An optimization algorithm for the calculation of the electrostatic discharge current equations parameters

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1 WSEAS TRANSACTIONS o CIRCUITS ad SYSTEMS Vasiliki Via George P. Fois Lambros Ekoomou A opimizaio algorihm for he calculaio of he elecrosaic discharge curre equaios parameers VASILIKI VITA GEORGE P. FOTIS LAMBROS EKONOMOU Deparme of Elecrical ad Elecroic Egieerig Educaors A.S.PE.T.E. - School of Pedagogical ad Techological Educaio Ν. Ηeraklio 4 Ahes Greece s: vasvia@aspee.gr gfois@gmail.com leekoomou@aspee.gr Absrac: - The ieraioal sadard IEC for he elecrosaic discharge does o provide a equaio for he elecrosaic discharge curre bu i jus defies a waveform for i. I he curre paper a ew opimizaio algorihm is preseed ha has bee developed i order o calculae he parameers of equaios proposed i he echical lieraure o describe he curre durig a elecrosaic discharge. Elecrosaic discharge curre daa obaied from real measuremes are also used i his work i order o compare he resuls produced usig he opimizaio algorihm i a effor o prove he efficiecy ad accuracy of he proposed algorihm ad o ideify he equaio ha describes beer he elecrosaic discharge curre. Key-Words: - Discharge curre; Elecrosaic discharge; Elecrosaic discharge geeraors; Opimizaio algorihm.. Iroducio Elecrosaic Discharge (ESD) is commo pheomeo ha is very crucial for elecroic devices such as iegraed circuis or fas complemeary meal oide semicoducor sysems. The IEC [] describes he es procedure for elecroic equipme uder elecrosaic discharges ad defies he shape of he discharge curre ha he ESD geeraors mus produce however i does o provide a equaio for he elecrosaic discharge curre. A accurae equaio is a idispesable requireme for he descripio of he ESD geeraors i simulaio programs. May sudies have bee coduced worldwide o sudy he ESD curre waveforms. I [] i has bee cocluded ha he ampliudes ad he rise imes deped o he chargig volages he approach speeds he elecrode ypes he relaive arc legh ad he humidiy. The parameers ha characerize he discharge curre waveforms of ESD esers have bee sudied i [3]. Muroa i [4] preseed he variaios ha appear o he discharge curre whe various codiios chage durig he es usig he simulaio program PSpice. A improved circui for he ESD geeraors wih a referece waveform close o he oe defied by he Sadard ad a equaio describig he referece waveform have bee proposed [5]. Aoher proposed equaio [6] for he referece waveform has bee developed i order o sudy he ESD pheomeo i coaial cable shields. Fially he dowhill simple opimizaio mehod i [7] ad geeic algorihms i [8] have bee used i order o deermie a accurae elecrosaic discharge curre equaio. The curre paper aims o calculae he elecrosaic discharge curre equaios parameers i a effor o obai a accurae discharge curre equaio. For his purpose a ew opimizaio algorihm is proposed ad he obaied resuls are compared wih elecrosaic discharge curre daa obaied from real measuremes provig he efficiecy of he algorihm.. ESD geeraors discharge curre The ESD geeraors are used for esig he robusess of elecroics owards elecrosaic E-ISSN: 4-66X 4 Volume 5 06

2 WSEAS TRANSACTIONS o CIRCUITS ad SYSTEMS Vasiliki Via George P. Fois Lambros Ekoomou discharges. Elecrosaic discharges ca occur eiher as coac discharges or as air discharges. The es level volages for he coac discharges rage bewee ad 8 kv ad for he air discharges bewee ad 5 kv. Accordig o he Sadard for he verificaio of ESD geeraors here are 4 parameers whose mus be cofied by cerai limis. These parameers are: he rise ime ( r ) he maimum discharge curre (I ma ) ad he curre a 30 s (I 30 ) ad 60 s (I 60 ). A ypical waveform of he oupu curre of a ESD geeraor is show i Fig. ad he limis of he 4 parameers (valid for coac discharges oly) are show i Table [9 0]. Fig. Typical waveform of he oupu curre of he ESD geeraor [] Table Waveform parameers Volage I ma r I 30 I 60 (kv) (Α) (s) (A) (A) iroduced by [] usig a double epoeial fucio: i( ) = i e i e () The referece waveform for he discharge curre accordig o [6] is: σ σ i ( ) = A e + B e (3) The waveform of Fig. may be viewed as he sum of wo Gaussias i he ime domai oe arrow ad he oher broad. Equaio (3) is closer o his observaio sice he facors σ σ A e ad B e represe he arrow ad broad Gaussia respecively. I [5] based o he equaio of he lighig curre of Heidler [3] he referred waveform is give by: i( ) k i i 3 4 = e + e (4) k k = e + ad k = e i i are curres i A 3 4 are ime cosas i s ad sigifies how may imes he equaio ca be differeiaed wih respec o ime. I order o aalyically describe he measured elecrosaic discharge curre he ukow parameers of he equaios ()-(4) mus be opimized. A equaio ha does o correspod o he discharge curre bu will be used i he furher aalysis is he lighig curre equaio []: i ( ) = i 0 e e () A approimae equaio of he discharge curre for commercial simulaors was firsly 3. The opimizaio algorihm The waveform of he discharge curre ha occurs for he opimized parameer daa of he four possible equaios mus be as much closer o he measured discharge curre. Cosiderig ha he accuracy of he compued discharge curre depeds o he model parameers hese ca be deermied by miimizig he fucio: E-ISSN: 4-66X 5 Volume 5 06

