[time-nuts] Stepping up the output of an OCXO

Dr Bruce Griffiths bruce.griffiths at xtra.co.nz
Sat Feb 3 05:56:20 EST 2007

Ulrich, Don
Ulrich Bangert wrote:
> Don,
>> What sort of SNR is necessary to prevent an uncertaincy 
>> of 1part in 10^13?
110dB or more for Tau = 1sec.
> I see, you are a non believer! But Bruce was talking about comparing
> zero crossings of signals at a few (!) Hz, which needs indeed tremendous
> amounts of SNR to get to an uncertainity of 1 part in 10^13! The reason
> is that for precice timing not the signal-to-noise-ratio is the figure
> of merit but the slope-to-noise-ratio. 
> With a 10 MHz signal and a 1 Hz signal having the same SNR the 1 Hz
> signal will be inferior 10E7 in terms of slope-to-noise-ratio which
> gives raise to the necessity of an 140 dB improved SNR on 1 Hz against
> the 10 MHz signal if you want to measure the zero crossings with the
> SAME incertainity as on the 10 MHz signal.
> If you are still critical about it: A zero crossing detector for a 1 Hz
> signal giving a uncertainity of better than 1E-6 (some universes  apart
> from your 10E-13) has been celebrated as an first grade scientifical
> breakthrough some years ago.   
> Best regards
> Ulrich Bangert
> P.S.
> Of course the above applies only to sinusoidal signal forms where the
> slope of the zero crossings depends on the signal's frequency. So one
> might pretend he is going to measure the zero crossings of DIGITAL
> signals of a few Hz which may be indeed easy to measure due to their
> high slew rates. The people that argument this way must ask themselves
> how to make a digital signal from a sine signal which is pretty much the
> same problem as measuring the zero crossing with high precision.  

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