[time-nuts] Metastability in a 100 MHz TIC

Dr Bruce Griffiths bruce.griffiths at xtra.co.nz
Fri Jul 20 06:56:48 EDT 2007

Ulrich Bangert wrote:
> Richard,
> metastability is an effect that happens when the setup times of an
> d-flipflop are not met. This can happen (with a certain statistical
> likelyhood) when the sources of the data input and the clock input of an
> d-flipflop are not synchronized. The important thing to know about
> metastability is that the likelyhood of its appearance might be directly
> computed from the setup time and the frequency of the d- and
> clock-signal as described in
> http://www.xilinx.com/xlnx/xweb/xil_tx_display.jsp?sGlobalNavPick=&sSeco
> ndaryNavPick=&category=&iLanguageID=1&multPartNum=1&sTechX_ID=pa_metasta
> bility
> Peter Alfke is THE expert in metastability at XILINX! I guess if you
> apply the data presented here to your case you will find that the
> probabilty of metastability in your case may be neclected. Roumors are
> that 99% of all assumed cases of metastability are due to other design
> flaws. 
> However I would like to draw your attention to an second point. From
> your posting it gets clear that you are not the pure user of the Shera
> design but have otherwise put a lot of brains into the question of how
> to improve it. 
> First, forget about the Shera design for a moment and consider the case
> that you have two 1pps sources and want to compare them by means of an
> REAL tic as the HP5370 or the SR620. Question: Since you are comparing
> TWO oscillators by means of an THIRD oscillator (the tic's time base),
> does the tic's time base stability influence your measurement results or
> not?
> Clearly so, if you think about it for a while. With this arrangement it
> is not possible to decide whether 1pps a or 1pps b or the tic's time
> base are responsible if you notice statistical fluctuations in the
> measurement results. The measured results will be an statistical average
> (not an simple arithmetic one but an more complicated one, but basically
> you can imagine it as an average) of ALL source's fluctuations. The
> situation changes if you have more sources and/or more tics available
> because there are statistical methods available to allocate which source
> and which tic is responsible for what but in the simple case of only
> three sources these rules cannot be applied. 
> Now that you aware of the fact that the tic's timebase has an impact on
> measurements made with the tic what would you do about it? In the real
> world you would synchronize the tic's time base to the best reference
> available, for example to the cesium in the backyard or the H2 maser in
> the kitchen. But what if you lack equipment like that and have only this
> one rubidium oscillator and this gps receiver? Clearly the second best
> choice is to use the rubidium also as the timebase for the tic EVEN if
> it IS the source that you want to discipline, just because you reduce
> the complexity of the problem back to TWO sources of fluctuations.
> Now let us come back to the Shera circuit. The question that must be put
> forward at this point is: If we have just recognized that the tic's
> timebase has pretty much the same influence on our mesurements as the
> duts itself, how can the Shera design work with an timebase consisting
> of a garden variety canned oscillator of the lowest class of stability?
> If the above explained claims are true and the measurement results are
> the statistical average over ALL sources then in your case this cheesy
> little timebase is by some orders of magnitude worse in terms of
> stability compared to the rubidium and the gps and what we measure
> should in theory be dominated by the bad time base and not by the duts.
> So, how can the circuit work at all ??? 
> At this point we come to one of the big but not commonly well understood
> tricks of the Shera design. The cheap canned timebase IS indeed the
> biggest source of fluctuations in the design. However the design
> includes precautions so that these fluctuation are hindered to show up.
> Howzat?
> Consider two 1pps signals. They can be as close as 0 s or they can be
> apart as much as 500 ms. Consider they are 500 ms apart and you have an
> timebase of 24.576 MHz to measure how far they are apart. With 500 ms
> your tic will reach something like 12288000 counts in that time. Among
> other environmental depencencies the coefficent of temperature will be
> the most prominent one with simple xtal oscillators being in the order
> of 1E-6/Kelvin. With 10 Kelvin temperature variation this will give you
> an change of app. 123 counts in the count result for the SAME 500 ms
> just due to temperature. This is an noticeable effect! Even the 10th
> part of it, 12 counts would be an noticeable effect. But now comes the
> clue: Both effects are noticeable because and ONLY because we made an
> HIGH RESOLUTION MEASUREMENT. With 12288000 counts 1 count equals less
> then 1E-7 of the result, so we made an measurement with better than 1E-7
> resolution. Now consider the case when we limit the measurement range of
> the phase comparator. Instead of allowing the pps signals to be 500 ms
> apart we now DEMAND that they are not more apart than say 500 µs for
> example because we claim that we cannot measure longer times. Within 500
> µs the counter may reach an result of maximum 12288 (and not more
> 12288000) and 1 count equals app. 1E-4 of the maximal result. Which
> effectively means that THIS measurement has only 1/1000 the resolution
> of the original 500 ms measurement. Can this be true? Think abaout it
> for a while and you will see its true. The 10 Kelvin temperature effect
> that made an count difference of 123 counts in 500 ms will make an count
> difference of 0.123 (!) counts in 500 µs. Which is less than 1 count and
> will be VERY difficult to be noticed if possible at all. So one or two
> clues of the Shera design is/are to make the measurement range of the
> phase comparator THAT small that all environmental depencies of the
> tic's time base are SMALLER than the RESOLUTION of the time base. Choose
> an resolution sufficiently low and all environmental effects of the time
> base will be masked by it.
> And that is exactly where your consideration is going to get wrong: The
> limited resolution of the Shera design (as well as the limted phase
> measurement range) is NOT an FLAW of the design that could be improved
> by your 100 MHz tic! It is an FEATURE of the design that may not be
> touched in order to give the proposed results! And the fact that you are
> NOT observing a real improvement although you increased the resolution
> by 4 is the proof for it all: Not only did you increase the resolution
> by 4, you also increased the count result's tendency to be influenced by
> environmental changes by the same factor. You should notice a big
> improvement if you throw away your 100 MHz oscillator to where it
> belongs and feed your counters with an 100 MHz signal that has been
> generated by an X10 frequency multiplication of your rubidium or by
> phase locking an 100 MHz VCXO to the rubidium.
> Best regards
> Ulrich Bangert 
> P.S.
> The reaction of rubidium oscillators to environmental changes like the
> day-to-day temperature changes to happen in a typical flat have not yet
> been discussed in the group in depth. However my own experience seconds
> your own results concerning the loop's time constant. While the overall
> temperature coefficient of of my rubidiums is an order of magnitude
> better than that of my best OCXO it is not possible to use a higer time
> constant with them compared to the OCXO when the day-to-day changes are
> expected to be removed by the loop. Over the last years a natural loop
> time constant of app. 1200 s has evolved to be the best compromise for
> both the OCXO and the rubidiums. Since my OCXO has MUCH less phase noise
> at small observation times I have come to the conclusion that an OCXO
> based GPSDO serves me better than an rubidium based one.  
If the 100MHz clock is derived from the OCXO or other standard being 
disciplined then the PPS source needs sufficent random jitter to ensure 
accurate averaging of the phase error.

