# [time-nuts] AVAR & Femtoseconds

Bob Camp lists at rtty.us
Sun Jun 20 11:32:10 EDT 2010

```Hi

The use of femtoseconds come from the AVAR it's self. It was originally defined by "time domain" people. It's delineated by a Tau dimensioned in seconds. The time domain "noise" that's 1x10^-12 or 1x10^-15 down at one second does indeed have units of 1x10^-12 or 1x10^-15 seconds.

As with any real world system one has to be very careful about the difference between resolution and accuracy. Resolution generally is easy, accuracy is more difficult. Any of the commonly used measurement techniques used to drive the AVAR are capable of enormous resolution. The problem is that past a certain point the added digits are simply internal noise and do not represent the DUT or the reference.

One very simple example:

A heterodyne system beats two 10 MHz oscillators down to a 1 Hz note. That gives you a 1x10^7 expansion. Drive the note directly into any of the common 11 digit per second counter (no limiters, no amps, straight in). You now have a LSD that has dimensions of 1x10^-18.  You could claim that you have a system with a resolution of 1 atto-seocnd. A quick look at the output of the counter would show you that a lot of those digits were simply random numbers. You could do equally well by taking a 6 digit / second counter and a simple PIC program to make up another 5 digits of data.

Bob

On Jun 20, 2010, at 10:46 AM, Robert Benward wrote:

> Steve,
> I am a professional engineer, but in this arena I am an amateur.  That is
> why I'm asking the questions, not to put down, but to understand some of the
> claims made.  And as I said in one of my previous emails, I've seen amateurs
> run circles around the professionals, and those professional admitting utter
> astonishment at those amateur accomplishments (this is in the area of
> amateur astrophotography).
>
> What I have heard throughout this thread is a lot of bashing of those asking
> the questions, surfacing as derogatory and berating comments on other's
> understanding.  I have also heard much claims to a certain procedure without
> one iota of numerical mumbo-jumbo to back it up.
>
> The issue here is an inability to describe a simple claim.  Pete has
> attempted to put things in simple numbers, and I see where he is going, and
> I concur with some of his calculations.  If one can not describe what
> appears to be a simple procedure, then I must question the basic
> understanding behind the explanation.  If you make a wild claim, and then
> you can't even get the bullet on the paper, then I must question the
> shooter's understanding.
>
> I guess I am not comfortable with the use of femtoseconds to describe
> frequency accuracy.  Technically, a locked PLL is at the exact frequency as
> the reference, as measured in the long term.  The phase between the two may
> not be at zero, that depends on the type of phase detector and the DC
> offsets in the system.  On the short term, phase noise of the reference will
> cause the loop to generate error terms which will change the phase of the
> DUT.  Oscillators are also specified using phase noise, e.g. 135dB down @
> 100Hz.  That specifies how much energy is not in the bandwidth of the
> carrier.  It also implies the phase is constantly changing!  If the phase is
> changing, the error term is changing, and so forth and so on.....Your
> measurement can only be as good as your reference oscillator.  A DVM can
> only average this error, it can't give you the instantaneous value of the
> peak deviation of the error signal, which is what you would need to claim fs
> cycle to cycle timing.  Fs units are appropriate for cycle to cycle
> variation, not long term or multicycle assements.  Even the best HP DVM is
> only good to 3ppm on the 100mV scale and the shortest reading is 167us.
> That's 10 orders of magnitude greater that the deviation you are trying to
> measure.  If you average the mixer output, you can no longer claim fs
> timing.  What you can claim is a long term frequency stability in ppm.
>
> This is my simple understanding of phase detectors and mixers.  You might
> get there by dividing down a bunch of numbers but I don't think the method
> supports the claim (of fs timing).
>
> Bob
>
>
>
> ----- Original Message -----
>  From: Steve Rooke
>  To: Discussion of precise time and frequency measurement
>  Sent: Sunday, June 20, 2010 2:00 AM
>
>
>  Bob,
>
>  Can I answer this one.
>
>  On 20 June 2010 04:36, Robert Benward <rbenward at verizon.net> wrote:
>> Warren,
>> I was responding to ke5fx comment "using a 12-bit, 480-Hz serial DAQ in
>> place of the voltage-to-frequency converter in the diagram above". A DAQ
>> is a multifaceted data acquisition system, where as in your annotated
>> diagram you showed an ADC.
>
>  The DAQ that Warren is referring to to has a 12bit ADC input capable
>  of performing up to 480 samples per second.
>
>> I understand it's analog, but you said: "Say you have a nice logic gate
> with
>> 1 ns delay" . So back to the analog loop, do you have an analysis that
> gets
>> you from EFC to femtosecond stability? PLLs are notorious for phase
> noise,
>> the phase noise actually representing the error term that brings the
> loop
>> back into lock.
>
>  I personally think the 1fs issue has become way out of hand and people
>  are now focussing on that instead of the big picture. Whilst I
>  understand that the professional engineers on this list wish to pounce
>  on every t that is not crossed, every i that is not dotted, and
>  requiring a complete mathematical breakdown of everything, it is not
>  going to happen here. If those professional engineers would like to
>  assist with the process of understanding and documenting this idea in
>  a way that pulls their chain, that would be great, but if it's down to
>  pointing the finger at the amateur engineers and laughing, then
>  perhaps they need more education in etiquette. Remember the golden
>  rule, do unto others as you would wish to be done.
