Approximate Simulation of the Shielding Effectiveness of a Rectangular Enclosure with a Grid Wall Ronald De Smedt l, Jan De Moerloose l, Steven Criel l, Dan3 De Zutter 2, Frank Olyslager2, Eric Laermans 2, Ward Wallyn2, Norbert Lietaert3 ’ : Alcatel Telecom, EMC Research, Francis Wellesplein 1, B-201 8 Antwerpen, BELGIUM 2 : University of Gent, Dept. of Information Technology, St.-Pietersnieuwstraat 41, B-9000 Gent, BELGIUM 3 : BARCO NV, Research & Development Dept., Th. Sevenslaan 106, B-8500 Kortrijk, BELGIUM Abstract: The shielding effectiveness of a rectangular enclosure, with one wall as a grid, is studiedin detail. An approximatetechnique is used:the holes of the grid are replacedby concentrated magnetic di- poles and the inside of the enclosureis regardedas a piece of a wave- guide with only the lowest TBto-mode present. This allows the constructionof a simpleequivalent circuit, from which the shielding ef- fectiveness can be quickly deduced. This simple model has been checked against dedicated experiments, proving its validness even above the first resonance frequency of the empty enclosure. INTRODUCTION Several mechanisms may cause leakage through a shielded enclosure and thus degrade its shieldingeffectiveness. As a result the total equip- ment (electronics + shield) may radiate too much or may become too susceptible to externalradiation. In this paperwe focus our attentionto the leakagethrough grids, which are, for instance,frequently used for ventilation purposes. Grids have been studied in the past by several authors [l-S], but re- stricted to the effect of a single plane. In most cases various numerical techniques are applied to study the transmission through a periodic array of apertures. In [5] the effect of the array is represented by an equivalent sheet impedance. When a shielded enclosure is studied,gen- eral numerical methods,such as Method of Moments or Finite Differ- enceTime Domain, can accurately predict the shielding effectiveness when a limited number of apertures is present[7-91.The Mdndez tech- nique is basedon a modal expansion inside the enclosure [lo-121. A very simplified, but effective equivalent circuit has recently been pro- posed by the Universities of York and Nottingham for the case of a single aperturein a rectangular enclosure [ 13,141. The present paper proposes a similar equivalent circuit for an enclosurewith a grid wall. The starting point in the theoretical development is representingthe holes in the grid by concentrated magneticdipoles and determining the coupling between thesedipoles and the waveguide modes, regarding the enclosure asa pieceof waveguide.To simplify the analysisonly the lowest ‘lIZlo-mode is taken into account and the summation over the large numberof holesis replaced by a suitableintegral. When applying an external incident field, we can derive in this way the sourcevoltage of the TBto-mode. To determine the source impedance we use a ‘l&o-mode asincident wave at the inside of the waveguide and calcu- late the reflection due to the presence of the holes in the grid. All this allows to build anequivalentcircuit where the voltagesandcurrentsare proportional to the electric and magnetic field respectively. From these we can derive the shielding effectiveness.The above analysis is vali- datedby measuring the shielding effectiveness of a dedicated test enclo- sure in which rive walls are perfect and with various grids as inter- changeable front panel. THEORETICAL DEVELOPMENT OF THE MODEL Low frequency apertures We consider a rectangular enclosurewith dimensions: length a, height b, depth d (Figure 1). All the walls are madeof perfect conductors.The only leakage,consideredhere, occurs through perforations (apertures, grids, ...) in the front panel. The five other walls act as a perfect shield. We start with a singleaperture in the front panel, which is illuminated by a plane wave (E’, H’) at normal incidence (Figure 1). b Figure 1. Rectangular enclosure with a grid wall We now assume that the aperture is small (compared to the wavelength) and that the front panel acts as if it was an infinite screen.In this case it can be shown that the aperturewill react as a magnetic dipole: P, = f Fcm * 2H: (1) (and an electric dipole, which is zero here),which is proportional to the tangential component of the incident magnetic field and in which 3, = n;,,u,u, + JC,,,~U~U~ is the magnetic polarizability (tensor) [ 1.5171. The + sign applies when consideringthe scatteringat the same side of the incident field, the - sign appliesat the other side. In caseof a circular aperture, with diameter D, the magnetic polarizabilities turn out to be: SC, = qy = $D3 (2) For the case of a rectangularaperture, with dimensions Lx and Ly (along the x- and y-axis respectively), approximate expressions are presented in [18,19]: 0-7803-5015-4/98/$10.00 0 1998 IEEE 1030