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Design >> RF Design >> Theory derivation of 6dB phase noise decrease after divider-by-2
https://designers-guide.org/forum/YaBB.pl?num=1349230093

Message started by jlee on Oct 2^nd, 2012, 7:08pm

Title: Theory derivation of 6dB phase noise decrease after divider-by-2
Post by jlee on Oct 2^nd, 2012, 7:08pm

Hi All,

As we all know, ideally the VCO phase noise near thermal noise region will be decreased by 6 dB, after the signal passes through a divider-by-2.

But I don't know the reason. Is there anyone can give the theory derivation, or any paper which explains the phenomenon?

Thank you!

Title: Re: Theory derivation of 6dB phase noise decrease after divider-by-2
Post by summi on Oct 2^nd, 2012, 11:53pm

Dear forum,
1. From lesson's equation phase noise depends on (Wo/Wm)^2, where Wo is carrier frequency and Wm is offset frequency. If Wo divide by 2 means, phase will decrease by 6dB.

2.Even from theory noise power depends on number of zero crossings, lesser the frequency, lesser zero crossings and hence less phase noise.

But remember if you keep on dividing like this at some point noise touches the noise floor and no more reduction.

Refer ali hajimirri pap on phase noise for further understanding.

Have fun.

Title: Re: Theory derivation of 6dB phase noise decrease after divider-by-2
Post by Frank Wiedmann on Oct 5^th, 2012, 12:48am

You can think of phase noise as a certain timing variability of the zero crossings of a periodic signal with respect to their ideal positions, referenced to the signal period. When you divide the signal frequency by two, this timing variability ideally remains unchanged. However, now this same variabiliby is referenced to a signal period that is twice as long, so the phase noise according to this definition is only half as large or 6 dB lower.

Title: Re: Theory derivation of 6dB phase noise decrease after divider-by-2
Post by Kevin Aylward on Jul 7^th, 2013, 2:31am

Arguably, it doesn’t reduce at all. It’s just a matter of definitions and comparing apples to oranges. Phase noise is specified at a specified offset frequency from the carrier frequency. This offset should, arguably, be treated as relative to the carrier frequency. If the carrier frequency is divided by two, so should the offset frequency, in which case for an ideal divider there will be no change in noise as the relevant noise frequency is now closer to the carrier. There is no such thing as a free lunch. For flat band noise, that is noise far away from the carrier, the noise will actually be increased due to the inherent noise of the divider.

Title: Re: Theory derivation of 6dB phase noise decrease after divider-by-2
Post by raja.cedt on Nov 3^rd, 2013, 5:28am

Dear all,
Sorry for slight diversion from the present topic, what happens to divider phase noise in -30dB slope region, i know for -20dB slope region it will decreased by 6dB @ same offset frequency.

Thanks,
Raj.

Title: Re: Theory derivation of 6dB phase noise decrease after divider-by-2
Post by Kevin Aylward on Nov 3^rd, 2013, 5:32am

The whole PN graph just gets shifted to the left.

Title: Re: Theory derivation of 6dB phase noise decrease after divider-by-2
Post by raja.cedt on Nov 3^rd, 2013, 9:40am

Dear Kevin,

Thanks for your reply.

Sorry, didn't get you. I mean after division is 6dB downshift can be explained from Leeson expression in case of -20dB slope region, but how about down shift near to -30dB slope region? What do you mean by left shift shift?

Thanks,
Raj.

Title: Re: Theory derivation of 6dB phase noise decrease after divider-by-2
Post by Kevin Aylward on Nov 3^rd, 2013, 9:50am

There is a graph of PN verses frequency offset covering ALL regions. Shift the the whole graph to the left.