I've asked several related questions, but I'm afraid that some of the answers that I received, while great answers, might be skewed because of incorrect assumptions or unclarity in my questions.

The answer to this question seems to indicate that any good conductor provides good shielding of both the E and H components of far-field EMR, because the fields are mutually dependent on one another for their existence. The up votes would indicate a reliable answer. But answers that I've received to some of my questions have left me with doubts. So, I'll ask a different way:

Given a box that has continuous, conductive, metallic walls with no gaps, and air at its exterior and interior, when a plane wave hits the box from the outside, are the E and H fields attenuated equally? Or, are there wall material properties that could cause EMR to emerge in the near field at the inner surface of the walls with E or H field dominant? For example, could a sealed enclosure provide good electric shielding and poor magnetic shielding of plane waves? Specifically, is thicker or higher-permeability material required to shield the H component of a plane wave at 500 MHz than is required at 1 GHz? Or, are considerations of thickness and permeability applicable only when shielding near-field AC magnetic fields or far-field EMR at frequencies below hundreds of kHz? Please assume that the box is sized such that all ingress radiation is in the near field.

Further, when I look at electromagnetic shielding equations and explanations thereof, I see no mention of field strength. A fairly well-known engineer assured me early on in my project that with attenuation in the neighborhood of 50 to 80 dB, field strength is not an issue, even under EMP conditions. Yet intuitively, I suspect that a pulse of 50 kV/m and 133 A/m would present unique challenges. So, how well will an enclosure whose walls contain less than 3 microns of metal with milliohmns of surface resistance stand up under an EMP? If your answer includes calculus equations, please include a brief explanation of the equations.

  • \$\begingroup\$ attenuation is also rise time dependent and affected by material properties for skin depth, conductivity etc and magnetic moment of the material ( polar property that affects eddy currents) . e.g aluminum vs copper vs iron vs silver. For a small object Aluminum Foil is a good shield but not for a long transmission line. \$\endgroup\$ – Tony Stewart Sunnyskyguy EE75 Mar 11 '18 at 17:46
  • \$\begingroup\$ Not only that but HEMP at some altitude has a different spectrum than EMP at ground levels with less 1/f attenuation from plane wave thermals and ionization can have a resonance effect on medium that depends on many factors and results in spectral differences are widespread. Even a xenon flash tube when it ionizes can resonate enough to wipe out indoor mobile reception. \$\endgroup\$ – Tony Stewart Sunnyskyguy EE75 Mar 11 '18 at 21:02
  • \$\begingroup\$ This might be part of an answer: Thicker material has lower resistance for the eddy currents. As the answer you link to states, these eddy currents are what shield against alternating magnetic fields. I believe the permeability of the material will help redirect the magnetic field around whatever it surrounds, thus shielding it, but I am not positive. \$\endgroup\$ – pscheidler Mar 11 '18 at 21:46
  • \$\begingroup\$ To divert magnetic fields, a magnetic circuit is implemented in parallel with whatever paths already exist. \$\endgroup\$ – analogsystemsrf Mar 12 '18 at 5:39
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    \$\begingroup\$ Articles in "Interference Technology" yearly magazine (conference papers + vendor ads) showed standard aluminum foil, overlapped 50% on the walls of a room, were excellent EMP protection. The 50% overlap implements a huge capacitance from one foil sheet to the next. \$\endgroup\$ – analogsystemsrf Mar 12 '18 at 5:43

This question relates to a special area of electrical engineering. Protection from intentional EMI and EMP was/is a big subject in defense industry, and tons of studies were conducted in 1960s -1980s on the subject, with some unclassified parts published and groups. There are published magazines as "Interference Technology", there are lots of IEEE publications, and books were written like this one or this.

Propagation of EM waves across complex media may be not an intuitive thing. To find answers on effects of complex layered materials, the right approach is to use 3D modeling software tools, like the one offered by Keysight. It will be difficult to answer your particular question about field strength without solving your case with details of particular materials and exact geometry.

