The Designer's Guide Community
Forum
Welcome, Guest. Please Login or Register. Please follow the Forum guidelines.
Mar 29th, 2024, 5:01am
Pages: 1
Send Topic Print
phase noise due to VCO control noise: 2 methods give different answers (Read 2838 times)
davetrouble
New Member
*
Offline



Posts: 3

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?
Back to top
 
 
View Profile   IP Logged
Ken Kundert
Global Moderator
*****
Offline



Posts: 2384
Silicon Valley
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
Back to top
 
 
View Profile WWW   IP Logged
davetrouble
New Member
*
Offline



Posts: 3

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?
Back to top
 
 
View Profile   IP Logged
Ken Kundert
Global Moderator
*****
Offline



Posts: 2384
Silicon Valley
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.
Back to top
 
 
View Profile WWW   IP Logged
davetrouble
New Member
*
Offline



Posts: 3

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




Back to top
 
 
View Profile   IP Logged
Pages: 1
Send Topic Print
Copyright 2002-2024 Designer’s Guide Consulting, Inc. Designer’s Guide® is a registered trademark of Designer’s Guide Consulting, Inc. All rights reserved. Send comments or questions to editor@designers-guide.org. Consider submitting a paper or model.