# [time-nuts] simple explanation of noise spectra with mixing

Mon Mar 2 08:45:50 EST 2015

```On 3/1/15 10:23 AM, Joseph Gwinn wrote:
>>
>> time-nuts Digest, Vol 128, Issue 1, Message: 8
>>
>> Date: Sat, 28 Feb 2015 17:46:18 -0800
>> From: Jim Lux <jimlux at earthlink.net>
>> To: Discussion of precise time and frequency measurement
>> 	<time-nuts at febo.com>
>> Subject: [time-nuts] simple explanation of noise spectra with mixing,
>> 	etc.
>> 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, fredlwalls at 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.
>

I'll look those up..

I was hoping that someone, somewhere had done a "guide to phase noise"
in 1 or 2 pages or a poster.

There's lots of pieces scattered hither and yon, but before I spent much
time generating my own..

Kind of like that cool plot that a time-nut has which shows the spectra
and allan dev of the various colors of noise in a table.

>
>> 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.

I assume you mean squaring..
True, the "2 f" term will have 6dB more.. But what about the baseband/DC
component..

>
> 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.
>

Short ranges (<1 km) so actually, lots of cancellation.  the round trip
delay is 6 microseconds, so a variation at, say, 10 Hz, is pretty well
cancelled out.

```