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Clock Jitter Explained

What is clock jitter in detail?

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MrEase Mon, 06/14/2010 - 10:24

PLEASE NOTE (AS KINDLY POINTED OUT BY BOSWELL) THAT I HAVE MADE A CARELESS SLIP IN MY MATHS IN THIS POST AND THE RESULTS I GIVE ARE FAR TOO OPTIMISTIC! PLEASE READ FURTHER POSTS IF YOU ARE INTERESTED.

Sorry but it's been some time since I could add to this thread, so I'll just get on with it for now!

Now I have shown some fairly typical, measured, results in measuring the true timing jitter of slaved clocks, we need to see what kind of effect it will have on our audio fidelity. I will first make a couple of assumptions.

1. The highest frequency of interest to us is 20 kHz.
2. The maximum level of the converters is 2 V p-p (peak to peak) before clipping.

These are straightforward assumptions however I'm sure some will contend the benefits of having audio bandwidth up to 40 kHz or more. If you are in this camp all you will need to do is adjust the appropriate figures I will give you.

So if we have a sine wave at 20 kHz, 2V p-p then the maximum slew rate of the wave is (approx) 125 V/s. If we now take the measured results of the jitter as 25 ns (I like round figures!) then the maximum possible variation on a sample is 3.125 uV. This is spread both sides of the ideal timing so the error is around +/- 1.55 uV. I will term this as the "maximum jitter modulation". This is 116 dB below 0dBFS and certainly, for my converters at least, is below the converter noise level.

That is not quite the end of the story though as the perception of a signal at this level depends on what the signal is. If the jitter noise happened to be the result of a sine wave modulation, the signal created by the jitter would be a similar sine wave. Because coherent signals can easily be perceived below noise then such jitter might be noticed, particularly in quiet passages (sadly not likely with a modern compressed CD).

This is why the nature of the jitter is important. In the two examples I gave, my 01V gave what appeared to be pretty random phase noise (note that I could not directly measure this with the set up I had) and therefore the jitter modulation is non coherent and therefore much less likely to be perceived. In the other instance, the MOTU 828 had what appeared to be predominantly very low frequency jitter and such modulation would result in signals outside the audio bandwidth. Relate this to the specification I gave much earlier, in reference to Soapfloats querie's, where the jitter bandwidth was given as part of the spec. Although that particular spec. tells us very little of what the actual jitter is, it does tell us that the jitter should not cause significant jitter modulation within the audio bandwidth.

I hope this gives some idea what the real magnitude of the problems arising from clock jitter really are. I hope that this description has been both useful and understandable and that will now have an appreciation of what clock jitter means in the "real" world. In essence, unless you have very poor clock circuits, it is very unlikely to impair your recordings. Of course it would be nice to have things perfect but it is also good to appreciate the engineering compromises we designers always have to make.

For those interested this last bit explains a little bit more of the maths and the reasons for the assumptions I've made in the calculations. Please skip it if you're not bothered by it.

A sine wave is described mathematically by Vout= A*sin(wt) (using w to represent omega), where the magnitude of the wave is set by A. In this case A=1 gives a sine wave of 2Vp-p. To find the maximum slew rate, we differentiate this expression with respect to time to give dV/dt (the rate of change of voltage) = w cos(wt), this is a maximum when cos(wt) = 1, hence dV/dt(max) = w. w = 2*pi*frequency = 125.663 V/s.

While I fully appreciate many musical instruments can produce much faster transients than this, the only implication is that frequencies above 20 kHz are present, hence this is a sensible assumption. I appreciate that many electronic circuits can also create high order distortions within the audio band as a result of these higher frequencies. The fact is that even with a 20 kHz square wave, if we could put that through a perfect "brick wall" 20 kHz LP filter, then there would be no dV/dt exceeding this figure. Indeed many high quality power amplifiers use a (simple) LP filter on their input stage in order to prevent fast transients causing any of the high order problems normally more prevalent in power stages.

If you prefer to take 40 kHz as a yardstick (although I have never personally seen a compelling reason to do so) then the only effect is to increase the jitter modulation noise by 6dB from the figure I calculated above, i.e. 110dB below 0dBFS.

