[time-nuts] Using Allan Plots, was(LPRO-101 with Brooks Shera's GPS locking circuit)
Brooke Clarke
brooke at pacific.net
Sun Dec 17 13:13:31 EST 2006
Hi Ulrich:
Thanks very much for your email of 16 December it's a big help for me to
understand how to use Allan plots. I would like to learn more about
their application to Time Interval Counters. For example I have the
SR620 and although the one shot resolution is 1 ps the one shot
precision is specified as 20 ps. What test can be done to determine an
Allan plot for a TIC?
Have Fun,
Brooke Clarke
w/Java http://www.PRC68.com
w/o Java http://www.pacificsites.com/~brooke/PRC68COM.shtml
http://www.precisionclock.com
Ulrich Bangert wrote:
>Brooks, Brooke and Bruce,
>
>1) I do not want to talk bad Brooks Shera's design. In fact i admire it
>a lot for its simpicity. It was the first to be published in amateur
>literature and that makes it easily the best available in amateur use
>for a long time. And I learned lots from it. Indeed i needed weeks to
>understand how some subtle ingredients go ahead hand in hand to make the
>whole thing work, the short measurement times that i talked about being
>one of them. The original QEX publication was surely a breakthrough in
>amateur technology.
>
>2) One of the things that the original publication lacks is a in-depth
>rule on how to set the loop time constant correct for a given LO. When i
>was new into this topic it was kind of my belief that choosing this
>parameter correct was the 'black art' in constructing a good frequency
>standard and I wanted to learn more about it. Today i know, that only
>ONE SIMPLE RULE applies to this question despite the fact that some math
>for drawing tau-sigma-diagrams is indispensable.
>
>3) This rule is: An OXCO has a banana like tau-sigma-diagram with the
>lowest ADEV anywhere between 10-100 s. A GPS receiver's
>tau-sigma-diagram is a straight line with a slope of -1 starting
>anywhere from ADEV 2E-8 @ 1 s to 1E-7 @ 1 s depending on the receiver.
>Note that these receiver figures apply to raw, not sawtooth corrected
>values. Now have a look to where the lines meet each other. Left from
>that point the OCXO's ADEV is smaller then the GPS receiver's. Right
>from that point the GPS receiver's ADEV is smaller the the OCXO's. There
>is no guessing or speculating at all: The loop time constant MUST be set
>to where the meeting point is. If it is set to anything else this will
>make the ADEV of the standard's output more worse than is necessary.
>Note that the OCXO's tau-sigma is already on its ASCENDING slope where
>the lines meet.
>
>4) From that simple rule a complete briefing for the construction of a
>good frequency standard may be deduced:
>
>a) Because left of the meeting point the standard's output stability is
>only a function of the OCXO's stability and NOTHING ELSE choose the best
>available LO in terms of ADEV up to the expected meeting point of the
>lines. For this purpose a GOOD xtal oscillator may by all means be
>better than a Rb! Perhaps the people that are going to discipline a Rb
>with GPS may be disappointed: While the Rb is much easier to discipline
>due to its smaller sensibility to environmental changes a good xtal
>oscillator (the key word is: good. And good means: better than a
>HP10811) may outperform a Rb based standard in terms of ADEV for short
>observation times. @1 to some 10 s the HP10811 is better in ADEV than
>most Rbs. However up from there its ADEV goes up steeper than that of an
>thermically better managed USO like a FTS1000/1200. An even better
>choice but beyond the financial scope of most of us were a BVA based
>oscillator.
>
>b) Because the meesting point is always on the the OCXO's ascending
>slope choose the best available receiver in terms of how high it's -1
>slope tau-sigma is located. The less high the absolute position of his
>tau-sigma is, the more left (=earlier) the meeting point will be. The
>more left the meeting point is the less the overall ADEV of the
>standard's output will be deteriored by the OCXO for observation times
>near the meeting point due to its ascending ADEV slope.
>
>c) The TIC measurement resolution must be high enough to not deterior
>the phase measurements by the sheer measurement 'granularity'.
>
>Some graphics might be helpfull in understanding this. Have a look to
>page 22 of
>
>http://www.ulrich-bangert.de/AMSAT-Journal.pdf
>
>which i wrote for the German AMSAT journal. Don't worry over the German,
>just look to the pictures. In this graphic both the tau-sigma of a
>HP10811 and a M12+ are drawn into the same diagram and according to 4)
>it becomes immediatly clear why we want the OCXO as stable as possible
>before the meeting point and the receivers tau-sigma as low as possible
>to make the meeting point as early as possible.
