Minimization of Radiation from a System of Interconnected Computer Equipment Inside an Anechoic Chamber

T he problem of electrom agnetic rad iation and scattering from a perfectly conducting system of arb itrarily-shaped intercon­ nected com puter equipm ent is considered. The method of mo­ m ents is used to solve the frequency dom ain electric field integral equation (EFIE). Two electrom agnetic interference E M I C A D tools are presented for the analysis of c o u p l in g and c ro s s ta lk th rough arrays of arb itrarily shaped apertures in such a sys­ tem . T he system , placed in an anechoic cham ber, is excited by in ternal sources produced by arb itrary P C boards circuitry. Two cases are discussed: a free-space case and a half-space case. For the la tte r, th e presence of an infinite perfectly conducting ground plane, which models the effect of the anechoic cham ber, is incorporated in the formulation. In bo th instances, the bod­ ies are modeled by the sam e planar tr iangular patches and the wires by the sam e series of straight-w ire segments. For the free space case we use free space vector functions. For the half space case, a new set of vector functions are introduced to account for the presence of the ground plane, yet keeping the same num ber of unknowns as if the system were in free space. Body expan­ sion functions are used on the bodies surfaces, wire expansion functions a t the wires and each of the body-wire junctions there is one junc tion expansion function. One program calculates the electric fields in s id e the system and the leaking fields a t the arrays of apertures. The o ther com putes the electric fields ra ­ d ia ted to the o u ts id e environm ent. The coupling of the inside solution w ith the outside one effectively dictates w hat the op­ tim um configuration and shape of the array of apertures ought to be to m in im iz e rad ia tion to the outside environment. IN T R O D U C T IO N C om puter an d o ther electronic equipm ent is, in general, con­ ta ined in conducting cabinets which have apertures for inputo u tp u t connections and cooling purposes. It is desirable to keep electrom agnetic transm ission through these holes as sm all as possible or a t least small enough to meet the FCC requirem ents. To investigate th e effect of such apertures, m easurem ents are m ade either a t open field test sites or in anechoic cham bers w here th e system s are placed on a ground plane. T he work in th is paper deals prim arily w ith the modeling of such systems to eventually come up w ith a general purpose electromagnetic CAD tool. For electronic equipm ent modeling purposes, a coax­ ial cable a ttached to a com puter box can be viewed as a wire m ounted and possibly driven against a conducting body. T here­ fore, the body plus the wire may be regarded as a rad ia to r of electrom agnetic fields produced by the current flowing on the surface of the composite system. A similar point of view holds if a system of several bodies interconnected by wires is consid­ ered. We view the system as a rad ia to r if the sources are on the system; if, instead, the sources are d is tan t from th e system we view it as a scatterer. Hence, by analyzing the system in an a rb itra ry im pressed field, we are effectively considering bo th cases a t once [1 ], T he w ire-to-surface junc tion problem has been exam ined by pre­ vious investigators beginning w ith A lbertsen e t al. [2], who analyzed wires perpendicular to sm ooth sections of a surface modeled by quadrila teral patches. Their form ulation is a hy­ brid one: namely, an E FIE form ulation is used for wires and a m agnetic field integral equation M FIE is used for closed sur­ faces. L ater, Glisson [3] used an E FIE form ulation alone to tre a t a ben t rectangular p la te w ith an arbitrarily-oriented wire a ttached , either on the flat portion of the p la te (but not near an edge or bend), or located directly a t a bend (but not a t an edge or vertex of the p late). The same problem was trea ted by Newm an and Pozar [4] using a sim ilar procedure, and the ir for­ m ulation has recently been extended to trea t a wire a ttached to a p la te a t or near a knife edge [5] or near a vertex or a bend [6 ]. Yet, the ir procedure excludes wires a ttached to doubly-curved surfaces or to vertices. M ore recently Shaeffer and MedgyesiM itschang [7,8] have trea ted the problem of wires a ttached to bodies of revolution (B O R ’s). However, none of the above procedures applies to wires m ounted on a surface w ith an edge, wedge, or a two-or three-dimensional vertex a t its junc tion region. Except for [7,8], the above pro­ cedures also do no t apply to curved junc tion regions. This is because the ir approaches require prior knowledge of the form of the curren t near the attachm ent point [9,10], Because for a filam ent curren t source w ith one end a ttached to the junc tion vertex of a canonical surface, there exists an analytical solution for th e curren t produced by it. A nd usually, ex traction