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Design >> RF Design >> Jitter from phas noise...who knows the answer
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Message started by Erez_Sarig on Oct 31^st, 2007, 7:05am

Title: Jitter from phas noise...who knows the answer
Post by Erez_Sarig on Oct 31^st, 2007, 7:05am

Hello,
Here is a hard question.
IF you want to compute a Jc (Cycle Jitter) from Phase noise there are 2 ways but results are different, which is the right one and why?
the ways are:

1) Jc^2=(1/(pi*fc)^2)*∫S(f)*sin²(pif/fc)df
2) Jc =(1/(2*pi*fc)))*√(∫(S(f)df)

S(f) is the PSD of phase noise

So.... who is the one to know the answer ?
Erez

Title: Re: Jitter from phas noise...who knows the answer
Post by Stefan on Oct 31^st, 2007, 8:12am

to my knowledge it can be calculated like this (assuming white noise sources only!) :

The PSD of the jitter

Stau(f) = Sphi(f) * sin^2(pi f/f0)/(pi f0)^2

For white noise sources Sphi(f) equals 2*Sw/(f)^2

Then you can use the Wiener-Khinchime Theorem to calculate the mean square value sigma^2

so

sigma^2 = int(0,+infinity) Sphi(f) * sin^2(pi f /f0)/(pi f0)^2 df=Sw/f0^3

with the definition of the phasenoise as

L(f)=Sphi(f)/2 this leads to

L(f)=sigma^2 f0^3/f^2

J = sqrt(sigma^2)

Ken Kundert uses a slightly different approach from Demir et Al. but comes up to the same result.

Does that answer your questions ?

Title: Re: Jitter from phas noise...who knows the answer
Post by Erez_Sarig on Oct 31^st, 2007, 9:13am

Hi,
Thanks for the answer but I don't understand.
Jc =(1/(2*pi*fc)))*√(∫(S(f)df) --> there is no Sin² , where did it go? is it only correct for White noise source to use this formula ? can you explain?
As I understand the sin² went because you can assume its 1/2 (rms of sin) intg(a*b) ~=intg(a)intg(b)=intg(a)*1/2 (where "b" is the sin²)

Thanks,
Erez

P.S can you direct me to files also ?

Title: Re: Jitter from phas noise...who knows the answer
Post by Stefan on Oct 31^st, 2007, 9:44am

You should start reading the papers from ken kundert about jitter and phase noise and from Demir et Al.
You can find them on ieeexplorer.

According to the white noise sources ... remember that the Phasenoise may have different steepness over the range. Assuming only white noise sources leads to 20dB/dec over the whole range (valid only in certain areas).

Title: Re: Jitter from phas noise...who knows the answer
Post by loose-electron on Nov 2^nd, 2007, 9:43am

What I find funny about the whole jitter question is that at the end of the day the theoretical expectations tend to be totally lost in the noise (bad pun) of the environmental noise of cross coupling, power and ground rail noise and similar.

Most of the time people dont model all of the second order effects. For ring oscillators, all the second order junk tends to dominate the performance and the theoretical expctations are created from a deficient model.

GIGO - results are only as good as the model simulated.

LC VCO's tend to be closer in correlation to the model due a simpler architecture and less sources of second order problems. However, in the RF world people tend to talk "spectral spreading" for these, rather than "jitter"

Title: Re: Jitter from phas noise...who knows the answer
Post by Sarig on Nov 2^nd, 2007, 10:06am

well people i know the answer to my question.
the cycle jitter is calculate exactly using the sin². this sin² is just coming from the fact you sample 2 egdes. it is exactly CDS.(Correlated duble sampling.)
the other equation "Jc =((1/(2*pi*fc)))*√(∫(S(f)df))" is worng it is Jee not Jc. for white noise you can assume Jc=sqrt(2)Jee

And about other noise sources... well, as I am an Analog designer so I know to find my way in PSRR,supply seperation and more...and I agree that they can kill your design.
Thanks,
Erez