>
>Exactly this is the point where i fear that you, Brookes, are the victim
>of a basic misconception, at least your comment makes me think so:
>
>
>
>>>I believe the sawtooth correction is of little or no value for a
>>>GPSDO,
>>>which typically requires a low pass filter between the GPS
>>>
>>>
>>1pps and the
>>
>>
>>>disciplined oscillator. This filter is quite effective in
>>>
>>>
>>removing the
>>
>>
>>>sawtooth quantization introduced by the GPS rcvr clock,
>>>
>>>
>>just as it removes
>>
>>
>>>the similiar quantization caused by my phase detector.
>>>
>>>
>
>This indicates that you are believing that it can all be done with low
>pass filtering. And this is wrong for two reasons:
>
>a) As Bruce and TVB have pointed out there are 'anomalies' in a GPS
>receiver's raw pps (well documented on TVB's web pages) where the idea
>that lowpass filtering the raw phase data will do the job is simply
>unsustainable.
>
>b) Low pass filtering is a trade with nature: You can get better
>precision due to low pass filtering but you have to pay for it in terms
>of time that you have to wait for the samples to avarage over. Look
>again at page 22 of
>
>http://www.ulrich-bangert.de/AMSAT-Journal.pdf
>
>and ask yourself what the noisefloor of you circuit would look like in
>this diagram. I tell you: Even if you had the best current GPS receiver
>available your phase measurements would be dominated by a noisefloor
>induced by the 4E-8s single shot resolution of your TIC giving a
>straight line starting at 4E-8 @ 1 s and having a slope of -1 i.e. a
>line that runs parallel to the M12+ graph but a factor 2 higher in
>absolute terms. Low pass filtering = averaging means nothing else than
>running up and down the line. Go to any point of time on the horizontal
>axis and draw a vertical line there. Where this line meets your
>noisefloor draw a horizontal line and on the vertical axis read the
>precision that you gain if you average over that time. It is as easy as
>that. And to find out when you reach a certain precision go to that
>precision on the vertical axix and draw a horizontal line. Where this
>line meets your noisefloor draw a vertical line and read the necessary
>averiging time on the horizontal axis. And note that this horizontal
>line drawn in the last example has crossed the M12+'s line by a factor
>of 2 earlier! That is: the sheer measurement resolution of 4E-8 s has
>DOUBLED the averaging time necessary to come to a certain given
>precision.
>
>At a first glance this may be not so impressive: Instead of 10 s we have
>to wait 20 s with your circuit to get the precision that the receiver
>alone has already after 10 s. Why do I make that heck out of it? Don't
>we have these 10 additional seconds? Please read on: The M12+'s
>sigma-tau shown un the diagram is the one for the raw phase data. If the
>sawtooth correction is taken into account the line starts at an ADEV of
>2E-9 @ 1 s. Unfortunately its slope is less than -1 so the factor 10
>increase in precision does not hold for all oservation times. At
>observation times of app. 1 day the two lines meet, giving an
>improvement in using the sawtooth corrected values only for observation
>times < 1 day. In
>
>http://www.ulrich-bangert.de/html/photo_gallery_44.html
>
>you can see the sigma-taus for the raw and the corrected data from a
>M12+ drawn into the same diagram. With a good OCXO the meeting point
>between receiver tau-sigma and OCXO tau-sigma is in to order of 1000 s.
>1000 s are small against a day, that means that almost the full possible
>improvement in ADEV by using the sawtooth corrected values apply to the
>case of a loop time constant of 1000. This factor of 10 in conjunction
>with the factor of 2 that we had before results in the factor of 20 that
>i claim that the noisefloor ot your circuit is inferior to that of a
>modern GPS receiver. And of course my claim stays intact!
>
>Some of you may now scratch your head and say: "Well...yes 20 is a
>handfull! With the Shera circuit we will have to wait 20 times the time
>that is necessary due to GPS 1pps jitter alone, but isn't it more
>important that we reach this precision/stability (in a sense these two
>words are synonyms in this discussion) AT ALL with the Shera circuit?"