>
>  Sure, some of us do not have the correct technical engineering banter,
>  so when we call the World a sort of round ball shape, please don't
>  play deaf until we say it's an oblate spheroid. Try to help us
>  communicate with you, we are trying to describe things in the best way
>  we can and we have something useful to contribute, IE. just take
>  Warren's TPLL implementation which seems to be producing good results.
>  So why don't we try to understand exactly how it is doing this instead
>  of ripping it apart and saying you shouldn't do it that way, you have
>  to do it this way. Remember that geezer who invented the lightbulb, he
>  didn't work it all out mathematically on paper before he chose
>  tungsten, no he did it experimentally and everyone seems to think
>  highly of him.
>
>  Steve
>>
>>
>>
>>> You are now averaging the "repeatable" jitter? YES
>> I was not questioning the procedure, I was questioning the conclusion;
>>
>>> Are you using a digital phase detector or a mixer as shown? Analog
>>> Phase detector
>> Why the digital analogy if it's all analog?
>>
>>> Do you have an analysis of the loop sensitivity/resolution? No
>>> analysis, No limit it is analog
>> I don't agree with you about the limit, and without an analysis or even
> a
>> simple calculation, how do arrive at femtosecond lock? if there is no
>> limit, why not a hundred times less?
>>
>>> Why do you say the results are repeatable in the short term vs the long
>>> term? Long term includes other factors such as non random drift, not
>>> just "random Noise"
>> Maybe so, but using the "short term" , is not a license to better jitter
>> figures by a factor of 100. Since you are not using digital, I don't
> know
>> where this example came from or why it is relevant.
>>
>>> Is there not a lower limit to how much you can average? Depends or
>>> everything, but not up to > 1 sec of averaging when the conditions are
>> I don't understand how you arrive at this conclusion
>>
>>
>> What attracted me to the TPLL question now was that you comment that you
> are
>> maintaining a femtosecond lock. Please don't dumb it down for me. I may
> not
>> understand all the statistical stuff, but I can understand an analysis.
>>
>>
>> Bob
>>
>>
>>
>> ----- Original Message -----
>> From: "WarrenS" <warrensjmail-one at yahoo.com>
>> To: "Discussion of precise time and frequency measurement"
>> <time-nuts at febo.com>
>> Sent: Saturday, June 19, 2010 3:27 AM
>>
>>
>>> Bob
>>>
>>>>> Don't know if I can explain it to you, I'm not so good at explaining,
>>>>> I'll give it *ONE* try.
>>>>> Example with some random picked numbers (JUST TO SHOW THE MAIN
> POINTS).
>>>
>>> I tried,
>>> All information and test that are available on the TPLL is on JOHN'S
>>> KE5FX
>>> site or in past postings.
>>> http://www.thegleam.com/ke5fx/tpll.htm
>>>
>>> One other thing I may not of made clear, The analog averaging thing
> does
>>> not
>>> help at low freq like at 1 PPS
>>> The TPLL works great because it is at a high freq like 5 or 10 MHz.
>>> DAQ == DataQ == ADC
>>>
>>>> I don't think 10ps is achievable under any dynamic conditions IMHO
>>> OK, I don't really care, use whatever number you want, you'll still end
> up
>>> below the Ref osc noise.
>>> but
>>> You may be surprised then by what the single shot "Aperture
> uncertainty"
>>> thing.
>>> But then none of that really maters AT ALL,
>>> because there is NO Digital anything in the simple TPLL before the ADC
>>> where
>>> a 10 Hz device would work fine for most.
>>> I just gave you an example to try and answer your question on digital
>>> logic
>>> which was:
>>>> How do you do fs when most digital logic has jitter several of orders
> of
>>>> magnitude greater?
>>>
>>> ws
>>>
>>> ***************************
>>> Robert Benward rbenward at verizon.net
>>> Sat Jun 19 03:18:05 UTC 2010
>>>
>>> Warren,
>>> Is there not a lower limit to how much you can average? Yes, it's the
>>> sqrt
>>> of the number of samples, but doesn't noise,
>>> hardware, and other perturbations limit the usefulness of this method?
>>>
>>>> Then one can get repeatable results say 100 times better from cycle to
>>>> cycle in the short term.
>>>> so down to 10ps repeatable.
>>>
>>> Why do you say the results are repeatable in the short term vs the long
>>> term? Isn't what you defined above
>>> (repeatability) the opposite of jitter? Jitter I thought was cycle to
>>> cycle
>>> variation in prop delay. On 1ns prop
>>> devices, I don't think 50-100ps jitter is unreasonable under the most
>>> optimum conditions, the most careful circuit
>>> layout, and constant repeatable inputs. I don't think 10ps is
> achievable
>>> under any dynamic conditions IMHO.
>>>
>>>> One can average 1,000,000 readings of the 10 ps jitter
>>>> If they are truly random, that can give you a 1e-3 improvement (square
>>>> root of number of samples averaged)
>>>
>>> You are now averaging the "repeatable" jitter.
