[time-nuts] Re: Phase Noise Measurement in Dallas

[Attila Kinali]

On Thu, 27 Oct 2022 10:46:03 -0400
Bob kb8tq via time-nuts <time-nuts at lists.febo.com> wrote:

> As you divide frequency, the phase noise gets better. It should improve by
> 20 log N where N is the divider. Divide 10 MHz to 1 MHz with a chip and
> phase noise gets 20 db better. Your -114 number is now -134. In an ideal
> world with perfect parts, it would just keep getting better the more you divide.

Small nitpick:

The 20*log(N) formula[1] is only valid if aliasing of noise can be prevented.
I.e. if one uses a digital divider (e.g. a bunch of D-flipflops) then the
aliasing will increase the relative noise and the noise scaling is reduced
to 10*log(N).

To achieve the 20*log(N) one needs a divider that generates a sinusoid
like a DDS or at the very least a trapezoid/triangular waveform like
a Λ-divider[2] in order to get the harmonics of the impulse sensitivity
function[3,4] to decay quickly with increasing frequency/harmonic number.

			Attila Kinali

[1] With log() being the logarithm of base 10. And result in dB

[2] "The Sampling Theorem in Pi and Lambda Digital Frequency Dividers",
by Claudio Calosso and Enrico Rubiola, 2013
http://rubiola.org/pdf-articles/conference/2013-ifcs-Frequency-dividers.pdf

[3] "A General Theory of Phase Noise in Electrical Oscillators",
by Hajimiri and Lee, 1998
https://doi.org/10.1109/4.658619
Note: Do not use the formulas in this paper for oscillators. The theory is flawed
and does not apply for systems with a feedback loop, like oscillators. Use [5] instead.

[4] "A Physical Sine-to-Square Converter Noise Model",
by yours truly, 2018
https://people.mpi-inf.mpg.de/~adogan/pubs/IFCS2018_comparator_noise.pdf

[5] "Phase noise in oscillators: a unifying theory and numerical methods
for characterization", by Alper Demir, Amit Mehrotra, and Jaijeet Roychowdhury, 2000
https://doi.org/10.1109/81.847872
-- 
In science if you know what you are doing you should not be doing it.
In engineering if you do not know what you are doing you should not be doing it.
        -- Richard W. Hamming, The Art of Doing Science and Engineering