> > time-nuts Digest, Vol 128, Issue 1, Message: 8 > > Date: Sat, 28 Feb 2015 17:46:18 -0800 > From: Jim Lux <jim...@earthlink.net> > To: Discussion of precise time and frequency measurement > <time-nuts@febo.com> > Subject: [time-nuts] simple explanation of noise spectra with mixing, > etc. > Message-ID: <54f26f6a.6030...@earthlink.net> > Content-Type: text/plain; charset=utf-8; format=flowed > > Is there a handy "one pager" kind of explanation of noise spectra after > some forms of signal processing..
The best source for the math is probably Fred Walls: F. L. Walls, “Correlation between upper and lower sidebands” IEEE Trans. UFFC, Vol. 47, pp 407-410, 2000. "PM and AM Noise of Combined Signal Sources", Fred L. Walls, Total Frequency, fredlwa...@cs.com, Proceedings of the 2003 IEEE International Frequency Control Symposium and PDA Exhibition Jointly with the 17th European Frequency and Time Forum, 0-7803-7688-9/03/$17.00 © 2003 IEEE, pages 532-540. > For instance, if you have a oscillator which has a 1/f characteristic, > and you mix it with itself, what is the spectra of the output of the mixer. Mixing is a multiplicative process, so this is equivalent to squatting the signal, which doubles its frequency, so the effect will be 20 Log10(2)= 6 db increase of phase noise on the double-frequency terms. Your bottom-line question will be if there is any cancellation of phase noise; this will involve the time delay for the rata signal to get to the target and return. My guess is that there will be no cancellation. > Or if you have a 1/f^3 characteristic (e.g. from a crystal oscillator, > very close in) or a 1/f^2 (from a VCO). The double rule will apply to each point in the phase noise as if it were alone. > Specifically, I've got some folks working with homodyne radars (where > you demodulate the received signal with a sample of the transmitted > signal, but sometimes with an offset mixed in, etc.) and I'm looking for > a quick intro to this kind of thing at a sort of > empirical/phenomenological as opposed to analytical.. > > "If you see X on a spectrum analyzer or FFT, it is because of Y"... > > Similarly, they're building PLLs and know about the 20log10(N) thing, > but what should the shape of things underneath be. The 20Loh10(N) applies regardless of offset frequency, so the whole phase noise spectrum will move up and down as a unit. Joe Gwinn _______________________________________________ time-nuts mailing list -- time-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
