Far Field Estimations and Simulation Model Creation from Cable Bundle Scans


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1 Far Fild Estimations and Simulation Modl Cration from Cabl Bundl Scans D. Rinas, S. Nidzwidz, S. Fri Dortmund Univrsity of Tchnology Dortmund, Grmany Abstract Th mission lvl of automotiv systms is oftn govrnd by th cabl harnss, it is oftn th dominant radiating structur and dtrmins th position of rsonancs. Th stablishd fild masurmnt mthods according CISPR 5 for valuation of missions suffr from th nd to us larg anchoic chambrs. Furthrmor masurmnt data can not b usd for simulation modl cration in ordr to comput th ovrall filds radiatd from a car. In this papr a simpl mthod to dtrmin th farfilds and a simulation modl of a radiating cabl bundl from narfild masurmnts is proposd. Th mthod masurs th lctromagntic filds at svral points nar to a cabl bundl. Masurmnts ar don in tim domain in ordr to gt phas information, to rduc masurmnt tim, and to corrlat diffrnt masurmnt data sts. From th fild masurmnt data an quivalnt currnt distribution in a cabl bundl can b computd. With this information a simulation modl of th stup can b gnratd, farfild stimations can b don. I. INTRODUCTION Elctromagntic Compatibility plays an important rol in th dvlopmnt of automotiv lctronic systms. Th intgratd Elctronic Control Units (ECUs and spcially th mainly usd unshildd cabl bundls ar sourcs for lctromagntic missions. Standardizd componnt fild masurmnt mthods, lik th ASE antnna mthod providd in CISPR 5 [] for valuation of lctromagntic missions from automotiv systms, suffr from th nd of larg and xpnsiv anchoic chambrs. Also a singl fild strngths valu is oftn not sufficint to charactriz th EMI bhavior of a complx systm. Furthrmor it is not possibl to us th masurmnt data for bhavioral modl cration for simulation. Having simulation modls, a statmnt about th radiating lctromagntic filds can alrady b mad in arly phass of dvlopmnt. Basically th lctromagntic mission must b distinguishd in th mission from circuit boards and thir housing and th mission from th conncting cabl bundls. To b abl to dtrmin th radiatd far filds it is ncssary to transfr th radiating ECU structur and th attachd cabls into an quivalnt bhavioral modl with rducd complxity. Knowing th filds in an indfinitly xtndd plan abov th tst objct all information is availabl to calculat any fild vctor abov this plan []. From thortical point of viw this would b sufficint to calculat th far filds. Thr ar svral problms with such an approach. E.g. accuracy of masurmnts is limitd and accuracy of fild calculation can b low. It is bttr to try to solv th invrs problm and thus to idntify by th masurd fild important proprtis of th tst objct. This approach is discussd in [3], [4], [5] and []. Focus is placd mainly on PCBs. Howvr, considring th small structur siz of most automotiv PCB and housings and compar it with th wavlngths in th frquncy rang blow MHz, radiation from cabls is oftn th dominant mission factor. To charactriz complx cabl bundls with standard voltag and currnt masurmnts on ach singl cabl is oftn not fasibl. This papr prsnts a spcial mthod for stimating th missions from cabl bundls. Th lctromagntic narfild at svral points nar a cabl bundl is masurd. With masurd dat an quivalnt currnt distribution in th bundl is calculatd and a simulation modl can b cratd. Th gnratd modl nabls diffrnt typs of postprocssing.g. far fild stimations. Th mthod can b combind with scans of th PCB and th nclosur structur, in ordr to dtrmin th full systm bhavior and to crat bhavioral modls for larg systm simulations. Accurat sourc idntification rquirs phas information [], most groups working on scanning mthods don t discuss this problm. In [3] an approach basd on frquncy domain masurmnts is prsntd. Disadvantags of th mthod ar th high complxity and masurmnt tim. In this papr a tim domain approach