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    \$\begingroup\$ I worked with a demo of Keysight EMPro for awhile and I ultimately learned that it couldn't do what I needed it to do. It's great for analyzing how fields behave on the scale of electronic components, but not for analyzing, for example, how fields behave inside a 1 ft cube with a skin of aluminum foil. A thin skin requires a smaller mesh grid size than EMPro can handle. Even if it could handle the required resolution, the computing power required would far exceed that of a PC. As I was getting closer to what I needed, simulations were taking days to complete. \$\endgroup\$ – dcorsello Feb 23 '19 at 16:37

When a plane wave in air hits the outer surface of an electrically conductive shield, part of the incident wave is reflected; part is propagated through the shield medium; and part is transmitted into air at the inner surface of the shield. Attenuation occurs through losses due to reflection and absorption. Shielding effectiveness is defined as the ratio between incident and transmitted field amplitudes. $$ SE = 20 \cdot\log(\frac{E_{inc}}{E_{trans}}) $$ From chapter 3 of Electromagnetic Shielding and Corrosion Protection for Aerospace Vehicles by Jan W. Gooch and John K. Daher, shielding effectiveness can be defined in terms of either the electric field (as above) or the magnetic field. When defined in terms of electric field amplitudes, it's known as electric shielding effectiveness (ESE). When defined in terms of magnetic field amplitudes, it's known as magnetic shielding effectiveness (MSE).

According to the authors, for plane waves and a shield with air on both sides, the two definitions are equivalent. $$ ESE = MSE $$ So, for far-field radiation, if a material provides electric attenuation that's sufficient for a particular application, it would follow that it also provides sufficient magnetic attenuation. Actually, this equivalency means that it’s meaningless to discuss the electric and magnetic fields of a plane wave as entities that act independently with respect to reflection and absorption.


Losses due to reflection are determined by the impedance mismatch between two media. The higher the difference, the more incident radiation is reflected. And, because good conductors have low impedance relative to air, the lower a material's impedance, the more it will reflect a plane wave in air. From the formula for impedance, $$ Z = \sqrt{\frac{i\omega\mu}{\sigma + i\omega\epsilon}} $$ it can be seen that low permeability (μ) makes for lower impedance (Z) and therefore, a better reflecting material.


Losses due to absorption are determined by factors that include the shield material's skin depth--the greater the thickness of material relative to its skin depth, the more it will attenuate an incident plane wave. From the equation for skin depth, $$ \delta ≈ \frac{1}{\sqrt{πfμσ}} $$ it can be seen that if minimal thickness is a requirement, then high permeability (μ) makes for smaller skin depth (δ), less overall thickness and therefore, a better absorbing material.

So, for far-field EMR, given two hypothetical materials that differ only in permeability, the material with lower permeability will provide more reflection and less absorption, and the material with higher permeability will provide more absorption and less reflection.

Therefore, given that the material in my application is thinner than its skin depth across most or all of the range of frequencies of interest, and it provides electric shielding that's sufficient for my application, I would conclude that the shielding effectiveness that I measure with a signal source in the far field is due almost entirely to reflection. Also, because MSE = ESE, I would predict that magnetic shielding will also be sufficient in the far field.

And, because the incoming signal will be attenuated significantly before it propagates through the shielding material, significantly less than the incident energy will be available to be absorbed and released as heat. So I don't think there will be complications due to overheating of the shield in EMP conditions as I had feared.

However, if unshielded conductors are located near an enclosure that’s optimized for far-field radiation, near-field radiation could be an issue in an EMP.

  • \$\begingroup\$ Doesn't MSE = ESE assume that you are in the far field of the shield itself as well as the signal? A conductive shield will attenuate the E field far more -- when the receiver is not pretty distant from the wall, won't low frequencies have a much higher magnetic component than high frequencies? \$\endgroup\$ – fuzzyTew Feb 22 '19 at 22:02
  • \$\begingroup\$ @fuzzyTew, yes, MSE = ESE in the far field, which is what I said ("plane wave" is synonymous with "far field"). I think it's not that low-frequency, near-field EMR contains a higher H component than in the far field. It's that the E and H components act independently in the near field (in the far field, they are inseparable--they actually create one another), and the magnetic component is more difficult to shield, i.e., requires shielding material of greater thickness and/or higher μ. \$\endgroup\$ – dcorsello Feb 23 '19 at 16:13
  • \$\begingroup\$ My understanding is that low frequencies are shielded more poorly by conductive shields, and I imagine it is because far-field is so much farther for them due to their long wavelength. When discussing shielding far-field or plane wave radiation, it seems obvious to me the shield is in the far field of the emitter, but it seems less obvious that the intent is that the receiver must be in the far field from the shield. MSE = ESE implies both to me -- did you mean this? \$\endgroup\$ – fuzzyTew Feb 25 '19 at 13:54

