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`IBG LLC ET AL. 1014
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`EXHIBIT 10
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`1
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`IBG LLC ET AL. - EXHIBIT 1014
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`"David "E! johnsoh
`"I3irminghiiin-SoL1t11o1‘n Cfollcgo
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`_
`Johnny R. lohnson '
`Unive1'.'~':it},: of North Alaxhzirna
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`John L. Hilbtzrn
`. Presideni, ';i\-1icro<':o1n])utor S}-=sLem.~'; Lvc.
`
`M
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`Peter D. Scott
`State Univcmsity of New You.‘1<--—Buft'z1E._<::
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`JOHN WE%.EY 8: SONS, INC.
`New York - Chéchester - Weinheim - Brésbane v Singapore - Toronto
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`4.3
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`.NODA!. ANALYSIS
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`uI1kI1ow;:s In 1~.<.~. 5122:2113. A cémw.-:;1iL‘11l C§‘d}iCf;‘. of V(!I‘.a£_£_:‘L't5S for .-$222123-' 21etw0r§<.<. is :}‘._<:
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`cacti of the mhcr nod:-:5.
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`Tiiese equtatiorzs may be estabiisiieti by applying KN-"1. artitmd the lcmps {tea} or iinaigineti}.
`Evitleutly. if we know all the node veltztges, we may "find {iii
`the L"lt3}11<'3!'1E vtziltages and
`thence all the eiemeni t;tm‘ent'».
`The it-lp‘[.'}li‘..)£!.l.i()I‘. of K{.'Tl.— zit u imde. expressing each tznimtwi-'11 curreni in terms" :11’ the
`zmtie \=niiages‘., results in a .=:<'ide eqttaririat. Clearly. simpliiittzttitin in writixig the resultiiig
`t-){{l££‘u'.'in11S is possible when 1l1e:‘et‘e1'ence node is she:-:91: to be at rmdc with E‘. large numb:-r
`of eieiiieaits cenncetetl In it.
`33.3 we shall see.
`itciwever.
`this is not the only criI.erio:i
`for selectitig the refe1‘ent':e iietie, zsitliuugh it is frequently the m-'er1'itiiz2g time. Since we
`cm: gtaing to apply KCL. siysiczmtticeilly at Circuit necles, the most straigi21i’erwai'd cause to
`L‘UIi3i£lCT is that of eii'cLtit.< whose only sources are intleperttient +:u1'rent f-i{I}1.i1'<.‘i£S. We begin
`with exzzrnpieaa of this type.
`In the network sltewu in F-"lg. 4.9{:t). there are three I‘t{,‘:{‘.l¢.")E-3, Li£1.\'il1E'd anti ntimhered
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`["l'i1is may be easier to see in the retirztwn versimi of Fig. —1.*)t_h)._§ Since there
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`£33’ the grnuiid .-aymbnt sham-=21.
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`"The re1’erei1ee 1".0LlL'.‘ is ‘£21123 at greumé potential or zero potential. and ea:
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`he Clillfi-i{lEl‘6K.l to be at some ptvtemiai above or below zero Spétci
`node veitage.
`' '31:: equatitins of nodal anzalyséx are obtained by £l.}3pl},’iI'ig KCIE- at the t1()ElL‘,:i. Recall
`shat eauii term in it
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`like any elcineut voitatge,
`is etgzzz-ti to Lt ntiaie
`mltzige {if one end of the eiement is tied it: the rei"ere11t:e time) in‘ the éiffereixee of two
`netie vzihxtges (if both ends are tied to ntnnrefereuee .'iL}Ll{’.'S}. E302" example, in Fig. 4.3 the
`reference and: is node 3 with zen) or gimmtl peteniizil. The :<y1nhol shows: attached It}
`made 3 is the standard .~;_vmhe!
`lei‘ gmuiid, ELS zttzteti in Cha;3te1' 3. Tlie ntanreference notice
`2. and 2 have nude v0lttige.~; T1;
`‘ind ug. Thus the elemen: VOlL£l.gL‘ i"|; with Lhe ptiltirity
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`us 10 write the. nude cqanatimxs r:;p'::i13r by z':1.'x'pcc1i<::': Lii1‘t:rcL]y E11. terms (=‘s" :1-:2 t1n:..: \':>1n.;:_
`New re1'L2rr2ing to "aim: CiI‘(;:.ii{ of Fig. 4.9.
`the .~eL:m of 82;: currenzs }a:av':ng ¥iUL.i{.‘
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`that rode. I»-lac? we (lime
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`is the sum of c0nduc1;'.mc::.<; of the clcnnczats L$O1‘:?.3£t{.‘1’{-.‘.d to zmdc E. wE1iEs
`iize <:<>e.i’f.cicn1 cf 2'; is the negaaive of the wmiuctailcc of the aaic-“meat cozaazccling
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`to notit: 2. The .~';au'ne szazcmerst holds fer (-'$.8b} if the numbc.‘.1's 5 and 2 are i11[1:I'£‘?m:‘§_=C.z.§.
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`!<L)E2E‘CCS that ezatas the c:c3z‘:'€sp(:r:(i?:r2g nods.
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`35.3.3.
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`Write 131:: nmial cqt1ai€:)m dirc::tE;_»'
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`ClRCUiTS CONTAINING VOLTAGE SOURCES
`
`At rirsl glance it may St‘J.:I‘[} that the presence of voftage Rottrccs in 21. circuit ‘tolnpiicaics
`nodal analysis. We can no longer write the KCL. node zsquattons.
`..<.-incc t['::‘.1'e is no w;=._v
`to express the currents tiurwgh these csircttit elements in ‘.ct'ms of their mode mttztgus. As
`discussed in Chapter 2.
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`no more ccaznpiicatssd, 1'<:q11ir'mg rmiy :1 s-:;'::a.l!
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`V“. ccrzsw vs
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`Example 4.8
`
`To illustrate the pt'0L‘,¢{it.££':3, Iet us czemsidur me circuit of Fig. 4.13.
`For cur1\=enicm':e we }i:J‘»’{: lzzbeieti the rcxismrs by their condt.1ctzmc:cr~:.
`Note that we: have enclosed voh-age sources in separate regions i-.~.<ii~
`catcd E3}; {flashed liaaas. Rccaliing that: the gtmcralized form of R531...
`states:
`:hat :1}! CLEI'1'Cl'lI.S enttttiltg El closati region must sum to mm
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`1 33
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`4.3.2.
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`U.'<ing Imdztl 2m:t}yr~ti.'~:. find lit.
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`10
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`11
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`EXHIBIT 11
`
`11
`
`

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`>§"'§%-“§“-§~§ 2<_.;ri':'§m;
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`
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`fiéel S. Sedra
`
`Uni}.-‘:2z';s‘;éz'_x-' of ’}"Ir)2z>z2£<.>
`
`Kenneth C. Smith
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