Two Port Handout

8/8/2019 Two Port Handout

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CHAPTER

TWO-PORTN ETWORKS

I Kno{ horto cal(!hte admlttan@,lnp.danc€,

liybrid,.nd tr.nsnissio. parumeters to. tvo-po.!

I B€ abl€ to cohve lettdeei adnlttaic6, lmped.nce,

hybnd, 6nd tratrenission pa.arnelers

I under5tand the inlerconnecllon oftwo-porlr.tworks lo form rnore compll(ated nelworks

irrr.! (tRcurr aolr0s, ot PCEs A3

[email protected] koown, provide a pLtfom

fortheiiterconnedionof va ou5eledronk

blods. The boards, which.retypi.ally nade olfibe€la$, are

.heap, easy to manuhctut€, andveryr€liabl€, and they hav.

goodele.tronkpropenies,tunhermore.theyarenormally

(o1tru. rpd 4irf ar\ip.e La/.a, {1irf perlirs re ooa o ro b,

planesaGinte6peEed i a iashion that best 5!its the purpose

orthe boad The ur. ofmulliple pldr€r Jor signar. t,ound, aFd

powerpemitverysho .onnodionwte5,be.ausatheconiec

ior poi' t. d'e neve''d..wa/ ne!e 9ror leaos en5r'e6.okq

r€siglanc. to t.ound, and lhe diel€(tiic propedies ofth€se

boards also serye io lsolate signaG from oneanother.

RecalLfrod Chapter5 how we ut Ll?ed Thev€nln! and Nortod\

I oeaniz€d sothatitssicnallav.G. ground planes, and pN.. theorcG to det€mine eq!ivalent ciftuil5 for liner circuits.

Colrtesy of Ma* [elms ard lo Ann Loden

809

From: BasicEngineering CircuitAnalysis, by Irwin.Wiley 2008.



8ro csepren r6 rwo-poR'r NErwosis

))) lfwe wae nor inrFrpsl€d in rhe intemal b€h|nor ol a ponion ola

circuit, w€ could d.temine a Ilra6nin ot No(on eqlivalent

.ircuii foruse in analysi5oltheov€ra[cncut.theseequlv6lenr

.n.uits are rorercd to as one porrrncuits or networks.4p91 5

thahdeiizedbvanan"rta,n-j. rheop4hplnChapGr4is

anetampleotatuono*i.iq^,k ThePCBshowntnlhephoro

conlalns several integGted circults (Ct aid othercomponents,

we may not be intere5ted in the detailed lntenalbehavlorofan

t, but na mult ponnetworknodeLlhatcan be Lrt Llzed ln ana,,

'i.o 'i5e l eboa.d. lFlL rponnode desdbestrebefav

ior ofthe lc ir terns ofthe voLtases add.uiientsat the tein dals.

MuLupo modelt forva ous.omponent,ontheboard cai be

intercoinected to peform an anaLysis ofthl5 boad,0n the top of

ftecircuit board shmn in the photo are fouroEgconndol'whi.i h& nine pine€ach. Ttis PCB could be conned€d toa latg

€r eledfta( syslem through th€s€ onnedo.s. We .ould lh€.

deveLop a muLtiport modelo'this cncuir boad and use it in

rnaLyzlrg this la€er eledi.aL eystem.

n many cases, modern eLectriRL systems aE so compL (ated

that the entire syrtem consGts of Bck5 of prinCd cift uit

board5thatafe coniigured like dche5 Lined !p on end ii a

cabinet,Becausela€esystemsareryplcaLLycoifiguredinthis

manner, it s inportantto understaid the iundarieital

p nciplesbeh ndthedevelopmentornuLtlpodnodeL!and

theirinter.onnecton nthischapter,wewlLLutlLketwo port

nekorks to illustrate these principLes. ( ( (

1.6.1.AdmittanceParameters

wcsay$ rhe lin.nr networt itr Fig. I6.lahasaygleeg! rhal n. a singl. pair ofr.rminah. Thc prir of rcrninah,a , rhar consdhre $is port €ould rcprcsem ! si.glc cl.nrcir(c.g.. &.4-. or C ), o. itcould bc some inter@nKrio. of thc* elcnenrs The lineur nctw. .

in Fig. 16 lb is cau.d a rwo'porl. As a eeneral rulc thc rernrinals I-A rep€sent the infupon. and thc tcmiMls C..D rct'.cscnr rheourpur port.

In drc tso-fofi nctwort shown'nFig.

16.2, ir n custon ) tolab.l the lolta8cr ardcutena

*shiw-niiiit is, tl]. uppc. tcminii;e posirive rirh Especr ro rh. lowcr r.lnirlls

'h .r,c1rree iN. tlE,qr.po 1r*.Lppe ,efl"l' r1d l.c,JU.eKCI flusrl.c{ri<ficdr "-.r p"n.-rh..-r:.nt,' jnof rhe ro.pon -r rhe .oqcr r!mn"ls. SrnrE r.\. nernrr}' blined { contains no jndwcnd.rl sources, rhe lnnciple otsup€rposilion !m bc lpplicd Lo

detei,liie thc cune l Ir, whichcan be writtcn as thc sur of trccompotle rs,o odueloVand oDc dlc !r V3. Urnrg $is principle, we can aiie

I = n V.+ v,i!Fhere yrj and ]D wc cscntially c.ncb.ts of Froponiondily with unns ofsicmcns.ln r !jn.llorinarner Il can bc writlen {s

lr: y:rv + ]!:v)

Th€refoe,llr two cqualioDs thar ddscnb€ $e t$Gponnerwor\ ffc

risurc r6j -.1



-

Notclhai $rb:qipt I rch^ k, the Lrpur poft lod bsript 2 refcrs to $e otrtpul pon, ladrhe cquat'o|x dcsrtbc wh!( wc wilt cn thc y,rdron.ra j",.

