Formulas for transforming the Alan deviation (AVAR)

[martis007]

transformation

How can I transform the Alan deviation (AVAR) into one-sided spectral density of the fractional frequency fluctuations Sy(f) and the sample time tau into Fourier frequency? I need exact formulas to do this .

 

[Debeli]

Re: transformation

White phase ((a*t*fo*2.565)^2)/fh

Flicker phase ((a*t*fo*2.565)^2)*(f^(-1))/(2.184+ln(fh*t)

White frequency (a*t^0.5*fo)^2*f^(-2)

Flicker frequency 0.361*(a*fo)^2*f^(-3)

Random walk frequency (0.276*a*t^(-0.5)*fo)^2*f^(-4)

a - Allan variance
t - measurement time
fo - carrier frequency
fh - measurement system bandwidth

Source: "Microwave and Wireless Synthesizers" U. Rohde pp 84.

Hope that's it

D.

 

[sergio mariotti]

transformation

I'm not so sure that a "transormation" from Allan Variance to SSB Phase Noise would be everytime possible.

For my modest opinion a transormation is possible when the sigma vs tau curve is "falling" or is "flat" (looking the curce from left to right).