>>>
>>> KE5FX's website shows a diagram and a link to your diagram as well. Are
>>> you
>>> using a digital phase detector or a mixer
>>> as shown? BTW, KE5FX refers to DAQ as your update to the design, where
> I
>>> believe he meant an ADC.
>>>
>>> You have my curiosity peaked. Do you have an analysis of the loop
>>> sensitivity/resolution?
>>>
>>> Bob
>>>
>>>
>>> ----- Original Message -----
>>> From: "WarrenS" <warrensjmail-one at yahoo.com>
>>> To: "Discussion of precise time and frequency measurement" <time-nuts
> at
>>> febo.com>
>>> Sent: Friday, June 18, 2010 6:49 PM
>>>
>>>
>>>> Bob posted
>>>>> can you explain it to me?
>>>>
>>>> Don't know, I'll give it ONE try.
>>>> I'm not so good at explaining, but it is pretty basic if one does not
>>>> start assuming that it can not be done at the
>>>> start.
>>>> It is mostly about averaging lots of those transitions, and the real
>>>> trick
>>>> is that it is not Digital.
>>>> Analog has no lower limits except manly for Johnson noise type effects
>>>> (mostly).
>>>>
>>>> Example with some random picked numbers.
>>>> and assuming all analog that has no digital steps in it to limit
>>>>
>>>> Say you have a nice logic gate with 1 ns delay
>>>> If you make it all nice and clean, and repeatable such as constant PS,
>>>> rise time etc.
>>>> Then one can get repeatable results say 100 times better from cycle to
>>>> cycle in the short term.
>>>> so down to 10ps repeatable.
>>>> Now make things even more clean with no variations and assuming random
>>>> noise.
>>>> Now if one is doing this at 10 MHz and only cares about the average
> over
>>>> 0.1 sec (10 Hz)
>>>> One can average 1,000,000 readings of the 10 ps jitter
>>>> If they are truly random, that can give you a 1e-3 improvement (square
>>>> root of number of samples averaged)
>>>> so now down to 10 fs of average jitter at 10 Hz for a 10 MHZ gate
>>>> starting
>>>> with a 1ns initial delay.
>>>>
>>>> OF course if Anything changes at all, it will drift much more than
> that,
>>>> which may or may not mater much depending on
>>>> what one is doing.
>>>> If you only really care about the difference between any two
> consecutive
>>>> 100 ms reading that are next to each other,
>>>> as is (mostly) the case in ADEV, then not a big deal.
>>>>
>>>> IF it does matter or you want to do better, the next step is to do it
> all
>>>> differential, so you are looking at only the
>>>> different of two separate independent but equal circuits. Differential
>>>> can
>>>> give, say a 1000 to one or better
>>>> improvement in drift due to common things such as temperature etc.
>>>>
>>>> If that helps explain the basics, good, if not you need to ask others
> to
>>>> explain it better.
>>>>
>>>> And yes there all kinds of things that can & do go wrong and many ways
> to
>>>> screw it up.
>>>> so as easy as it sounds, it does take a bit of skill and art to do it.
>>>> Especially when one realizes that you are measuring things << 0.001 in
> of
>>>> distance change will have major effects on
>>>> because of the speed of light.
>>>> (approx 1ft /ns, 0.01 in/ps, 1 micron/4fs)
>>>>
>>>>
>>>> Now if one starts out, not with a gate but a phase detector that is
>>>> for such things, and averages enough (but not
>>>> to long) and is real careful,
>>>> 1fs resolution is possible in the 100 Hz range with 10 MHz
>>>>
>>>> 10 MHz & 1fs at 100 Hz gives 1e-13 freq variation resolution at tau
> 10ms
>>>> The simple BB TPLL is only getting about a tenth of that, (as shown on
>>>> John's test plots) so it can be made much
>>>> better with enough care, if anyone has a ref osc that needs it.
>>>> But as I am always so quick to point out, the BB tester was not
> optimized
>>>> for any one thing, It's performance was
>>>> selected as a compromise for 'KISS' reasons. (KISS = Keep It Simple so
>>>> the experts can understand.)
>>>>
>>>> please let me know on or off line if I'm wasting my time trying to
>>>> explain
>>>> this to the non "nut experts" without the
>>>> help of the fancy math papers.
>>>>
>>>> ws
>>>>
>>>> *********************
>>>> Robert Benward rbenward at verizon.net
>>>> Fri Jun 18 20:23:40 UTC 2010
>>>> Method
>>>> Messages sorted by: [ date ] [ thread ] [ subject ] [ author ]
>>>>
>>>> Warren,
>>>> I'm a newbie, so can you explain it to me? Femto anything is something
>>>> mostly reserved for a well equipped lab. How do you do it when most
>>>> digital
>>>> logic has jitter several of orders of magnitude greater?
>>>>
>>>> Bob
>>>>
>>>> *************************
>>>
>>>
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>
>
>
>  --
>  Steve Rooke - ZL3TUV & G8KVD
>  The only reason for time is so that everything doesn't happen at once.
>  - Einstein
>
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