I'm trying to determine the thickness of copper foil required to construct an enclosure that attenuates a very fast-rising, very brief pulse of AC magnetic field at a frequency of 1 MHz and field strength of 133 A/m by 50 dB. Using the equation $$ A = (3.338)(10^{-3}) t\sqrt{\mu fG} $$ where A is attenuation, t is thickness in mils, μ is relative permeability referred to free space, f is frequency and G is relative conductivity referred to copper, I get a thickness of 380 microns.

Someone answered a previous, related question of mine with the following equation, which he identified as "Maxwell's equation plus Stokes",

$$ \oint_{\partial \Sigma} \mathbf{E} \cdot d\mathbf{l} = -\mu\int_\Sigma \frac{\partial \mathbf{H}}{\partial t} \cdot d\mathbf{A} $$

which means that the electric field, integrated along a contour Σ (i.e, potential) is equal to the integral of the time-derivative of the H field times the medium's μ. He concluded that according to this equation, a strong AC magnetic field at the frequency of interest would induce a current strong enough to fill a thickness of copper, calculated as above, and couple to the contents of the enclosure. I've asked the poster for clarification, but they haven't responded in 5 days.

So, my multi-part question is:

  1. Would someone please confirm that the Maxwell/Stokes equation is applied properly to answer my question, and that the poster was correct in concluding that my copper foil and its contents would be in danger in the presence of a 133 A/m H field, and if so, why?
  2. Could it be because skin depth is greater at 133 A/m than it is at a lower field strength? "The relative permeability of any material at a sufficiently high field strength trends toward 1 (at magnetic saturation)" (Wikipedia). And lower μ means greater skin depth. But I don't think this affects copper, because its relative permeability is 0.999994. Also, I'm not sure if magnetic saturation applies to copper in an AC magnetic field. So is there another property of copper that results in increased skin depth in a high-strength H field? Or,
  3. Does the formula that I used to calculate thickness provide only skin depth, so that an additional thickness of copper is required to separate the point of deepest current penetration from the inner wall of the enclosure? Or,
  4. Does heat build up in the copper due to the high induced current, causing it to melt? (This seems unlikely to me, because the EMR of interest is produced as a very fast-rising but very brief pulse.) Or,
  5. Have I specified insufficient attenuation? If a 133 A/m H field is attenuated by 50 dB, the resulting field strength is 420 mA/m. The only electronic components that might couple strongly at 1 MHz might be things like the coil antenna in an AM radio. Given that the H field of an AM broadcast signal might have a field strength of 76 mA/m at a distance of 100m (see this article), and that an AM radio must be sensitive to much lower-power signals, would 420 mA/m be enough to fry an AM radio? Or,
  6. Does some other phenomenon apply?
  • \$\begingroup\$ Also consider plating on Cu. Zn is good. Ag is better but $ and consider seam resistance and inductance to gnd \$\endgroup\$ – Tony Stewart Sunnyskyguy EE75 Feb 26 '18 at 18:43
  • \$\begingroup\$ Even better,Also consider mu-foil tape with mu >10k and Bsat >0.5 T \$\endgroup\$ – Tony Stewart Sunnyskyguy EE75 Feb 26 '18 at 18:51
  • \$\begingroup\$ "the EMR of interest is produced as a very fast-rising but very brief pulse" - 'very', 'fast', and 'brief' are not specifications. Exactly how 'fast rising' and 'brief' is the pulse? \$\endgroup\$ – Bruce Abbott Feb 27 '18 at 6:46
  • \$\begingroup\$ @bruce, it rises to peak in about 5 nanoseconds, decays to half of peak within about 200 nanoseconds, and is fully decayed by about one microsecond. \$\endgroup\$ – dcorsello Feb 27 '18 at 8:44
  • \$\begingroup\$ I'm confused. You said it was an AC magnetic field with a frequency of 1MHz, but you seem to be describing a DC pulse with a width of ~1us (and a repetition rate of ???). A non-sinusoidal pulse may contain significant harmonic content which will affect the attenuation calculations. \$\endgroup\$ – Bruce Abbott Feb 27 '18 at 9:04

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