>
>This is EXACTLY where the misconception starts. If someone is claiming:
>"I can average over 30s to get an improved measurement precision." I am
>going to ask him: "Hey, why don't you average over 300 s, giving you an
>additional factor 10 improvement." The answer might be: "Yes, perhaps I
>could do. It depends.." My next question were: "Depends? Depends on
>what? If every factor 10 in measurement averaging results in a factor 10
>in measurement precision, why not even average over 30000 or 300000 s
>??" I know the next answer very well in advance: "Oh no, i can't do
>THAT. While the argument of improving the measurement precision is
>right, i can't make use of this precision because my OCXO has drifted
>too much away if I wait THIS long!" AAHH! You have to take your OCXO
>into account? And yes, that is correct, but it is correct in a different
>sense than you may think!
>
>It is correct in the sense that i tried to explain before: The
>tau-sigmas of the OCXO and the receiver meet each other and where they
>meet depends ONLY on
>
>a) receiver quality in terms of ADEV
>
>b) OCXO quality in terms of ADEV
>
>c) TIC's noise floor
>
>In reality you are not free to choose "I want to average over 30 s" or
>"I want to average over 100 s". Instead the simple rule DICTATES that
>you HAVE to set your averaging time to the meeting point's x-axis value
>and to nothing else. There is simply no use in saying: "But with such
>and such averaging times i would reach a precision of such and such".
>You cannot choose! The physical properties of your receiver, your ocxo
>and your TIC dictate it!
>
>Since we now know what 'averaging' is all about let us now consider
>again at which ADEV the two tau-sigmas meet. Clearly we want to make the
>ADEV at this point as small as possible as it represents a local maximum
>in the overall tau-sigma of the standard's output. Since we are on the
>ascending slope of the OCXO our interest must be that the lines meet AS
>EARLY as possible. Since we cannot do anything on the -1 slope of the
>receiver's tau-sigma we achieve this only by shifting the absolute
>position of the tau-sigma as low as possible. This in turn is achieved
>by using the best available receiver AND using the sawtooth correction.
>A TIC resolution of 4E-8 shifts the meeting point a factor of 20 more to
>the right than would be necessary with a good receiver. Since I admire
>it a lot what you do, Brookes, i would be glad if you could gain the
>insight that averaging over raw phase data is something VERY DIFFERENT
>from using sowtooth corrected values.
>
>
>
>>Hi Ulrich:
>>
>>I think the answer is what other low cost options
>>are available? I would like to have a more modern
>>TIC capability to add to the clock I'm working on.
>>But although there's been a lot of discussion about
>>different ways of making TIC measurements, it's not
>>clear to me how to do it on a budget.
>>
>>For example the TIC232 circuit by Richard H McCorkle
>>is easy to implement, but how good is it's noise floor.
>>See:
>>
>>http://www.piclist.com/techref/member/RHM-SSS-SC4/TIC232.htm
>>
>>Then there's the low cost frequency counting TIC that appeared
>>in QEX that we know trades performance for low cost so it's
>>not a candidate.
>>
>>Any ideas on what circuits have a noise floor that's compatible
>>with the M12+T or it's newer equivalents and at the same time are
>>in the low cost category?
>>
>>
>
>Brooke, looking at the web page and the circuit diagram I second
>everything that Bruce has already said to it. This one uses a 16 MHz TIC
>time base and therefore its performance is even worse compared to
>Brooks's circuit. This one has its tau-sigma starting point at 62E-9 @ 1
>s, abt. 30 times worse than the M12+.
>
>If it can be done 'on a budget' as you say depends a bit on what you
>would call 'a budget' but it can surely not being done better if you
>have the Shera design prices in your head! In my own DIY GPDSO I do it
>using a delay chain out of the fastest interconnection elements
>available in a ALTERA Flex10K10 gate array, giving 110 ps resolution.
>That chip is surely not more than 50 US$ in single quantities.
>Unfortunately the delay of a single element of this delay line depends
>on chip temperature and supply voltage so that the lines need to be
>'calibrated' on a cyclic base. While this is done in the controllers
>firmware it makes the whole circuit a bit tricky. I currently try to
>migrate the design into a XILINX Spartan III fpga XC3S400 worth 25 US$
>in single quantities. Let us see what 2007 has to bring for us.
