How is the formula of X-correlation obtained?

build correlation phase noise measurement

Dear all
In the phase noise measurement, there is a method called cross correlation that reduces phase detector noise and increases the accuarcy of measurement.
I want to know How is the formula of X-correlation obtained.
Thanks.
rf2000

phase noise measurement

Brief explanation here:
**broken link removed**

On a quick look, it looks like they have trouble with close-in phase noise of the agilent internal LO source. So they build two independent LO's (they would have to be really independent--not sharing the same xtal clocks, etc) so that they are uncorrelated in phase noise. Then they down convert the DUT signal in two parallel paths and just average the pooh out of the result. Every time you do another average, you get a better idea of the DUT phase noise and you reduce your background system LO phase noise. If you average N times, you improve your signal to phase noise floor by √N . By "averaging" I mean they are averaging the FFT outputs in a narrow bandwidth, so that the phase of the background noise gets vectorially cancelled out.

This assumes a couple of things, like the phase noise of your DUT is stationary and repeatable statistically. If you were measuring an oscillator on a sine vibration table, for instance, I would think this would really screw up the accuracy of the phase noise measurement.

Re: phase noise measurement

Dear biff44,
I Thank you for your attention to the topic.
But I want to know If I average N times, How my signal to phase noise floor improves by √N . I mean How can I obtain the "√N relationship" mathematically?
Thanks.

Re: phase noise measurement

Oh, I do not remember. It has something to do with the signal vector adding coherently each time, but the backgrond noise adding incoherently.