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Shielding theory: reflection, absorption, apertures

Guide, EMC fundamentals

The material a shield is made of almost never decides how well it works. The arithmetic below shows why: plain metal offers hundreds of decibels, far more than any product needs, and the achieved figure is set instead by the openings, the seams and the cables crossing the boundary. Understanding that ordering is the difference between buying a solution and buying an expensive box.

Shielding effectiveness is conventionally split into three contributions, added in decibels:

SE = R (reflection) + A (absorption) + B (multiple-reflection correction)

Reflection occurs at the surface, because the arriving wave meets a huge impedance mismatch. Free space presents 377 ohms; a metal surface presents a few thousandths of an ohm. Most of the energy never enters.

Absorption attenuates whatever did enter, as it crosses the thickness. It follows directly from skin depth:

A = 8.686 x t / delta [dB]

where t is the wall thickness and delta the skin depth. The constant is not empirical: it is 20 log10(e) = 8.6859, the conversion from natural logarithm units to decibels.

The correction term B accounts for energy bouncing between the inner and outer faces. It is negative and only matters when the wall is thin compared with a skin depth, which for a metal enclosure above a few megahertz it never is.

Far-field reflection loss for a good conductor works out as:

R = 168 - 10 log10(mu_r x f / sigma_r) [dB]

for f in hertz, with permeability and conductivity relative to copper. That expression is not a fitted rule: computing the surface impedance from first principles and comparing with the free-space impedance gives the same answer to a tenth of a decibel.

FrequencyReflection loss, copper
1 MHz108 dB
10 MHz98 dB
100 MHz88 dB
1 GHz78 dB

Absorption through half a millimetre of copper:

FrequencySkin depthAbsorption, 0.5 mm
1 MHz66.1 um66 dB
10 MHz20.9 um208 dB
100 MHz6.6 um657 dB

At 100 MHz the wall is seventy-five skin depths thick, giving a theoretical total near 745 dB. That number is meaningless for a real product. Nothing achieves it, no measurement could confirm it, and quoting it is a sign that apertures have not been considered.

A slot leaks according to its length relative to the wavelength. For a slot shorter than half a wavelength:

SE = 20 log10(lambda / 2L) [dB]

Longest openingat 100 MHzat 1 GHz
1 mm63.5 dB43.5 dB
10 mm43.5 dB23.5 dB
50 mm29.5 dB9.5 dB
100 mm23.5 dB3.5 dB

Set that against the material figure. An enclosure offering several hundred decibels of copper delivers 23.5 dB because one lid joint is 10 cm long, and at 1 GHz that same joint delivers 3.5 dB, which is nothing.

Two consequences follow, and they are the whole of practical shielding.

Leakage follows the longest dimension, not the area. A ventilation pattern of many small round holes outperforms a single slot of the same open area by a wide margin. A seam that touches only at widely spaced screws is a row of long slots however tightly each screw is done up.

Halving the longest opening buys 6 dB. That is the same 6 dB as a factor of two in decibels for EMC, because the relation is a straight 20 log.

The figures above are far-field, plane-wave numbers. Against a low-frequency magnetic field a non-magnetic shield performs far worse, because reflection loss depends on the wave impedance and a magnetic near field presents a low one. The shield then acts only through induced eddy currents.

This is why mu-metal exists and why it is used for mains-frequency magnetic problems while copper is not. It is also why a shield that solves a radiated emission problem at 200 MHz may do nothing for a 50 Hz hum problem, which is a different mechanism entirely.

Left floating. A shield without a deliberate return path is a conductor coupled capacitively to what it surrounds. It can pick up and re-radiate, raising emissions.

Cables crossing the boundary. This is the one that defeats otherwise good enclosures. A cable passing through an opening carries common-mode current directly from inside to outside, and from coupling mechanisms, common-mode current on a cable radiates roughly ten thousand times more efficiently than differential current in a loop. A few uA are enough. The enclosure is then irrelevant, because the antenna is outside it.

The remedy is to treat the boundary rather than the box: filter or bond every conductor where it crosses, and terminate cable shields to the enclosure in a full circumferential contact rather than a pigtail, since a pigtail is an inductor in exactly the wrong place.

