On Fri, 05 Jan 2018 21:54:58 -0500, [email protected] wrote: > Message: 13 > Date: Sat, 6 Jan 2018 01:08:45 +0100 > From: Magnus Danielson <[email protected]> > To: [email protected] > Cc: [email protected] > Subject: Re: [time-nuts] AM vs PM noise of signal sources > Message-ID: <[email protected]> > Content-Type: text/plain; charset=utf-8 > > Joseph, > > On 01/05/2018 09:16 PM, Joseph Gwinn wrote: >> On Fri, 05 Jan 2018 12:00:01 -0500, [email protected] wrote: >>> Send time-nuts mailing list submissions to > >>> If I pass both a sine wave tone and a pile of audio noise through a >>> perfectly >>> linear circuit, I get no AM or PM noise sidebands on the signal. The >>> only way >>> they combine is if the circuit is non-linear. There are a lot of ways >>> to model >>> this non-linearity. The “old school” approach is with a polynomial >>> function. That >>> dates back at least into the 1930’s. The textbooks I used learning it >>> in the 1970’s >>> were written in the 1950’s. There are *many* decades of papers on >>> this stuff. >>> >>> Simple answer is that some types of non-linearity transfer AM others >>> transfer PM. >>> Some transfer both. In some cases the spectrum of the modulation is >>> preserved. >>> In some cases the spectrum is re-shaped by the modulation process. As >>> I recall >>> we spend a semester going over the basics of what does what. >>> >>> These days, you have the wonders of non-linear circuit analysis. To >>> the degree >>> that your models are accurate and that the methods used work, I’m >>> sure it will >>> give you similar data compared to the “old school” stuff. >> >> All the points about the need for linearity are correct. The best >> point of access to the math of phase noise (both AM and PM) is >> modulation theory - phase noise is low-index modulation of the RF >> carrier signal. Given the very low modulation index, only the first >> term of the approximating Bessel series is significant. The difference >> between AM and PM is the relative phasing of the modulation sidebands. >> Additive noise has no such phase relationship. > > May I just follow up on the assumption there. The Bessel series is the > theoretical [basis] for what goes on in PM and also helps to explain one > particular error I have seen. For one oscillator with particularly bad > noise, a commercial instruments gave positive PM numbers. Rather than > measuring the power of the signal, it measured the power of the carrier. > Under the assumption of low index modulation the Bessel for the carrier > is very close to 1, so it is fairly safe assumption. However, for higher > index the carrier suppresses, and that matches that the Bessel becomes > lower. That's what happened, so a read-out of the carrier is no longer > representing the power of the signal. > > However, if you do have low index modulation, you can assume the center > carrier to be as close to full power as you want, and the two > side-carriers has a very simple linear approximation.
Yes. This is exactly right. There is a modulation index for which the carrier is totally suppressed. That must have been a very bad oscillator. You mentioned elsewhere that we now have to consider AM, not just PM. This has been my experience as well, especially with power supply noise fed to a final RF power amplifier, especially if that final amplifier (or its driver) is not fully saturated. Joe > Cheers, > Magnus > End of time-nuts Digest, Vol 162, Issue 9 > ***************************************** _______________________________________________ time-nuts mailing list -- [email protected] To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
