[time-nuts] LF power supply noise
Mike Monett
xde-l2g3 at myamail.com
Sun Jun 21 14:27:54 EDT 2009
> Mike,
[...]
>> One of the reasons I was attracted to the 543310A was it could
>> display 14 digits of frequency in one second. Sine then, I have
>> figured a way to resolve 16 digits in one second, so that part of
>> the spec is no longer interesting.
> As was described by J. J. Snyder in "An Ultra-High Resolution
> Frequency Meter" in the FCS 1981 (as available from IEEE UFFC) I
> assume, basically using the fact that adding more measurements in
> a dense time raises the degrees of freedom and allows for quicker
> interpolation.
> Modern counters like HP 53131, HP 53132 as well as Pendulum CNT-90
> or Fluke 6690 uses similar approaches.
I can't find any copies that are not payware, but it is unlikely
there is any connection between the methods.
Conventional averaging methods are limited by the exponential rise
in number of samples that are required to improve the SNR. The
measurement ends up taking too long, or the system drifts which
renders the mesurement useless.
This provides an effective barrier to the amount of improvement
possible in SNR, and the available precision that is possible with
conventional technology.
Binary Sampling works a completely different way. It ignores the
amplitude of the sample, and only records the direction of the
error.
According to the Central Limit Theorem, the mean of Gaussian noise
is zero. This forces the Binary Sampler to converge on the true
value of the signal, and ignore the error caused by the amplitude of
the sample.
This is a really big thing. The problem of using averaging to
improve sigma has existed for over 109 years. And nobody has been
able to solve it up till now.
With a heterodyne sampling system, or conventional mixer technology,
the sample delta is the offset frequency divided by the square of
the reference frequency:
Delta = Offset / Ref * Ref
With a delta of 1Hz and reference of 1 MHz, the sample delta is
1 / (1e6)^2 = 1 / 1e12,
or 1 picosecond.
Since the Binary Sampler discards noise, the result is 1 picosecond
resolution in 1 second.
I show this on my web site. The schematic for the measurement is
shown in Fig. 1 at
http://pstca.com/sampler/design.htm
A simple boxcar smoother is used to integrate the samples. The
result with different smoothing values is shown at
http://pstca.com/sampler/smooth.htm
A system with 18.38 ps rms jitter would require averaging 338
waveforms to obtain 1ps rms jitter. With conventional sampling
technology, this would require 169 seconds, and the system would
probably drift during the measurement, rendering the measurement
invalid.
So it is not possible to obtain this amount of improvement in this
system, and the measurement is impossible.
The Binary Sampler gives 1ps resolution in 1 second. This is shown
in Fig. 4 at
http://pstca.com/sampler/binsamp.htm
No other system can achieve this performance. And anyone with
sufficient skill can duplicate this result at home.
Extending this to higher frequency, it should be possible to obtain
a 1Hz offset at 100MHz with 1 uHz resolution. This gives
1 / (1e8)^2 = 1e-16 resolution in 1 second.
I do not think any existing equipment from HP, Fluke, or Pendulum or
anyone else can come close to matching this level of performance.
Also, existing technology must deal with noise and the averaging
problem. This eliminates much of the performance boundaries from
consideration.
As a result, conventional technology cannot reach 1e-16 in one
second.
> As being reported, such mechanisms does not fair well with ADEV
> calculations, and especially the overlapping variants of ADEV and
> den MDEV and TDEV which was inspired by that particular article,
> so using it twice forms unwanted filters.
My approach delivers continuous samples. No missing or extra bits.
>> The 543310A can do a single-shot time measurement with a
>> resolution of 200ps, and gets down to 1ps with averaging. The
>> HP5370B does 20ps single-shot, and will resolve 100fs with
>> averaging. But I have figured a way to measure 2ps single-shot,
>> and a bit better with averaging. So that part of the spec is not
>> so interesting any more.
> I assume you really mean HP 53310A and not HP 543310A, even if
> your typing is consistent. The listed numbers is when weigthing in
> how various jitter sources combine upon averaging and should be
> considered a bit conservative.
> By all means describe what you mean by 2 ps single-shot
> resolution.
That will cure me of trying to type complex numbers when copy and
paste works so much better. But now I have to try and figure out
what your "weigthing" really means:)
The 2ps single shot is dead straight conventional time-to-time
conversion. Nothing new there, except I think I have some new tricks
on stabilizing the circuits against drift, and providing a much
faster response to the zero-crossing at the end of the timing
interval. All these reduce the noise in the sampling process.
But the real trick is applying the Binary Sampling technique to the
result. That allows a huge reduction in the noise from the sampling
process, and converges rapidly on a much more precise solution.
>> The 543310A will display the phase and frequency changes in a PLL
>> step response. But you can get the frequency response just by
>> looking at the VCO DC error voltage. And if you look at the
>> voltage across the bottom capacitor in a type 3 loop, you get the
>> phase response. Here's a picture:
>> |
>> --- C1
>> ---
>> |
>> |----------O < - Phase Error
>> | |
>> --- C2 \
>> --- / R1
>> | \
>> | |
>> --- ---
>> - -
> You should recall that when HP built their line of analyzers, they
> where thinking "what can we make this cool ZDT core do?" rather
> than attempting to build the best analyzer for all responsens.
I have a slightly different impression. I sold a lot of equipment to
Boisie, Idaho, and I used to make a lot of trips there in my Piper
Malibu, which was about the only realistic way of getting there from
San Jose:
http://www.jetphotos.net/viewphoto.php?id=5874208&nseq=0
There was a lot of political infighting at Boisie involved in
development of new equipment. The winner pretty much had whatever
say he wanted in the direction, and he ignored the input from other
competent engineers.
As a result, the equipment was limited by that individual's scope
and abilities. The result is much of HP's equipment suffered.
One example is the 20ps single-shot resolution of the HP 5370B has
never been matched by any later equipment, as far as I know. A few
engineers at Boisie complained bitterly about the loss.
>> So about the only thing left of interest is histograms of the
>> jitter. Unfortunately, the 543310A cannot store enough samples to
>> really make an interesting graph. What I would like to be able to
>> do is similar to an invention I made for the disk industry long
>> ago, called Phase Margin Analysis. There is a brief description
>> on my web page at
>> http://pstca.com/patents.htm#phasemargin
> Somewhere in my map of apps there is a HP appnote for doing the
> same, to discs, intended for disc industry, back in the days.
That may very well be a result of my invention, which occurred in
1970, was published in 1979, and was copied by IBM in the 1990's.
But I have all the HP appnotes for disk. I don't recall any of them
describing what I show above. Can you provide more information?
[...]
> The 53310A was a nice convenient tool at its time, but it's
> performance isn't up to spec with modern times. It seems like HP
> didn't pursue it into much deeper levels after its VXI
> instruments, where as others went deeper.
I'm not sure about this, but I don't think there is any later HP
equipment that can approach what the 53310A does.
But I can now match or beat it by orders of magnitude. This is
sufficient for our current needs, but I will always be working on
newer technology to break through the limits we now have.
> Cheers,
> Magnus
Thanks,
Mike
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