with a standard oscilloscop is prsntd. Advantags ar, th dirct availability of th phas information, th possibility to masur 4 fild componnts simultanously, i.. synchronizd, and th fastr simulation tim. II. SCANNING METHOD FOR SYSTEM CHARACTERIATION Typical automotiv systms consist of on or mor ECUs and thir conncting cabl bundls (Figur. Ida of th prsntd approach is to stimat th lctromagntic filds of an automotiv cabl bundl by crating a bhavioral modl basd on scannrmasurmnt data. Th ECUs ar considrd hr as black boxs, using a linar bhavioral modl approach. As th voltag amplituds of RFdisturbancs ar oftn not big,
2 small signal approachs ar valid and linar modls can approximat th mission bhavior of th lctronic systm. In th approach prsntd hr, ECUs ar considrd as non radiating lumpd circuits. An xtnsion with radiating structurs is possibl, but not discussd in this papr. ECU Figur. Systm to invstigat For crating th bhavioral modl th currnt distribution on cabl bundl must b approximatd. Complx nar fild data is collctd at svral points on lins paralll to th bundl. Thrfor th masurmnts ar don in Tim Domain, followd by a transformation in Frquncy Domain for furthr procssing. With H ( z I ( z πd π (h + d th corrlation btwn th magntic fild and currnt distribution is givn for a long homognous cabl placd clos abov a ground plan. Whr d is th distanc from bundl to masurd fild point and h is th hight of th cabl bundl abov th ground plan. Th closr to th cabl th filds ar masurd th highr is th accuracy of (. Th hight h is also assumd to b small. Th modl cration procss is prsntd in Figur. Frquncy Domain R i V (t E(t,H(t Cabl Ground Plan NarFild masurmnt H z at z z n DFT ECU ( Tim Domain Estimation of th currnt I z on cabl at z z n A. Masurmnt Stup For masuring th magntic fild a small loop antnna is usd. Th voltag V i is inducd by th magntic flux through th ara A of th loop. Vi t A Bd A If th fild is homognous and th prob diamtr is considrably smallr than th wavlngth, th flux in th loop can b considrd as constant. For th magntic fild componnt orintd normal to th loop plan th quivalnt circuit prsntd in Figur 3 can b drawn. V i Figur 3. Equivalnt circuit of magntic fild prob Th prob voltag V is calculatd by V Vi R + Basd on th masurd magntic fild at position z nar th cabl th corrsponding currnt on th lin can b computd. For that purpos th transfr function btwn th masurd prob voltag and th quivalnt currnt on th lin can b drivd from (, 3. Th constant µ dscribs th rlativ prmability and r s givs th loop radius of th magntic fild prob. R Masurd Prob Voltag V,z R H ( s ( + µ r s s S d h + d V ( (3 Equivalnt bundl modl Currnt on lin I z Prconditiond modl paramtrs Figur. Procss of modl cration Radiation computation with MoMSolvr FarFild Computation Figur 4. Transfr function for magntic fild prob Th masurmnt stup consists of a signal gnrator for fding th cabl bundl, th magntic fild prob (Figur 5 and a tripod for prob positioning. Th cabl undr tst is placd abov th ground plan. Th prob voltag is masurd in Tim Domain with a 4 channl standard oscilloscop. By synchronizing th channls and diffrnt masurmnt sts with a rfrnc prob signal accurat phas information can b
3 obtaind. Anothr important advantag of th Tim Domain masurmnts is th dcras of masurmnt duration. loop antnna Figur 5. Magntic fild prob (diamtr d 9 mm B. Tim Domain  Frquncy Domain Transformation Tim domain masurmnts hav svral advantags discussd abov. For th following postprocssing I z is transformd in th frquncy domain. For obtaining th Frquncy Domain information of a masurd Tim Domain signal th FourirTransformation is usd. This transformation provids th complx information in a continuous Frquncy Domain, from which spctrum and phas information can asily b drivd. Furthrmor th FourirTransformation is fully rvrsibl. F jωt x( t dt { x( t } X ( ω As th continuous FourirTransformation rquirs continuous