[time-nuts] On some pitfalls of the dual mixer time difference method of horology

[Magnus Danielson]

From: "Ulrich Bangert" <df6jb at ulrich-bangert.de>
Subject: [time-nuts] On some pitfalls of the dual mixer time difference method of horology
Date: Sun, 1 Oct 2006 11:29:52 +0200
Message-ID: <000001c6e53c$28191a10$03b2fea9 at athlon>

> Hi folks,

Ulrich,

> Now it seems we have really created the universal workhorse of horology:
> We have amplified the effect to be measured by a factor of 1E7 by simply
> mixing down the signals to 1 Hz and the transfer oscillator's influence
> completely cancels out due to the difference measurement. That is how we
> find it described in the textbooks!
> 
> I do not know how many of you readers really built a DMTD circuit or
> used one. I know at least that some of you are planning to build
> circuits like that and that TVB owns an instrument (a TSC 5110) that
> works according this principle. 
> 
> I built a DMTD and made measurements with it on the few good oscillators
> that I own. While my experiments have shown that the principle works
> INDEED as described they also have shown that the DMDT has some pitfalls
> which you will find ABSOLUTELY NOTHING about in the textbooks. I get the
> impression that a lot of the authors explaining the method simply reecho
> what the have read elsewhere and that only a very small number of
> experts have an experience of their own with this method. I would like
> to explain what I have found out and discuss this stuff with you.

This is why textbooks are textbooks. They learn you a number of methods, but
does not go into the nitty gritty of them all. That is left over as an exercise
to the reader. Many times the author didn't spend much time on each of them
either. Few have the time.

Luckilly, there are other sources.

> First Pitfall of DMTD: Transfer oscillator effects do NOT cancel out
> completely
> 
> The explanation above gave you the impression that any effect in phase
> or frequency of the transfer oscillator cancels out due to the
> difference measurement between the down mixed signals, didn't it? And
> hey, this argument is not really wrong. But we need to be precise: Any
> transfer oscillator related effect cancels out completely if we look at
> the two down mixed signals at the SAME time! This is due to the fact
> that at the same time the transfer oscillator is in the same state
> concerning both channels.

Good point. It is obivous when you know it.

> But do we really do so? No, we do not! We look at one signal when its
> own zero crossing takes place and we look to the second signal when its
> own zero crossing takes place. With 1 Hz beat notes the zero crossings
> may be up to 500 ms apart of each other. No means of "at the same time",
> but anything between 0 and 500 ms. Of course: We may have a certain hope
> that the transfer oscillator's properties do not change completely
> within the maximal time of 500 ms. However, the principal idea that the
> transfer oscillator is in absolutely the same state concerning both
> channels is wrong because we do not look at both channels at the same
> time and for that reason its effects will not cancel completely but only
> up to a certain degree. 
> 
> Some authors (seldom to be found) will show you schematics that include
> phase shifting elements in the OUT's or the reference oscillator's
> signal path BEFORE the mixers. By means of phase shifting one of the
> original signals the zero crossings of BOTH down mixed signals can be
> forced to happen at the same time or at least app. the same time. In
> this case the transfer oscillator's effects do indeed cancel out and you
> may assume that this author knows what he's talking about. 

Also, if you do as in the TSC 5110 and sample the signal there, you will
measure over the complete time and will be able to cancel out the phase
differances. The note about the transfer oscillator should have a low phase
noise too is to keep the amplitudes down.

> But the measurement itself gets more complicated this way because for
> the comparison of the oscillators we do not only the have to take the
> TIC's measurement into account but also the phase shift that we now have
> applied artificially which is not measured easily with the same
> precision. If you see a TIC being part of a DMDT system WITHOUT phase
> shifting elements then be prepared that the author has not the definite
> in-depth knowledge about his topic. However, if DMTD is THAT standard
> and common in horology one would expect this property of the DMTD being
> discussed in hundreds of scientific articles available in the internet.

These things where banged out in the labs before Internet had hit the curb
big time.

> But it is not. I suggest you search yourself a bit for that! If you are
> lucky then you may come across the very ONE SINGLE source of information
> about this fact that I have been able to find at
> 
> http://tmo.jpl.nasa.gov/progress_report/42-143/143K.pdf

While this is indeed a good publication, it is not the single publication out
there. You should look at NIST TN1337 and in particular TN190 "Phase Noise and
AM Noise Measurements in the Frequency Domain" by Lance, Seal and Labaar and
TN241 "Performance of an automated high accuracy phase measurement system" by
Stein, Glaze, Levine, Gray, Hillard and Howe.

