[time-nuts] Examples of noise processes

[Attila Kinali]

Did someone say "noise processes"? :-)

On Fri, 15 Mar 2019 10:03:11 -0400
John Ackermann N8UR <jra at febo.com> wrote:

> For a presentation on basic time-nuttery, I'd like to find 
> non-oscillator examples of the various noise processes -- white PM, 
> flicker PM, white FM, flicker FM, random walk.  (I'm not sure if FM and 
> PM have any relevance outside oscillators, though.)

First you have to define what you mean by FM outside of oscillators.
If you look at frequency just as integral of phase, then there is
a very straight forward relation. Ie frequency noises are just
phase noises with the exponent going up by two. 

white noise (~white phase):
The most important white noise source is thermal noise, ie movement
of atoms that disturb(scatter) the flow of electrons due to thermal energy.
The second most important noise is shot noise in semiconductors.
This is mediated by the fact that the current carriers (e.g. electrons)
are discrete objects that pass through a potential barrier.
There is also avalanche noise which is present in p-n junctions with
high electric fields where electrons are accelerated to the point where
they gather enough energy to knock out secondary electrons from atoms
in the lattice before leaving the active zone. Avalanche photo diodes
and zener diodes with voltages over 6V are the most common devices that exhibit
predominantly avalanche noise.

1/f noise (~flicker phase):
This noise comes mainly from defects in conductors or other structures
that trapp or scatter the electrons (or phonons in crystal resonators).
This type of noise is very common and can be found in almost all physical
systems (even weather patterns), but it's exact source is not well understood.

1/f^2 noise (~white frequency):
There are two types of noise here:
1) Popcorn noise: Like 1/f noise, this is not well understood, but
is also related to the activity of single traps in regions of high
current density. It was more a problem back in the vacuum tube and
germanium semiconductor times. Current silicon semiconductors show,
if any, only very low levels of popcorn noise.
2) generation-recombination noise: when electron-hole pairs form or
get recombine, the carrier density changes localy. Above the frequency
that is inversly proportional to the recombination time, this type
of noise shows a 1/f^2 characteristic (below it's white)
Additionally to those two real noise sources, you also have the
integration of white noise. This can either happen due to a real
integrator or by a device that has integrative properties within
the circuit (e.g. the Q of the resonator in Leeson's formula)

higher order noises (~flicker frequency and above):
>From what I've read in the last years, I have formed the hypothesis
that most (all?) noises with higher exponents are formed either due
to integration of the above noise sources[1] or are mediated
through environmental effects that make it look like noise sources[2]
when analysing them with our tools, but in reality are not truly
random and/or not Gauss distributed. E.g. in Enrico's paper[3]
you can see that thermal effects lead to a 1/f^5 type noise.
I still need to figure out a way to prove/disprove this hypothesis
and I do not think this way of thinking is generally accepted (I have
not seen anyone else formulating this), so please take this with a
grain of salt.

HTH
	
			Attila Kinali


[1] Eg. Leesons formula for oscillators. Similarly, passive frequency
standards which do a frequency detection that exhibits white and 1/f noise,
which thus turns the output noise in into white frequency noise and
flicker frequency noise.

[2] I use here a somewhat more strict definiton of noise surces.
Namely sources which generate random, Gauss distributed values
with an 1/f^a, a >= 0 power spectral density. While for practical
purposes using this strict definition does not make sense (if it
looks like noise, then it is noise), but from a theoretical point
of view it is important to distinguish other effects that can be
explained and thus potentially removed (e.g. by measuring temperature
of the device itself very accurately) from "real" noise sources.

[3] "Low Flicker-Noise DC Amplifier for 50Ω Sources", by Enrico Rubiola
and Franck Lardet-Vieurdrin, 2004
http://rubiola.org/pdf-articles/journal/2004rsi(rubiola)low-flicker-dc-amplifier.pdf

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