Tim Domain data it is not usabl in cas of digital signal procssing. Thrfor th Tim Domain data is discrtizd at fixd tim stps according to a chosn sampling frquncy that should b idntical to th scop sampling frquncy. t f S Additionally, th chosn sampling frquncy spcifis th maximum frquncy dtctabl by th FourirTransformation, which is limitd by th NyquistThorm. f max Hnc all frquncy componnts highr than f max should b supprssd by a lowpass filtr to avoid problms originating from AliasEffct. In this cas th transformation is known as Discrt Fourir Transformation (DFT F d { } s( n S( k f s( n t f S N kn jπ N Th DFT is working on a fixd lngth data squnc s(n that is assumd to b rpating priodically. Th lngth N of th sampling squnc hrby dfins th discrt frquncy rsolution of th DFT. f S f N N t smirigid coxial cabl (5 Ω SMA connctor (4 (5 (6 (7 (8 For achiving good rsults th frquncy rsolution should b chosn as an intgr dividr of th most intrsting frquncy, but in gnral th frquncy componnts of a signal ar not known prior to th masurmnt. An fficint ralization of th DFT is achivd by th Fast Fourir Transformation (FFT, which taks advantag of symmtris along roots of unity usd in th calculation. Diffrnt algorithms for th FFT xist, which mainly diffr in thir fficincy concrning diffrnt input squnc lngths N. Anothr aspct in th usag of th DFT is th windowing of th original squnc in Tim Domain. Th input squnc s(n itslf can b undrstood as part of th original masurmnt data windowd by a rctangular function of lngth N. s( n x( n w ( n Th multiplication of th data squnc with a window function in Tim Domain corrsponds to a convolution of th transformd data squnc with th transformd window function in Frquncy Domain. N { x( n } F{ w( } S( k F n (9 ( This causs a crtain distortion in th FrquncyDomain rsult dpnding on th usd window function which is also known as akageffct. To obtain th ncssary prcision of th frquncy data usd in this work, without wasting computing tim, masuring tim and mmory, th frquncy rsolution f is carfully chosn btwn. and. tims of th dsird minimum frquncy. To furthr optimiz ths fficincis critria th sampling frquncy f S is chosn in rlation to th dsird maximum frquncy. In Figur 6 masurmnt rsults of a pulsd input signal into a singl cabl mad with a tst rcivr can b sn. Hr th puls has an amplitud V V, a fundamntal frquncy of f MHz, a puls/paus ratio t h /t l. and a rising and falling dg of t r,f.5 ns. In comparison th rsults from th FFT basd on a Tim Domain masurmnt ar shown in Figur 7. Hnc, th FFT rsults ar vry accurat. Th main diffrncs btwn both mthods ar th nois floor lvls causd by th masuring dvic and th spctrum shap around th paks causd by rsolution bandwidth (RBW and window shap. As xplaind abov th dynamics of th FFTmthod mainly dpnd on th usd sampling frquncy and th duration of th masurmnt. Thortically any frquncy rsolution blow th Nyquistfrquncy (6 can b achivd. Th signal s shap and frquncy do not hav considrabl ffcts on th rsult in gnral. A physically limiting factor to th rsults is st by th usd masurmnt dvics, mor prcis its nois floor lvls and attnuations. Th diffrnc in th amplitud valus, which is quit constant along th spctrum, is xplaind with th masurmnt mthod itslf. Th tst rcivr masurs th ffctiv valu, whras th usd FFT calculats th pak valus of th Fourir componnts of a givn signal.
