Effect of the Apertures

This is the final article in a series [1-7] devoted to the topic of shielding to prevent electromagnetic wave radiation. All the previous articles assumed a solid shield with no apertures. This article addresses the impact of slots or apertures in the shield on radiation. It is shown that apertures can be as effective radiators as antennas of the same dimensions.

Apertures and Shielding Effectiveness

In practice, most shields are not solid, since there must be access covers, doors, holes for cables, ventilation, and displays, like the ones shown in Figure 1.

All of these apertures reduce the effectiveness of the shield. Consider a solid shield shown in Figure 2.

The incident field induces a surface current in the shield, which may be thought of as producing the reflected field that tends to cancel the incident field [8]. In order for the shield to perform this cancellation, the induced currents must be allowed to flow unimpeded, as shown in Figure 3a.

The slot will impede the current flow. Figures 3b and 3c illustrate that the thickness of the slot is not critical, but the length of it is. An obvious solution might be to place the slot parallel to the current flow, as shown in Figure 4a, to minimize its adverse effect.

The problem with this solution is that it is not feasible to predict the direction of the induced current. A reasonable solution is to use a large number of small holes (Figure 4b), as these small holes disturb the induced current to a much lesser degree.

Electric Dipole and its Fields

The electric (Hertzian) dipole and its complete fields are shown in Figure 5.

The far fields of the electric dipole are

(1)

(2)

(3)

The simplified far-field model of the dipole (oriented along the z axis), and the fields at an observation point P at the location (θ = 90°, = φ = 90°) are shown in Figure 6.

Electric source, J, produces the fields and at an observation point P in the far field of the antenna. The medium with intrinsic impedance η_O is infinite with no other objects present.

Babinet’s Principle Applied to a Slot Antenna

Babinet’s principle, modified by Brooker for antennas [9], provides a way to analyze the radiation from slot antennas by treating a conducting strip (of the same dimensions as the slot) like a complementary antenna to shield with a slot.

Figure 7 shows an infinite thin flat metallic shield with a slot cut out, placed between the source and the observation point in the far field.

Now, the fields at an observation point P are and , as shown in Figure 7. Next, the shield is replaced by a complementary thin metallic strip of the same dimensions as the slot, as shown in Figure 8.

Now, the fields at an observation point P are and.

The fields in Figure 7 and Figure 8 are related by [9]:

(4a)

(4b)

Next, consider the situation shown in Figure 9a where the electric dipole is rotated and oriented along the x-axis.

Figure 9b shows the fields at the observation point in far fields with the shield containing a slot cut out, placed between the source and the observation point. Figure 9c shows the fields with a metallic strip of the same size as the slot placed between the source and the observation point.

Figure 9 leads to the two additional relations [9]:

(5a)

(5b)

Equations (4) and (5) lead to the conclusion that apertures can be as effective radiators as antennas of the same dimensions.

References

1. Bogdan Adamczyk, “Shielding to Prevent Radiation – Part 1: Uniform Plane Wave Reflection and Transmission at a Normal Boundary,” In Compliance Magazine, June 2025.
2. Bogdan Adamczyk, “Shielding to Prevent Radiation – Part 2: Uniform Plane Wave Normal Incidence on a Conducting Shield,” In Compliance Magazine, July 2025.
3. Bogdan Adamczyk, “Shielding to Prevent Radiation – Part 3: Far-Field Shielding Effectiveness of a Solid Conducting Shield – Exact Solution,” In Compliance Magazine, August 2025.
4. Bogdan Adamczyk, “Shielding to Prevent Radiation – Part 4A: Far-Field Shielding Effectiveness of a Solid Conducting Shield – Approximate Solutions,” In Compliance Magazine, September 2025.
5. Bogdan Adamczyk, “Shielding to Prevent Radiation – Part 4B: Far-Field Shielding Effectiveness of a Solid Conducting Shield – Approximate Solutions,” In Compliance Magazine, October 2025.
6. Bogdan Adamczyk, “Shielding to Prevent Radiation – Part 5: Near-Field Wave Impedance of Electric and Magnetic Dipoles,” In Compliance Magazine, November 2025.
7. Bogdan Adamczyk, “Shielding to Prevent Radiation – Part 6: Near-Field Shielding Effectiveness of a Solid Conducting Shield,” In Compliance Magazine, December 2025.
8. Clayton R. Paul, Introduction to Electromagnetic Compatibility, Wiley, 2006.
9. C. A. Balanis, Antenna Theory Analysis and Design, Harper & Row, New York, 1982.