>
>
>
>>One can only achieve the subnanosecond resolution required to avoid
>>degrading the performance of an M12+ by using a clock
>>frequency of 1GHz or more. Thus this method is probably too
>>expensive and difficult to implement.
>>
>>
>
>Bruce, the clue is NOT to go out for a high clock frequency. Instead
>search for sub-clock interpolation schemes. Lots of them are available!
>
>Best regards
>Ulrich Bangert, DF6JB
>
>
>
>
>>-----Ursprüngliche Nachricht-----
>>Von: time-nuts-bounces at febo.com
>>[mailto:time-nuts-bounces at febo.com] Im Auftrag von Dr Bruce Griffiths
>>Gesendet: Samstag, 16. Dezember 2006 02:00
>>An: Brooks Shera; Discussion of precise time and frequency measurement
>>Betreff: Re: [time-nuts] LPRO-101 with Brooks Shera's GPS
>>locking circuit
>>
>>
>>Brooks Shera wrote:
>>
>>
>>>----- Original Message -----
>>>From: "Ulrich Bangert" <df6jb at ulrich-bangert.de>
>>>To: "'Discussion of precise time and frequency measurement'"
>>><time-nuts at febo.com>
>>>Sent: Friday, December 15, 2006 05:47
>>>Subject: Re: [time-nuts] LPRO-101 with Brooks Shera's GPS
>>>
>>>
>>locking circuit
>>
>>
>>>.......
>>>
>>>
>>>
>>>>I second Bruces's opinion about what is an overshot or
>>>>
>>>>
>>not. When ps
>>
>>
>>>>reolution is ready available then why not use it? I attach
>>>>
>>>>
>>a online
>>
>>
>>>>output from my DIY GPSDO from a few minutes ago that shows
>>>>
>>>>
>>the M12+'s
>>
>>
>>>>signal properties when measured with abt. 110 ps
>>>>
>>>>
>>resolution against a
>>
>>
>>>>FTS1200. The yellow line reperesents a prefiltered version of the
>>>>sawtooth corrected values (blue). The filter time constant
>>>>
>>>>
>>is 1/3 of
>>
>>
>>>>the loop time constant as in a PRS-10. The yellow values
>>>>
>>>>
>>are the ones
>>
>>
>>>>to feed the regulation loop.
>>>>
>>>>
>>>>
>>>
>>>
>>>
>>>>What I wanted to explain is the Shera concept noise floor
>>>>
>>>>
>>is a factor
>>
>>
>>>>20 above what a modern receiver can deliver (again inc.
>>>>
>>>>
>>the sawtoth
>>
>>
>>>>correction). And yes, you are right: There were different numbers
>>>>when this concept was thought out! And exactly because different
>>>>number were there when this concept was thougt out I am
>>>>
>>>>
>>going to ask
>>
>>
>>>>why people still built it today.
>>>>
>>>>
>>>>
>>>
>>>
>>>
>>>>Best regards
>>>>Ulrich Bangert, DF6JB
>>>>
>>>>
>>>>
>>>I believe the sawtooth correction is of little or no value for a
>>>GPSDO,
>>>which typically requires a low pass filter between the GPS
>>>
>>>
>>1pps and the
>>
>>
>>>disciplined oscillator. This filter is quite effective in
>>>
>>>
>>removing the
>>
>>
>>>sawtooth quantization introduced by the GPS rcvr clock,
>>>
>>>
>>just as it removes
>>
>>
>>>the similiar quantization caused by my phase detector.
>>>
>>>For example, reading from your graph I averaged the raw
>>>
>>>
>>data (as best
>>
>>
>>>I
>>>could by reading the blue line). The running average of
>>>
>>>
>>the raw data over
>>
>>
>>>40 sec (starting at 12:31:30) was -4.5 nsec, after 60 sec
>>>
>>>
>>it was -4.2 nsec.
>>
>>
>>>These values appear to be indistinguishable from the values
>>>
>>>
>>you get by
>>
>>
>>>averaging the "sawtooth corrected" data (the yellow line).
>>>
>>>It appears from your plot that the sawtooth correction has
>>>
>>>
>>contributed very
>>
>>
>>>little or nothing that averaging does not already provide. Have I
>>>misunderstand something?