3 WSEAS TRANSACTIONS o CIRCUITS ad SYSTEMS Vasiliki Via George P. Fois Lambros Ekoomou I e = c ( ) I I ( ) m m ( ) 00 I c ( ) is he compued discharge curre ad I m () is he measured discharge curre. (5) The equaios ()-(4) ha ca describe he discharge curre are cosised of differe parameers whose may have various. Equaios () () (3) ad (4) have ad 7 parameers respecively. The objecive is he miimizaio of he absolue error of (5) which is a fucio of or 7 variables depedig o he model. The parameers of each equaio form a colum vecor : [ ] T = [ i ] T 3 0 = (6) [ ] T = [ i i ] T = (7) 3 4 [ ] T = = [ B σ σ ] T A = (8) [ ] T = = [ i i ] T 3 4 = (9) The applicaio of a opimizaio algorihm will deermie he opimal i wih is goal he miimizaio of he relaive error which is a fucio of several variables. e() is he relaive error where is he colum vecor preseed i (6)- (9). The opimal soluio ca be foud afer he ieraio of a formula of he form: colm (0) + = λ X is he value of he desig characerisic vecor a he h ieraio λ is he coefficie vecor which acceleraes he covergece colm is he colum vecor formed from he Jacobia mari M ad M is he Jacobia mari defied as: e e... N M (... N ) = () en en... N N equals o or 7 depedig o he equaio. This mehod compues he firs parial derivaives of he objecive fucio i referece o he depede variables [4]. I is ierally made by wriig a suiable approimaio of he objecive fucio up o a desired degree. The followig algorihm based o quasi-newo mehod has bee implemeed. Sep : Se iiial for he i 0 i i 3 4 A B σ σ of each equaio (6)-(9). Sep : Calculae e i from (5) M from () ad + from (0). Sep 3: As log as: + < ε repea Sep where ε is a posiive parameer which defies he desired covergece precisio. Sep 4: Display coverged X. 4. Resuls Tables -5 prese he compued parameers for each oe curre equaio described i secio as well as he opimum parameer obaied usig he proposed opimizaio algorihm. Table for equaio () i 0 [A] [s] [s] Table 3 for equaio () i [A] i [A] [s] [s] Fig. preses i a sigle figure he compariso bewee he discharge curre waveform ploed usig eperimeal daa ha have bee obaied hrough real measuremes [5 6] ad he discharge curre waveforms ploed usig he obaied opimized parameer for he equaios ()-(4). E-ISSN: 4-66X 6 Volume 5 06