While you may consider this to be a significant degredation to the highest performance converters it is also important to compare like with like. Converters boasting up to 120dB of dynamic range are available but bear in mind that these will be "weighted" figures, whereas the calculations I have given here are not. I could only weight them if I knew the spectral density of the jitter noise. It is also highly unlikely that you will have a recording facility with a low enough ambient noise to ever achieve such dynamic range figures in any case.

Scott Griffin Mon, 04/19/2010 - 11:28

BobRogers, post: 346251 wrote: I think that (well deserved) reputation comes from pop culture, history, politics, and the "soft" sciences. I find Wiki to be as reliable as any other general reference source that I know of in math and classical physics. Compare it to a modern Encyclopedia Britannica. Wiki is also more comprehensive and the price is right. As always, check it twice. In the word of Ronald Regan, "Trust, but verify." (Which means, "Don't trust.")

As someone who moonlights in the medical field, I can assure you, Wiki blows it in that department regularly.

MrEase Mon, 06/14/2010 - 14:49

What I should also point out (as I have not made it clear) is that the figures I have given are absolute worst case. It is not possible for the 125 V/s slew rate to exist more than instantaneously and this will only occur with a signal of 0dBFS at 20 kHz. Real audio waveforms will be very unusual (effectively impossible) if they contained anything remotely near this level. The net result is that normal audio data will have a very much reduced jitter modulation noise from the figures I gave. This all tends to suggest, to my engineering side, that jitter noise will very very rarely be the cause of any problems.

I hope that I have not only explained what jitter clock jitter is, as originally asked, but also shown what effect it will have and finally, that for all intents and purposes, it would never, under any normal circumstances, cause us any real problem.

Of course if you find any part of this explanation unclear or incorrect I would welcome your comments in this thread. I will then try to explain further or correct any errors. Equally if you find you agree with this explanation, please chime in as that could also add weight to what has been a purely solo effort!

jasonthomas Wed, 10/06/2010 - 02:12

You hear that expression used in top of the line Blu-ray players now. That they have improved clocks to eliminate clock jitter.

MrEase Wed, 10/06/2010 - 02:25

Clock jitter affects any product that uses either A-D or D-A converters so of course it affects Blu-ray just as it does DVD, CD etc. etc. While they may claim to have improved clocks, it certainly will not ELIMINATE clock jitter. Read through my posts and you will see why.

bigtree Tue, 09/28/2010 - 02:19

man, deep topic. I see this is a very important when we enter very high end audio. I also see the importance of very good power and conditioners that work. Most of this is over my head but I get it. Clean power is critical area in high end digital audio and mastering?

Good converters vs poor converters must deal with how they filter and are effected with the power.

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djmukilteo Mon, 06/14/2010 - 21:28

Good technical stuff....always exciting and interesting to me when I can read some tech talk!
I've been following another forum thread where the ongoing discussion is external clocks. The discussion for the most part is high end clocks....
I guess I won't mention any names but the debate is 10Mhz atomic master clocks creating better perceived audio.
The science on the one side makes claim that a properly designed internal clock and jitter suppression circuitry within a well designed converter is a better clock than using one of these 10M external master clock units. The other side claims that highly renowned, experienced producers and engineers have no problem discerning a noticeable difference in the quality of the audio being converted and monitored from their A/D/A's when using said high end clocks.....
While I lean toward the science and engineering side of this and not having any expert listening experience (I think I have good ears LOL)...or even really high end equipment at my disposal ($6000 for an atomic clock is a little out of my price range!)...do you think there is something going on here that has a reasonable explanation? Or is this high end clock thing hyped and is there possibly "listening bias" going on here with experienced people hearing a perceived improvement?
In my mind and understanding with A/D/A reaching 120db of dynamic range and possible sideband artifacts down in the -110 range....is it really possible that these extremely accurate timing circuits could produce a perceived improvement in the audio and where (if at all) could this be shown or proven?
So thanks MrEase, Boswell and Scott for your contributions to this thread!
I'm reading it.....
And FWIW RO is far more professional, open and truly free from the incredibly augmentative nonsense that goes on over there!
Thank you for that audiokid!

