Jan Frank wrote: <snip>
Hmm. Well inside the loop bandwidth of a perfectly noiseless PLL, the instantaneous frequency of the VCO in a PLL N-tupler is N times the reference frequency.
Phase is the time integral of frequency, so the output noise phase is also N times the reference phase, up to an additive constant of integration.
It takes about three lines of algebra to show that (in the high SNR limit) phase noise PSD goes as <delta phi> ** 2, so the output of a perfectly locked PLL has 20 log N decibels worse phase noise than its reference.
We know that sin phi ~= phi for small angles, so weak phase noise behaves like additive noise. Thus that 20 log N is independent of the phase noise spectrum as long as the total
<delta phi> << 2 pi radians,Seems pretty conclusive to me.
How does your magic box avoid this?
(I'm familiar with various tricks that reduce the additive phase noise of dividers and phase detectors, but that's beside the point here--we've assumed they're noiseless to begin with.)
Cheers
Phil Hobbs