On Fri, 05 Jan 2018 21:54:58 -0500, time-nuts-request@febo.com wrote: > Message: 13 > Date: Sat, 6 Jan 2018 01:08:45 +0100 > From: Magnus Danielson <magnus@rubidium.dyndns.org> > To: time-nuts@febo.com > Cc: magnus@rubidium.se > Subject: Re: [time-nuts] AM vs PM noise of signal sources > Message-ID: <d286e789-d466-ed27-d436-d2bdbdb30a1c@rubidium.dyndns.org> > 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, time-nuts-request@febo.com 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 > *****************************************

Hi Joe, On 01/06/2018 10:26 PM, Joseph Gwinn wrote: > On Fri, 05 Jan 2018 21:54:58 -0500, time-nuts-request@febo.com wrote: >> 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. Yes, the first of a series of zeros is at 2,4048. > That must have been a very bad oscillator. It was. None of mine, and not my measurement, I just helped triage it. > 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. Indeed, and the risk of AM-to-PM conversion makes huge difference in AM and PM levels allow circuits to ruin the PM properties. If you consider it as an act of isolation and the need for balance to ensure the isolation, it becomes easier to understand conceptually. Cheers, Magnus