MrEase Thu, 07/15/2010 - 10:00

It has occured to me that I have not really done any sort of summary to these posts. As they have happened over a month or two not all my thoughts have made it into my posts. So I'll try for more of a summary....

First of all it is very important to realise that the amplitude of any noise arising from clock jitter is entirely dependent on the source material as the noise arises from modulation of the recorded signal. Thus it is definitely NOT a fixed level problem. If there is no signal there is no noise caused by jitter. This is crucial to understand as I have already presented calculations infering worst case noise at -56 dBFS on my own system. More accurately that maximum noise is -56 dB relative to a 20 kHz signal of whatever amplitude. Now I do not know of any musical instruments that produce fundamentals above 5 kHz (with the one exception of some instances of pipe organs) - although I stand to be corrected on this. This would reduce the figure of -56 dB to -68 dB relative to a 5 kHz sine wave. Now for a real instrument there may well be harmonics that slightly increase the rise time which is why I went for the absolute worst case scenario of 20 kHz which is highly unlikely to be produced by any instrument in a none transient manner!

The problem with this noise is that it is not at all harmonically related to the recorded signal (only the amplitude is) but is directly linked to the characteristics of the jitter noise itself. Just suppose we had jitter noise that comprised solely of 1 kHz sinusoidal phase noise (this is never going to happen - this is just an illustration). In the presence of my full scale 20kHz signal and with the jitter noise at 25ns p-p, then the jitter noise would be a 1 kHz sine wave at -56 dB. Clearly not very good but also a completely contrived example. In reality the jitter noise would be predominantly low frequency (with my MOTU) or essentially pink noise (as with my 01V). In neither case would this be particularly noticeable except that my ageing ears would not be able to hear the 20 kHz signal so I would only hear the noise! The good thing is that with "real" music being presumably audible to mere humans and therefore jitter noise would be a) lower in level and b) significantly masked by the "real" signal. In essence, the annoyance factor could possibly be equated to an amplifier with very poor intermod distortion creating a similar none musically related low level "mush".

Also it is important to understand that it will only be any slaved sound cards that are going to contribut any significant jitter noise, as the internal clocks of almost any sound card should have inherently low jitter. This may be interesting to those who use an external reference such as a big ben. I would only use this when using multiple soundcards and even then maybe not, depending on the jitter performance of the various soundcards when slaved.

It is also clear that most modern soundcards/converters are paying more attention to jitter noise so they will perform better than my set up but in fact they will not be so much better as to ignore jitter noise completely. These newer cards also generally seem to focus the jitter outside the audible band. They can only do this by focusing the noise as much as possible in the sub audible band. Thus it is more important than ever to make sure that you use high pass filters set appropriately to the recording. This is standard good practise but will also avoid any build up of low frequency mush arising from jitter noise as well as the other more usual sources.

I hope this puts a lid on this with a few practical tips on how to minimise any effects you may get from jitter noise.

As usual, please feel free to comment, criticise, question (or even acclaim!!! LOL) whatever these ramblings mean to you!

MrEase Sat, 05/15/2010 - 10:18

I've managed to find a bit of time to get some basic photo's together!

Rather than just spout on about how jitter arises and what the spec's mean I think these photo's will show what happens a bit more clearly. What I've done is to use my Yamaha 01V (original) together with my original MOTU828.

These are linked together via ADAT lightpipe and I've used both devices as the clock source to measure the relative jitter on the S/PDIF outputs. In both devices the cycle to cycle jitter is in the order of a few tens of picoseconds (as are, I expect, just about all soundcards that are slaved or not). I've never bothered to do this before and the exercise has proved what I expected but also thrown up one small oddity I did not anticipate.

OK, the first photo is of the 01V slaved to the MOTU on a coarse scale to see the timing variations. I'm afraid my "best" scope is currently dead so I have used an older digital scope which is quite adequate to show the problems and also allows me to display the full range of the timing variations over a period of time.

