

Helmhurts:  Placing a WiFi router with the Helmholtz equation - signa11
http://jasmcole.com/2014/08/25/helmhurts/

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physPop
Good fun here, and a neat exercise! However, a few comments for people looking
to do the same:

\- Ignoring the 3D nature of antenna placement, you need to model the concrete
walls properly to get an answer that is semi reliable. All materials have
frequency dependent reflection and transmission (attentuation) coefficients.
Its pretty easy to extend a toy FDTD sim to include these.

\- For the reasons above, inferring 2.4Ghz behaviour from ~1GHz (30cm) signal
isn't really a good thing to do (even in a "hand waving" manner).

\- When displaying E-fields, you usually want to plot the ||E||^2 averaged
over one complete wave cycle -- the nodes shouldn't jump around. If they do,
it means the simulation hasn't reached a steady state.

Cheers!

~~~
sitkack
Given a 2.4Ghz pure sine wave and a couple signal strength detectors couldn't
one iteratively modify the frequency dependent values for the various walls?

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Stwerp
Not for any practical measurements. This would work in say an anechoic
environment – save for the wall under test – but you'd end up sampling
multipath constructive/destrictuve interference instead of the wall
reflections.

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mgraczyk
Did you solve that system by inverting the helmholtz matrix? Your steady state
time independent solution looks like it's suffering from major numeric
instability. If you didn't already, you should solve the system with
linsolve() and see if your results stay the same.

~~~
GFK_of_xmaspast
Reading between the lines I wonder if he's just using the backslash operator
when he says 'inverse'.

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Rabidgremlin
Someone should build a web app that lets you upload a floor sketch to run
these calcs on :-)

~~~
onli
At least if the solution of this is not normally "place the router in the
middle of the flat", as this is the standard advice.

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mattdotc
Got me thinking...could you integrate a wireless AP into a light fixture
without fear of interference, either EM or physical? I'm sure there is a
clever solution for something like a hanging chandelier.

Maybe there are products out there already that allow people to hide their
networking hardware in plain sight?

~~~
fennecfoxen
Aruba Networks used to make a model called the AP-65WB. The WB means "wall
box" \-- it basically fits in a standard wall-box, the same kind of fixture
that could also hold a couple of outlets or light switches (or a combination
thereof). Not sure if that unit's been replaced or retired, though. Also, it's
not exactly targeted at home users.

Many of the enterprise APs with integrated antennas are designed for ceiling
installation. They often have an antenna that's intended to radiate its best
coverage down from the ceiling in a cone.

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xwintermutex
Now it would be a nice next step if he uses his wifi card's RSSI + Helmholtz
reciprocity to verify the theory.

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sbierwagen
Which would work if zero of his neighbors had wifi routers too, which isn't
true in 2014.

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leni536
_More precisely, if the time-dependence of an electromagnetic wave can be
assumed to be of the form sin(\omega t)..._

It's not quite true. It assumes that the electric field oscillates with the
same phase at every point. Normally the Helmholtz equation is solved assuming
that the time dependence is _exp(I\omega t)_ , where _I_ is the imaginary
unit, and we search for a complex _E(x)_ solution. _arg(E(x))_ deals with the
phase factor, _abs(E(x))_ is the amplitude. _Re( E(x)exp(I\omega t) )_ is a
solution to the Maxwell equations.

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pawelkomarnicki
Isn't it kind of obvious that the best coverage will be when the emitter is in
the middle of the area to cover? ;-)

~~~
plg
for a uniform sphere maybe