>>>
>>>I believe that your "noise floor is a factor 20 above what a modern
>>>receiver
>>>can deliver" statement is incorrect. With an HP 5720B
>>>
>>>
>>(about 100 psec
>>
>>
>>>resolution), I have measured the phase difference between
>>>
>>>
>>the GPS 1pps and
>>
>>
>>>the phase of a 5 MHz oscillator controlled by my
>>>
>>>
>>controller. This data has
>>
>>
>>>been compared with simultaneous phase serial output from
>>>
>>>
>>the controller as
>>
>>
>>>determined its maligned 24 MHz asynchronous internal phase
>>>
>>>
>>measurement
>>
>>
>>>circuitry.
>>>
>>>ADEV Stable 32 plots of both data sets are essentially identical.
>>>From this
>>>I conclude that nothing would be gained, for the purpose of
>>>
>>>
>>discipling an
>>
>>
>>>oscillator, by using a more elaborate and expensive phase
>>>
>>>
>>detector (the
>>
>>
>>>phase detector in my controller costs $6.61, including
>>>
>>>
>>$5.35 for the dual 24
>>
>>
>>>MHz osc that is shared as the PIC clock). It was my goal
>>>
>>>
>>when I designed
>>
>>
>>>the controller was to make the design transparent to the
>>>
>>>
>>builder and to use
>>
>>
>>>as few parts as necessary consistant with performance
>>>
>>>
>>limited only by
>>
>>
>>>available GPS receivers and VCXOs. When I wrote the QST
>>>
>>>
>>article I was
>>
>>
>>>totally ignorant of the fact that I could buy the HP58503
>>>
>>>
>>with similiar
>>
>>
>>>performance for $5400.
>>>
>>>Your earlier comment about the capture range of the phase
>>>
>>>
>>detector is
>>
>>
>>>well
>>>taken. For the past several years the PIC software I
>>>
>>>
>>provide has included
>>
>>
>>>an option designed for use with inexpensive TCVCXOs. It
>>>
>>>
>>requires only an
>>
>>
>>>external 128 divider chip and produces EFC voltages
>>>
>>>
>>suitable for inexpensive
>>
>>
>>>oscillators. It works very well and provides sufficient
>>>
>>>
>>performance for
>>
>>
>>>many applications.
>>>
>>>Regards, Brooks
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>----------------------------------------------------------------------
>>
>>
>>>----------
>>>
>>>
>>>
>>>
>>>
>>>>_______________________________________________
>>>>time-nuts mailing list
>>>>time-nuts at febo.com
>>>>https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts
>>>>
>>>>
>>>>
>>>_______________________________________________
>>>time-nuts mailing list
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>>>
>>>
>>>
>>>
>>Brooks
>>
>>Your comparison of your circuit with measurements taken with
>>the "5270"
>>(is this a typo? did you mean 5370? which is known to have
>>differential
>>non linearities well in excess of 100 picoseconds, at
>>least according
>>to the designers - some later modifications to the circuitry reduced
>>this effect somewhat) demonstrates very little unless the
>>measurements
>>were corrected for the sawtooth error.
>>
>>The only true test is to compare a sawtooth corrected
>>GPSDOCXO alongside
>>a sawtooth corrected GPSDOXO. Both should of course use equivalent
>>performance oscillators and GPS timing receivers.
>>
>>The short plot that Ulrich furnished doesn't include any
>>hanging bridges
>>which occur when the GPS oscillator drifts through a harmonic
>>of 1Hz. Most M12+ GPS timing receivers produce sawtooth
>>correction errors in
>>which such "hanging bridges" are not infrequent.
>>
>>No one is disputing that with an low performance oscillator its not
>>worth going to too much trouble in improving the phase
>>detector performance. However some of us have oscillators
>>with much better performance than
>>such cheap oscillators. We also have a need to achieve an oscillator
>>instability of less than a few parts in 1E12 which your
>>circuit cannot
>>reliably provide in the presence of hanging bridges and aberrant PPS
>>pulses which do occur from time to time.
>>
>>The existence of a commercial GPSDOCXO that achieves an Allan
>>variance
>>of 2E-13 or better from tau = 1 sec to 1 year, indicates that it is
>>possible to do much better than your circuit is capable of.
>>All we are
>>doing is exploring cheaper ways of approaching this
>>performance within a
>>factor of 10 or so.
>>
>>Bruce
>>
>>_______________________________________________
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>>
>>
>>
>
>
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