[time-nuts] What is the best counter for a Time Nuts?

Magnus Danielson magnus at rubidium.dyndns.org
Sat Oct 11 20:17:08 UTC 2008


Mike,

Mike Monett wrote:
>   The Allen deviation is used to describe the performance of  a stable
>   clock. Measuring the performance of a good clock requires  a counter
>   with resolution  down  to picosecond levels. As  Dr  Griffith points
>   out, some  modern counters may have internal signal  processing that
>   makes them unsuitable for this task.

Hold on!

What modern counters do is to use various means to improve on frequency 
and period measures. This makes the frequency and period measures 
unsuitable for futher processing as well as evaluation of expected 
performance when doing measures for Allan Deviation. However, what we do 
is usually not that measure, we to Time Interval measures for individual 
trigger points. When doing those measures these smoothing methods cannot 
be utilized. Then you are running on the bare-bone hardware performance 
with only the normal (traditional) translation skews.

I specifically cautioned Ulrich from making Allan Deviation performance 
estimate from the frequency performence for this reason. The smoothing 
will make such rule-of-thumb comparisions much harder.

>   Another thread  discussed using a mixer to  generate  the difference
>   frequency between  two oscillators, then measuring the  stability of
>   the resulting beat note:
> 
>   http://www.febo.com/pipermail/time-nuts/2005-July/019006.html
> 
>   The basic  principle  is sound. If the oscillators  were  running at
>   10MHz, and  the  frequency difference was 1 Hz, then  the  beat note
>   would be 1 Hz.
> 
>   This represents  one  part in 10 million, or  1e-7  of  the original
>   frequency. If  the  beat   note   is   measured  with  1 microsecond
>   resolution, the  overall resolution is 1e-7 / 1e-6 = 1e-13.  This is
>   beyond the capability of most commercial counters.
> 
>   The difficulty  with this approach is the output of a mixer is  at a
>   fairly low  level, perhaps 50 millivolts or so. The  frequency would
>   also be very low, perhaps 1 Hz. This means the counter would have to
>   trigger accurately on a very slow-rising, low amplitude signal.

This is not the actual problem. The actual problem is the slew rate of 
the signal. Even if the amplitude was several volts peak-to-peak the 
slew rate of the beat note is the main problem as the wideband noise of 
at the output added with the wideband noise of the counter input causes 
a random additive voltage modulation which can pre/post trigger around 
the ideal position with a RMS value of t_jitter = N_total / SR (this is 
a traditional trigger jitter formula).

The gain stages / slew rate amplifiers that Bruce and I have discussed 
contributes a significant gain which significantly goes beyond what a 
can come out of a mixer. Signal is clipped and filtered in order to 
improve signal to noise properties such that a minimal of noise is 
amplified while the slew rate is raised significantly.

>   This is  a very difficult measurement problem. The accuracy  will be
>   degraded by  noise,  such  as the 60Hz  AC  line  frequency  and its
>   harmonics, switching noise from the pc power supplies  and monitors,
>   radiation from nearby fluorescent lighting, plus thermal  noise from
>   the mixer and input stage of the amplifiers.

Not too hard really. The thing which makes it complex is that good 
signal to noise is needed both at the carrier frequency and beat 
frequency. Some knowledge of suitable measures should give adequate 
measures.

>   This low-level noise is very difficult to eliminate, especially when
>   coax cables are needed to transfer the desired signal from one place
>   to another.  The result is the measurement system is not as  good as
>   it could be.

Is it? Fighting ground loops to handle H fields is no big magic. Using 
mixers which ports is galvanically isolated helps. E fields is easier to 
handle at lower frequencies.

For the output port, the difference frequency needs the signal to noise 
properties. Traditional diffrential signal handling deals with both E 
and H field issues to such a level that other sources will dominate.

It should also be pointed out that carefull adjustment of both input 
port levels and the loading on the output port will have impact on 
performance as recorded in literature.

>   There is a solution to this problem. Another kind of mixer  called a
>   "digital mixer"  is ideally suited for this application.  It  uses a
>   d-flop, with one signal going to the clock pin, and one going to the
>   "D" input.  The resulting signal on the "Q' output is  the frequency
>   difference between the two signals.
> 
>   The output signal is a full logic level swing, perhaps 5 Volts, with
>   a risetime  of a couple of nanoseconds. This is an  ideal  signal to
>   pass on  a terminated coax cable to the counter.  The  schematic and
>   waveforms are shown in the attached GIF.

You will not solve the requirements for good dynamics. The digital input 
is highly non-linear and thus behaves like a mixer so due care is still 
needed, both at the beat frequency and carrier frequency. The benefit is 
the high slew rate.

It behaves like a sample and hold system, but with the quantization 
occuring before the sample action rather than after, which would could 
debated which is best, but the sampling action is certainly the mixing 
action causing problems, regardless of methods it is realized through.

Regardless of method, to achieve performance, you would need to maintain 
a certain degree of signal hygene to achieve the inteded or possible 
limit of the system.

>   The output  of  the  first d-flop is passed to  a  second  d-flop to
>   eliminate glitches due to metastability in the first stage. This can
>   occur when  the signal on the "D" input is exactly on  the switching
>   threshold when the clock transition occurs. The resulting glitch can
>   severely disrupt the following logic stages.
> 
>   In practice, it might be difficult to offset two  stable oscillators
>   by 1  Hz.  In this case, the frequencies can be  multiplied  to some
>   higher value. For example, the frequencies could be multiplied  by a
>   factor of 10 to 100MHz, and offset by 1 Hz.
> 
>   There may be some jitter in the leading edge of the beat  note since
>   the d-flop  may  or may not catch the transition as  it  crosses the
>   threshold on  the  "D" input. Instead of the  standard  +/-  1 clock
>   ambiguity in  digital circuits, the output could  be  several clocks
>   late. However,  if the counter had a resolution  of  100 nanoseconds
>   (10MHz clock),  the  extra  delay  is  much  less  than  the counter
>   resolution and should have no effect.

No, they add up unless you use the CLK signal for couting the beat 
frequency, in which case this is really the input trigger of a 
non-interpolating counter. If you use different clocks the beating 
pattern between them will introduce the additional noise signal.

>   The overall resolution in this example would be 1e-8 / 1e-7 = 1e-15.
> 
>   This is  achieved in one second, which is an impossible  task  for a
>   counter. This means the Allen deviation can be measured  much faster
>   than before, and with much higher accuracy.
> 
>   A simple LTspice analysis is included in the attached ZIP.

Where is the added noise? What D flip flops do you use? What is the ref 
inverter and what properties does it have?

It's an analogue world after all, so we need to evaluate it as an 
analogue system.

Cheers,
Magnus



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