BSTJ 50: 7. September 1971: Crosstalk in Outside Plant Cable Systems. (Foschini, G.J.)

10.7 MB·English

Crosstalk in Outside Plant Cable Systems

By G. J. FOSCHINTE
Meme sil Fobra 4 197)
A toauaiaion mode of ots plan wire pair cabic sytem is ger.
‘Ti wel vende eva wih eae wit na as bees apd
for somputes wanipuintion so th [ov of @oigefroaney si
rogea The program ea sala the feminal behsior af a eern
Tous syatorcompove of a useade of wiznd pause of pulp and PIC
fable, ont evs, nd Deied tape, There ve aden thatthe siveaton
mpabiisy can prone wll eainatee of te! within unit, FRAT at
Tons up tote high sie freq region Pacory data on eupactaice
anbaance ace te eomntiot dos aura Jor he eon: pation of the
"Pir weny maton sca a narinaly opecied cable aka he eee.
seid wockentoaly fu stsewssinpnsst a Do rower
iol io wind the atckasse Sekorer nf te exparitance eblenee, The
Gifs cones forte sore pete ade eambinetins of capuetene
Cove sa Be aves sn forms of ble geometry. The dc
Gf this ecovessan vaing eapactonce wninlonee da ora a bas
‘etn pa ia el.

A transmission model of outside pl. win arene systems whieh
snoes dice eomstall ie develowed ern. We begin by’ presening
Algerninisie mel of eutede plans systems by mane of mate reptr=
seoutiene of tho vasioue eeuans. The posturbation ebuigue far
Tending puic-lrpair onnting i= develop in deli Ax adgptetion
of toe made fa #3e Zor of a Hime stion program: ie doused snd
foxuonrisins Intercalation av axperante cme, seas
tie tearm of paie-panr eapwrilive enaping is givea whieh is
hover to lead ta met af uotinal Ua Teng selzeton

"We suns thatthe shoory se eeeut ere hea origm in he woe
of athe fae for extol, Ref. 1 through ). Tae ions ef Mite eons
Tate and of tenting capiitance uabslanee as radon Senet With
2422 mum amu srorust Meu teal JOURNAL, SHMENHER 1672

‘sla Cunetion covatianee an femiliar ko thoes who have worked on
‘rosetak, We organine and extend available techniques in he direction
oT furnishing a siete psteme engineering mode! of ercartalk.
leanerrnation of air ode ina a practical ergincering tool extads
{he wus oF routine data on peiete-pai capastance tnbatcave thee
fe akon at Weslo Bleie® erie nenufenaring “ovations om a
diy asi

Toe simplicity we limit fhe dengan ta an ealiaed wetion of che
ontsie plant. We assume thut « pat eysvem ie comprised uf w eas
‘a of passive n-portnetmasks ae dopisted ing. 1

"These nets ate primary wine pa eves, elthough we inlude
toad nis, sles, and open crete bridged taps. The objective ist
beable lo sinilate (he manonse of » Ion clas of cutee pl spe
ere to singlefrequoney exeitatinns, We seek a programmed sinla-
jou capeilily Gia ill enable the evaluation of erostalk per
lance. The erostualk pecformce (oenr end of IW ene) is erally
Capresed ine form af the smnlative dsrinitian funeton af pi
orp ermal vals. These euunt've liabutions form the sie
fer uaowering w lange cs of ryan erg ering enti eonserning
creaetlle

‘At thie pin: is the developmat ef this work only the stoshastio
native oF paisto-pair copeeitaree unbalance ie included. ‘The aeera
Uf moisture, cenpersture, aging, extra ganersted noe, oF man
Taotuving variability of other cable parameters aze act considered
Artive devioes are aleo aot included. or many probleme snvalving
nove devicos iti important te ehurnteriae the beluavor of the past
‘ive porcions ofthe plant cot snterconnect these devise. Furthermore,
Ihe technique we prosent for handling erostali appears toe exten.

