Auxiliary Sources for the Near-to-Far-Field Transformation of Magnetic Near-Field Data

Transcription

1 Auxiliay Soucs fo th Na-to-Fa-Fild Tansfomation of Magntic Na-Fild Data Vladimi Volski 1, Guy A. E. Vandnbosch 1, Davy Pissoot 1 ESAT-TELEMIC, KU Luvn, Luvn, Blgium, vladimi.volski@sat.kuluvn.b, guy.vandnbosch@sat.kuluvn.b Rliability in Mchatonics and ICT, KU Luvn Kulab, Ostnd, Blgium, davy.pissoot@kuluvn.b Abstact A novl algoithm to pfom a na-to-fa-fild tansfomation, stating fom th magntic fild masud ov a finit plana aa abov th dvic-und-tst, is poposd. Th algoithm is basd on th intoduction of auxiliay soucs that appoximat th magntic fild in th scanning plan outsid but th scanning aa. Numical sults show that ths auxiliay soucs significantly incas th accuacy of th na-to-fa-fild tansfomation. Indx Tms Elctomagntic compatibility, Na-fild, Radiation pattn. I. INTRODUCTION Radiation missions gnatd by lctonic dvics a of intst in many aas. Nowadays almost vy lctonic dvic has to pass EMC adiatd mission tsts bfo it can b put onto th makt. Standadizd missions tsts a usually don in a smi-anchoic chamb and basically dtmin th fa-fild of th dvic-und-tst. As such facilitis a quit xpnsiv to build, most companis must go to xtnal labs to do ths tsts. This not only maks EMC tsting quit xpnsiv, but also limits th possibilitis to fficintly dbug an EMC issu. A mo flxibl and ofthn chap altnativ appoach is to masu in th vy na fild of th dvic-und-tst and to pfom a tansfomation btwn th na fild masud data and th fa fild componnts. This tchniqu was oiginally dvlopd fo antnna masumnts, but lat it was succssfully usd fo oth typs of masumnts. Th quivalnc thom [1] povids a thotical backgound fo such tansfomations. Unfotunatly, this thom quis that th na fild is known on a closd sufac fully suounding th adiato. In pactic th scan data vy aly cov an nti closd sufac and nomally only th scan data abov a dvic-undtst a availabl. As a consqunc spcial algoithms a ndd to cop with this. Most of th xisting mthods in litatu [-8] a basd 1 on th intoduction of quivalnt soucs (mainly infinitsimal dipols). Ths soucs gnat simila na fild componnts ov th scan aa. Th gnal ida actually lads to a classical invs poblm, which in many cass dlivs non-uniqu solutions and involvs opations with ill-conditiond matics. In od to stabiliz th solution sval mdis alady hav bn poposd in litatu, involving spcial optimization algoithms with many gulaization paamts, combinations with full wav solvs, tc. [-8]. Th main goal of this pap is to popos a simpl flxibl algoithm capabl of pdicting th lvl of adiation mission fom a plana PCB basd only on plana scan data ov a final aa and topological infomation about th boad dimnsions. Th poposd algoithm is simpl and lis on cla guidlins and wll-known matix opations only. Its implmntation is staightfowad. Moov, in many cass this algoithm can b asily combind with oth mthods to impov th accuacy of th xisting mthods. Th majo diffnc with xisting appoachs found in litatu is th fact that th auxiliay soucs appoximat th filds in th plan only outsid th scan aa and not ov th scan aa itslf. It will b shown that this tchniqu has hug advantags. In this pap w wok out th thoy fo magntic fild componnts which a widly usd in pactic fo EMI na fild scanning [1]. II. THEORY A. Dict na to fa fild tansfomation Basd on th quivalnc thom [1], th fild outsid a closd volum can uniquly b constuctd fom th lctic and magntic fild componnts tangntial to th sufac of th volum. This thom has th diffnt vsions, on wh both lctic and magntic componnts a considd, on wh only lctic componnts a considd just in font of a magntic conducto, and on wh only magntic componnts a considd just in font an lctic conducto. Applying this gnal pincipl to th masumnt plan, and using th scond vsion, quivalnt lctic cunts can b intoducd basd only on th magntic na fild componnts. In pactic it is asi to masu magntic fild componnts. Fo a plana stuctu th quivalnt lctic cunt ov a pfct magntic conducto can b xpssd in tms of a doubld lctic cunt adiating in f spac using th imag pincipl [1] J = ( i H) = H i + H i (1) z y x x y This wok is pfomd within th famwok of th IWT pojct NEATH

