Shielding to Prevent Radiation

EMC concepts explained

Part 4B: Far-Field Shielding Effectiveness of Solid Conducting Shield – Approximate Solutions – Version 2

his is Part 4B of seven devoted to the topic of shielding to prevent electromagnetic wave radiation. The first article [1] discussed reflection and transmission of uniform plane waves at a normal boundary. The second article, [2], addressed the normal incidence of a uniform plane wave on a solid conducting shield with no apertures. The third article, [3], presented the exact solution for the shielding effectiveness of a solid conducting shield. In Part A of the fourth article [4], Version 1 of the approximate solution was derived. In this article, a more practical Version 2 of the approximate solution (obtained from Version 1) is presented.

Shielding Effectiveness – Approximate Solution – Version 2

An approximate solution for the reflection loss (Version 1) was derived in [4, Eq. (10)] as

Substituting h₀ = 120p and using Eq. (24) (from [4]) in Eq. (1), we get

resulting in

This is an alternative expression to Eq. (1) for the reflection loss for good and thick conductors in the far field. Note that the reflection loss is greatest for high conductivity-, low permeability- materials, and at low frequencies.

Now, let’s derive an alternative expression for the absorption loss. The exact formula was given by Eq. (11) in [4] as

Skin depth in good conductors is given by [4]

Using Equations (22) and (23) (from [4]), in Eq.(6), we get

Substituting this result into Eq. (5), we get an alternative formula for the absorption loss of good conductors in the far field as (with the conductor thickness t in meters)

When the conductor thickness is expressed in inches, this formula becomes

This is the alternative expression to Eq.(11) in [4] for the absorption loss for good and thick conductors in the far field. Note that the absorption loss is greatest for high conductivity-, high permeability- materials, and at high frequencies.

The total shielding effectiveness is

or, utilizing Equations (3) and (9)

Table 1: Relative conductivity and permeability of copper and steel

Far-Field Shielding Effectiveness – Copper vs. Steel – Simulations

In this section, we compare far-field shielding effectiveness of copper and steel (SAE1045). Table 1 shows the relative conductivity and relative permeability of these two shield materials.

Let’s begin with the reflection loss, computed from

Figure 1 shows the reflection loss in the frequency range 100 Hz – 1 GHz. Note that the reflection loss of copper is higher over the entire frequency range.

Figure 1: Reflection loss – copper vs. steel

The absorption loss, for 20-mil thick shields, is calculated from

It is shown in Figure 2. Note that the absorption loss of steel is higher over the entire frequency range.

Figure 2: Absorption loss – copper vs. steel

The total shielding effectiveness is calculated from Eq. (10b) and is shown in Figure 3.

Figure 3: Total shielding effectiveness – copper vs. steel

Note that up to the frequency of about 4200 Hz, the shielding effectiveness of copper is higher than that of steel. Beyond that frequency, the opposite is true.

References

Bogdan Adamczyk, “Shielding to Prevent Radiation – Part 1: Uniform Plane Wave Reflection and Transmission at a Normal Boundary,” In Compliance Magazine, June 2025.
Bogdan Adamczyk, “Shielding to Prevent Radiation – Part 2: Uniform Plane Wave Normal Incidence on a Conducting Shield,” In Compliance Magazine, July 2025.
Bogdan Adamczyk, “Shielding to Prevent Radiation – Part 3: Far-Field Shielding Effectiveness of a Solid Conducting Shield – Exact Solution,” In Compliance Magazine, August 2025.
Bogdan Adamczyk, “Shielding to Prevent Radiation – Part 4A: Far‑Field Shielding Effectiveness of a Solid Conducting Shield – Approximate Solution – Version 1,” In Compliance Magazine, September 2025.

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Dr. Bogdan Adamczyk is professor and director of the EMC Center at Grand Valley State University (http://www.gvsu.edu/emccenter) where he performs EMC educational research and regularly teaches EM/EMC courses and EMC certificate courses for industry. He is an iNARTE-certified EMC Master Design Engineer. He is the author of two textbooks, “Foundations of Electromagnetic Compatibility with Practical Applications” (Wiley, 2017) and “Principles of Electromagnetic Compatibility: Laboratory Exercises and Lectures” (Wiley, 2024). He has been writing “EMC Concepts Explained” monthly since January 2017. He can be reached at adamczyb@gvsu.edu.

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