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

Magnus Danielson magnus at rubidium.dyndns.org
Fri Jan 5 19:08:45 EST 2018

```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 npose has no such phase relationship.

May I just follow up on the assumption there. The Bessel series is the
theoretical for what goes on in PM and also helps to explain one
particular error I have seen. For one oscillator with particular bad
noise, a commercial instruments gave positive PM nummbers. 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 happen, 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.

Cheers,
Magnus
```