"r.,*",r. tf ih",:;;;;;

ill-,1:l;l,l-ltt:"J y,: 0,. rnnqn. ,hc input/uurpu,"1,".r." .r rr," r"..i.n i.

,From tit. { 16. D w @n d.&mj.c thc y pararul.rs in rhc folk,wine manncr Note rrcm ftccquarons flror y,, is qul to lr (tivi&d b, V *i(h UE oorput shun-"t-irot 1i..., V.1.

-

' =r'l ? .^',r.,*,",\" vt". " I i"1,1"1,,9.., 16.2

soa'-r

s d adnitran4 at rlE inpu n€rlBd iD siemcis vrrn th. oulptrr shon-cieuned. il

[.:i:Tg::1fr]#,11 ;i,fr'd,,irdn."rh€ €qkions

indi*" o.io. ,l_ v p-"i".

pr nruere ns grr

t tlgur.6.2

.:L<Lz,'1 . 'v{''

r, .r

Ji^^l^ .'t'lr*'

[r,l _ [r,, r,,lfr,]Lr,l Ly, y,, _lL r,l

I,J

,^ - ill

::::!:: :.!:",,:: " 1. grue rhi\ pd!,hcrcF dr.rcftd rJr.r rh".o n..^,i,,a- u,,,)

crcmr'oi.rFhmenrcl' forJ rs.Gpon nerwo whas. &iurt ..nusu;drnn is untn*n

Wr wrsh ro dcl.|fuc rhc y p.nnEres for lhc lsu-port ncrwo{ rhown in F.i8. tr,,;me rh.s pamers alt trown, *c wil d.|qminc ihc c!ftnr In a 4lt to.d, which isconnetql to lh. ourprr pon when a 2_A cuncnr sowc is lppti.d at 6c inD mn.

EXA|T|PLE 16.1

sotur|otmn Ea. l6.lb, s€ mre ftar

As shown ii lji8. 16.3c,

,,=v/.!*l)'\t 2/

r" =;s

-2



8rz c "ocreq

ll h

+l

vL :1r' 3nl vl

(q (!r

YD = ti

Ako, y: ir oomputcd fen Fig. 16.3b uring rlr€ equ.llbn

.vj

!r.i (hcrefore.

!^I = .r'

F!. ilj. \ ..r rderr'c.r..'nirs. lu'-L.rd

l -\l:' )_ _\l t/

5

Thereiore, dre equatiods tlar d$cribc lhe tvo pon nFlfarc

'u *iu.r=tx-;vr Il-.t" .Thcse equatbns cu now bcenrplotedto delentrine lbe openlion of th; t*o por iorsomegiletr set of lemind condniois. The lenrinal condirions ve *ill eraqinc ae show. in

Fig. 16.3d. Flon tlris fillre we nolc that

I,=2A and \- ,1t:r

Cooljf,nrg these with tlre precednig I$o-poftc{toatiens yiells

,=lr lro--lr"fv.

:|

$



', i 11I - -l' 'tI r. lrl=lolr ll

N.r. c{erull\ rh.rt th.sc.qudon\ ue simplt dre DoJal cllulr.ns n! rh. nc(uorh

lis 16ld Sorirgti.qud(,ns,\eabrain\r =t,ll\ rrJllr:.tur.l.= ] ll.1

Find rhc Y Wifrere^ tutlrc twGpon n.rworkshosn in lii8. El6.1.

R1r

,:lri'.

fi{re E$.1

ANSWER:

',=

t4S:

':=t:i=ts:lrr=ts

ANsWER:

r: = -,r.29 A16,2

tirl0 A

$uces.Dineckdroiheinpur otlnerM-p.n nerworkrn I-,g bl6.l.1tnrrlr cu .rrn)a 5 OEshror.orneded to thc drrut portH

(r.r...,L.ti.:i$..-$L:rx iid rh. r\,, f.n rr(\,yl i\r iiri.rrner\Lrt rl,i \!DL in: N rrtt.f.rJ.n1 $!r.r(. rrien b\ mci,r\,, 50perpo\ir nr \ c ran srilr Lli. rnDrr rnrl oL rffr \oh,:rc\,N rli. {Lnr .i r\,, (urp.nrn'\ ,,n. rltr. to I, rn,l !,n. d!. r, I

T[\..qul ,r]\. tr[i.lr d3\rLl,c r])! tr\. Inrl n.6\nrk crn rL\( b. \r'tr.i'd'.i'r\ ior n h

fr-.- ..11r

I

ri'

Lrl. rh. Y frrrftrcA. th.r. I /,rn,rrrc,:! (un 1,. d..i!eil xs ft,llt,\\

. =llr,,,, =! l, r

. =\ L

... = t:_' I: r=

lr rhr t'..cLiiri gqi.rrfnt. .rL !r! | .r l. = o r\ rtlonll.nr r, .,f.n . r.u rnL, rtr. tit rr ..!f!fur

l[rIh.rflni!'rh.Zfrr.,nrcrersu..!lL(Jrh..,p.nt|,rt!i.t!..tn!,

\onr!.t,j7 l\.J l.J rlr i7\r, ,,rfr f,/tr rrl).J.,ir 7-. ir.ilL.J rhe q\ | \rtt: I rll\lt rr!,.tttN.ni\l z I rnLr 2. r.. rernrcn ff! 11 tittut tn!r1.t r,!nl.Dt..s

ro.llmpedanceParameters

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Two Port Handout