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MODELLING OFATTENUATION AND CROSSTALK OF CASCADED
TRANSMISSION LINES
Pa el LAFATA1
1Depa men o Telecommunica ion Enginee ing, Facul y o Elec ical Enginee ing, Czech Technical Uni e si y in
P ague, Technicka 2, P ague, 166 27, Czech Republic
la a pa @ el.c u .cz
Abs ac . This pape deals wi h he measu emen s and
modelling o a enua ion and nea -end (NEXT) and a -
end (FEXT) c oss alk o cascaded me allic ansmission
lines. The ansmission pa ame e s o homogenous
me allic line can be easily desc ibed by eleg aph
equa ions o cascade ma ix; he e a e also se e al
models o NEXT and FEXT equency dependence. Bu
hese models and equa ions could no be applied in he
si ua ion o wo o mo e di e en cascaded ansmission
lines, because hese cascaded lines do no mee he
essen ial condi ion o o e all homogenous ansmission
line. Howe e in such case, i is s ill possible o es ima e
he o e all ansmission cha ac e is ics o he whole
combina ion hanks o he cha ac e is ics o each
sepa a e elemen . This pape b ings he desc ip ion o
complex measu emen s pe o med o he combina ion o
h ee di e en me allic cables and based on hese
measu emen s, se e al conclusions abou he possibili ies
o modelling he a enua ion and NEXT and FEXT
c oss alk o cascaded ansmission lines a e p esen ed.
Keywo ds
T ansmission lines, a enua ion, NEXT, FEXT,
cascaded lines, modelling.
1. In oduc ion
The me allic cables a e s ill he mos equen
ansmission medium o local access elecommunica ion
ne wo ks and also local da a ne wo ks, while hey o e
decen ansmission capaci y balanced oge he wi h ai
cos s [1]. The ypical access ne wo ks usually consis o
a ious di e en mul i-pai and mul i-quad me allic
cables and hey se e as a local da a ne wo ks o local
access elecommunica ion ne wo ks o xDSL digi al
subsc ibe lines [2]. His o ically, hese me allic
in as uc u es can be composed o a ious me allic
cables wi h di e en ansmission pa ame e s and
cha ac e is ics based on hei in e nal cons uc ion ypes
(pai s, s a -quads, Diesel Ho s -Ma in quads), wi e
diame e s ( ypically 0,4; 0,5; 0,6, some imes e en 0,8 o
0,9 mm), ypes o insula ions (PE-polye hylene, PVC-
poly inylchlo ide, o he polyme s, pape , e c.), wis ing
sys em and adius, e c. [3]. The esul ing me allic
in as uc u e i sel can be c ea ed by splicing and
coupling hese a ious me allic cables wi h di e en
ansmission pa ame e s, he e o e i is usually no a
homogenous ansmission ne wo k. Mo eo e , in he
in as uc u e i sel , he e a e also splices o mechanical
couplings, which a e used o moun wo me allic cables
(ac ually hei pa icula symme ical pai s) oge he and
which also in luence he esul ing ansmission
pa ame e s [4].
Thanks o ha , i is no possible o simply use
gene al o mulas, such as eleg aph equa ions o nea -end
(NEXT) and a -end (FEXT) c oss alk models [5], o
calcula e he ansmission pa ame e s o hese cascaded
me allic lines. These equa ions and models a e usually
alid only o homogenous ansmission lines and hey
a e based on an assump ion, ha he ansmission
pa ame e s a e cons an along he whole line and
independen on he ac ual posi ion [6]. Bu in case o
cascading se e al ansmission lines wi h di e en
ansmission pa ame e s, he condi ion o homogenous
line ceases o be alid and he ma hema ical calcula ions
could become inco ec . This e o is signi ican
especially o NEXT and FEXT c oss alk modelling,
while he c oss alk couplings a e gene ally di e en o
each combina ion o symme ical pai s in a cable and a e
usually unique o di e en me allic cables and he e o e
canno be app oxima ed o se e al a ious cascaded
me allic cables wi hou he knowledge o c oss alk in i s
each elemen [7].
This pape p esen s he esul s o complex
measu emen s pe o med o h ee di e en me allic
cables wi h di e en cons uc ional and ansmission
cha ac e is ics. Based on hese measu emen s, se e al
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gene al conclusions abou he a enua ion and NEXT and
FEXT c oss alk a e p oposed. These conclusions a e
u he used o es ima e and o calcula e he o e all
a enua ion and c oss alk cha ac e is ics o cascaded
ansmission lines based on he esul s measu ed and
modelled o i s each elemen . These calcula ions a e hen
compa ed wi h measu ed esul s and inal conclusions
abou he accu acy o he calcula ions will be p esen ed.
