[time-nuts] TIC Characterization

[Club-Internet Clemgill]

Hi, 
Looking to testing my HP53132A in TIC mode. 
I considered the Time Interval measurement technique: 
The start channel is connected to a 1 PPS signal, and to the stop channel though a coax cable (constant delay line).
I found some references on the web, but no one with the associated maths.
So I tried the following :

1/ AVAR  =  (1/2*Tau^2) * < [(Xi+2 - Xi+1) - (Xi+1 - Xi)]^2 >
with (Xi+1 - Xi) = phase difference = time interval 

2/ Phase difference = To + Ti 
where To is the constant delay between start and stop (coax line)
and Ti is the counter's resolution at time i

3/ Assuming that Ti is a Central Gaussian distribution then:
mean = < Ti > = 0 and variance = < Ti ^2> = SigmaTIC^2

4/ [(Xi+2 - Xi+1) - (Xi+1 - Xi)]^2 = [(To + Ti+1) - (To + Ti)]^2 = (Ti+1 - Ti)^2 
=  (Ti+1)^2 + (Ti)^2 - 2(Ti+1 * Ti)

5/ <(Ti+1)^2> #  < (Ti)^2> for large samples and 
<2(Ti+1 * Ti)> = 0 because Ti+1 and Ti are independent
Then AVAR =  (1/2Tau^2) * 2< (Ti)^2>  = (1/Tau^2) * SigmaTIC^2

6/ Hence ADEV = SigmaTIC / Tau

So ADEV (log log) is a straight line with -1 slope
And ADEV(Tau=1) provides the standard deviation = SigmaTIC  of the Time Interval Counter's resolution 

Is this right ? 
Thanks to point me at related articles or web pages if you know any.

Gilles.