The lower trace is the 01V S/PDIF output and the upper is the MOTU output in all cases. Horizontal scale is 50ns per division. The first thing to notice is that the 01V output is delayed by approximately 250ns relative to the MOTU. This is a systematic error and although a perfect system would show the signals in perfect sync., in practise a fixed delay of 250ns is not large enough to cause any phasing issues. Bear in mind that the period of 20kHz is 50us so 250ns equates to 1.8 degrees of error - absolutely insignificant compared to moving a mic a fraction of an inch! What you can also see is quite a timing variation on the upper trace. Bear in mind I am always triggering the scope from the 01V signal so that variation is effectively the jitter on the 01V output relative to the MOTU output. This is shown more accurately later but note that the relative jitter is around 20ns or so. Forget cycle to cycle jitter, this measurement is what is REALLY important as this shows that timing of when you will actually get your samples.

Photo 2 is the same set up but with the MOTU slaved to the 01V.

Here we see that the jitter is similar but this time the MOTU output is delayed realtive to the 01V but this time by the smaller amount of 200ns. Again, for our purposes this is not really relevant. The amount of jitter is similar to the first photo. What I cannot easily show you here is the "nature" of the jitter, so I'll just have to try and explain the differences I noted. The jitter caused when the 01V is slave is apparently relatively wideband and appears to be essentially guassian noise. Without resorting to my spectrum analysers (and I'm NOT lugging them from my lab to the studio) I don't know what the full bandwidth of the noise is so this is just my judgement. With the MOTU as slave, as we can see, the magnitude of the jitter is about the same but the character is quite different and is predominantly low frequency (you can actually see it bouncing around as the scope picture builds). These different characteristics will alter how the sampled signal becomes modulated by the jitter.

The third picture is the same as #1 but zoomed in to see the jitter more precisely showing the peak to peak jitter of around 26ns

#4 is as #2 showing about 23ns jitter.

While I was doing these tests, I was storing the results over about 45 seconds or so which seems adequate to catch all the variations however I did get diverted and noticed the MOTU, when slaved, occasionally has a "blip" which causes a significant increase in the jitter. This is shown in the last photo, #5.

This happens infrequently (every few minutes or so) and I can only ascribe this to some systematic fault in the logic of the system. It certainly does not appear to be a character of the phase locked loop circuit.

The most important thing to take from these photo's is that the real world jitter is actually in the order of tens of nanoseconds rather than the tens of picoseconds that it seems the manufacturers specifications would have us believe and also there is simply not enough information in the "cycle to cycle" measurements for us to calculate the real world jitter figures that I have given here.

Next will be a few simple calculations to show roughly what all this means to our recordings!

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Boswell Tue, 06/15/2010 - 03:07

MrEase, post: 350248 wrote: A sine wave is described mathematically by Vout= A*sin(wt) (using w to represent omega), where the magnitude of the wave is set by A. In this case A=1 gives a sine wave of 2Vp-p. To find the maximum slew rate, we differentiate this expression with respect to time to give dV/dt (the rate of change of voltage) = w cos(wt), this is a maximum when cos(wt) = 1, hence dV/dt(max) = w. w = 2*pi*frequency = 125.663 V/s.
....
So if we have a sine wave at 20 kHz, 2V p-p then the maximum slew rate of the wave is (approx) 125 V/s. If we now take the measured results of the jitter as 25 ns (I like round figures!) then the maximum possible variation on a sample is 3.125 uV. This is spread both sides of the ideal timing so the error is around +/- 1.55 uV. I will term this as the "maximum jitter modulation". This is 116 dB below 0dBFS and certainly, for my converters at least, is below the converter noise level.

Great analysis, but I think you dropped the K in KHz, making the figures 60dB worse than you suggested!

At 20KHz, the angular frequency is 125664 rad/sec, so the max gradient of a 1Vpk sinewave is 125.664V/ms or 0.125664 V/us. Your (huge) 25ns jitter translates to a 3.14159mV (pi) uncertainty pk-pk. This is -56dBFS, which would be very audible.

MrEase Tue, 06/15/2010 - 05:20

Big thanks to Boswell for pointing out the slip! I can only say "woops", this type of thing always happens when you try to fit these things in with the time available. I actually have the slip of paper in front of me where I have written down 125.663 V/s instead of 125.663 V/ms! I must admit that the consequent results took me by surprise and I thought had got me out of going in as deep as I originally anticipated!

Of course Boswell is correct and this is more the result I had been expecting (never having bothered to calculate this before) and which my earlier posts had been "teeing up" so to speak.

