[time-nuts] AM vs PM noise of signal sources

Joseph Gwinn joegwinn at comcast.net
Sat Jan 6 16:26:48 EST 2018

On Fri, 05 Jan 2018 21:54:58 -0500, time-nuts-request at febo.com wrote:

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


> Cheers,
> Magnus

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