Shielding Effectiveness Studies of Rectangular Enclosures with Apertures against EM fields with Arbitrary Angles of Incidence and Polarizations

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Shielding Effectiveness Studies of Rectangular
Enclosures with Apertures against EM fields with
Arbitrary Angles of Incidence and Polarizations
Zulfiqar Ali Khan Oklahoma State
UniversitySchool of Electrical and Computer
EngineeringStillwater OK 74078 e-mail
zulfiqa_at_okstate.edu [phone]
Charles F. Bunting Oklahoma State
UniversitySchool of Electrical and Computer
EngineeringStillwater OK 74078e-mail
reverb_at_okstate.edu(405) 744-1584
Funded under NASA Grant NCC-1-01032
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Overview

• Formulation of Modal/MoM for oblique incident and
  arbitrary polarized plane waves
• Effects of following factors on SE
• Angle of Incidence
• Polarization
• Location inside cavity
• Frequency
• Number of apertures
• Conclusions
• Future plans

(M.D. Deshpande, Electromagnetic Field
Penetration Studies, NASA/ CR-2000-210297, June
2000.)
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Basic Geometry
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Assumptions and Limitations

• The thickness of the walls very small
• Diffraction from the edges of the walls
  neglegible
• Rectangular cavity and apertures
• (can be easily extended to other regular
  geometries)
• Lossless and empty cavity

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Formulation of the Problem

• Use Equivalence Principle to replace apertures
  with equivalent magnetic currents
• Use Greens function for a rectangular cavity to
  determine the internal cavity fields
• Use free-space Greens function to determine
  external scattered field
• Match external and internal fields at the
  apertures
• Use Galerkins method to obtain final matrix
  equation to be solved numerically

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The Incident Wave
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Aperture Fields
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Equivalent Magnetic Currents
Using equivalence principle, we can replace the
aperture fields by equivalent magnetic currents
as follows
Replacing the apertures with equivalent magnetic
currents allows splitting the problem into two
parts Internal and External
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Scattered Fields
Internal Fields due to equivalent magnetic
currents can be determined using Cavity Greens
functions
External Fields due to equivalent magnetic
currents can be determined using free space
Greens functions
The scattered Electric fields can be determined
similarly.
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Boundary Conditions
Matching the internal external fields at the
apertures
Using Galerkins method and noting the
orthogonality gives us the final matrix equation
that can be solved numerically.
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Final Matrix Equation
Final Matrix Equation
where
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SEx vs Incidence Angle (Single Aperture Case)
SE calculated at the center of the cavity.

• SE minimum for normal incidence
• Increasing polarization decreases SE
• Increasing frequency decreases SE
• Aperture radiation pattern has more lobes at
  higher frequencies.

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SEx vs Incidence Angle (Two Apertures Case)
SE calculated at the center of the cavity.

• SE not minimum for normal incidence at 3.0 GHz
• Increasing frequency decreases SE
• Aperture radiation pattern has more lobes at
  higher frequencies.

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SEx vs Incidence Angle (Four Apertures Case)
SE calculated at the center of the cavity.

• SE not minimum for normal incidence at 3.0 GHz
• Increasing frequency decreases SE
• Aperture radiation pattern has more lobes for
  higher frequencies.
• Appearance of a null at the center of cavity at
  10 GHz

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SEy vs Incidence Angle (Single Aperture Case)
SE calculated at the center of the cavity.

• SE minimum for normal incidence
• Decreasing polarization decreases SE (opposite
  to SEx)
• Increasing frequency increases SE (opposite to
  SEx)
• Larger field penetration for Ey than for Ex
• Similar behavior for two and four apertures
  (results not shown here)

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SEz vs Incidence Angle (Single Aperture Case)
Polarization 0 degrees
Polarization 42, 90 deg
A null has appeared at the center of the cavity
for Ez field for polarization angles greater than
zero degrees
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SEx vs Polarization (Single Aperture Case)
SE calculated at the center of the cavity.

• Increasing polarization decreases SE
• Increases frequency decreases SE
• Negative SE at 20 GHz

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SEx vs Polarization (Two Apertures Case)
At different frequencies
At different distances from the aperture

• SE decreases with increasing frequency
• Minimum SE at the center of the cavity

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SEz vs Polarization (Single Aperture Case)
SE calculated at the center of the cavity.

• Appearance of null at certain polarizations
• The null appears to shift with frequency towards
  lower polarization
• Higher SE compared to x and y components of E
  field
• SE decreases with increasing frequency

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SEz vs Polarization (Two Apertures Case)
SE calculated at the center of the cavity.

• Minimum SE at the center of the Cavity
• Null appears at different polarizations at
  different points inside cavity

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Conclusions

• Dependance of SE upon
• Angle of Incidence
• Polarization
• Frequency
• location inside cavity
• Maximum Field Penetration for Normal Incidence
  Only for single Aperture
• Careful sampling of cavity fields due to their
  modal structure
• Future work
• Adding loss
• Cylindrical Cavity and apertures
• Statistical Investigation