  • SE = reflection + absorption + correction, and for any metal enclosure the first two are far larger than needed.
  • A = 8.686 t / delta, where 8.686 is 20 log10(e), not a fitted constant.
  • Copper at 100 MHz gives about 88 dB reflection and 657 dB absorption through 0.5 mm. The material is not the design variable.
  • A 10 cm seam caps the enclosure at 23.5 dB at 100 MHz and 3.5 dB at 1 GHz. Apertures set performance.
  • Leakage follows the longest dimension. Many small holes beat one long slot of equal area.
  • Cables crossing the boundary defeat the shield, because common-mode current outside the box is the antenna.

Sources & references

  1. Henry W. Ott, Electromagnetic Compatibility Engineering (2009), Wiley , Wiley onlinelibrary.wiley.com/doi/book/10.1002/9780470508510
  2. IEEE 299, standard method for measuring the effectiveness of electromagnetic shielding enclosures , IEEE standards.ieee.org/ieee/299/4262/
  3. IEC 61000-5-7, degrees of protection provided by enclosures against electromagnetic disturbances (EM code) , IEC webstore.iec.ch/en/iec-search/result?q=IEC%2061000-5-7
  4. CISPR 16-1-4, radio disturbance and immunity measuring apparatus, antennas and test sites , IEC webstore.iec.ch/en/iec-search/result?q=CISPR%2016-1-4

Frequently asked questions

What are the three terms of shielding effectiveness?
Reflection, absorption and a multiple-reflection correction, added in decibels. Reflection happens at the surface because of the impedance mismatch between the arriving wave and the metal, and it is the dominant term at low frequency for a good conductor. Absorption is the attenuation of whatever got in as it crosses the thickness, and it grows with frequency, thickness and conductivity. The correction term accounts for energy bouncing between the two faces, and it matters only when the shield is thin compared with the skin depth, where it reduces the total. For any practical metal enclosure above a few megahertz the first two are enormous and the real performance is set by something else entirely.
How much shielding does plain metal actually give?
Far more than anyone needs, which is exactly why the number is misleading. For copper at 100 MHz the reflection term alone is about 88 dB, and 0.5 mm of thickness adds roughly 657 dB of absorption, because the skin depth there is 6.6 micrometres and the wall is seventy-five skin depths thick. The theoretical total is several hundred decibels, a figure with no physical meaning for a real product. No enclosure achieves it, no measurement could confirm it, and treating the material as the design variable is the most common way shielding money is wasted.
Why do apertures dominate?
Because a slot leaks according to its length compared with the wavelength, and that has nothing to do with the metal around it. A useful approximation for a slot shorter than half a wavelength is 20 log10(lambda / 2L). At 100 MHz a 10 cm seam gives about 23.5 dB and a 1 cm seam about 43.5 dB. At 1 GHz the same 10 cm seam gives 3.5 dB, which is to say nothing at all. So an enclosure whose material offers hundreds of decibels delivers twenty-three because of one lid joint. The rule that follows is that shielding is a problem of seams, gaskets, ventilation patterns and connector openings, not of material choice.
Why is a slot worse than a round hole of the same area?
Because leakage follows the longest dimension, not the area. A slot radiates like a slot antenna, and its performance is set by its length. This is why a ventilation pattern of many small round holes vastly outperforms a single long slot of equal open area, and why a seam that is nominally closed but makes contact only at widely spaced screws behaves like a series of long slots. Halving the length of the longest opening buys 6 dB; doubling the number of short openings costs far less than that.
When does a shield make things worse?
When it is left without a deliberate return path, or when cables carry current through it. An ungrounded shield is a floating conductor that couples capacitively to what it surrounds and then re-radiates, which can raise emissions rather than lower them. Cables are the bigger problem: a shield with a cable passing through an opening gives common-mode current a direct route from inside to outside, and since common-mode current on a cable radiates roughly ten thousand times more efficiently than differential current in a loop, the cable defeats the enclosure. A shield is only as good as the treatment of everything crossing its boundary.