200B IEEE EMC SymposiumOverv~ew

Introduction to the P< rtial Element

Equivalent Circuit (10 EEC) echnique

(MO-AM-1-2)

'G. Antonini!JAq e~c laooratOlY

Universit.;" of L'Aquila, ITA.LY

Acknov.ie.:lgment: Albert E. Ruehli

IBM T, J. Watson Research Center

Y, k " In Heights, NY, USA.

• Introduction to Partial Element Equivalent Circuit(PEEC) Method

• IPEEC Fundamentals

• Assembling Equations by enforcing KVl and IKOL

• Multi-function partial elements evaluation

• CompleXJity redllction, non-orthogonal formulation

• IPEEC Model [Examples

• Conclusions

• How can I get started with PEEC - References

_,I

IEM and Circuit Solution Approaches

L r-------;;C IRe LlII T 11 _L... I EO UAli IONS

IPEEC fundamentals

Ea<1! (I!Jr'Bm~ i 'JI1i8 in '11'01­nmes, lO(iI~,ed ,iI~ iI pDint ,,1

illJh~n tl. a no! each charge onsurfaces. (iI~ed ,i1t ,i1 II' "lit '~

o 51 II od' (le, an il1o!ame ,eJ­

iec~ at iI o:int • at time t.

Inside the' ndoct,.w, at a point. " at time t, t.he foil ~'ing equat' n

holds

.1'''',t . A.,.tE,"',t =-",- =E' "',t ,---'-' -V, ',t

, t

",mere ,Ei "', t is the electric field eventually' inddent in l' at ti me t .

.-. ....lll,La. ........ u;..X«i

978-1-4244-1699-8/08/$25.00 ©2008 IEEE

IPEEC fundamentals IPEEC fundamentals

+\1'·I/",8

.,. E ""',8

'1J:l "',8

\1' . .1(.,. 8

fl. . .1 .,., 8

The pl<!violE equatilolrr.> can be re-mitten in the Lapl~e domain, in a mOl<!atmpart fufm I as:

mere = I'" - f"I/IlJ, 8 is the Laplac.e variable aoo CO is the spee:l ofIight in the free spaor.e.

et!ofS

f side coodLlet!or51od.u r, t 00 SIUr<IJ e or [[011

at

r! = t - I .,. - .,.' Io

""; .1 '.,.,t) 8A "',t Vir,.." "',t =--+---+, ,.." "',t.., {It

= _ { .1 .I,t" af!4T ••' 11' - ., 1'

'OJ .,J' r,t

. .1 'r,t'

A "',t

In the q;uas'i-static case t' = .

A.~.. Aipi. .iD:lIli

lDevelOp ment of a IP EEC olver IPEEC fundamental

Five steps process1. disc etiza'foll of vdunles into elelnentary volume ce 51

surFaces into 'elementary surface oells'

C.onductCf' and diele::tri c vol umes an d 51urfa GeS are diSGretized in el­ementary wlumes :hexahedra and patches (quadrilaterals) respec~

tivefy.".,.

discretizafon of the Electric Fie d Integral Equation

HIE·

----.....-.+.J-,.....r--- r---- -----<

..3. circuit inte ;etatio of the EFI E'

4. evaluilfon of partia e e nents describin~ m~etic andelecu'c lield couplng (time c'!lllsum'

5. solution of the linear system into the l'requency 0 land

time do 'lain (tin e consufllin~' .

ins

Charges are as ned on the surFace of (JOfiductOll'1S

to

IPIEEC fundamentals

J,V1

.J"

~ 2:b,. '1'

I'J-l.

1'.".

i7 .' ~ LPm Qmm-l

" I" and Qm , I are the basis function ..-eights ·h ir:h must be

determi n- at each angu lar frequenli:'i ,

" .rIj'. and N. r,;,present the number of volume and surface basis furr::­

tmrn and the cOl'feSlJ'!illdi ng elementary ViIJ/ ume and surface sub­

reg .. rn

IPIEEC fundamentals

The so-ca lied 'Galerklll1J's test n,g or \\i1i!i,gll1tiJll!; process is used tl!!l.gener­

ate a Y)'5tem ofequatioos for the unliflo- ns Y. ights In 'I. ,= 1·· ·N.and Qm " ., m = 1 .. ,N. ,. enforcing the resi::lual9 of equatioos to be

orthcgonal to a set of ~~ighting fUrd mre, cl)!llS:E!n t be mincident 'lith

the basis functions.

