Talk:Leeson's equation

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Possible typo

I think there is a typo. The factor 1/2 should actually be a factor of 2.

-BillH1234 BillH1234 (talk) 21:43, 15 September 2015 (UTC)[reply]

agree OBg75 (talk) 21:24, 19 July 2024 (UTC)[reply]

I think the page was correct originally before it was changed - it is now wrong. please explain the reasoning behind this.

This is SSB phase noise density to carrier, there are other ways to express this concept.

The below links I believe show it was originally correct, so is now wrong.

https://ietresearch.onlinelibrary.wiley.com/doi/pdf/10.1049/el.2016.1021

https://www.jstage.jst.go.jp/article/elex/1/5/1_5_109/_pdf

https://www.youtube.com/watch?v=WAilXeo5PNI Paul B isle of wight (talk) 23:03, 9 March 2025 (UTC)[reply]

Quoting Leeson's original publication "Leeson, D. B. (February 1966), "A Simple Model of Feedback Oscillator Noise Spectrum", Proceedings of the IEEE," (reference #1):

"... a suitable composite expression is [for the spectrum of the phase]": Sphi(wm)= Sdtheta(wm)*[1+(wo/(2Qwm))^2].
"the additive noise component of Sdtheta(w) is identical to the spectral density of noise voltage squared relative to the mean square signal voltage. For white additive noise [...], effective oscillator noise figure F, and signal level Ps at input of oscillator active element, the two-sided" PSD is Sdtheta(w)= 2kTF/Ps.
Sdtheta(w) is two-sided here (w over frequencies -inf..+inf); it would be 4kTF/Ps if one-sided PSD (w over 0..+inf)
Sphi(wm)= 2kTF/Ps*[1+(wo/(2Qwm))^2, which is two-sided (since Sdtheta(wm) is two-sided)
single-sided phase noise L(w): L(w)=Sphi(w) because Sphi is two-sided (it would be L=Sphi'/2 for one-sided Sphi')
therefore: L(w) = 2kTF/Ps*[1+(wo/(2Qwm))^2 (fc/fm 1/f-noise term not included here).

OBg75 (talk) 21:15, 11 March 2025 (UTC)[reply]

also see MIT OpenCourseWare Lecture Notes, added to external links - especially pages 21-22 OBg75 (talk) 22:43, 11 March 2025 (UTC)[reply]

sorry for delay, busy.

we have the problem here that things are being expressed in ways that the meaning is not always clear.

phase noise to carrier ratio should not be dependent on whether we are meaning single sided spectrum or double sided spectrum. It is the ratio of carrier to noise, both carrier and noise add coherently on the two sides, so in principle the concept of single sided vs double sided is only only of significance for the noise in isolation. It is very important to be clear whether we are talking of single sideband phase noise or double sideband phase noise, because here it is only the noise that adds. Up until recently everyone accepted that the numerical factor in the equation for SSB phase noise was 1/8, you can see the references I mentioned (IET ought to be trustworthy), and my working on youtube, I dont think there is an error in it. The only thing that was disputed about the equation was the meaning of Ps. I am not convinced that these other claims of a different factor are correct. I will try and investigate but I dont have much time. Paul B isle of wight (talk) 18:12, 23 March 2025 (UTC)[reply]