2 Thn th vcto potntials can b intoduc to calculat th fa fild componnts as jk jk( x'sinθcos θ+ y 'sinθsin + z 'cosθ) Aα = Jα ( V' ) dv ' 4 () π V wh α = x, yk, = π / λ, = x + y + z Aθ = Axcosθ cos + Aycosθ sin Azsinθ A = A sin + A cos x y Th vcto potntials a coupld with th fa fild componnts as E E θ θ = jkwa = jkwa and W 1π is th f spac impdanc. Ths fomulas (1)- (4) a th co of th dict na-to-fa-fild tansfomation. In pactic th scan aa of a PCB of intst is always finit. As a consqunc th quivalnt cunts (1) also hav a finit domain. This stiction can sult in hug os vn if th scan aa is lag. Th analysis of (3) and (4) dmonstats that ths quivalnt cunts (1) a.g. not abl to gnat any thta fa fild componnts in th hoizontal plan ( θ = 9 ). Fo typical antnna applications, lctic cunts gnat dictiv adiation in th upp hmisph. In this cas th os a lss significant. Howv fo a small PBC and spcially at low fquncis, this fa fild appoximation can b vy inaccuat. As a consqunc spcial masus should b takn to sto th coct mission fom th PCBs. B. Asymptotic coction using auxiliay dipols As w hav shown in th pvious sction, a fundamntal poblm of any scanning tchniqu is that th scan aa is always limitd. This can sult in lag os bcaus th contibution of th magntic fild outsid th scan aa is nglctd. Th a sval possibl ways to tackl this poblm. In this pap an appoach basd on th intoduction of auxiliay adiatos ( J ) is slctd. This stp looks vy simila to oth mthods basd also on th intoduction of auxiliay soucs. Howv th a two majo diffncs. Th oiginal contibution fom th quivalnt cunts (1) will b taind and th main goal of th auxiliay soucs is to appoximat th magntic fild componnts not ov th scan aa (as is nomally don), but mainly outsid it. Consid a dvic und tst (DUT) with lctic cunts DUT J flowing on top PCB tacs and a PCB gound plat makd by black solid lins in Fig. 1. Consid a finit plana scan aa S scan in font of th DUT. Th maining pat of th nti plan is dnotd S out. (3) (4) Using th quivalnc pincipl, th lctic fild abov th scanning plan can b wittn in tms of th magntic fild in th scanning plan DUT ( ) = ( scan ) + ( out ) EJ EH EH (5) Unfotunatly, th scond tm in (5) is unavailabl. Fo any auxiliay adiato J, th situation is diffnt. It gnats known fild componnts vywh in spac, and thus also in th scanning plan, i.. H scan and H out. Th us of th quivalnc pincipl dlivs an quation in which all tms a known. ( ) = ( scan ) + ( out ) EJ EH EH (6) Figu 1. Intoduction of auxiliay adiatos. Subtacting (6) fom (5) and using th supposition pincipl, on obtains th following quation DUT ( ) = ( ) + ( scan scan ) + EH ( out Hout ) E J E J E H H It bcoms now obvious that if th auxiliay adiatos a capabl to mimic th fild outsid th scan aa coctly thn out S out H H (8) out and (7) can b simplifid S scan DUT ( ) ( ) + ( scan ) ( scan ) S out EJ EJ EH EH (9) In this quation all tms in th ight pat a known. It is absolutly cucial to mphasiz that in pincipl th pocdu dos not qui a good appoximation of th fild H scan by th fild H scan insid th scan aa as nomally quid by oth mthods. Th appoximation of th magntic fild componnts has to b of sufficint quality but in gnal this is a now simpl task bcaus th a no hotspots o vy fast vaiations of th filds outsid th scan aa. (7)

