[time-nuts] Advantages & Disadvantages of the TPLL Method

[Magnus Danielson]

On 06/19/2010 12:49 AM, WarrenS wrote:
> Say you have a nice logic gate with 1 ns delay
> If you make it all nice and clean, and repeatable such as constant PS,
> rise time etc.
> Then one can get repeatable results say 100 times better from cycle to
> cycle in the short term.
> so down to 10ps repeatable.
> Now make things even more clean with no variations and assuming random
> noise.
> Now if one is doing this at 10 MHz and only cares about the average over
> 0.1 sec (10 Hz)
> One can average 1,000,000 readings of the 10 ps jitter
> If they are truly random, that can give you a 1e-3 improvement (square
> root of number of samples averaged)
> so now down to 10 fs of average jitter at 10 Hz for a 10 MHZ gate
> starting with a 1ns initial delay.

The square root improvement assumes white noise, and will work when 
white noise dominates. A logical gate or any other amplifier will also 
have flicker noise, which doesn't average out like that. The meaningful 
length of averaging thus depends on the cut-off frequency between white 
and flicker noise. To analyse it, Allan variance and friends needs to be 
applied. Thus, only for short-term stability may straight averaging work 
for estimation.

Cheers,
Magnus