2. Measu emen s and Desc ip ion o
Used Me allic Cables
The i s cable used o he measu emen s and modeling
was a TCEPKPFLE 75×4×0,4 mul i-quad cable om
P akab a.s. p oduc ion. This cable is ypically used o he
ealiza ion o access elecommunica ion ne wo ks in
Czech Republic and o las mile xDSL digi al subsc ibe
lines ne wo k [8]. I consis s o 75 s a -quad di ided in o
3 g oups o 25 s a -quads each, ha means 50 pai s in
one. These g oups a e u he di ided in o 5 subg oups
wi h 5 s a -quads each. The diame e o a Cu wi e is
0,4 mm, while he insula ion is om oamed PE and he
in e s ices be ween quads a e illed wi h a wa e p oo gel.
The leng h o a cable used o he measu emen s was
100 m. The second cable was a s anda d UTP ca . 5e
cable acco ding o he ANSI/TIA/EIA-568-A s anda d.
The diame e o a Cu wi e is 0,5 mm and he
measu emen s we e pe o med o a cable wi h he leng h
o 100 m. And he las cable used o c ea ing cascaded
me allic in as uc u e was SYKFY 4×2×0,5 cable, again
om he po olio o P akab a.s. This cable is usually
used o local in e nal in as uc u es (phones, da a
ne wo ks, signaling ne wo ks) inside la ge buildings
(schools, hospi als, business cen e s). This cable con ains
4 symme ical pai s wi h he diame e o a Cu wi e o
0,5 mm and PE insula ion. The measu emen s we e
pe o med o a cable wi h he leng h o 100 m.
The measu emen s o a enua ion, NEXT and
FEXT c oss alk and cha ac e is ic impedance we e
pe o med using Rohde&Schwa z Vec o Ne wo k
Analyze 10 Hz/9 kHz, 4 GHz-ZVRE, in a equency
band om 100 kHz o 70 MHz. No h Hill’s balun
ans o me s wi h impedance a io 50/100 W we e used
o p ope e mina ion and o co ec ma ch o he
analyze o he cable. The unused pai s o unused ends o
all pai s we e p ope ly e mina ed du ing he
measu emen s. The a enua ion and cha ac e is ic
impedance (inpu impedance wi h opened and sho end)
was measu ed o each pai o all h ee me allic cables
indi idually and also NEXT and FEXT c oss alk
a enua ion was measu ed o se e al combina ions o
dis u bing and dis u bed pai .
The c i ical ansmission pa ame e s ega ding he
digi al ansmission sys ems a e a enua ion and NEXT
and FEXT c oss alk (i is also possible o calcula e ACRN,
ACRF – A enua ion o C oss alk Ra io NEXT, FEXT
cha ac e is ic) [9]. These pa ame e s can be de ined by i s
a enua ion alues in dB, o as a a io be ween inpu and
p ope ou pu signal powe as powe ans e unc ions
[9]:
()
()
[ ]
()
()
[ ]
()
()
[ ]
dBHz H
dBHz H
dBHz H
A
FEXT
A
NEXT
A
FEXT
NEXT
;,10
;,10
;,10
1,0
2
1,0
2
1,0
2
-=
-=
-=
×-
×-
×-
, (1)
whe e |H( )|2 is a powe ans e unc ion o a pai ,
|HNEXT( )|2 is a NEXT powe ans e unc ion be ween
he gi en combina ion o dis u bing and dis u bed pai
and |HFEXT( )|2 is a FEXT powe ans e unc ion o he
same combina ion o me allic pai s. The si ua ion and he
de ini ions o hese pa ame e s a e illus a ed in he
ollowing Fig. 1.
Fig. 1: To he de ini ion o he a enua ion and NEXT, FEXT
a enua ion.
All hese powe ans e unc ions a e de e mined
exclusi ely by he p ope a enua ions (a enua ion o a
pai , NEXT and FEXT a enua ions). The e o e hey can
be di ec ly calcula ed using measu ed alues o
a enua ion, NEXT and FEXT a enua ion, o hey can be
calcula ed (e en ually modelled) by se e al pa ame e s o
gi en me allic cable and he en i onmen . These o mulas
a e usually ma hema ically complex (especially o
NEXT and FEXT powe ans e unc ions) and hey can
be ound o example in [2]. The cha ac e is ics and
alues o powe ans e unc ions o pai s, NEXT and
FEXT powe ans e unc ions used in his a icle we e
ob ained by measu emen s o he a enua ions o each
si ua ion and hen calcula ed by using o mulas (1).
The ansmission unc ion H( ) (ei he o a pai o
NEXT, FEXT c oss alk) has always complex cha ac e
con aining i s eal and imagina y pa . This unc ion is
de ined by p opaga ion cons an
g
( ) o a pai (which is
also complex) o simila NEXT, FEXT p opaga ion
complex cha ac e is ics ha ing hei ampli ude and phase
componen s. Howe e , using powe ans e unc ion
wi h p opaga ion unc ion’s squa e makes he esul ing
powe ans e unc ion eal (i co esponds o he powe
o a p opaga ing signal). Mo eo e , when s udying
NEXT, FEXT c oss alk, he phase cha ac e is ic is also
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usually unnecessa y and he powe cha ac e o a
c oss alk is he mos impo an pa ame e o analyses.
