FDTD ANALYSIS OF ELECTROMAGNETIC FIELDS DUE TO SPARK

8/7/2019 FDTD ANALYSIS OF ELECTROMAGNETIC FIELDS DUE TO SPARK

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FDTD ANALYSIS OF ELECTROMAGNETIC FIELDS DUE TO SPARKBETWEEN CHARGED METALS WITH FERRITE MATERIAL ATTACHMENT

Osamu Fujiwara and Kei KawaguchiFaculty of Engineering, Nagoya Institute of Technology,Gokiso-cho, Showa-ku, Nagoya 466-8555,Japan

E-Mail: [email protected]

Ab st ra ct The electromagnetic fields due to the elec-trostatic discharge (ESD) between charged metals are sig-nificantly affected by the presence of the metal. For suchESD fields, we have previously analyzed them, using thefinitedifference time-domain (FDTD) method, and haverevealed that the metals increase the field level accordingto the metal dimension. In this paper, we analyze theESD fields due to the metals attached by ferrite cores,which are being commonly used for electromagnetic inter-ference (EMI) countermeasure. The computation resultsshow that the cores attached close to the discharge gapsuppress the magnetic field level.

INTRODUCTIONIt is well-known that, the electromagnetic fields duet o electrostatic discharge (ESD) include broad-band fre-

quency spectra over the microwave region [l], whichcauses serious damage to high-tech information devices.For the ESD fields, several kinds of analytical studies [2]-[4 ] have been conducted, while the effects of metals onthe ESD fields were unclear. We therefore previously an-alyzed the electromagnetic fields caused by the spark be-tween the metals, using the finitedifference time-domain(FDTD) method, and showed that the metals enhance thefield level according to the metal dimension [ 5 ] .

In this paper, paying attention to ferrite material beingused for electromagnetic interference (EMI) countermea-sure, we analyze the ESD fields due to the metals attachedby the ferrite cores. The FDTD method is also used tocompute the ESD fields. A FDTD algorithm for the mag-netic field inside the ferrite core is newly derived.

FDTD ANALYSISFigures l(a) and l (b ) show a discharge model between

metals attached by ferrite cores and its FDTD model,respectively. As for the metals for consideration, twocylindrical metals with a radius of a and a length of Lwere used and they were spaced at a gap of e . For theferrite material, two commercially available ferrie coresbeing frequently used for EM1 countermeasure, were em-ployed. They had an internal diameter of 2d , an external

diameter of 2 0 and a length of s, which were attached tothe cylinders at a distance of s from the gap end. Whenthe spark between the gap occurs, the electromagneticfields caused by the discharge are analysed here using theFDTD method.

Consider the current due to the spark as a single shotimpulsive current. Then the current i ( t ) flowing throughthe gap can be expressed as 141

i(t)= I , ' F(t/.r), (1)where I and T are the current peak and nominal dura-tion period, respectively, and F( . ) s the non-dimensionalfunction that represents the waveform of the spark currentand the following relation holds:

F(z )d z= 1. (2 ).ImNext let us derive a FDTD algorithm for the electro-

magnetic fields inside the ferrite core. The complex rela-tive permeabilty i , of the ferrite core used for the EM1countermeasure can be assumed to follow the Naito's pro-posed frequency dispersion equation [6] which is given by

Metallic cvlinder(3 )

Figure 1 (a) Discharge model between metals attached byferrite cores and (b) FDTD model.

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18P405where pa is the permeability of free space, pv a is the initialrelative permeability related to the spin rotation motionof the ferrite core and U, is the spin resonance angularfrequency.