mi BE ee ae

t n a ee

Tig 1A ound of psi prt senor,
mewstai MOORE 2103

ible ethane of modeling etiatians i ec ewe paramere ae
lle heated in the nee! aioe. However, the write dsts on
{ho win iaiey of othor else assaaerara be ase a ie therefore
prewatine fo atiacp” hv ilide #3080 at Uh ow in € wuneloed
‘madel

"The marcmal'ral rpmeseitalu of he sermial Rebar of these
systema generated fron the mtn oh divencal equation tat
Tharuerine lie poysiel laws Thee tee oolilaent ssbapateme aber,
find Lie Inga relates Wo chapseenie she merlin aren

enim sbyatem. To sss adel the sytem ie chartered at
Shc pin apse> 1) tte (by he eho pair Waltages wis,
fred pit currents sc, That lorltaieal symmetry i smplethy
teamed, tees is wrlalie mege prooagating 22 nt ffouted ne omy

Teve ut chart pvimary eoastant salir, Each of the setwures 5
Tsrsiled bs a mahonaties iy wel bebuvel Traarder horeogenccus
ystean af es offcentiql otis. We mae the siandardsipuiea-
tion of exppressing Ue time tariils hy rezeeing Ue entinions tn
Devos che sas Irony gc pve. he elation matrices to shes
Aizscenal nota nosh iit vvln mt to Bae dati ste are
Selly sited Lo coseedad sieugrage, Fellvevng ty inrnolage
“apart ebook beers se all this alton He ABCD eeain mantis
of 2 alee hese

“(8

1 then allows th

Bol A nT oe

shave che on af mulipintinn neon:
(Gererolly in strc 8 spusted Tove some ear a=

aims oneer ig ie Lebaron, kimi mcecled by aeaming
fang ream taat?n vol bee frm> Bf «Sf were Diy Ue cus
Aint Sot iss nates atone poceos wilh seen mesa. The pune ¢,
‘shich i calf the persarberian eaten, wl he azoded 20 flitate
Gat aval, Since diferent syrem sleaente gave Wiens phyaeal
furans unify tae thers by tcsing these ene «1s parameters
inthe visin aatnoes, Thu ie rit natrioes ur indeed ever» eet of

fpaarsciy ale and sw tiny ataehaete proms

Sa os aed adie rondo see psa a ore wees
ies we dal with the deter fabio a nr alana, The
swe disrnsfstuss hat aseromnn el realactions of sheatatetie
fystoam, ‘horse, in -e went setior ve at the ate ells
raing ‘ith scoezitie subsyscets b unieivorlent wal is neler

We expres bev the keane far tlt wale! opting hemes
‘ene pale i w exble syst peoes Tow-leve Inverter ona pine
Pproxriy went ener! save. Ph jsmnrete > O sen be thot
fof te mse sy nnosn ji’ lone serysiem ta Heel fe —
1) in whi the paite ave reouple. Ya sll evelay sone eisapltiee=
oye I ott recs to nme

“Wie ee by sowing foe eemural ile af the pet chation onesie
sn seéanng the sie ofa clo cress eomanataton, Aa spake eeble
ff Length fy 4 Liar psive laure Bx. ntaerk, wn nC ty
roqacaey fe bes edn maiiy (ABCD) elt eran bio oe
shall donate he PUL)

= 14) w

‘eine the 3s and ths vs asthe vont ca ements ab the de pana
be tae setwans Wo coe Uh Pal delves by Use untae at
ame I 2a
ole
where Je ide is sn The ws ie) epi we
Tnpedsate ceri wth nse Ci ae ona emule huelone
tthe sel raneols = cel ho disona wz ace all eal abd ate
Getoted ov msi eran. Ser hve ntlree sate
Yin. We wale 260) = Tt 7 nis hte te
hud Ge) nave te danas ea 2 dy are ete ith Se
deal wei os Be” tt eee pert a
“We se heirs in nzsng erate panto tts

teak end 105 ~

shore ine pir in w ene i euengzed and ube wec-c ella ti
re voller tha afar pat mete be sed oe. Using TUE),
fn arin charastereal vn ol the nly sl the beurcbae