If the 100MHz source isnt as stable as desired then this instability can 
be alleviated somewhat by using the 100MHz clock to measure the period 
of the OCXO (or a multiple of this period), and using this result to 
correct the phase measurement. If one measures 1E7 periods of a 10MHz 
OCXO then the calibration error in the 100MHz clock will be around 1E-8 
or so, allowing the calibration error (due to the 100MHz clock frequency 
calibration error) in a 100us phase measurement to be held to within 1 
picosecond or so. Almost any well designed XO mounted within an 
enclosure with adequate thermal time constant will drift slowly enough 
in frequency for this correction technique to be effective.

Re calibrating the 100MHz clock once a second should allow the effect of 
its frequency drift to be minimised provided the critical parts of the 
100MHz clock have a thermal time constant of a few tens of seconds or more.

However this method requires dividing the OCXO down to around 1Hz or so 
to allow accurate calibration of the 100MHz oscillator against the OCXO 
The circuit complexity is greater than that required when using hardware 
correction of the PPS sawtooth error followed by a simple D flipflop 
(plus following synchroniser) where the corrected PPS clocks the 
flipflop whose D input is connected to the OCXO output frequency or 
submultiple thereof as suggested a few weeks (months??) back.
The D flipflop will typically have a resolution of a few picoseconds or 
so depending on the logic family chosen. This is far higher than can 
reasonably be expected when using an inexpensive variation of the Shera 


More information about the time-nuts mailing list