4 WSEAS TRANSACTIONS o CIRCUITS ad SYSTEMS Vasiliki Via George P. Fois Lambros Ekoomou Table 4 for equaio (3) A[A] B[A/s] [s] [s] σ [s] σ [s] Table 5 for equaio (4) i [A] i [A] [s] 3.5. [s] [s] [s] shape similar o he eperimeal resuls. The hird more suiable equaio is () ha alhough i cao simulae he firs peak of he elecrosaic discharge curre i ca calculae accuraely he parameers of he double epoeial fucio. 5. Coclusio The ieraioal sadard IEC for he elecrosaic discharge does o provide a equaio for he elecrosaic discharge curre. I his paper a opimizaio algorihm was developed i order he opimum equaio for he descripio of he elecrosaic discharge curre o be deermied. The obaied resuls have bee compared wih real elecrosaic discharge curre daa obaied hrough eperimeal measuremes i a effor o jusify he efficiecy ad accuracy of he proposed mehodology. The proposed opimizaio algorihm ca be proved very valuable i he achieveme of more accurae ad reliable resuls i he sudy of he ESD pheomeo. Refereces: [] Ieraioal Sadard IEC Elecromageic Compaibiliy (EMC) Par 4-: Tesig ad measureme echiques Elecrosaic discharge immuiy es Basic EMC Publicaio 008 [] D. Pommereke M. Aidam ESD: Waveform calculaio field ad curre of huma ad simulaor Joural of Elecrosaics Vol pp Fig. Compariso bewee he eperimeal daa of he discharge curre ad he discharge curre for he opimized parameer of ()-(4) (chargig volage = +4kV). Comparig he curves of Fig. i is obvious ha he equaio ha has he bes fiig o he eperimeal daa is equaio (4). This is he mos suiable of all he eamied equaios for he elecrosaic discharge curre descripio sice i simulaes he discharge curre i he bes way. The secod mos suiable equaio is (3) sice i has a [3] O. Fujiwara H. Taaka Y. Yamaaka Equivale circui modelig of discharge curre ijeced i coac wih a ESD gu Elecrical Egieerig i Japa Vol pp. 8-4 [4] N. Muroa Deermiaio of characerisics of he discharge curre by he huma charge model ESD Simulaor Elecroics ad Commuicaios i Japa Vol pp [5] K. Wag D. Pommereke R. Chudru T.M. Dore J.L. Drewiak A. Shashidraah Numerical modelig of elecrosaic discharge geeraors IEEE Tras. EMC Vol pp E-ISSN: 4-66X 7 Volume 5 06

5 WSEAS TRANSACTIONS o CIRCUITS ad SYSTEMS Vasiliki Via George P. Fois Lambros Ekoomou [6] S.V. Berghe D. Zuer Sudy of ESD sigal ery hrough coaial cable shields Joural of Elecrosaics Vol pp [7] G.P. Fois L. Ekoomou opimizaio of he elecrosaic discharge curre equaio Ieraioal Joural o Power Sysem Opimizaio Vol. 3 No. 0 pp [8] G.P. Fois I.F. Goos F.E. Asimakopoulou I.A. Sahopulos Applyig geeic algorihms for he deermiaio of he parameers of he elecrosaic discharge curre equaio Isiue of Physics (IOP) Proceedigs Measureme Sciece & Techology Vol pp [9] L. Ekoomou G.P. Fois T.I. Maris P. Liasis Esimaio of he elecromageic field radiaig by elecrosaic discharges usig arificial eural eworks Simulaio Modellig Pracice ad Theory Vol. 5 No pp [0] T.I. Maris L. Ekoomou G.P. Fois A. Nakulas E. Zoulias Elecromageic field ideificaio usig arificial eural eworks 8 h WSEAS I. Cof. o Neural Neworks (NN '07) Vacouver Caada 007 pp [] D. Kid K. Feser High volage es echiques Newes 00 pp [] G. Cerri R. Leo V.M. Primiai ESD idirec couplig modellig IEEE Tras. EMC Vol pp 74-8 [3] H. Heidler Aalyische Blizsromfukio zur LEMP-Berechug 8h ICLP Symposium 985 pp [4] D.F. Shao Codiioig of quasi-newo mehods for fucio miimizaio Mahemaics of Compuaio Vol pp [5] G.P. Fois L. Ekoomou S. Kouresi E. Zoulias A. Nakulas Measureme of he elecric field a he ear field radiaig by elecrosaic discharges 6 h WSEAS I. Cof. o Isrumeaio Measureme Circuis ad Sysems Hagzhou Chia 007 pp [6] G.P. Fois C.A. Chrisodoulou C.D. Pippis L. Ekoomou I. Zafeiropoulos T.I. Maris D.C. Karamousaas G.E. Chazarakis I.F. Goos I.A. Sahopulos Measureme of he elecromageic field radiaig by commercial ESD geeraors wih he Pellegrii arge o isulaig maerial Measureme Vol. 4 No pp E-ISSN: 4-66X 8 Volume 5 06

Experiment 2: Waveform Analysis

Experiment 2: Waveform Analysis Specrum aalyzer Experime : Waveform Aalysis 8/3/6 his experime is o familiarize you wih he aalysis of sigals ad eworks usig he HP 358A Specrum Aalyzer. he aalysis of sigals is achieved i he ope loop mode