Hi Chris, have you been away, or have I just been more than typically oblivious of my surroundings?
>It's commonplace to obtain resolutions much more precise than the oscillator period simply by measuring the phase... <
Okay, I apologise for the expression "significantly more precise”. However you will note that the theme of that point was: "resolution". It remains true that the higher the frequency (shorter the wavelength), the greater the practically attainable resolution, no?
By way of analogy it has long been something of a cliché that one cannot achieve greater resolution with a light microscope than the wavelength of the light permits. Usually naive biologists take that as meaning that you cannot resolve anything smaller than the wavelength, although a half or even quarter wave would be more appropriate as an estimate for such a purpose. However, recent techniques based on quite venerable principles have managed far greater resolution. Mind you, one still does not ultimately escape the relevance of the wavelength and it does require different hardware!
> Stability: <
>The instability which tends to cancel out over time is called phase noise which is ... not really relevant in timekeeping applications. More relevant to timekeeping are temperature coefficient and ageing which do not cancel out over time.<
Those are rather curious remarks, Chris. You do not make it clear what the temperature coefficient and ageing have to do with the relevance of stability in timekeeping, whether they are more relevant than stability or not. Try this as an experiment: write the simplest, most naïve timer program, in Microsoft BASIC if you like, simply including a counting loop that prints out its estimate of elapsed time every few seconds. It is trivial to get something close enough for jazz. Now modify the program to include a small, more or less random, reasonably unbiased, perturbation in the count. You will find (assuming your programming is as ineffably brilliant as I am sure it must be) that the resulting inaccuracy of your programmed timer is surprisingly large to anyone expecting that the average error will cancel out, but surprisingly small to anyone who expects the error to be simply proportional to the average deviation. In fact, I am sure that you must recognise that the situation incorporates a variation of the drunkards walk, so that it is reasonable to expect a deviation proportional to the square root of the time. This will remain true, even if other factors concerning instability are reduced notionally to zero. I cannot see why you reason that (in)stability is not really relevant. Could you please elaborate?
>Quote "3. The higher the frequency, the smaller the possible range of error per cycle, and the greater the number of cycles in any measurement, so the greater the cancelling out of errors."
>I think this again refers to phase noise which is not really relevant to timekeeping...<
Well Chris, I was not deliberately referring to phase noise in general, unless you can relate that to the notionally symmetrical kind of instability I was referring to and demonstrate the irrelevance of the drunkards walk. I unhesitatingly and ungrudgingly bow to your patent theoretical and hands-on knowledge of the field, and of the factors that are of practical importance, but could you please clarify how these items negate the aspects that I did address, and if possible respond also to the original question of the apparent association of high frequency with high accuracy and high resolution timing?
>A high Q will proportionately reduce the effects of noise, temperature, ageing, etc. on the stability of an oscillator. Watch crystals can have Q values as high as 100,000 and are engineered to have minimal temperature coefficient at the average wrist watch temperature of about 25 degrees C. <
I liked the bit about the Q factor, and was quite startled by the figures you gave for watch crystals. Do you refer to the crystal itself, or the crystal in its circuit as the power decays?
Thanks in anticipation,
Jon
