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phase noise due to VCO control noise: 2 methods give different answers (Read 343 times)
davetrouble
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phase noise due to VCO control noise: 2 methods give different answers
Jul 28th, 2017, 1:30pm
 
what bothers me is that I can calculate VCO phase noise due to VCO control noise 2 ways and I get different answers.

1. use eq 34 from Abidi "Phase noise and jitter in cmos ring oscillators"
L(f) = (1/4) * (Ko**2/f**2) *Sv(f)

2. use LTI  phase domain model of VCO as described in Kundert "Predicting the phase noise and jitter of PLL-Based Frequency Synthesizers" proceeding as follows

a linearized model of the vco in terms of voltage in and phase out is H(s) = 2*pi*Ko/s where Ko has units of Hz/V.

let the input voltage variable be v and the output phase variable be phi

let the input be a random variable with psd of Sv(f) and let the output psd be Sphi(f)

These should be related by the magnitude squared of the transfer function which would be Ko**2/f**2 so that

Sphi(f) = (Ko**2/f**2) * Sv(f)

Now according to the definition of phase noise L(f) = Sphi(f)/2 (eq 27 Kundert) so in this case the phase noise at the output from the noise at the input would be

L(f) = (1/2) * (Ko**2/f**2) *Sv(f)

method 1 and method 2 differ by a factor of 2. What is the explanation?
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Ken Kundert
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Re: phase noise due to VCO control noise: 2 methods give different answers
Reply #1 - Jul 28th, 2017, 4:16pm
 
It probably has to do with the derivations using different form of the Fourier coefficients. Double sided and single sided Fourier coefficients differ by a factor of two. I remember that being an issue.

-Ken
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davetrouble
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Re: phase noise due to VCO control noise: 2 methods give different answers
Reply #2 - Jul 29th, 2017, 4:16am
 
Thanks for a quick reply. Based on your reply I would add the additional question of which method is correct. As far as I have been able to determine both of these methods are using the same defintion for phase noise L(f) so i don't think they can both be correct. For the same input voltage noise shouldn't the vco only be entitled to one output phase noise?
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Ken Kundert
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Re: phase noise due to VCO control noise: 2 methods give different answers
Reply #3 - Jul 30th, 2017, 12:08pm
 
Which is correct depends on which form of Fourier coefficients you are using.
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davetrouble
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Re: phase noise due to VCO control noise: 2 methods give different answers
Reply #4 - Jul 31st, 2017, 6:12am
 
Ken,

I have read through the Kundert paper (version 4i)  with an eye to double check if quantities being used are single or double sided.

Sphi(f) seems to be chosen to be a single sided PSD (pg 14)
L(f) seems to be chosen to be a SSB phase noise  (pg14-15)
For the phase domain model of the vco (pg8-9) it seems if the output phase is taken to have a single sided  PSD then the input noise should also be taken to have a single sided PSD.

For the Abidi paper I have tried to do the same thing.

L(f) seems to be chosen to be a SSB phase noise (pg 1808).
Sv(f) seems to be a single sided PSD but this leads to the 2 equations for L(f) to disagree as mentioned in the OP. Another problem is that even if I interpret it as a double sided PSD it only makes the discrepancy between  the L(f) from the 2 methods even worse since Sds(f) = (1/2) * Sss(f).

Dave




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