Why mixing two harmonics can't improve phase noise?

I am wondering the following questions:
1) Assume two independent freq sources: one is 900M with -130.9dBc/Hz@1KHz, and the other is 1100M with -129.2dBc/Hz@1KHz. Then mixed two signals, we can get 2000M signal with about -128dBc/Hz@1KHz.
2) Assume one 100MHz OCXO, multipliz it to its 9th harmonics with -130.9dBc/Hz@1KHz and 11th harmonics with -129.2dBc/Hz@1KHz, then filtered other harmonics respectively. After that mixed two signals, we can only get 2000MHz signal with about -124dBc/Hz@1KHz.
Why the result is different? Is it because the noise-correlations?

If you multiply two harmonics of a single source, the noises of the harmonics will be-more or less- correlated, that's why this correlation will degredade the PN performence..If this correlation is one, the noises will be added and thus noise vector will be bigger-maybe two times- than single one..this is the worst case..
But if you multiply two independent signal source, because of uncorrelated signals, the PN performance will be better..If noise vectors can be done out of phase, the ideal PN performance can be obtained.
All of those are noise vector summation problem..
This is my thinking..

If you have two free running saw oscillators, one at 1 ghz and the other at 1.1 ghz. Lets say either one of them has phase noise at -100 dBc/Hz at 10 khz off set. You mix the two, and the phase noise at 2.1 ghz is going to be -97 dBc/Hz.

You now take the two saw oscillators, and phase lock both of them in a big control loop bandwidth to the same 10 Mhz ocxo. If your ocxo had poor phase noise, so that the saw oscillators still both have -100 dBc/Hz phase noise at 10 khz, now when you mix them together you will find the total phase noise at 2.1 Ghz is going to be -94 dBc/Hz.

In the later example, you don't normally realize what is going on, because the oscillators typically get better when you phase lock them, so you often overlook the correlated phase noise addition.

If you wanted them to be 3 dB better, you could phase lock them to two independent 10 MHz ocxo's, but the 3 dB is usually not worth the extra hardware.


Sometimes this works in your favor. Lets say you have a 100 Mhz system clock at -120 dBc/Hz phase noise. You multiply it by X10 (1000 MHz), and the resulting signal is -100 dBc/Hz phase noise. You also multiply the 100 MHz system clock by x6 (600 MHz), and the resulting phase noise is -120 +15.56 dB= =105. BUT, if you mix the two together to get 400 MHz (i.e. 1000 MHz -600 MHz), your phase noise will only be -120 +20Log4= -108, better than either of the components that made it up! Correlation helps you in that case.

Rich

thank you very much.