In the FDTD computation, by using the differenceequations related to the electric field E and magnetic fieldH satisfying the Maxwells equations, one-by-one com-putation is conducted, while for the case where intrinsicproperties of the medium depend upon frequencies, thefrequency-dependency must be considered [7]. In this pa-per, in differentiating. the electromagnetic fields inside theferrite core, the computation of magnetic fluxB is newlyadded. First substituting the frequency dispersion equa-tion of Eq.(3) into the following equation:

B = i ( j w ) H (4 )and then transforming this into the time domain, we have

Denote by 6x = 6y = 6z = 6 the difference interval ofspace, and by 6t the difference interval of time. Let thedifference function of W = W(z,y , z , t )be W ( i , j , k ) =W(iSz,jdy, 6z ,n6 t ) . Under the assumption that thespark discharge between the cylindrical metals as shownin Figure l(a) occurs in the z-direction, the z-componentof the magnetic field, for example, can be given by

H p + * ( j + i , j+ , k ) =1

1+{1+/~~~(i+i,j+$,)}w,(i+f, j + i, )r6 t +{l+w,( i+ f , j+, k)76t}Bkn+((i+ , j+f,)-B ,

[H:I-4 i+ ; j+ , )(6)In- & (i+ 1,j+ f ) ]

and the z-component of the electric field is expressed asELn+(i,j,k + $) = ELn(i,j,k + f )

2Er (i , j , + f) - 6 t r ~& j , + i) E o 2~~ (i,j, + t) + 6tru (i,j, + ?) E O-,

1 26 t Fn f1 ( i , j ,k + f )612 2E r (i,j, + 4) +6tru (2 , j , + 4) E O- -

where E= E / ( ZoHo ) , B = B / ( h 0Ho ) ,H = H/H,,Zo =m, oc is the speed of light.

The values of pra and ws in Eq.(G) have those of themedium equivalent to each cells, and they thus becomezero except for the cells constructing the block modelfor ferrite cores. The function P+*,hich is the sec-ond term of the right-hand side of E!q.(S), is given byFn(i , j ,k)= F(n6 t j2 ) for the cell through that the sparkcurrent flows, but 0 for other cells. Permittivity &?( i , j , )and conductivity u(i , j , ) in Eq.(8) have numerical valuescorresponding to the medium of the cell. The first orderM u r absorbing boundary condition IS] was applied to theboundary surface of the computational region to simulatean unbounded region.

I,/cr, 6t = 6t/r , 6 6 / n , and

NUMERICAL COMPUTATIONSFigure 2 shows the FDTD computation region and ar-

rangement of the cylindrical conductors. The region con-sisted of (101 x 101x 101) cells with 6= 1.0 mm. Thefollowing three cases for the FDTD model were consid-ered: the first model attached to the near end of the gap( z= OS), the second model attached to the far end of thegap ( z = 356), and the t.hird model without a ferrite coreattachment.

The FDTD model was placed at the center of the com-putation region and it was aligned along the z-direction.For the implementation of the spark path, only one cellwas used. The discharge point was taken as the originof the coordinate system. When the spark between thegap with a length of e occurs at a voltage V,, he sparkcurrent of l?q.(l)s given by 141

(9)

.I1+ exp{3&(f - O)}]-.~ (10)

-0-0

Figure2 Computation region and arrangement ofFDTD model.

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where C is the capacitance between the gap, a s the sparkcoefficient and xo s the integral constant and was takenas 20 = 1.5.

Figure 3 shows the waveform of the function F ( . ) . Asfor a material of the cylindrical metal, brass (conductivity:U = 2.0 x 10 S/m) was used. The size was taken asa = 1.0 mm and L = 4.5 cm. The intrinsic propertiesof the ferri te core were taken as U = 0 S/m, &.. = 300,w. = 6.28 x lo7 rad/s and E? = 14.0. The core size wastaken a ~ i = 2 mm, D = 8 - 16 mm and s = 1.0 cm.The normalized difference time st(= 6 t / 7 ) was chosenas 6t = 0.5 x ~ / C T r 0.01 from the solution stability [8](CT N 5 cm was used, which was obtained from ou r sparkexperiments for the metal spheres [4]).