A'~I ,1. ..... 1, ,0KIIi 9 ... J.o

IPEEC fundamentals

Each term of the EFI E is 'Ui!ighted and integrated aifer elementary volume

cells I,~:

IPIEEC fundamentals

Cih ce Of the basis allli ~'Ei,gl1till1,g full1 ct illS

for conductor vollJmes and colltdlllCt,or S!!J: faces

<t ' ,13; l' ~', = L. t .. b; l' r; fur"1.=l···N.

{

Unb,. , = "Tn"

if)

if1' E T"

. hel"l't1SE!

",.1-.ere fln is the unit vector irdicating tl-.e current rientation in volume,n'

if EA m

otl-.erwise

!II .... ]]

Enforcing Kirchhoff Voltage Law (KVIL) Etlforcing Kirchhoff Voltage law (KCl)

The pl'elil is ,eql!l<Jitlicn is eql!lirv ~em: 'to Km:II1'lmff's vcrtaJ!;e I N

(IKVL)

The application fthe alerkin's t.esting p ca!l uIB t.o t.he equation f the

electrior sor:a lar potent.ia I leads ..rit.e:

~=PQ

relati n,g the f»1Bnt.ia I of eaorh su rfaor:e cell 00 the charges located on aII

the surface orells.

Kirdil fif's 'Cllment raw i(I(CL) is E'lilfOll'(;ed 'to 'Bilidil node In the

LaJ:Xace domai n, it. ream:

Nu

Qm - L m,~,l!c~ S =1.m

k-:L

....here 6m,k = -1,+1,0 depending on the coonert: nand directioo of

branch.ll 'it,h respen t.o node m,

r&~ =_"'_1 ~ =RkJ'Lk,~

JI1

'rel: = - LQm ~m -..F"k,"mm-l

1'0'

'rL'" = 8 Ll.ykn1Ln,,-I

",.here:

rand ,~are the length and t.he cross section of cell k and

L:p~n s =~ :on LLnis the ~ called partia lind utt.ance beti>een vol ume orells i and

Example Example

IE'lllLlwalent ar;:uit fOIl' mill8J1.et·c fiefl!! (OOIlIJIlJl:

IKVn. Is enforced 1.'0 eillcih mesh,

",

1Di'scretJizilIt[ 'iii process:

• nodes, 3 pIl)t.entia Is t.o infinit" iIok, Ii = 1 :2',3

R1 + L.,nlIz.:L + L"l:1L2 + lell = 0

R2 + sl.pz;Jhz. +sl.F21hl + 1,'Ct!' =0

• braoche9,' currents 1L", = 1,:2'In a matri form, KVL ream:

-,A,.p 8 - ,lUI. 8 - 8L" ,8 1L 8 - 0 8 = 0

....i-.ere A i9 the oronna:.tivi~' matrix

A.....I. J.;..3:Ui 9"']~

Electric field coupling Electric field coupling

Pllql + PJ20Q2 +PU 3

Paql +Pl2~ + Pl3 3

P31 ql +P32i'J2 +1\3 3

In a matri fOrm, KC L reads:

1. .s - A'1.[, .s = 1 •

Di's:pacelll1.ent. (l!ffH''1ts 1. =.sQ = .sp-1if!'

Severn I derom ~tioos of p-l are p!!l5'Sible.

l~l1 PI:;'

~l=.s-iIoJ-.s- -.s3111' Pll Fll

102_1_ iIo'2

_ .. PlI &2=

Pl2 Pz.! 1-.s~3

1.s sQ3 = 1. Pn P:!2-iIos-"- 1- ..~2P33 1\s ~ ..

10:: = .sIJifo - 10::

""here 1. .s represents the lumped current Sl!IU n.::es.

EqlilvalEmrt dm.lit fur electlr[c field (QI.IpI1IlJJ:

A I!JUI, .Be1

PEEC equivalent circuit

P rtLa'I element eq\.llva1ellt drcui':t

Lu m linear and non linear elements can be, nnected to the equivalent.c.irc.u it throogh nodes.

Basic Derivation of PEEC Model

Unlknowns antities:

1. cond tive cunents flowing in volunles Ii..·

potentials to infinity 1..'.

The nlagnetic fie d a xl elect ·c feld ooupJinss are cles'Cr ed

by the p tial inductance and cJO'enicient of pot'enti matri­c~es.

........ Ui.3:Oi

Multi-Function IElement Evaluation

I.

Example: Evaluation of Partial Inductances

• "INiear" a,nd "Far" Coeff,icients:

Full Wave solution: circuits have delays

L =_Pf f ,~'Um,Fkm 4rrS/r.Sm'".' .... ITk - T m I

Spacing T/;rn delays the coupling

• 2 Cell Exalillples

Partial L Cin.uit Equafoo

"••.1lI,ua. .

