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

[Ulrich Bangert]

Hi folks,

Let me say sorry in advance for this lengthy posting but I did not
manage to make it shorter. 

If one reads the common literature on oscillator characterization then
he quickly finds out that one of the standard methods for oscillator
comparisons is the "Dual mixer time difference" method, or short: DMTD.
While most of you readers may know the principle of DMTD very well
please allow me to describe the method in a few words for those who are
not so familiar with it:

In the DMTD the signal of the OUT (Oscillator Under Test) as well as the
signal of a reference oscillator are mixed down to the low frequency
domain (say 1 to some ten Hz) by means of two double balanced mixers and
a third oscillator which I will call the transfer oscillator. The down
mixed low frequency signals have an interesting property. 

Let us assume the OUT signal changes its phase on its working frequency
of 10 MHz by an amount of 1 ps (expressed in absolute time) then this
absolute change can be expressed as a 1 ps / 100 ns = 1E-5 change
relative to the period length of 100 ns. Please note that a 1 ps change
in phase is orders of magnitude smaller than we are able to measure with
direct methods. 

The down mixed signal of the OUT experiences a relative phase shift of
1E-5 in this case as well because it is a fundamental property of mixing
to preserve phase/frequency information of the input signals to be mixed
(That is the reason why phase and frequency modulation can be used with
superhet receivers). 

Now comes the clue: While the relative phase shift stays the same, the
phase shift expressed in absolute time is MUCH bigger now because the
relative phase shift value now applies to a much smaller frequency and
therefore to a much bigger period length! Say we have a down mixed
frequency of 1Hz then the 1E-5 relative phase shift is 1E-5 * 1 s = 10
microseconds absolute. Wow! We have amplified the effect from the domain
of un-measurability to something that can be measured with a garden
variety counter.  

Who has followed the explanation closely up to now might argue that the
down mixed signal preserves the phase/frequency information of the OUT
as well as that of the transfer oscillator so that any phase/frequency
change that we observe on the down mixed signal may relate to the OUT or
the transfer oscillator or both of them. This argument is correct!  And
that is why we have the second mixer which is used to down mix the
reference oscillator's signal with the transfer oscillator. 

Assume the transfer oscillator experiences a phase shift. Then this
phase shift is the SAME in both down mixed signals. If we make a time
difference measurement between the two down mixed signals any phase
shift of the transfer oscillator is believed to cancel out completely.
This is what the DMTD is all about and usually in schematic diagrams
explaining the DMTD we find two zero crossing detectors for the down
mixed signals followed by a TIC (time interval counter) measuring the
time between a zero crossing of one signal to the zero crossing of the
second signal. 

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.

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.

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. 

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.
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

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. 

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. 

For a better understanding of what's coming next I suggest you download
 
http://www.ulrich-bangert.de/AMSAT-Journal.pdf

from my homepage. This article is in German but you are not expected to
read it. However, it contains some graphics which I would like to refer
to.

Consider the case that we need to make a timing measurement on a
sinusoidal signal, for example to determine its period length. While he
may not be able to explain completely why, every technician would decide
to use the zero crossings of the signal as the timing reference. That
is: He would build a zero crossing detector and measure the time between
two zero crossings from negative to positive values. 

Had we a noise-free signal available then there were no problem at all
because the noise-free signal crosses the zero line at a sharp defined
point in time. However, noise-free signals are an idealization not given
with real-world signals. There is always a certain amount of noise,
sometimes more, sometimes less, a fact that documents itself in the well
known signal to noise figure. 

In "Abbildung 6" on page 12 I have drawn a noisy sinusoidal signal
crossing the zero line. Please note that I have chosen a real bad signal
to noise figure but that has just been done to show you the principle of
this effect. The effect itself I am explaining now takes place at every
signal to noise figure even at very good ones.

Because the amplitude of the sinusoidal signal contains amplitude noise
it becomes immediately clear that the signal now has a certain chance to
cross the zero line also at times before the cross point of the noise
free signal as well as behind that. It may even cross the zero line
several times.