Figures 4 and 5 show the computed waveforms of themagnetic fields on the y-axis at locations of (06,36,06)and (06,306,06), respectively. The abscissa is the timenormalized to T . The ordinate is the magnetic field nor-malized to Ho = I ,JcT. he thick and thin solid linesare the waveforms for the case attached to the near end( z = 06) and fa r end (2 = 356) of the gap, respectively.The dotted line is the waveform without a ferrite core at-tachment. As seen in Figure 4 , in the near region of thedischarge portion t he ferrite core attachment does not al-most affect the rising part and first peak value of th emagnetic field, whereas in the far region shown in Figure5 the core attached to the near end considerably suppre-ses the first peak and makes the waveform gentle. On theother hand, the core attachement in the far end does notsignificantly affect the magnetic field waveform.

Figure 6shows the dependence on the distance of thefirst peak value of the magnetic field. The thick solid linesis the first peak value of the magnetic field when the ferritecore is attached t o the near end of the gap (t= 06). Thethin line line is the case for the core attached to the far end( z = 356). The dashed line is the case without a ferritecore attachment, which almost corresponds to the thinline. It was found that when the ferrite core is attachedto the near end of the gap, in the fa r region of T > 0.1 x c rthe magnetic field peak decreases, while in the near regionfrom the discharge portion the core attachment does notalmost affect the field peak.

2 4 6 8Normalized time f/zn

Figure 3 Computed waveform of nondimensionalfunction F(ti7) for the spark current.

r

,0 2 4 6 8Normalized time t/zFigure 4 Computed waveforms of magnetic fieldsin the near region from the spark portion.

Normalized time f/z

D = 1 6 60 2 4 6 8........without ferrite core

-0.2Normalized time f/z

Figure 5 Computed waveforms of magnetic fieldsin the far region from the spark portion.

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18P405to a ferrite core attachment.

........

Normalized distance dcz3 10 30 6

94 1 0 7 ID = 16 cell I= 16 cell

....... without fenite core0.010.02 0.05 0.1 0.2 0.5 1 2.5 1 2Normalized distance dcz3 10 30 6

Figure 6 Dependence on the distanceof peakmagnetic fields.

CONCLUSIONSThe magnetic field due to ESD for the metal cylinder

attached by the ferrite core has been analyzed, using theFDTD method. As a result, we have found that the ferritecore attached to the near end of the discharge portionsuppresses the magnetic field.

Future subjects include experimental confirmation andmechanism elucidation of the field suppression effects due

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REFERENCESfor instance, Greason, W.D.: Indirect effect ofESD: modeling and measurement, Proc. 11thInt. Zurich Symp. Tech. & Exh. on EMC,116R1, Mar.1995, pp.613-618.P.F.Wilson and M.T.Ma:Field radiated by elec-trosta tic discharges JEEE Trans. Electro-magnetic Compatibility, EMC-33,1, Feb.1991,pp.10-18.S. Ishigami and I. Yokoshima:Measurements offast transient electric fields in the vicinity ofshort gap discharges, Proc. of 1994 Interna-tional Symposium on Electromagnetic Compat-ibility, May 1994, pp.90-93.0.Fujiwara:An analytical approach to modelindirect effect caused by electrostatic dis-charge,IEICE Trans. Commun., Vol.E79-B,No.4, Apr.1996, pp.483-489.O.Fujiwara, K .Kawaguchi and N.Kurachi:FDTD computationmodeling for electromagnetic fields generated byspark between charged metals, Proc. Inst. Wro-claw Symposium on Electromagnetic Compatibil-ity, EMC98 Wroclaw, Poland, June 1998, pp.268-271.Y. Naito:On the frequency dispersion of the per-meability of spinnel type ferrite, Trans., IEICE,Vo1.56, 2, Feb. 1973, pp.113-120.R. Luebbers, F.P. Hunsberger, K.S. Kunz, R.B.Standler and M. Schneider:A frequency depen-dent finite-difference timedomain formulation fordispersive materials, IEEE Trans., VoLEMC-32 , 3, Aug. 1990, pp.222-227.G.Mur:Numerical solution of initial boundaryvalue problems involving Maxwells equations inisotropic media, IEEE Trans., VoLAP-14, No.8,May 1966, pp.302-307.

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FDTD ANALYSIS OF ELECTROMAGNETIC FIELDS DUE TO SPARK

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