2 ublain 2r egutions wits 24 uremia: TE where ate
10D pase the ele we ae avee 290 3 AN eagle ain
salve for she ezostals yultawes.Trectica consdoratons ‘a inverting &
onosenena oo aa

si of this ste pages the ower ak af eocch of the compas
We sll nye ah epprosiresion wherchy the computation is dee
compuoal nin The ingersien af 0. £3 4 sewn This erables she
fnlenlaton toe hulle ita easy’ Ey the eoneouter

inept ial fllows esha ganar tant at both onde the
able. pass ae tersinntod in thelr “emuraeensie inpumee’
Ba Vistas Nb wm shall wetmaabrs be gas shal he een
pele ie intorovell ais velege genoentar of wellage (32 2 valle,
Ein ovine Speen Z, so Us ore we ees sean the
erm of le energized poi We skal flow she cumin “hal
the reared ers BAT, fh — fesO} (0H and hs fared
froeae FET iyo) = [ie tl dante tho rte af Ue vulag
four j dan to the dsvarbiny wollnge ma pair ¢ at the enble termina

Tring ae banda soll ome so rbeiuing inte equavien {11 we
can obtais tae qutions ee NEXT, J) ond PENT. §

‘Chssider the Aepothulial cable containing only two pare whone
setning en

Do os
ee ee)
= |, um oo
Ini» 98
oy] PPPS gag] BIND »
WK 1 = ye, |
exncne. NNT, 9

‘us basal cavgblen NENTG, § awd FANT, 3) ate calles dis
rvs Tw tect eros oie counder ualy the exetenes of
pba fan jit te eae en ho eosstalls which gorsicom Sue wines
Dall opis tv able ave agapzoccally equvlor am is bw
the appordn, Tha: i

sin ESTES
Tin Rene

‘Toor iy strone esresimentl wane that inthe stems of alee

Giese szall tha for inoeeprigten. uxpaeseaaymplie oqsivclnee

fan be incerprvel eau
2108 mmr men avarene TpEIsIOML JENOVA, SETS Ht

‘Woxt wm desorapose tse plone af delenining a 4X 4 mame 2
iy w poo 0 dstacmaing tio 2 X 2 alive Tor noe his
sve truce some arte voltages ted ewermte Fae), Pace Fah
ud i), vin the Golloming trator, wir wr sat ll P

re | Lo 8 0 eal
vata} [120 Of ate
nap mo al ten
nisl on 0 1 al batal

The ahnsa traefermation maps tee pHoblem ef 2vo unifam eoupled
pie fo that determining th sain atsoos for to anne bat
Imnooupled puis, The deynilence °F on « wll be impareant acy. $0,
fine 2 ia undertugd toe fied a: L > 0, Wesbel wre Pa) itout
ot TL), Telling Te) dexove the chain matrix of the spexum of two
‘unecuplo jmim we howe oe) = 2 'Te Abu eensequouee Te) bys
tho falowing form:

AME AG) Ml — AB 1

AGS Al AGI Ade Ble
GEFGH CH Gd Od DAL Dile — Dx]
GiB GH GN 1 CH BL = DLA DL) — BE)

te -

whens the rnc
fA‘ B19]
lesa Die

ae

dans the ABCD matmes for cho “oman lines thou eauping
Fqaren 2a and Bb portray be teworviion ie detail $0 Ase) =
dna), Bile) = Bye) Gels) — Cxi—e, a Dale) = DiC a. Ung
Ue datntion of dorivwtive er obtain shat for euiiant smell