4 V a I a b b I( z I ( z (4 Magnitud [dbuv] Amplitud [dbuv] Frquncy [Hz] Figur 6. Signal masurd with a tst rcivr j ( l z j ( l z a ( β β, jβ ( l z jβ ( l z b ( + j ( l z j ( l z a ( β β, jβ ( l z jβ ( l z b ( + (5 To minimiz rrors in th modl gnration procss th possibility to masur a local minimum of currnt distribution on lin must b rgardd. This fact can caus a low signalnoisratio. Two approachs ar possibl hr. Th amount of data sts is incrasd by masuring th cabl bundl at N >> fild points. N is dpnding on th dsird maximum frquncy to b masurd. This lads to an ovrdtrmind systm of quations. It can b solvd with th mthod of last squars or ls approximatd to a sinusoidal function. A prprocssing scanning is don bfor masuring th two magntic fild points. Basd on this scanning th local maxima on lin ar stimatd and th masurmnts ar don hr. With th prdfind intrnal rsistanc of th sourc R i sourc voltag V can b computd (Figur Frquncy [Hz] Figur 7. Signal masurd in Tim Domain and transformd into spctrum C. Equivalnt Transmission in Modl To approximat th cabl bundl bhavior a singl transmission lin modl with quivalnt currnt distribution is gnratd. Th prsntd approach is basd on th losslss transmission lin quations. Th voltag and currnt at position z on th transmission lin can b calculatd as Vz I z jβ ( l z jβ ( l ( V ( z + I + V I jβ ( l z jβ ( l ( V ( z + I + V I ( ( with wav impdanc and th propagation constant β. As shown in Figur 4 th currnt I z on transmission lin can b calculatd from th magntic fild masurmnts. For modl gnration procss som modl paramtrs hav to b prdfind. Ths ar th lngth l of th transmission lin, th radius r of th lctric conductor and th hight h ovr ground plan [8]. ngth and hight ar chosn corrsponding to th cabl bundl undr tst. Basd on ths input paramtrs th trminating impdanc (Figur can b calculatd as V I (3 whr V and I ar voltag and currnt at th nd of th transmission lin. For stimating V and I only two sts of data ar ncssary. a + R V V a i a (6 a + j tan( βl + j tan( βl (7 D. Equivalnt Dipol Modl As dscribd in chaptr C th currnt distribution on a cabl bundl can b stimatd. Thrfor masurmnts ar don in N >> fild points on a lin abov th bundl and approximatd to a sinusoidal function. Aftrwards th rsulting currnt distribution function is approximatd by lctric dipols with dipol momnt M I d k k k (8 whr I k is th currnt on lin lmnt and d k is th discrtization siz. Th dipols ar arrangd abov a ground plan in hight h, adoptd from th cabl bundl undr tst. III. RESUTS Th dvlopd mthods wr tstd to confirm applicability. For th invstigations a pulsd signal is gnratd. Th puls has an amplitud V 5 V, a fundamntal frquncy of f 4 MHz, a puls/paus ratio t h /t l and a rising and falling dg of t r,f.5 ns. It is imprssd by a 5 Ohm systm. A. Singl Conductor Equivalnt Transmission in Modl Th cabl (Figur 8 consists of a singl conductor placd in th hight h 5 mm ovr a ground plan. It has a lngth of l 49 mm and a thicknss of d mm. It is trminatd with a
5 5 Ω impdanc. Th prdfind modl paramtrs ar adoptd from th cabl undr tst. Th intrnal rsistanc of th sourc is st to R i 5 Ω. Th magntic fild is masurd at two positions at a hight h S mm abov th cabl. magntic fild prob V R i h Figur 8. Singl conductor undr tst l ground B. Multiconductor Equivalnt Transmission in Modl Th invstigations for th multiconductor prsntly ar don basd on computr simulations. Th systm (Figur consists of a thr singl conductors with lngth l 5 mm and thicknss d mm placd in th hight h 5 mm ovr a ground plan. Th distanc btwn th conductors is st to D mm. Th transmission lins ar trminatd with 5 Ω, 5 Ω + s µh and 3 33 Ω. Th xcitation is imprssd in th cntr lin. Th prdfind modl paramtrs ar adoptd from th multiconductor. Th intrnal rsistanc of th sourc is st to R i 5 Ω. Th magntic fild is masurd in two fild points at a hight h S mm abov th cabl. With th quivalnt modl radiations from th transmission lin at any position and distanc can b obtaind. Th lctric far filds E θ and E φ ar prdictd and shown in Figur 9 and Figur, rspctivly. Exmplary th far filds of th 7 th (f 6 MHz and th 5 th (f 4 MHz harmonic of th pulsd input signal ar prsntd. As a comparison a full fild simulation of th cabl undr tst givn by a MoM solvr [] is shown. Th two rsults agr in trms of pattrn and amplitud with a maximum rror of.5 db at most angls. V R i D l h ground Figur. Multiconductor undr tst In Figur and Figur 3 lctric far filds E θ and E φ ar approximatd with