So the explanation continues with what I had originally anticipated saying.

Unfortunately I can't do this immediately but I will be back soon....

Thanks again Boswell!

MrEase Tue, 09/28/2010 - 15:33

Boswell, I haven't seen that particular app note before and it is certainly one of the better ones. Thanks for posting it here, very worthwhile. For the more mathematically adept readers it is nice for me that it covers almost exactly what I tried to in the non technical way - which I suppose is to be expected! The best bit to me though is that it does not talk of cycle to cycle jitter, probably because it is written from the RF perspective. Sorry folks if I'm like a dog with a bone on this! ;)

audiokid, yes of course, good clean power is always the best starting point and should be a must in a studio. Unfortunately you cannot always record "in house" (or maybe you can!) so it should always be incumbent on the designer (of whatever equipment) to try and deal with any mains borne noise within the box. This should be regarded as "de rigeur" on top end gear but, as usual, things like this adds an expense that becomes an easy saving on budget gear when they do little for the spec. sheets. While that may be a good general rule there will always be exceptions in either case. Caveat Emptor as usual...

MrEase Thu, 10/29/2015 - 10:06

Hi Chris (audiokid),

I wasn't making a comment as to why you might do something a particular way and certainly not saying I disapprove of your methods or whether you are mad or not! :)

Hi Chris (Perra),

Chris Perra, post: 433339, member: 48232 wrote: So, unless something is totally noticable noise, buzz etc, jitter isn't a concern?

That's sort of putting words in my mouth but in essence, true. What I was really trying to say is that clock jitter only comes into play whenever you move from analogue to digital or vice versa. If you're happy with the recorded sound of individual tracks then the mixing process will have no impact whether tracks had high jitter when tracked or not. There should be no accumulative errors due to jitter and the mixing process. Note that when mixing, you are constantly playing back and the playback clock jitter comes into play. If you really had a clock jitter problem then it should be noticeable then, even if the tracking was "perfect" (which it can never be, sadly).

I guess it's worth noting that even if you're just listening to a single track, you have two lots of jitter involved, once when recorded and again whenever you play it back.

To all, I only came back here as I was interested in the samples provided in the link given earlier and had some comments I thought people should be aware of. I hope it helps!

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audiokid Thu, 10/29/2015 - 10:19

MrEase, post: 433430, member: 27842 wrote: Hi Chris (audiokid),

I wasn't making a comment as to why you might do something a particular way and certainly not saying I disapprove of your methods or whether you are mad or not! :)

no worries, but I am Mad for getting into the business. Somehow I'm able to function remotely well on the outside world. :)

I have more questions for you, just need to think about the wording. Thanks as always for your contribution here.

MrEase Mon, 04/19/2010 - 15:34

I certainly agree with Boswell's comments but I do have something to add. In just about all spec sheets for audio interfaces jitter is quoted as error between consecutive clock edges rather than the more key aspect, as Boswell infers, of errors in absolute time. Nor have I seen any figures given for clock jitter when externally referenced. Phase noise (particularly in PLL's) when clocks are slaved can be very poor and often do not follow the WIKI suggestion of Guassian noise. This is one of the areas where I certainly think improvements can be made and I think will only happen if we can get better specification of jitter from the manufacturers. Indeed, what is mostly quoted as jitter, to my mind at least, is not a true measure of jitter.

OK this is the tech talk forum, so my question is how far do we want to go into this topic?

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Chris Perra Thu, 10/29/2015 - 11:30

For me.. listening to this examples nulled and hearing super exaggerated jitter I'd treat it like part of your sound like any other part of the chain. You either like or don't notice the sound or notice and dislike what you hear. If it sounds good it's good if it sound bad it's not.

Scott Griffin Mon, 04/19/2010 - 15:49

This forum could use a topic like the legendary 96K argument on George Massenburg's old (now defunct) forum on Musicplayer....

Go as deep as you like, and offer as provocative an opinion as you dare! *grin*

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Boswell Fri, 07/16/2010 - 03:26

I wanted to say thanks, Mr Ease, for all the time you have spent explaining this tricky subject to a wider audience. It's contributions like yours that make RO stand out among the many audio forum websites.

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