# Wavelengths blocked by a certain metal mesh

Introduction: I've heard about a theory, according to which you can check if there is any leakage in your microwave oven by putting your mobile phone inside and call it. However, I gave it a try and the call was successful.

I realized that the two devices are working on different frequencies (and wavelengths, of course), thus the metal mesh in the door of the oven may be unable to block anything different from the intended working frequency. I came across similar results on the Internet.

Calculating the free-space wavelengths for 1.8 GHz and 2.45 GHz, we get ~0.167 and ~0.122 meters, respectively. This means a 40% increase in wavelength for the unintended usage.

Problem: Still, I don't understand why I was able to call my phone. First of all, I vaguely seem to remember a 'thumb of rule', namely that a metal mesh blocks electromagnetic waves of which the wavelength is in the same order of magnitude as the dimensions of the holes (or smaller). Well, that looks absolute stupidity, as the holes appear to be no more than 2-3 mm each side (almost a hundredth of the wavelengths).

Secondly, those wavelengths are practically the same in comparison with the holes.

Question: Given the dimensions of a metal mesh, how can you determine the range of wavelengths blocked by it?

A few points to consider:

• the frequency of your microwave and of a cell phone are "similar enough" - although depending on where you live, the frequency of the cell phone could be typically between 800 MHz and 1900 MHz - I am guessing you know that 1800 is the right number for your phone.
• A cell phone (and the tower) will adjust the power to communicate depending on the path loss - so if your shielding is 99% efficient, the two will increase their power by 20 dB and keep right on talking...
• The electromagnetic waves in a microwave tend to be standing waves - and there are nodes in the corners of the oven for all modes I can think of. Thus a gap in the shielding (quarter-wave trap, Dave calls it) doesn't have to be terribly efficient, even at the frequency of interest.

That leaves the question "how efficient is a mesh". The answer, as always, is "it depends". It depends on the shape of the hole, it depends on the polarization of the E/M wave, and it depends on the conductivity of the material. I found a paper at http://dx.doi.org/10.1109/15.3309 whose abstract reads:

The electromagnetic shielding behavior of bounded-junction wire-mesh screens is discussed in the frequency range where the individual meshes are electrically small. The screen, whose meshes are assumed to be square, is described by a equivalent sheet impedance operator. The plane-wave shielding effectiveness of a planar-mesh screen is derived. The problem of coupling between antennas on either side of the planar mesh is addressed, and its applicability to the measurement of mesh properties is described. The low-frequency electric and magnetic shielding afforded by mesh enclosures is considered. Because of the reactive character of the mesh surface, the plane-wave shielding effectiveness decreases with increasing frequency. The enclosure's magnetic-field shielding effectiveness increases with increasing frequency, but saturates at a maximum value that depends on the geometry of the enclosure, the mesh size, and the mesh wire radius. The enclosure electrostatic-field shielding effectiveness depends only on the enclosure and mesh geometries

Unfortunately I don't have access to the full paper - but this should give you some ideas...

• Thank you! I'll try to get access to the paper through the university network to get further information. – hryghr Aug 22 '14 at 23:19

It isn't the metal mesh leaking so much as the joint around the door. Rather than employing a continuous metal-to-metal contact around the edge of the door to seal it when closed, most microwave ovens use a quarter-wave "trap" — basically a shaped "groove" of the correct dimensions that surrounds the door opening (usually hidden behind a dielectric gasket of some sort) — to create a "virtual short circuit" for the microwave energy that prevents it from passing from the interior to the exterior of the oven.

This trap is fairly specific to the frequency that the microwave uses, and it isn't surprising that it wouldn't have much effect on cellphone signals.

• Thank you, this perfectly answers the basic situation. This really was a two-in-one question after all. But I'm now curious about the "spin-off" question about the relation of mesh size and wavelengths. – hryghr Aug 21 '14 at 21:55
• For that, you should look up "slot antenna". Basically, a hole will pass radiation if its circumference is greater than the wavelength in question. – Dave Tweed Aug 21 '14 at 22:46
• Also, the microwave's shielding only has to be good enough to prevent harmful radiation. Phones are very sensitive and can (obviously) pick up signals that are below the level of being harmful. – RJR Aug 22 '14 at 6:06
• @Dave: So, this mesh has more of a decorating/eye-protecting (?) function? – hryghr Aug 22 '14 at 23:12
• No, the mesh is what forms the conductive surface that prevents the microwaves from leaking directly through the glass of the door. – Dave Tweed Aug 23 '14 at 2:43