stock here: Having spent thousands of hours protecting the militaries most critical assets, I am aware of "Waveguides" of certain size in relation to Wavelength creating a certain amount of attenuation of the signal. At the farthest bottom I have placed some formulas that with certain assumptions can provide guidance on the attenuation which can be shown to be in the form of an exponential decay.
As I was ready to close out the article, I finally ran across this....perfect! Like a Psycrometric chart for air and moisture properties!!
And they have some nice Decibel Attenuation formulas too. I capped the formula sheet and put at far bottom.
Disaster Preparer has many products that are focused on EMP protection.
https://disasterpreparer.com/product/emp-gaskets/
EMP Doctor
https://www.youtube.com/user/disasterprepper
Should you ground a Faraday Cage? Answer, it makes little or no difference.
But for sure, dont run the wire into the Cage! 460Mega hZ Typical Radio Garbage Can, as a Faraday Cage Recommended Book, from this link on EMP misconceptions
https://www.youtube.com/watch?v=GYLn7wgGxPo
https://www.amazon.com/Disaster-Preparedness-Attacks-Storms-Expanded/dp/1478376651
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https://physics.stackexchange.com/questions/546449/faraday-cages-size-of-holes
The optimum hole size depends on the compromise you seek between screening effect and accessibility through the holes. The thickness and electrical and magnetic properties of the material you make the holes through are also significant. Aluminum foil is a cost-effective screen but it is not a high-quality one. It gets complicated. As a rule of thumb, a hole size of less than one-tenth of the wavelength is a good starting point. – Guy Inchbald Apr 24, 2020 at 21:01
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General rule of thumb is that the opening in a Faraday cage should be smaller than 1/10th of the wavelength that should be blocked.
For example, in order to block EM fields with frequencies of 10 GHz and lower, the hole size of the Faraday cage should be smaller than 3 mm.
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The most important concept relating Faraday cage hole size to cell phone signal attenuation is the idea of a cutoff frequency. For round holes, you would model them as cylindrical waveguides. For simplicity, we'll consider rectangular waveguides instead.
Matching the boundary conditions at the metal wall, you get so called transverse electric (TE) and transverse magnetic (TM) modes. These look like partially standing waves, with a traveling wave component for the third. For TE modes, they're of the form (for polarization in the y direction):
There's a multitude of standing wave modes. These are described by different values of
and, which are solved by setting the above expression to zero at the walls of the waveguide (for the sine portion), or derivative zero (for the cosine portion). The solutions:
Where
and are the width and height of the waveguide, and and are integers. Substituting the above expression into the wave equation, we get the relation between the differentcomponents and frequency.
The lowest possible such frequency is when
andThis is the cutoff frequency. Below this frequency, the signal exponentially decays as it propagates through the structure. To show this, solve for
, and write it in terms of cutoff frequency.
Evidently, at frequencies below cutoff,
becomes imaginary. Substituting this into our travelling wave expression, it becomes exponential decay.
Notice that for our rectangular waveguide, the cutoff frequency depended only on the width. In general,
(This is exactly true for a rectangular waveguide, and should hold approximately for other shapes.)
For Faraday cages with openings in the size of centimeters, the cutoff frequency is around 20GHz, which is quite large compared cell phone signals in the range of 2GHz. We can approximate the decay constant
To figure out the amount of decay, we need to assume some length
to the opening (equivalently, thickness of the cage material), and then substitute forin the wave expression. Converting this to a decibel scale, we get the following power loss:
Another important point is that the signal will mostly negatively interfere with itself in the cage, except at a few spots within the cage where it is effectively amplified (probably the center). If the cage features are fairly large, you might be able to notice this signal hotspot.
Edit: There are also complex effects where the fields in one hole can induce fields in another hole. The above analysis is a simplified description of a complex field problem, but I expect the general principles to hold.
------------------------------------------- These guys make Faraday cages for running sensitive experiments in.
https://www.gamry.com/application-notes/instrumentation/faraday-cage/
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