Jaco Bor aero ‘

ros | +t
cear eget, * “lerwsr na

where
on

“This forsale patiolacly useful fox gonsteticg tee lirear eppeoni=
analive fo the i) mater forthe cam of eonstt oping, Heat
the cnss whan win) arc £5) are cosy nels "The nse is
fellows, with TP Vay,
estan om 2a

or the esse wen 9 snavbitray onsen fusetons We
brain the eloming ove ronan 0 1%
219K ay sou Seon auaicen Jovan, s¥erosRe un
noserau ot 2320

Sutstinting tis eve
the Tinea ayprosimati

ion of et nt sqvation (9) and solving for
to the crests yl the elasical formula

= 20H oe

wexng,a—+ f°

tele) ZNO

PANT, DS me

Jn this sotion we have achitved » eanonienL reorstencation of
‘oupled pairs in w exile, Uur mpreonlatign & euuplete rough (0
permit prir-tooir erawalk ealrulations to be wd, but a repo
citations are approxinase, We have not veloped? sng snalytial
Felatvshipe belvecr the magiitee of soes bvatved acl, Prag
tically We Ive no etd gy mee for anh wtionsinn a we are
been able to sely om experimsnial vetfetion of our estanptions

"The savetise of the eable easia ua this we bave developed
cexpedives ihe leterminatinn of the chain matrix experimentally sing

[ee ve =

were] 3 of ~ por! 7. eis:

fouiy fe 6 2 simp pusny

Fig, tos el coe imines feos ant cr
i Too wonuifora wooed anenirioy Toes and taie eres
ia
24g mp meta arate YRNSHOAL SORA, SEBTIMEEN 92

1 genesalid open oizeuit-ezert ire, technique. Spesifcally cach of
the 4, R, C, and 1 aneries hes the form o! » perluchation of come
ronsero multiple of Ue itstity. A etrcghtforwad genortination of
the slawsical oon vires sont iret tesbniqus, eupiaiving othe
fppwoimmation that eu be unten lnverting'9 matrix of the aiaro-
tnettioned form, sees fora smote delerminstion of he a, B,C, and
1D muteces. Since the experaonia] fchniee le stonlghorward we
shallot ses eSorther

Ti This setion we have divs talk enmpntations fr a single
coble The extanaion to oeade af cables i staightorwand. We need
‘nly modify (8 by ryhsing T(Z) by the ordaced product []é-, Toes
fod Zy on be rphul hy sadly dstinet impedances we 2 ~ O and
Em Len the Appendie we have proven asymptotic aquivaones int
Special ease ofa snule ve. (Wo spate the ceader the general roof for
fable sytem} We shall ue nayepatia equivalence of erste wad
‘ict eostole Zp eublo eyes a the eaetions that fale. We note
hes if bridged tase ane essed the extension of the asymplotie
feauivalenes to xb ein is immeeias

1 sncenavise: THR Pram A eHow eRBgUTNeMA

‘The fe phase (ie somparer emulation ef tbe oatede plone has
boo lites 20 voce frenercien. "The poogran gancrats the eubeys-
tem choi teacices wal rnligles van eogeeer ve acta scalzaien of
the ABCD mesic for Uv system The progeare can einalate an exten
sive cage of exrerminmie elena} speettealy, the oop ea bo com
prised of uny exetace-o" PTC ies, pulp cubes, lcd eis, and bridge
tape Thus, givew Ihe lersinecion apedanecs and exeinsions we ea
solve for aay sf the feminal rosges and eurrents, The important
feline of the prograe is tht it provides the enpabiliry to make oross-
{atk computatis.

‘there were» nvurhor of weacons Why We began the simulation effort
with te vows plan, Fist the very vastness of the overall proeet of
fulsile plat eabie sinseetion dictotes that one shoul begin Ty
handling x eomcwt elf-ooaine portion of the projet that could
form the buss (or folie for. The susphication that arse in deal-
ing with vos plant makas it an stnsetive tasting place ws me no

shor

‘Osonsily the basis forthe siolation wf individual euble ie gue
tion (3). Tho chain madrees for load coil and Bridge taps exc be
beained fom ‘We note tal the enees ofthe