3 C. Slction of auxiliay dipols Infinitsimal lctic dipols a slctd as auxiliay adiatos. Goups of dipols a abl to mimic vy complx topologis but th distanc btwn adjacnt dipols should b chosn in a pop way. Guidlins usd in th mthod of auxiliay soucs [9] can b consultd. All fild componnts gnatd by infinitsimal lctic dipols J can b calculatd analytically T z y iy + iz J x jk 1 z x H( J ) = jk x z Jy i + i y x J z ix + y i (1) jk3qαβ δαβ k Qαβ k + jk W Eα = J jk 3Q β αβ jk 1 4π + + δ αβ (11) xαxβ Qαβ = ; δαβ = 1 if α = β & δαβ = if α β Th positions and amplituds of all auxiliay dipols a dfind in two stps. At fist th positions and th polaizations of th dipols a dtmind. Th analysis of th scan data H scan vals sval s with high lvls of masud magntic filds. Ths s cov all dominant soucs of unwantd mission causd by th PCB tacs. Thy can b asily fomd by kping all points fom th scan data on th upland platau aound th local maxima. Thn th quivalnt hoizontal dipols a placd at th top of th PCB insid ach H z top J = i H, z = z (1) As w hav alady mntiond only hoizontal dipols a not abl to pdict coctly all fa fild componnts. So th psnc of z dictd auxiliay dipols is mandatoy in J z many cass. In pactic, th optimal positions of th J z dipols should coincid with vias suppoting vtical cunts and aas wh vtical polaization cunts in th substat a lag. Unfotunatly, th a no simpl ways to xtact th quid infomation fom th na fild scan data. As a consqunc sval appoximations should b usd. Vtical cunts flowing on vias a tansfomd into hoizontal cunts spading thoughout hoizontal tacs. Ths hoizontal cunts gnat claly distinctiv aas with a high fild lvl in th scan data. So it is ath logical to assum that th vias a locatd within th s alady slctd to cov dominant mission soucs on th PCB tacs. J z dipols a placd insid ach using a simpl quidistant gid. In contast to th J H dipols which can blong to th sam goup within ach, th J z dipols a indpndnt within ach bcaus th xact positions of th vias a unknown. Th combination of both dipol typs ( J, J ) foms a fist lvl H z appoximation. Th magntic fild outsid th scan aa in th hoizontal plan can b dscibd as a supposition of outgoing wavs gnatd by th al lctic cunts. Th auxiliay dipols a also gnating outgoing wavs th. Ths two sts of wavs a quatd in a sufficint numb of points at th dgs of th scan aa, sulting in an m x n lina quation systm. Th following quations a usd fo th k-th point on th dg ( ) ( ) ( ) ( ) scan xk H + xk z = xk H J H J H dip scan yk H + yk z = yk H J H J H (13) Th obtaind systm (13) can b solvd using th Gauss Lgnd last squa o minimum algoithm. Th solution in matix fom is -1 T T T T AJ B A AJ A B J A A A B (14) = = =( ) Onc th amplituds of th auxiliay dipols a calculatd using (14), all fa fild componnts can b found using (9). III. NUMERICAL RESULTS In od to illustat ou mthod w consid a simpl PCB with sval tacs on th top as shown in Fig.. Th PCB thicknss is 1 mm and its siz is 1 mm x 8 mm. Th distibution of magntic fild componnts abov th PCB at a hight of mm at MHz was calculatd using th FDTD solv that is includd in Agilnt Tchnologis 3D EM platfom EMPo [11]. Th scan aa is 16 cm x 1 cm (.17λ x.8λ) and th usd solution is.5 mm in both dictions. Figu. Scnshot of th PCB tst stuctu with multipl tacs Th combind fnc magntic fild componnts a shown in Fig. 3. As xpctd th fild lvl bcoms vy high abov th PCB tacs.

4 .5 3 x 1 3 Oiginal Asymptotic 1.6 x Oiginal Asymptotic 1. 1 abs(hx) 1.5 abs(hy) points points Figu 3. Calculatd x componnt of magntic fild ov th scan aa Auxiliay dipols a placd insid ach using an quidistant gid. Its solution is diffnt fom th solution of th scan aa. In this pap, th distanc btwn adjacnt dipols is slctd as sdip =.1λ = 15 mm. Fo th stuctu in Fig. th total numb of auxiliay dipols is 4 and thi positions a shown in Fig. 4. Thy fom 16 goups (unknowns) containing sval o singl dipols. Th tst points at th dgs a also slctd using an quidistant gid ( s =.1λ = 15mm ). dg Figu 4. Oiginal positions of all auxiliay dipols As w hav alady mntiond th imposd bounday condition is satisfid at th dgs of th scan aa. Th last squa os minimum algoithm is usd. Th fficincy of th appoximation can b chckd onc th amplituds of all dipols a calculatd. Th two magntic fild componnts at th dgs a plottd in Fig. 5. As xpctd, a fw dipol goups a capabl to gnat almost th sam fild at th dgs of th scan aa. Th a small diffncs bcaus th numb of quations is diffnt fom th numb of unknowns. Figu 5. Bounday conditions fo magntic fild componnts Th fnc fa fild pattns and two calculatd pattns a plottd in Fig. 6. Th figus in th fist column cospond to th fnc pattns. Th scond column shows th sults obtaind using only th dict tansfomation of th na fild scan data. Th last column illustats th coction intoducd by ou appoach. As alady mntiond th quivalnt cunts a not abl to mimic th thta componnt ( E θ ) of th fa fild pattn clos to th hoizontal plan bcaus thy gnat no adiation in ths dictions. This is a sious disadvantag of a small scan aa. Howv, th oth componnts ( E ) of th fa fild pattn a appoximatd satisfactoily. Th application of ou mthod allows to impov noticably th appoximation of th fa fild pattns in all angula sctos using just a fw dipols. This xampl illustats th fficincy of ou appoach. CONCLUSIONS In contast to many xisting algoithms th appoach intoducd in this pap is vy simpl and staightfowad. It lis on cla guidlins fo auxiliay dipols and simpl opations with matics. Moov, th basic ida can b asily implmntd in any oth mthod using auxiliay dipols. It significantly impovs th accuacy of th dict appoximation fo all fa fild angula sctos as shown in Fig. 6. A futu wok will b focusd on an advancd algoithm fo th optimal placmnt of auxiliay dipols and spcial masus to avoid possibl poblms causd by th opation with ill-conditiond matics. REFERENCES [1] C. Balanis, Antnna thoy: analysis and dsign, Wily, 1997 [] X. Tong, D.W.P. Thomas, A. Nothof, and P. Swll, C. Chistopoulos, Modling Elctomagntic Emissions Fom Pintd Cicuit Boads in Closd Envionmnts Using Equivalnt Dipols, IEEE Tansactions on Elctomagntic Compatibility, vol. 5, pp , 1

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