Fu II Wave Solution: P Elements ,ith De'lays

Pl"., = 4\TElAm L. I..... ITk ~ m Id.t4dAm

Spacing T/;m delays the coupling

• 2 Cell Exalillples

P C" uil Element Equatron

P EEC Equivalent Circuit Model

Bas"c partial element FOI" 3-D I odel

" ....u.

tion of PEEC Model Validity of IP EEC Solution

A dvantages over other integra I metho ds

• lilhe same formulatioll1 equivalent circuit can beused for botlrn time and lirequency domain analysis

• All time metlrnods for cimuit analysis can be used:nodal analysis. rI1Ieslnl ~nalysis, Modified NbdalAnal'ysis (MNA)

• lEas;' incorporation of linear and non linear lumpedelements and/or electronic devices

• Spice-ilike solVers can be used eventually includingdelays

IRREQUENTLY ASKIED QUESTIONS

'. \lVhat is a Full Wave Solution?'. Highest Frequency, Pm..,. 'Given by Meslrning'. Not limited by Quasi Static Models delay involVed)

'. What is a Full Spectrum Solution?'. Works for lo.v Frequencies, Including DC

'. Limits of Lumped Circuit Element Solution?'. Same as Other Numerical Solution Teclrnniques

'. HO'I'J Can We Add New Features?'. Very Flexible Circuit Based Solution A,pproaclrn'. MNA (Spice) Circuit JlStampS"l Technique

IPEEC Model Spice Cir uit IElement IPIEEC Model Complexity Redu tion

[ SCI IC;a,pa.c j'tance:;;]

iI

6ign"'l P1J'o;p..,g..~ti"",nM,sodell i'ttlg··I •, .·, ,

[ Lip.C)PEJEC

-------.:-------..

(t __

_ (Lp,P.A.'" ) IPEEC

[ ,eLI> PEEl::; _ ,( ...R!PEEC ]

iII

L~ow 1m pcd.ancePower SUpply Moolcling

From Geometry to Circuit Representation

• Zero PotetlUal1 Ground Reference Node at Iinfil!llilty!

• N - Termin::ll Spice Circuit Element

• lin dIU dedi lin Spice Inpl!.lt language Synt:3lx

GENIERAL FULL WAVE PEEC MODEL

B. s.i IF'IEEe Cir uit Cell for Diele tri s.

Coupled Loop Few Two Basic PEEC Cells of aNon-Dispersive Dielectric Barlll

PEEC equiva ent circuit fur die ectricsExcess capacitance ...~ = ..,e· l-I.)S

Non Orthogonal Fewmulation• lForl11llli1btiolfl \iVork [2]• Extension, 'Generalliizatrion of the PEEC Method• Hex:anedra: Very Gener;;/I Building Blocks• 1fl,i1la,1<e AJrbirtrary Non>-IRectangullarr Sha,pes

.3

6

"'.IJUI,.~

IFa t lime O'omain Solution Spa ime D'omain Solution

Sparse Circuit Matrix Solution

Pl!I1s.1:Time (KJIlO !l11l)'

V,II

.. ..l

d • ( i • T)LPij-d-t--

x

P resent Time

• Sparse L/U GrclLllit l/i.ibtriiX Solver. 0 N 1.5

• One Matri,iX Sol~e. Tlil11e Steps Back SLllbstiitUitrions

• Overa,lI Solll!lJti Olm Till11 eO_7\,(2 Not 0 l [3

Delay Differential Equation Fonllulation

• Del ayed Modllifi ed Nodla,11 An allysi,s For111 ulla,bon

• MlliIlltiplle lip;. DellayedlllndlLlcbve (olJlpllings

• IMlIliIliti pile Pij Della,yedl lPotentila,ll (oLlpllilngs

Co 1: t +GD~'t +LGi~ t-.., +LCi' t- i =LUi t-..,

"'1If,

lossy Example lightning Protection Stern

1..=·....'