In addition, the HP AN358-12 is a quite practical approach to it rather than
theoretical.

> The fact that this topic is covered by only one publication is why I
> think real experience with the DMTD method is the domain of a very few
> experts. Greenhall is one of the really big guns in horology and has
> published a lot of intelligent stuff about it. He clearly shows in this
> publication that a time interval counter is not sufficient for the DMDT
> method without artificial phase shifting. Instead two independent
> time-tag counters are necessary and a bunch of mathematics that most of
> these DMDT people do not even have an idea about. 

While I think you exaggerate a little, I agree that it is now a very wellspread
technique compared to others (like interpolating frequency counters). There is
a lack of sources that go into the deeper issues (publicly on the net).

> Second Pitfall of DMTD: Decreasing slope to noise ratio counteracts the
> magnifying effect of down mixing
> 
> In a textbook I once read the remarkable sentence: "When it comes to
> precise timing measurements the slope to noise ratio and not the signal
> to noise ratio is the true figure of merit" Remarkable because I found
> it in a textbook about instrumentation in nuclear physics. And
> remarkable because it mentions the "slope to noise ratio" which I had
> never heard about before. 

This is standard counter trigger noise issues. Just look in a HP manual or
HP AN you find it perfectly well explained. The trigger noise is the noise
divided by the slope. The slope is proportional to the amplitude of the signal
and the frequency of the signal. Infact, the slew-rate is

S = 2*pi*A*f

where A is the amplitude of the sine signal (sqrt(2) times the RMS value) and
f is the frequency in Hz.

The timing error becomes:

t = N/S

where N is the noise power.

You can fight this two ways:

* Reduce the noise - usually acheived by filtering and choice of low-noise
  components
* Gain

One should however be carefull about limiters. They bite you if you don't
think about it.

> As it turns out there IS a clever way to handle this situation at least
> up to the principal limits. Again there ARE a very few specialists who
> know about this problem very well but they are rare to find animals. If
> you ever want to build a DMTD system by yourself then be sure that you
> have read 
> 
> Dick / Kuhnle / Sydnor: "Zero-crossing detector with sub microsecond
> jitter and crosstalk" 
> 
> before! Some people will tell you that you need "low noise zero crossing
> detectors" but only these guys will explain you in full detail how to
> build them! This text is a bit difficult to get from the net. If you do
> not manage to download it please ask me for help. Basically the authors
> use a cascaded chain of low pass filters and combinations of
> non-limiting and limiting amplifiers to increase the slope of the signal
> in several steps while at the same time they try to filter out as much
> noise as possible. As you can see from the title anything better than 1
> microsecond jitter (!) is considered state of the art.

While I have figured it out myself, it would be nice to see what these guys
have come up with, so please send it if you are able to. It sounds very much
like what I have proposed to do to some fellow colleagues. I would not use
limiting amplifiers until the very end, the back-end to the TIC.

I agree fully with this pitfall of DMTD, and the filter/amplification is the
engineering natural path out of this trouble.

It is also covered HP AN358-12 (in a practically oriented description).

> Third Pitfall of DMTD: Phase corruption due to mutual crosstalk

This is indeed another issue. In particular, the highly increased gain of the
coincidens events may affect the voltage of the (late) signal such that it
triggers early, regardless of the injection being between the incomming
signals, tigger of one signal to the input of the other or trigger to trigger
signals. Especially trigger-to-input signal insertion is serious. Infact, part
of this can be cured by not matching the signals as tight as possible. You will
infact find that this is commonplace in may TI cases. Trigger events being very
close to each other is indeed a plauge even today. 

> I would like to hear from you if you ever experienced one of the
> pitfalls yourself. Especially the owners of equipment like the TSC 5110
> are asked to explain if they ever noticed crosstalk effects. Or do these
> instruments perhaps involve some tricks that I am not aware of? 
> 
> One of the ideas I have is: If it is already clear that the zero
> crossings of OUT and reference channel ARE apart from each other why do
> I need the second channel WHILE I measure the zero crossing of the first
> channel? Perhaps equipment like the TSC 5110 uses a very high isolation
> switch to keep the second signal completely out of the box while it
> measures the zero crossing of the first channel? And then re-computes
> them to the same epoch as described in the Greenhall paper?

The TSC 5110 is a different animal altogether. You may infact internally
compensate for cross-correlations. The most dangerous intermodulation path
(trigger-to-input/gainstage) isn't there. It is a different set of problems
in there, even if it is very similar indeed.

I could scan the AN358-12 if anyone need it. I also beleive have I have some
other document lying around related to it.

Cheers,
Magnus