Introduction

Electronic equipment can be effectively shielded by the use of a conductive barrier placed between the source of electromagnetic waves and the equipment to be shielded as shown in Figure 1.

The shielding effectiveness (SE) factor may be expressed as the ratio of the transmitted field magnitude to the incident field magnitude. The shielding effectiveness figure may be expressed as:

                                                 (1)

• Relative permiability, permittivity and conductivity on a specific shielding material and on the material surrounding the shield, as well as the frequency of the interference (Hz). This is achieved by using the appropriate text fields provided,
• parallel or perpendicular polarization of the incident wave, by selecting the relevant check-box,
• the thickness of the shield, by dragging a vertical line to the right, away from a fixed vertical line representing the left-hand-side of the shield,
• the angle that the incident wave is inclined to the shield normal by clicking and dragging a red ball representing the source of the incident ray anywhere in a region left of the left-hand-side boundary of the shield.
• Choosing a particular check-box that will give a preset selection of variables for a particular material, e.g. copper, glass, etc.

The hyper-linked document ShieldingCalc.doc develops the relevant equations that are used by the applet in calculating the shielding effectiveness. Also calculations for determining the Brewster angle, which is also included in the applet are given in this document. A calculation for the angle of refraction derived from complex angles is presented in the hyper-linked document Refraction.doc. A knowledge of electromagnetic theory is assumed. Should the reader require an introductory reference book, an excellent book is "Introduction to electromagnetic fields - 3^rd Edition, Clayton R. Paul, Keith W. Whites, Syed A. Nasar - 1998, ISBN 0-07-046083-3" available from http://www.amazon.com. All units are SI. For the shielding effectiveness, two sets of calculations are performed. The first is where the incident wave has parallel polarization and the other, where the incident wave has perpendicular polarization. The equations developed use oblique incidence of a uniform plane wave and are made general. This means that air does not have to be the surrounding media to the shield, although, the media surrounding the shield must be the same. Similarly, for the determination of the angle of refraction. However, as only the plane of constant phase is required in the calculations of the angle of refraction, only the total field at the boundary is considered. The angle of refraction is derived in the companion document Refraction.doc using complex angles and not by using Snell’s law.

The applet

The applet has a series of six radio buttons on the top to enable pre-programmed parameters for a particular material (Copper, Iron, Aluminum, etc.) to be automatically entered into each of the input parameter text fields. After these have been entered, the choice of polarization (TE - perpendicular or TM - parallel) is selected and the frequency (Hz) of the interfering signal is entered. The results are as appears in Figure 2 below, using Copper as the material, with TE as the preferred polarization, at a frequency of 3GHz.

By dragging the right-hand vertical line to the right, the thickness of the material, t m m, can be varied and the screening effectiveness in decibels will be given, together with the argument of the transmitted to incident wave, arg(SE). As the thickness of the material is varied by the action of dragging the mouse, the screen will be updated with the new thickness in m m. These three outputs are shown in red.

By dragging in the region left of the fixed left-hand vertical line, an angle of incidence , can be established. Automatically, the reflected wave , and its correct angle of reflection on the first boundary will appear. If the angle of incidence is the Brewster angle for the material, then the reflected signal will disappear and "No reflection!" will be printed on the screen. For Media 2, the refracted wave , together with it's reflected wave , will correctly appear automatically for the chosen angle of incidence and the material parameters entered in the text fields. Finally, the wave transmitted from the right-hand side of Media 2 into Media 1 , is shown at the same angle as the incident wave.

The angle of incidence, angle of refraction , and angle of transmission , are shown in dark blue at the bottom left-hand side of the screen. These values are automatically updated as the angle of incidence changes.

For the particular material chosen, its parameters, , relative permiability, relative permittivity and conductivity respectively, are either entered manually in each of the text fields in the MEDIUM 2 row, or for the choices offered, by means of the radio buttons. For material in MEDIUM1, which is defaulted to that of air, the material parameters , again can be entered manually or, for the choices offered, taken as that of air.

Finally, the frequency is entered into its text field. The value entered must be in Hz. If the value is say, for example, 7.8Mz, then it is easier to enter it as 7.8E6. Figure 2 shows 3 GHZ entered as 3E9. This form of entering values can also be used for the other material parameter text fields, as shown in Figure 2.

The screen outputs, shown in blue in Figure 2 are the various parameter equations that are derived for each of the media used, in the course of developing the final equation. These plane wave parameters are:

, the attenuation constant (Np/m), shown as "alpha1" and "alpha2",

, the phase delay constant (rad/s), shown as "beta1" and "beta2",

, the impedance at the boundary (W ), shown as "z1" and "z2",

The value of the Brewster angle, or that it does not exist

, the reflection coefficient, shown as "refl.1" and "refl.2",

, the transmission coefficient, shown as "Tx1" and "Tx2".

This applet has been designed for oblique plane waves. To activate the applet: after inserting the input parameters, enter the frequency and press "enter". Also, the applet can be activated by pressing enter from any "text-field" input parameter box. If a letter is inserted into any of the text fields instead of a number, an error message will appear. The polarization can be changed without effecting the graphics layout or the text field entries if "Click here to enter your values" checkbox is activated. This is convenient if comparisons are to be made between polarizations. However, the preset text field entries will remain if the "Click here to enter your values" is not activated, so before pressing enter, check that all of the text field entries are correct and this checkbox is activated or the required preset checkbox is activated.

Figure 2 Screen shot of the applet using a pre-programmed parameter input

The Microsoft Word *.doc" files; "Shielding.doc" (this document), "ShieldingCalc.doc" and "Refraction.doc" are available for download together with the code for this applet in a zip file format called "Shielding.zip".

Tony Townsend, tonyart@ieee.org