International Journal of Engineering Trends and Technology (IJETT) – Volume 34 Number 3- April 2016 Analysis of Shielding Enclosure using Numerical Electromagnetic Techniques R.Seetharaman, R.Vandana, K.Venkata Srinath Department of Electronics and Communication Engineering College of Engineering, Guindy Anna University, Chennai-600 025,INDIA Abstract A comprehensive study of shielding enclosures using various CEM methods has been dealt here. The inherent advantages and disadvantages of these methods have compared and analysed. Various aperture considerations have been taken into account. The frequency is considered to be in GHz range. Various softwares such as ADS, CST and HFSS characteristics have been illustrated and a further extended study using these softwares will be done. Widespread methods for numerical analysis of enclosures include FDTD (Finite difference time domain), FEM (Finite Element Method), FIM (Finite Integration Method) etc. They are efficient at predicting shielding effectiveness but added computational time as well as enormous unknowns confines their usage. Analytical techniques such as MoM (Method of Moments) or the Boundary Element Method (BEM) are effective in confronting shielding quantification. Keywords-Shielding, EMC, Apertures, Sheilding Effectiveness I.INTRODUCTION Shielding is an important concern in EMC concept. Shield is a metallic casing basically used to provide susceptibility to interior electronics from external fields. Shielding effectiveness (SE) [1] is defined as the ratio of magnetic (electric) field incident on the shield to magnetic (electric) field transmitted by shield. A shield may not always be an enclosed structure it will have may some perforations inside it such as a personal computer casing. These slots act as proficient radiators influencing shielding effectiveness. Therefore, EMC modeling of metallic shielding enclosures proves to be extremely byzantine due to massive expansion in high speed electronics. Determination and substantiation of SE becomes relatively significant as the integrity of enclosures is compromised by apertures, cable penetrations, power supply cables etc. Radiation characteristics of an enclosure can be corroborated by numerical as well as analytical techniques. These analyses are carried out keeping in mind that energy penetration is mainly through apertures. ISSN: 2231-5381 II.METHOD OF MOMENTS Method of Moments is a technique used to solve EM boundary or volume integral equations particularly in frequency domain. Most EM problems can be modeled in terms of inhomogeneous equation of the form[2]: LΦ=g (1) Where g is a source function or excitation which is primarily voltage or current source. MoM is a general procedure for solving equations of the form as stated in equation 1. Since EM sources such as voltages and currents are primarily considered as quantities of interest, this technique becomes prevalent in solving radiation and scattering problems. For MoM formulation a Perfectly Electrically conducting (PEC) [3]-[5] cavity whose walls are thin and lossless are considered for the experimentation. As an excitation, a plane wave is made normally incident on one of the faces of cavity. Varying degrees and polarizations of angle can be encountered. Depending on the angle of incidence this technique is subdivided into two: MoM http://www.ijettjournal.org Page 141 International Journal of Engineering Trends and Technology (IJETT) – Volume 34 Number 3- April 2016 for Normal Incidence(MNI) and MoM for slanting angles(MOI). A.Normal Incidence A wave normally incident on an enclosure can be expressed as [6]: Internal domain fields can be quantified by dyadic Green’s function for cavity[8].An apposite boundary formulation[9] for finding aperture current distributions using continuity of tangential component of magnetic field on the apertures can be stated as: × + × = × (6) = (2) k =wave number of free space=ω where is the incident magnetic field, is the scattered magnetic field, and is the magnetic field inside the enclosure. = The electric field on apertures can be illustrated as [6]: = 1)Galerkin’s Method Finally using method of Galerkin [10] where the basis functions themselves are used as the testing functions a matrix representation[11] of MoM can thus be obtained of the form [C][X]=[D] sin cos = cos sin (7) (3) -M×M matrix obtained from the arithematic configuration of MoM. [X] - M×1 column matrix which contains unspecified modal amplitudes of the aperture fields. [D] - M×1 column matrix depends on incident wave. Upmn, Vpmn -unknown modal amplitudes of the mnth mode at pth aperture, nonzero at aperture (in general),zero otherwise; Lr,Wr -length and width of pth aperture; P - total number of apertures; (xcp, ycp ) -center of p-th aperture. Applying equivalence principle [7] for z=0 plane and reinstating aperture fields by magnetic currents: = × (4) This has the advantage of enforcing the boundary conditions throughout the solution domain, instead of at discrete points. B.Oblique incidence Oblique incidence used in MoM involves random angles and polarizations. Khan[12] developed this method and further validations for statistical investigations are being carried out in this area. -normal vector of aperture. The complete analysis of MoM solution can be devised into external and internal domain. External fields are calculated using free space Green’s function [2]: (r,r )= (5) (r,r ) + (r,r ) + (r,r ) III.FEKO METHOD (r,r ), (r,r ) and (r,r ) correspond to infinitesimal, elementary sources pointed in the y and z direction, ISSN: 2231-5381 The advantages include the fact that MoM is fast, conceptually simple and accurate [13]. It does not require special boundary conditions. The infinite ground plane assumption in Modal/MoM suggests a restriction that the apertures be smaller than the walls they are located on. Varying EM complexity and electrical size offers no single numerical method which can handle all problems efficiently. These problems can be handled by a single method known as field computations http://www.ijettjournal.org Page 142 International Journal of Engineering Trends and Technology (IJETT) – Volume 34 Number 3- April 2016 involving bodies of arbitrary shape (FEKO) [14]. By offering a selection of different solvers, this tool offers the option to choose a method that is most suitable for a required problem. FEKO is an allinclusive computational electromagnetic (CEM) simulation software tool. The diverse range of modernized numerical simulations and hybridization allows precise elucidation of Maxwell’s equation extending the applicability to 3D configurations. Essentially devised in frequency domain time domain can be extracted by applying Fourier transform on frequency domain data. FEKO is basically a Method of Moments (MoM) code hybridized with techniques such as Physical Optics (PO), Ray-launching Geometric Optics (RL-GO), Uniform Theory of Diffraction (UTD). Such an hybridization enables solution of computationally massive problems on small computers, full wave analysis, using estimations whenever required to different parts of the same model better optimization of solution and time. This aspects of FEKO makes it vulnerable to EMI\EMC investigations including shielding enclosures. Both Electric Shielding effectivenness(SE) and Magnetic Shielding effectiveness(SM)for the above illustrated enclosure having apertures can be experimented in two scenarios: (1) A plane wave can be made incident on the casing and fields inside enclosure are calculated.(2)Internal components inside the casing can be modeled as dipoles or patch source wherein near and far field outside the cavity are computed. Both metallic casings as well as enclosures made of non-perfect screening materials can be investigated here. It is predicted that Shielding effectiveness of the order of 200 dB or more can be quantified. Since quantification of shielding effectiveness requires a wide band of frequency a method known as Adaptive Frequency Sampling (AFS) is adapted to scan the entire frequency range of interest in fewer frequency points, still resolving all resonances and other features of the problem. So, electrically large and complex problems can be handled with this simulation software. A FEKO 4.2 version is used to model a metallic box with a slot before computing the shielding effectiveness of the structure in a typical EMI/EMC problem. The applications of FEKO involve lightning, mitigation studies antenna analysis including interpreting radiation patterns and RFI mitigation studies. The finite element analysis of any problem involves basically four steps [13]:discretizing the solution region, deriving governing equations for a typical element, assembling of all elements in the solution region and solving the system of equations obtained. A. Basic development of three dimensional FEM problem Consider a volume V occupied by a lossy material with constitutive paramaters є and μ surrounded by free space characterized by parameters and .An EM wave from a source with angular frequency ω is incident on the body. All the equations pertaining to this explanation can be illustrated from [16]. The electric fields inside and outside the volume satisfy the following vector partial differential equations: × × The finite element method is a tool for resolving problems with partial differential equations [15]. Its × E - ω²є E=0 (8) × ×E- ² E=0 (9) =ω is wavenumber of free space The field inside volume V can be expressed as: F= { ( [( ] – μ[ - ² + ² + ² ] dV + )dS (10) l and m are two orthogonal unit vectors tangential to the surface S. From discretization of volume V into 3d elements fields within each element can be illustrated as: = (11) IV.FINITE ELEMENT METHOD ISSN: 2231-5381 ability to deal with complex geometries makes it a very prevelant technique. Since evaluation of shielding effectiveness of a rectangular cavity is quite tedious FEM modeling becomes quite appropriate. (x,y,z) ; = (x,y,z) n number of nodes within element interpolation functions http://www.ijettjournal.org Page 143 are International Journal of Engineering Trends and Technology (IJETT) – Volume 34 Number 3- April 2016 , ) represent field at ith node Using Rayleigh –Ritz procedure and substituting eqn (12) into (11) yields final formulations: { }+[ ]{ }=0 { }+ { }+ (12) { }=0 (13) denotes electric field at the nodes interior to the surface S denotes tangential electric field at nodes on S and is the tangential magnetic field at the nodes on S. denotes a matrix having three dimensions. A complete formulation using these equations cannot be obtained and therefore hybrid procedures combining fem with surface integral equations such as Hybrid FEM/MoM [17] has been developed.FEM is enable to hand easily complex geometries. Generality of FEM makes it possible to construct general purpose program for solving wide