EMC concepts explained
Shielding to Prevent Radiation
Part 4A: Far-Field Shielding Effectiveness of Solid Conducting Shield – Approximate Solutions
T
his is the first part of the fourth installment in a series 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 normal incidence of a uniform plane wave on a solid conducting shield with no apertures. The third article, [3], presented the exact solution for shielding effectiveness of a solid conducting shield. In this article, two approximate, yet accurate, solutions are obtained from the exact solution.
Shielding Effectiveness – Approximate Solution – Version 1
The approximate solution for the shielding effectiveness is obtained from the exact solution of the previous article, [3]:
where
Let’s investigate the consequence of the assumption that the shield is made of a good conductor. Intrinsic impedance of a good conductor, at the frequencies of interest, is much smaller than the intrinsic impedance of free space. That is 
<< η0. (For instance, the magnitude of the intrinsic impedance of copper at 1 MHz is 3.69 × 10-4 << 377 Ω).
<< η0. (For instance, the magnitude of the intrinsic impedance of copper at 1 MHz is 3.69 × 10-4 << 377 Ω).
It follows,
If the shield is thick, t << δ, then we have
and the right-hand side of Eq. (1) can be approximated by
or
Furthermore, for a good conductor, we have
and Eq. (5) simplifies to
This is the approximate solution for a good and thick conductor in far field. In dB, this solution becomes
or
where
Note that the approximate reflection loss is different from the exact reflection loss, (Eq. (49) in [3]) while the absorption loss is the same as in the exact solution. Also note that the multiple-reflection loss is not present in Eq. (8), which means that for a good and thick conductor in far field, it can be ignored.
Shielding Effectiveness – Approximate Solution
The approximate solution for the reflection loss given by Eq. (12) and the exact solution for the absorption loss given by Eq. (11) can be expressed in more practical forms. To derive these alternative forms, we need some parameter relationships. Recall the expressions defining the propagation constant and the intrinsic impedance (Equations (6) and (7) in [2]).
Thus,
or
We will return to this equation shortly.
The propagation constant in Eq. (12) can be expressed as
For good conductors, [4],
Thus, the propagation constant in Eq. (16) can be approximated by
Using this result in Eq. (15), we get
or
and thus
Absolute permeability can be expressed in terms of relative permeability (with respect to free space) as
Absolute conductivity can be expressed in terms of relative conductivity (with respect to copper) as
Using Equations (22) and (23) in Eq. (21) we have
In the second part of this installment, we will utilize the above parameter relationships and present a more practical solution for the far field shielding effectiveness of a solid conducting shield.
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, Principles of Electromagnetic Compatibility – Laboratory Exercises and Lectures, Wiley, 2023.
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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.