quivalnt T modl and compard with a full fild simulation. Hr xmplary th far filds of th 5 th (f 44 MHz and th 7 th (f 6 MHz harmonic of th pulsd input signal ar prsntd. Th rsults agr in trms of pattrn and amplitud with a maximum rror of 3 db at most angls full fild simulation masurmnt basd quiv. T modl full fild simulation masurmnt basd quiv. T modl Figur 9. Elctric far fild (dbv/m at distanc r m (ft: E θ, Right: E φ, f 6 MHz full fild simulation simulation basd quiv. T modl full fild simulation simulation basd quiv. T modl Figur. Elctric far fild (dbv/m in distanc r m (ft: E θ, Right: E φ, f 44 MHz full fild simulation masurmnt basd quiv. T modl full fild simulation masurmnt basd quiv. T modl Figur. Elctric far fild (dbv/m at distanc r m (ft: E θ, Right: E φ, f 4 MHz
6 full fild simulation simulation basd quiv. T modl full fild simulation simulation basd quiv. T modl Figur 3. Elctric far fild (dbv/m in distanc r m (ft: E θ, Right: E φ, f 6 MHz C. Singl Conductor Equivalnt Dipol Modl Th quivalnt dipol invstigations for th singl conductor wr don basd on computr simulation. Th cabl consists of a singl conductor placd in th hight h 5 mm ovr a ground plan. It has a lngth of l 5 mm and a thicknss of d mm. It is trminatd with a 5 Ω impdanc. Th prdfind hight of th dipol modl is adoptd from th cabl. Figur 4 shows th magntic fild at a point mm abov th dipol arrangmnt in comparison with a full fild simulation. Th rsults agr with a maximum rror of lss db up to a frquncy of 4 MHz full fild simulation quivalnt dipol modl 33 REFERENCES [] CISPR 5 Ed.3: Vhicls, boats and intrnal combustion ngins Radio disturbanc charactristics imits and mthods of masurmnt for th protction of onboard rcivrs. [] Constantin A. Balanis, Antnna Thory Analysis & Dsign, Wily, 996. [3] Yolanda Vivs Gilabrt, Modélisation ds missions rayonés d composants élctroniqus, Univrsité d Roun, 7. [4] D. Baudry, M. Kadi,. Riah, C. Arcambal, Y. VivsGilabrt, A. ouis, B. Mazari, Plan wav spctrum thory applid to narfild masurmnts for lctromagntic compatibility invstigations, IET Scinc, Masurmnt and Tchnology, 5. Jun 8. [5] Tommaso Isrnia, Giovanni on, Rocco Pirri, Radiation Pattrn Evaluation from NarFild Intnsitis on Plans, IEEE Transaction on Antnnas and Propagation, Vol. 44, No. 5, May 996. [6] Gorg Monin, Di Binflussung dr Mßabwichung von Fldsondn und Stromzangn durch ral Umgbungsbdingungn, 3. [7] Edgar Vogs, Hochfrqunztchnik Baulmnt, Schaltungn, Anwndungn, Hüthig Tlkommunikation, 4. [8] G. iu, D. J. Pommrnk, J.. Drwniak, R. W. Kautz, C. Chn;, Anticipating Vhiclvl EMI Using A MultiStp Approach, IEEE Intrnational EMC Symposium 3 [9] S. Fri, T. Nägl, R. Jobava, Bstimmung dr Störaussndung im KF durch di gtrnnt Btrachtung dr lktrischn und magntischn Vrkopplungn, EMV Düssldorf, 4 [] Spigl, R., Booth, C., Bronaugh E., A Radiation Masuring Systm with Potntial Automotiv UndrHood Application, IEEE Transactions on Elctromagntic Compatibility, Vol. 5, No., 983, S [] EMCoS Consulting and Softwar, [] Xin Tong, D.W.P. Thomas, A. Nothofr, P. Swll, C. Christopoulos, A Gntic Algorithm Basd Mthod for Modling Equivalnt Emission Sourcs of Printd Circuits from NarFild Masurmnts, APEMC Bijing, Amplitud (dbua/m Frquncy (Hz Figur 4. Magntic fild in hight h mm abov th cabl IV. CONCUSION In a frquncy rang up to MHz radiation from cabls is th dominant factor in automotiv systms. Two mthods to dtrmin farfilds and simulation modl of a radiating singl cabl or cabl bundl wr introducd in this papr. Mthods ar basd on nar fild masurmnts of th magntic fild nar th radiating cabl. Masurmnts ar don in Tim Domain in ordr to gt propr phas information and to dcras acquisition tim. Applicability of Discrt Fourir Transformation (DFT for postprocssing is discussd and vrifid. Th approachs wr tstd by mans of and in comparison to numrical full wav simulation data.
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