range of problems. FEM has its own drawbacks. Harder to understand, it is difficult to program than both methods (FDTD and MoM). It requires preparing a set of input data, which is tedious. If apertures are present in the casing, the FEM solver requires an ―air-box‖ to correctly model the radiation characteristics and its performance deteriorates rapidly. V.FDTD METHOD FDTD plays a significant role in modeling of microwave problems whose geometrical dimensions are comparable to wavelength. Application of the FDTD method is usually very straightforward: the solution domain is typically discretized into small rectangular or curvilinear elements, with a ―leap frog‖ in time used to compute the electric and magnetic fields from one another. Considering the aspect of shielding enclosure with apertures, a lot of work has already been done in evaluating shielding effectiveness of electrically large physically small casings using this CEM tool. The loss necessary for FDTD [18] analysis of shielding enclosures technique is introduced by using a specific resistance at the end of the monopole probe. S-parameters, EMI, Far field, Near fields etc. are quantified. Modeling of fields outside enclosure is done using equivalence theory for apertures taking into consideration surface electric and magnetic currents of enclosure. The FDTD method has the ISSN: 2231-5381 following inherent advantages and disadvantages [2] over other modeling techniques such as Method of Moments. Advantages include: The algorithm does not require formulation of integral equations, and relatively complex scatterers can be treated without the inversion of large matrices. It is simple to implement for complicated, inhomogeneous conducting or dielectric structures because constitutive parameters can be assigned to each lattice point. The algorithm makes use of the memory in a simple sequential order. It is much easier to obtain frequency domain data from time domain results than the converse. Thus, it is more convenient to obtain frequency domain results than the converse. The disadvantages include: Its implementation necessitates modeling object as well as its surroundings. Thus, the required program execution may be excessive. Its accuracy is at least one order worse than that of the MoM example. Since the computational meshes are rectangular in shape, they do not conform to scatterers with curved surfaces, as in the case of the cylindrical or spherical boundary. VI.PROPOSED SOFTWARES A.Computer Simulation Technology CST [19] offers an extensive range of features and solvers suited to all kinds of electromagnetic (EM) problems. It is computationally efficient and accurate. The solver range includes: time domain, frequency domain, integral equation, asymptotic, fast resonant, eigenmode , static and stationary fields, charged particles, temperature, mechanical stress, and circuit simulation. Specifically speaking, CST PCB STUDIO (CST PCBS) used for the simulation of signal and power integrity and EMI/EMC on printed circuit boards and CST DESIGN STUDIO (CST DS) a versatile tool that facilitates 3D EM circuit cosimulation and synthesis plays a trivial role in enclosure analysis. B.High Frequency Structure Simulator Ansoft High Frequency Structure Simulator[20] is a full-wave, FEM based electromagnetic field solver for simulating arbitrary(3D) structures such as computing behavior of high-frequency and highspeed components. With HFSS, engineers can extract parasitic parameters (S,Y,Z) to visualize 3D electromagnetic fields (near – and far-field) , generate broadband SPICE models and optimize design performance. HFSS is widely used for the design of on-chip embedded passives, PCB interconnects, http://www.ijettjournal.org Page 144 International Journal of Engineering Trends and Technology (IJETT) – Volume 34 Number 3- April 2016 antennas, RF-microwave components, and highfrequency IC packages. constructed for shielding effectiveness vs. frequency for comparative study. C.Advanced Design System VIII.CONCLUSION Advanced Design System[21] abbreviated as ADS is the world’s leading design automation software for RF, microwave and high speed digital application. It versatility of solvers such as the momentum, momentum microwave and FEM make it a high end tool for 3D electromagnetic simulation. It offers a powerful and easy to use interface ADS pioneers in most commercially and successfully used industrial tool. The proposed paper here illustrates the comparison of various CEM techniques used for the analysis of shielding enclosures. These techniques can be henceforth applied for the modeling of casings with distinct aperture compositions. CST, HFSS and ADS are the anticipated softwares used for 3D EM simulation and modeling. The operation frequency is considered in GHz range. This work will be further extended to the aspect of PCB modeling and its components in shielding enclosures with versatile solvers using ADS tool. VII.APERTURE CONSIDERATIONS All the techniques here mentioned FDTD, MOM, FEM and FEKO will be run for single, double and multiple aperture cases. Low frequency as well as high frequency analysis is encountered. Multiple square apertures of size 1cm forming an (1) (2) (3) (4) Fig 1. Illustrates the example of different aperture plates to be analysed array of approximately 250 are also considered. Smallest to largest apertures cases are investigated. 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