• Input Wave~m Sine Square Current Sou ree, Rise Time 100 ps,Fall Time 100 ps, Wklth 1.9 ns

• 20 non uniform cellg alons the lengtl1, 10 cells alons the width, 1.

cell aloos the thickfless, largest Cell hi[kness to length ratio

1:4750

.' (ross Sect~n: VFI Skin Effect Uniform Model

1",= =30kA., = l,k, = t/ 1 rith 1 = 0.5 .S, 2 = 10,ru and

"'.IJUI,.~

Iinterferometer fo 'Gravitational 'Waves

D re(;l: [jgtilJm Jig 's:llToke ,of iI ~ rge .s:mu:ct e c. .lIlstilJUted lby iI 100 m

~ns s:em~cyll1ldr call CQ.\lering Virgo-Project

ICNIRS-fraJ1lce+~NIFrJ-ltilrf)4(CaSdllllii. PiSiI, [tal] )

2500 pilitdtes - 1.2001) ~atl,allbasis functions (;,ons:ld!E'J'llIlg both

currelilts and potential's to, [nfilllit;t

Connectors

Summary

PEEC fiJlodel Evolution• IExcelllellilt for Combinedl ElM and Ckt. Modlellilllilg• lHIelps IlJIndiersta'lJldl EIMllPmMem Beha,vior, CoulphllilgS

Etc.• ndl1ucta,IIiIce, Ca pa cita>lIiIce, Time a'lIiIdi FrE{Jlll!Ienc.y

Do ma,illlil Sollll!luions• IFI!.IIIII Wave a'lIiId Fulill Spec.tlfUll1ll1 Solll!lltion (dc to

dayllilglitt '

PEEC fl,l1odeling and 5 lution Efficiency• Careiiul Allgoritnms Wlith ElIiIgineerling Accmac.y• Fast solvers freC!luency and time domain• 3D PEEC Method Development is Continuing

Recent IPEEC 'Oriented Works• Original Full Wave Paper [3]

• Time Domain PB!l'E'r [4]

• Ne Direct Sp4tl:e Implementatioo [5]

• New GSI Skin Effect 1.1 I [6]

• Mooel Order Reductioo [1, 8]

• Wavelets PEEC [9, 10, 11]

• Nlln Ortoogooal PEEC [12, 13, 2]

• Time-Frequency domain FMM-PEEC BJl'lIf"OOch [14, 15, 16]

• Dielectritl: rm>del ing [1]

• Dispersio-e Bnlll lo~ dielectri€:s [17, 18, 19]

• B . dband model ing [20, 21, 22, 23]

AI!JIlI..DG A....L .>DXi

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Mc4II 03i.. ~'IIIm~"imf"..·,.,. i'mry:a.'Id'r-....m"f'."iUt~::JOs-J :l,~' r»n

ITI J.C• ..".A. Ruhl~ T.DIIII~.Ji.rni'lt»cIra...bc:»-ar"'r~"I"'lIh.bIUQrbr!ll'n.~dP:d1ll»CIlail'''u~.IQ~ ~.!Ii1nl"ll,~.~~ ~'Um~i1lrl'1l"'W1=!t.......,.....",.i'" MI.........."ftII:lI»:I.

1'1 .... """"', r.~ 1 ....."" "''''''*\1 "'~ "f'''''' DO"""" ..,." ..... ",,1<v~ ...d.~~rnDlI.S~ "JnLI!Ct\1'II41 a"l:1i'n N''s)'ZH'U,L\.f, ..fJ~D.XOJ.

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LLq G. "'mII"~ A. c.unI~ Ii.. bill. !bu... 51:111"11111 I'D' PliliC r,"'I~. II ~. 07..~r/)J S .. itE. ~'q1 on

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LL~ Jt.. Ii. R......... .v.u.... :III1I A. OrtJniIL littuIlC41 d'n~ ifMnlllI.iI,.tdll"II: I:ftUL I'III~ IQ

lce-ncl.II"pbrflC'fttIl' hiAr".:.;c "d:rtV'SSSli'lf.~np.""~~Q,,,,,.u:fi ':fi p.Iij,II j1.&-."".l~.

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LUI G.htulll~".R."I.J.~ Nc4 0nII~FG: I=«rUJmnbTm.1I rw...~ Do:ITaIll ~I'I''''

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I., """,*". rm ...' _ ... P<I>: "''''''"'Y''''-''''''.'''''"",,~"'~'&T~ 'S«!cJ ~, Ji'(.3)::n-.JI, H~r..."btr.~

L~ G..... tulll~ A." BIt F:alL 1.oU1fd'1II'I:i N.tl-Rn:llc.. r~ I:titttUlL S~ ;.In..Ittb... ",.,;l;Il:tt,

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[~ 5. 'i. K:o:huw, G.WoIIltarg. slJlt.l.,.'Jr,..I4'7.·.. ~t(rT1Il4Ib:t: ..=--- I:wnUlblkl":II~~. Ix'~ SIJ ;~\nl""'~~~CD_..,....i~,",r ·~~21-'ND.Na.--lIrDtr:nz.

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