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Spectrum of an oscillator with phase noise (Read 84 times)
iVenky
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Spectrum of an oscillator with phase noise
Feb 06th, 2019, 8:30am
 
We can represent oscillator as

y(t)= A cos (wt + Φ(t)), where Φ(t) is phase noise.

If Φ(t)=cos(wnt)  then, we can show using Narrowband approximation that

y(t)≈ A cos (wt) + A sin (wt) sin ( wnt)

Which one of the figures attached (a or b) is the actual spectrum of the oscillator?

I used to think it's (b) and the entire carrier power is spread throughout, but I can't explain it mathematically. Only (a) makes sense mathematically since we have a carrier term (highlighted above) and then a phase noise term.

Question 2:

Also when we measure SSB phase noise it's overlaying both left and right of the carrier, resulting in 3 dB more phase noise compared to DSB phase noise, right? In the plot (a), the dBc that I am plotting is DSB phase noise, which is 3 dB lower compared to SSB phase noise, right?

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spectrum2.JPG

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Ken Kundert
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Re: Spectrum of an oscillator with phase noise
Reply #1 - Feb 7th, 2019, 2:47pm
 
It's b.

The narrow band approximation does not work with oscillator phase noise. Fundamentally the narrow band approximation is a small-signal approximation, it assumes Φ(t) is small. But in oscillator phase noise, Φ(t) is unbounded over long time intervals. It is this unbounded nature that leads to the Lorenzian distribution.

Also, when you plot S(f), you should distinguish between SΦ or SV.

-Ken
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iVenky
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Re: Spectrum of an oscillator with phase noise
Reply #2 - Feb 9th, 2019, 7:04pm
 
Hi Ken,

Thanks for the reply, I got it now. I was plotting Sv, I understand S_phi goes to infinity due to flicker but not Sv.
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