of the ra ­ dial variation of the surface curren t from th a t analytical solution is sufficient to provide a good model. Nevertheless, this is pos­ sible only w hen the junction region resembles the actual canon­ ical surface geometry. Consequently, those schemes rely on the existence of a canonical problem having an analytically obta in ­ able G reen’s function. Hence, the ir approach is seriously limited since there exist m any practical configurations where either the G reen’s function is unatta ibab le or its com putation extremely difficult. T hen, because of its lack of generality, the ir approach is no t easily incorporated into a general-purpose com puter code for trea ting a rb itra ry systems of bodies interconnected by wires. T he tr ian gu lar patch surface modeling scheme developed a t the University of Mississipi by R ao et al. [9] obviates, in our view, the need for determ ining this variation th rough a G reen’s func­ tion of a re lated canonical problem. In addition, as seen in [11,12,14,16], p lanar tr iangular patches conform easily with the shape of the ventilation holes required in electronic equipment. However, for th e junction problem , R ao’s junction trea tm en t rendered some anomalies by v irtue of linear dependencies. A b e tte r alternative, in our opinion, is to use only one expansion func tion per junc tion as we do in this work. This compares w ith R ao ’s use of n expansion functions [9]. In addition to resolving th e linear dependency problem our scheme reduces 139 C H 2 1 16-2/85/0000-139 $1.00 © 1985 IEEE th e num ber of unknowns. Furtherm ore, R ao’s im plem entation was restric ted to one body and one wire only and ours is not. So far as our results show, our procedure gives excellent results in com parison w ith either available exact or m easured data . For m ultip le configurations, no such d a ta are available to com pare w ith , yet the results look quite reasonable. Consider the com posite system to be bound by a perfectly con­ ducting boundary surface S . We s ta r t by assum ing the system to be placed in free space and subject to an a rb itra ry impressed field E ,nc. T he problem reduces to solving for the surface cu rren t density J on S'. An E-field solution can be obtained by enforcing the tangentia l com ponent of the to ta l electric field to vanish everywhere on the conducting surface except a t the sources. T he electric field integral equation (EFIE) so obtained is then solved numerically by m eans of the method of m o m en ts ; [l] to solve for the currents induced on the boundary surface S of the system . In th is paper only a frequency dom ain solution will be considered. T he induced surface curren t distributions are the unknowns in th is electrodynam ic problem and the surface charge d is tribu ­ tions are derivable from the currents. Low frequency results can be ob ta ined as indicated in [12,15]. O ur approach in modeling a com puter system uses p lanar triangular patches for the bod-r ies an d a series of straight-w ire segments for the electrically th in wires. A m om ent solution is effected by using G alerkin’s m ethod as a s ta rting point. Each geometric p a rt of the system has its own class of vector expansion functions. T hree sets of vector functions are utilized as bo th the expansion and testing func­ tions: the body expansion functions approxim ate the current density on the surfaces of the bodies, and are a generalization of R ao ’s [11 ]. An extensive bibliography on surface modeling is also given in [11]. The wire expansion functions approxi­ m a te the cu rren t on the wires w ith pulses th a t have a vector direction coinciding w ith the wire axis. A t the junctions, each ju nc tion region has one vector expansion function composed of two term s: one is half a pulse w ith an axial vector direction into the wire, and th e o ther is a surface te rm in which the current density is radially directed tow ard the wire a ttachm ent point, the jun c tion vertex. This surface te rm is, in tu rn , composed of n d is tinct te rm s, each defined in triangles th a t touch the junction vertex. This junc tion expansion function is constructed so as to satisfy the K irchhoff curren t law (K C L) a t the junction vertex. T he problem of free-space electrom agnetic rad iation and sca tte r­ ing from a perfectly conducting system of bodies interconnected by wires, of a rb itra ry shape, will be considered first. In this case, free-space vector functions are used to effect a mom ent solution. Free space body expansion functions are used on the bodies sur­ faces, free space wire expansion functions a t th e wires and a t each of the body-w ire junctions there is one free space junction expansion function. T hen a half-space solution, in the presence of a perfectly conducting ground plane, is effected by introduc­ ing half-space vector functions, by using image theory and keep­ ing th e sam e free-space G reen’s function. The same modeling is used in b o th instances, i.e., the same patching schem