# Phase noise spectrum question

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#### neoflash

In document from designer's guide, it is stated that there is a relationship between
SΦ(f) and L(f): SΦ(f)=2*L(f):

L(f) is Leeson function;
SΦ(f) is phase noise spectrum;

However, Hajimiri's paper on Phase noise in Ring Oscillator stated that SΦ(f)=L(f). Which one is real?

How we get L(f) function? Direct measuring from PLL output by spectrum analyzer?

Here is the doc from that website.

#### biff44

If you look at a clean signal on a spectrum analyzer, it looks like mount everest with a sharp peak and slopes that tail off to the right or left. Normally, the right side is identical to the lefts side of peak. So, statistically, people often measure only one side of the spectrum, and say that if they doubled that amount of noise they would know what both sides of the noise spectrum would be. Obviously, half of the noise spectrum is not equal to the full noise spectrum, so your book is in error.

The only time S(s) ≠ 2 L(f) is when there is a complicated correlated relationship between the AM and PM noise, so that one side is enhanced and the other side is diminished (kind of like how an image reject mixer works). You usually only can see this in discrete sidetones, where the upper sideband is a different height than the lower sideband.

#### neoflash

biff44:

In my understanding, L(f) is what we can get from spectrum analyzer. We just normalize what we measured to the fundmental tone to get L(f).
Is it correct?

Isn't it the same thing when we refer to SΦ(f)? Their only difference is definition of single sided or double sided?

thanks,
Neoflash

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