# How to increase the "dynamic range" of shielding problems in FEKO

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I need very high dynamic range for a shielding problem, but I don't seem to get more than about 60 dB shielding. Is this correct or is there a problem with my model?

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Users attempting to achieve shielding levels in excess of 40 dB find it unachievable. This is due to the formulation of the MoM and not a bug in FEKO. The MoM uses the electric field integral equation (EFIE) by default. This integral equation leads to a limit on the amount of shielding that can be provided by metallic surfaces. This how-to shows that the surface equivalence principle (SEP) is a valuable tool to model problems with high levels of shielding. This method is also applicable in cases of high permeabilities.

## Why the MoM (with EFIE) gives poor shielding for metallic problems

The total electric field is given by the sum of the incident electric field and the scattered electric field:

`E_total = E_incident + E_scattered`

For example, assume E_incident is 1 V/m (plane wave). If we have, say, 40 dB of shielding, then we must have E_total = 0.01 V/m, and thus E_scattered = -0.99 V/m. Therefore slight errors in E_scattered (e.g. 1%) result in huge errors in the shielding factor (error amplification). E_scattered depends directly on integrating the currents, and the effect of the discretisation is large.

To avoid such cancellation effects of the MoM, the SEP is used to decompose the problem into two regions: (a) outside and (b) inside. One then has to mesh the apertures also and FEKO will set up equivalent electric and magnetic currents. The big advantage of this method is that on the inside the E_incident is zero, and thus E_total  = E_scattered, and the error amplification due to cancellation is removed.

## Example 1 description

Consider a 1m x 1m x 1m cube with a circular aperture of diameter 0.07 m. The shielding inside the box is computed by calculating the near fields caused by an incident plane wave at theta=0. The frequency range is 120 to 180 MHz.

Figure 1: Geometry of the cuboid

## Model setup

To show how the SEP improves the (available) shielding, we create two models.

The first model consists of a cuboid in free space with a circular aperture (hole). The model is made as follows: Create a cuboid. Set the region of the cuboid in the details tree to "Free space". The hole is made by simply subtracting a circular surface (ellipse with equal radii) from the cuboid.

The second model is made as follows: Create a dielectric with permittivity of 1 and no loss. Create the cuboid. Create the ellipse that will represent the hole on top of the cuboid. Union the cuboid and ellipse. Set the region of the Union to the dielectric. Set all the faces of the Union to "Perfect electric conductor". Set/keep the face property of the aperture (ellipse) to dielectric. If necessary, set a local mesh size on the aperture, depending on the size of the aperture.

Figure 2: Close-up view of the aperture for the two models
Aperture of dielectric cuboid Aperture of free space cuboid

An initial mesh size of lam0/10 is used but with finer meshing set on the aperture - in the case of the free space cuboid the edge of the aperture has a local mesh size set; in the case of the dielectric cuboid the face of the aperture has a local mesh size set.

## Results

The near field is computed inside the box and plotted versus frequency. The shielding is given by the ratio between the incident field (in this case 1 V/m) and the field inside the box. Figure 3 compares the shielding for the free space case and the dielectric case. The shielding for the dielectric case is as expected - the aperture size grows electrically with frequency and we would expect the shielding to deteriorate with frequency. However, the free space case shows a much lower shielding and is not consistent with the expected trend.

Figure 3: Shielding compared for the two models

In general, the free space MoM with PEC triangles gives a maximum shielding of the order of 40 dB. This figure deteriorates when the mesh is made coarser than the recommended 1/10th of the free space wavelength.

## Example 2 description

Consider a fully closed sphere of conductivity 1e7 and relative permeability 112. Shielding is computed from 60 Hz to 100 kHz.

Reference: R. Jobava et.al. “Interaction of Low Frequency Magnetic Fields with Thin 3D Sheets of Combined Resistive and Magnetic Properties”, Proceedings of the 40th European Microwave Conference

## Model setup

A sphere is drawn and the inside of the sphere is again set to an air dielectric similar to example 1. Surface properties of conductivity and permeability are assigned.

Figure 4: Geometry of the sphere

## Results

Figure 5: Shielding results: FEKO vs analytical solution and code E

FEKO agrees very well with the analytical solution over the entire frequency band. Note that the numerical solution from code E fails to predict high shielding values due to cancellation effects (avoided in FEKO because SEP is used to separate the interior and exterior regions).

The SEP is clearly the method of choice to model shielding problems. But it must be remembered that the SEP increases the computational resources in that 2 basis functions are assigned per triangle compared to the free space MoM where only 1 basis function is assigned.

There are limits to the shielding that can be computed with FEKO. Reducing the aperture size in example 1 requires a finer mesh on/around the aperture. Eventually a very inhomogeneous mesh will result (a warning or error will be given), casting doubt on the accuracy of the results. In addition, numerical noise will eventually dominate the results as the number of significant digits is limited and fixed. Attainable shielding values will strongly depend on the problem, that is, what is contained inside the box, whether there are connection points, whether there are dielectrics inside the box and so forth.

It is also recommended to use double precision and symmetry (if possible) to increase the accuracy of results.

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