This is an interesting question for which I’ll give a hand-waving answer. I worked in Santa Clara for several years; one stint at a particular company involved large semiconductor manufacturing inspection equipment, which had both large and smaller modules containing various sources of EMI. I was tasked to bring this up to EMC compliance for emissions and (reception).

There was an expert in the valley, Mark Montrose, who did just this type of work. Part of his approach was the approach of the problem with respect to rise times, or edge rates, of incident and emitted EMI. With a “fast” edge rate, the approach required consideration of transmission line effects, as the knee bandwidth was, to a good approximation, the reciprocal of twice the rise time, or edge rate. In unterminated or poorly shielded scenarios, the reflections, edge effects, and leakage (did) cause issues in what is a precisely defined standard for these effects.

The above is the short version of his introductory comments to me. The short answer is that for large manufacturing equipment, there is a boilerplate approach in which sensors are placed around the equipment and a large list of measurements are made, compared to standards, and then troubleshooting done when required. For, say, single PCBs, an anechoic chamber was used, and similar boilerplate torture was performed.

There is also a simulation approach.

In any case, he’s taken a workmanlike approach to the questions of EM compliance and, in his words, turned Maxwell’s equations into algebra. He’s well known in “the valley” and will take your call. You can google him;, he’s all over and prolific within IEEE, etc. Tell him Robert from the blue building on San Tomas sent you.

He’s a very approachable, knowledgeable professional, and will answer your questions as if doing a magic trick.

  • \$\begingroup\$ The knee is the sin(x)/x point where response is -3dB. Thus 1nanoSecond edge, doubled to 2nanoSeconds, and inverted to product 500MHz, gives the -3dB energy value of 1nS edges. \$\endgroup\$ – analogsystemsrf Mar 12 '18 at 5:38
  • \$\begingroup\$ @analogsystemsrf, would you pleas explain? \$\endgroup\$ – dcorsello Mar 12 '18 at 14:11
  • \$\begingroup\$ A mechanical engineer friend of mine recently told me that electromagnetics isn't science, it's magic. Maybe he was right. I'm having trouble understanding how edge rate would be an issue with a single pulse. Would you please explain? I did call Mark, and I was very surprised by his characterization of EMP as a large, predominantly magnetic pulse. I wasn't sure how a magnetic field could dominate in the far field, so I emailed him for clarification. I might have misunderstood him. \$\endgroup\$ – dcorsello Mar 12 '18 at 23:28

Actually, analog, while I understand you, the difference sometimes lies with “edge rate” and “rise time” and sometimes depends on to whom you are speaking. 1/(2tr) is used as a good approximation for power spectral density, but is usually expressed as 0.5/tr. You can see why it is used if you consider this edge as exactly 1/2 of a period, then find the corresponding frequency. I went to a Howard Johnson seminar back in the 90s and was pretty sure I remembered it right. Then I went to https://www.conted.ox.ac.uk/courses/webfiles/HSDD_Student_material.pdf and found a pretty good replica. That is to say, his presentation is still lifting even after some years.

You will also see 0.34/tr

Finally, it was also discussed here: How is rise time related to bandwidth of the signal?

It always pays to define context and vocabulary. I’m new around here.. I’ll get the hang of it.


  • \$\begingroup\$ Robert, I think the way the site works is that this should be added as a comment to your original answer, not as an additional answer. Yes, some definitions of vocabulary would be helpful. As-is, your answers might demonstrate that you have highly specific knowledge of the subject, but without simple, brief definitions of terms, they are not helpful in providing understanding of general concepts, which is what I'm asking for. Are you saying that in a single pulse, a very small rise time adds high-frequency harmonics to the incident wave? \$\endgroup\$ – dcorsello Mar 13 '18 at 16:42

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