quartz and atomic clocks are well-known to exhibit 1/f^4 noise, and so I won't be surprised if folks in physics know the various pathways to 1/f^4 noise. Having said all that, I don't think one should worry about 1/f^4 noise that is very close to the carrier, unless designing applications for GPS, satellite comm, .., where maintaining precise timing over a long time interval (long-term time/frequency stability) is needed.

Title: Re: 1/f3 noise.
Post by Ken Kundert on Mar 16^th, 2006, 12:16am

David,
Having the frequency vary in a random walk implies the frequency can drift without bound; that there is nothing pinning the frequency. White phase noise (∝ Δf^-2) is created because the phase can drift without bound. Clearly in a free-running oscillator this is the case because it is autonomous. But the frequency of an oscillator is pinned by the natural frequency of the resonator. It can vary somewhat as it is affected by its environment, but it cannot drift without bound. Consider this difference. If an oscillator is perturbed by some distrubance, its phase will be permanantly affected. If the disturbance is later removed, the phase does not return to its original value. However, in the case of sensitivity in the frequency to mechanical vibration or temperature, once the vibration stops or the temperature returns to its original value, so too will the frequency return to its original value. As such, the variation in the frequency is not a random walk process.

I still don't understand how one can end up with a Δf^-4 component in the phase noise produced by an oscillator.

-Ken

Title: Re: 1/f3 noise.
Post by David Lee on Mar 17^th, 2006, 9:58am

Hi Ken,
Aging and environmental factors are commonly accepted explanation for crystal oscillator's natural frequency to drift signficantly from its nominal value. What phase noise spectrum would you expect due to this long-term frequency drift? Surely, this spectrum ought to fall faster than the usual white FM noise.

Title: Re: 1/f3 noise.
Post by Ken Kundert on Mar 17^th, 2006, 2:02pm

David,
Okay, I can kind of see it now. If you model long term aging as a linear drift in the frequency then the phase spectrum would be 1/Δf⁴, though it would not be a random walk. However, it seems like the frequencies would be so low (< 1μHz) that very few people would bother mentioning it.

-Ken

Title: Re: 1/f3 noise.
Post by David Lee on Mar 17^th, 2006, 8:34pm

Hi Ken,
In "The Science of Timekeeping," Figure A1 on page 60 shows that for quartz oscillators, frequency stability curve starts to increase for time longer than 100 seconds. So, random walk FM noise becomes observable after 100 seconds. For the recent chip-level atomic clocks (http://tf.nist.gov/timefreq/ofm/smallclock/LongTermStability.htm), one can observe (flicker walk FM?) noise that falls -10 dB/decade faster than random walk FM, after 10 to 100 seconds. It is customary to remove systematic trends when frequency stability measurements are made and reported. So a linear frequency drift does not fully explain the observed random walk FM noise. While it is true that the oscillator's natural frequency is utimately bounded, I think it is sufficient that over a finite observation window, the variance is increasing with longer time interval in order to observe power law noise similar to random walk FM noise.