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Let us calculate the shielding
effectiveness of a PEC box with a slot, excited with a plane wave
incident in the direction perpendicular to the slot.
A rectangular metal enclosure with an aperture on one face can be
modeled as a waveguide, shorted at the far end, with the aperture at the
entrance to the waveguide. The model is quickly created with just a few
plates in WIPL-D Pro (Fig. 1).
The electric field shielding effectiveness is calculated as the ratio of
the impinging field to the field measured at some point within the
waveguide, distant from the slot.
The theory assumes that a single TE10 waveguide mode propagates from the
aperture and normal to it. Higher order modes, and modes propagating in
other directions may exist which will complicate the results, and
introduce need for EM simulation in order to predict the shielding
effectiveness. The box is taken to be empty. The results of EM
simulation are in excellent agreement with results obtained by using
intermediate level simulation tools from University of York, and easily
obtainable by using their online calculator [1] .
The objective is to investigate the influence of changes in box and slot
geometry as well as in position inside the box at which field is
calculated on shielding effectiveness (Fig. 2).
For fixed dimensions of the box and of the aperture (a=30 cm,
b=12 cm, d=30 cm, l=10 cm, w=0.5 cm), shielding
effectiveness at various positions within the box (at the symmetry
plane) is displayed in Figs 3 and 4. The shielding effectiveness is
worst close to the slot while it increases as we move away from the
slot. The subsidiary depth-wise resonance shifts up in frequency as the
probe moves towards the back. The principal resonance is due only to the
box dimensions, so its frequency is unaffected.
|
Fig 1. Rectangular box with an
aperture |
Fig 2. Explanation of geometry of
the box with a slot (taken from [1]) |
|
Fig 3. Shielding effectiveness of
electric field for p varying from 5 cm to 20 cm. |
Fig 4. Shielding effectiveness of
magnetic field for p varying from 5 cm to 20 cm. |
If we fix everything except the width of
the box (a), then for b=12 cm, d=30 cm, l=10
cm, w=0.5 cm and p=15 cm, and by varying a from 20
cm to 40 cm, we get Figs 5 and 6. The principal resonance frequency
shifts as we change the box size, as expected.
By fixing all parameters except the length of the slot to a=30
cm, b=12 cm, d=30 cm, w=0.5 cm and p=15 cm
and varying l from 3 cm to 17 cm, we get Figs 7 and 8. Shielding
effectiveness is directly related to the size of the slot, and it
decreases as the slot grows.
|
Fig 5. Shielding effectiveness of
electric field for box width a varying from 20 cm to 40
cm |
Fig 6. Shielding effectiveness of
magnetic field for box width a varying from 20 cm to 40
cm |
|
Figure 7. Shielding effectiveness
of electric field for l varying from 3 cm to 17 cm |
Fig 8. Shielding effectiveness of
magnetic field for l varying from 3 cm to 17 cm |
A closer look at the fields inside the
box at several frequencies within the range from 700 MHz to 1.3 GHz was
done in order to illustrate higher order modes that form. Fig. 9 shows
near fields at different frequencies in case when the incident plane
forms an angle of 75 degrees with the normal to the slot.
a)
b)
c)
d)
e)
f)
Fig 9. Electric field amplitudes inside the box at: a) 700 MHz, b) 800
MHz, c) 900 MHz, d) 1 GHz, e) 1.2 GHz, and f) 1.3 GHz.
All models used in this paper required
around 750 unknowns (4.5 MB of RAM). In many examples, this can be
further diminished using symmetry planes to about 200 unknowns.
Simulation in 100 frequency points takes about 40 seconds on a Intel
Core2 Duo CPU with 2.66 GHz clock.
References
[1]
http://www.emc.york.ac.uk/examples/screening/screening.html
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