[time-nuts] Notes on tight-PLL performance versus TSC 5120A

[Bruce Griffiths]

Steve Rooke wrote:
> On 4 June 2010 08:32, Charles P. Steinmetz
> <charles_steinmetz at lavabit.com>  wrote:
>    
>> If I may be allowed to summarize, it appears that Warren and Bruce agree
>> that integration is necessary to produce true ADEV results.  Warren asserts
>> that the low-pass filtering his method uses is "close enough" to integration
>> to provide a useful approximation to ADEV, while Bruce disagrees.  So, the
>> remaining points of contention seem to be:
>>
>> 1.  How close can a LPF implementation come to integration in ADEV
>> calculations, and
>>      
> Well, Warren uses two stages of integration. There has already been
> talk of the simple R/C filter in the feedback loop. Unless my
> education in electronics was completely wrong, the series R/C circuit
> forms a simple LPF and is an integrator (assuming that the resistor is
> in series with the input and the capacitor is in parallel with the
> output). See http://en.wikipedia.org/wiki/Integrator_circuit,
> http://en.wikipedia.org/wiki/RC_filter. Sorry these are not academic
> papers but if you spot something wrong please feel free to edit them
> appropriately. This first stage of integration is set at a much wider
> frequency than tau0 and forms the PLL-loop filter allowing it to track
> the FAST changes of a noisy unknown oscillator. That last bit is very
> important and something some previous attempts at this method failed
> to resolve.
>    
A cascaded low pass filter and and a finite time interval integrator are 
required.
A single RC LP filter can't approximate this.
Its either a low pass filter or a crude approximation to an integrator 
not both.

> Now there is a noisy control voltage on the reference oscillator and
> it is absolutely no good trying to make a single measurement at tau0
> because the settling time of the filter has not been constrained to it
> so it will not give an integrated mean value. This where the second
> stage of integration comes in which is the oversampling which takes a
> number of readings during tau0 (please correct me if I have the
> terminology wrong here) which are then averaged to give a mean,
> integrated, value of the control voltage for tau0.
>    
Speculative nonsense sampling by itself integrates nothing unless one 
uses an integrator to do the sampling.
Even when the finite bandwidth of the sampler is taken into account the 
equivalent "averaging time" will be too short and not under user control.
However the samples (if the sampling rate is sufficiently large) contain 
sufficient information for the required finite time integrator output 
values (or frequency averages) to be calculated.
A simple rectangular integration approximation may not be sufficient in 
all cases.

The sampling process actually tends to whiten the sampled phase noise 
spectrum.
The amount of false white phase noise contributed by the sampling 
decreases as the sampling rate increases.
A simple RC low pass filter may not be a a particularly good choice in 
this regard.

> So why two stages, look closely above, until the idea of oversampling
> was tried, the PLL-loop filter had to have a settling time, IE. cutoff
> frequency, equal to tau0 so that the measurement at tau0 reflected the
> mean, average, integrated, value for that tau0 period. But if a filter
> with that sort of cutoff is used then the reference oscillator is not
> able to track noise on the unknown oscillator at all and it would give
> results for things like flicker noise, random walk, etc, which were
> lower than the actual values. Now have a look at the top end of John's
> graphs where there is a divergence.
>    
The divergence at the top end of the graphs should be treated with 
extreme caution one needs to know the size of the associated error bars 
to be able to make statistically meaningful conclusions. In general the 
error bars tend to be large in this region.

>    
>> 2.  How close to true ADEV is "good enough"?
>>      
> well, considering we have integrated frequency measurements at tau0
> intervals, there is little wonder that it correlates closely to ADEV
> because that's exactly what it is.
>
>    
This cannot be so for each and every signal source if the weighting 
function ("equivalent filter") doesn't closely match that used in the 
definition of AVAR.
Without the integration/averaging the "equivalent filter" closely match 
the required filter at all frequencies.

>> I humbly submit that trading insults has become too dreary for words, and
>> that neither Warren nor Bruce will ever convince the other on the latter
>> point.
>>      
> Well, I've been on this list long enough to know that Bruce will
> always resort to that sort of behaviour when he is boxed into a corner
> or cannot get his point of view accepted. Anyone who speaks up against
> him is usually put in their place. This saga has come about because
> someone dared to challenge him so we have been subjected to his
> tantrums.
>
>    
The saga originated because of the wildly inaccurate claims and very 
woolly explanation as to what signal processing was used.
A few equations and a circuit diagram or 2 would have made it perfectly 
clear months ago what methods were used.
Vague statements on the lines of: "any person competent in the field 
should be able to figure it out for themselves" are not useful if the 
originator has made some fundamentally incorrect assumptions.

>> I thus humbly suggest (nay, plead) that the discussion be re-focused on the
>> two points above in a "just the facts, ma'am" manner.  One can certainly
>> characterize mathematically the differences between integration and LP
>> filtering, and predict the differential effect of various LPF
>> implementations given various statistical noise distributions.  If one is
>> willing to agree that certain models of noise distributions characterize
>> reasonably accurately the performance of the oscillators that interest us,
>> one can calculate the expected magnitudes of the departures from true ADEV
>> exhibited by the LPF method.  Each person can then conclude for him- or
>> herself whether this is "good enough" for his or her purposes.  Indeed,
>> careful analysis of this sort should assist in minimizing the departures by
>> suggesting optimal LPF implementations.
>>      
> Ask yourself what is the difference between a simple R/C LPF and
> integration, what is integration in fact. What is the difference
> between an electronic LPF and an integrator designed in electronics. I
> think we are getting hung up between the mathematical term integration
> and the electrical term. Although I should say that of course ADEV is
> a mathematical derivation taking frequency data and finding the
> averages of various positional averages. Whether the frequency data is
> provided as the inverse of the measured period of the unknown
> oscillator or the voltage reading of a fancy VCO (ref osc), makes no
> difference, providing that each data point is accurately represented.
>
> In terms of "optimal LPF implementations" as I see mentioned here,
> this is the trap that previous people trying to use the tight-PLL
> method have fallen into. An "optimal" LPF will give a very accurate
> average value of the frequency for each tau0 point but only at the
> fundamental. It will get the effects of noise wrong unless its
> bandwidth is sufficient to encompass that but then the LPF will not be
> "optimal" and the resulting frequency data will be incorrect.
>
>    
The above statement misses the point entirely and illustrates a 
fundamental misconception of what the measurement of ADEV and other 
frequency stability metrics actually require.
AVAR (tau) can be viewed as measuring the output noise (ordinary 
variance) of a phase noise filter with a particular shape and bandwidth 
for the chosen value of Tau.
Each Tau value requires a different filter.

The equivalent filter of any method purporting to measure ADEV needs to 
match that required by the definition of ADEV for all frequencies in the 
filter pass band for which the source phase noise is significant.
This requirement is made more difficult to meet by the fact that the 
equivalent filter bandwidth and maxima locations change for each end 
every value chosen for Tau.

> Best regards,
> Steve
>
>    
>> Best regards,
>>
>> Charles
>>      
Bruce