3. Realiza ion, Measu emen s and
Modelling o Cascaded Lines
The i s s ep was he ealiza ion o cascaded
ansmission in as uc u e, which consis ed om he
TCEPKPFLE cable and UTP cable. Fou pai s om each
me allic cable we e connec ed oge he using K one cable
dis ibu ion ame o p ope high- equency impedance
in e connec ion. The summa y leng h o he cascaded line
was 200 m (100 m TCEPKPFLE + 100 m UTP cable).
Nex pic u e, Fig. 2, desc ibes his si ua ion oge he wi h
a de ini ion o a enua ion and NEXT, FEXT c oss alk in
each elemen .
Fig. 2: Cascading he TCEPKPFLE and UTP cable.
The second cascaded in as uc u e was composed
o TCEPKPFLE 75×4×0,4, UTP ca . 5e and SYKFY
4×2×0,5 cable in his sequence. Again as in he p e ious
si ua ion, 4 pai s om each cable we e connec ed
oge he using K one dis ibu ion ame. The o al leng h
was he e o e 300 m (100 m TCEPKPFLE + 100 m UTP
cable + 100 m SYKFY cable). Figu e 3 illus a es he
whole si ua ion.
Fig. 3: Cascading he TCEPKPFLE, UTP and SYKFY cable.
3.1. Modelling and Measu emen s o a
TCEPKPFLE and UTP Cascade
The TCEPKPFLE and UTP cables we e cascaded
acco ding o he Fig. 2. The measu emen s o a enua ion
and NEXT, FEXT a enua ion we e pe o med om he
bo h side o he cascade. The p ocess o modelling o
cascaded ansmission lines wi h di e en pa ame e s
could be qui e di icul , while o accu a e and exac
calcula ions, many e ec s should be conside ed and a
complex ma hema ical model would be necessa y [3].
Bu i is possible o assume se e al simpli ica ions and
condi ions, which may simpli y he p ocess o modelling,
while main aining su icien accu acy:
·Impedance misma ches – he cha ac e is ic
impedance o each cable wi h di e en
cons uc ional and ma e ial pa ame e s is p obably
di e en [6]. The di ec e ec o impedance
misma ch in cable join s a e e lec ions and o he
dis u bances. We can assume ha he modulus o
cha ac e is ic impedance in case o ypical
me allic cables, used o elecommunica ion
pu poses, is usually be ween 90-150 W [5]. Which
means he e a e e lec ions in he poin o wo
cables joining oge he , bu he in luence o hese
impedance misma ches should no be signi ican ,
while hanks o he a enua ion o a cable hese
e lec ions a e also pa ially a enua ed.
·Mul i-pai and Mul i-quad e ec s – in he case o
mul i-pai and mul i-quad cables, pai s
su ounding he signal pai o m a Fa aday cage,
which ep esen s a i ual sc een [3]. The signal
cu en s in such su ounded pai induce eddy
cu en s in his i ual sc een and ep esen a
u he sou ce o loss in he signal conduc o .
·C oss alk ia su ounding pai s and quads – he
c oss alk in mul i-pai and mul i-quads cables does
no o m only be ween wo pai s (dis u bing and
dis u bed pai s), bu he c oss alk can be
dis ibu ed also ia su ounding pai s. Again as in
he p e ious simpli ica ions, he in luence o his
pa o a c oss alk could be igno ed wi hou a
signi ican e ec on he esul ing accu acy [5].
·Wa y cha ac e o FEXT, NEXT c oss alk – he
equency cha ac e o NEXT, FEXT c oss alk
con ains many dips, peaks and basically i usually
shows wa y cha ac e . This cha ac e is no
en i ely pseudo andom, bu i was p o ed ha i
depends on se e al pa ame e s o a cable and also
on he a io gi en by he leng h o a cable and he
wa eleng h o a p opaga ing signal [10], [11].
Tha ’s why i is no possible o calcula e (model)
he exac wa y cha ac e o mul iple cascaded
ansmission lines by using hei sepa a e NEXT,
FEXT cha ac e is ics, while he a io be ween he
leng h and wa eleng h is di e en in each case.
The in luence o his e ec will be p obably mo e
signi ican in case o he measu emen s pe o med
om he side o a cable wi h he lowes
a enua ion (UTP cable in his case). The
possibili ies o modeling his wa y cha ac e o
NEXT, FEXT c oss alk will be u he s udied.
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Acco ding o he p e ious simpli ica ions, i is
possible o p opose a calcula ion and modelling o
cascaded TCEPKPFLE and UTP cables’ cha ac e is ics
based on he measu emen s o each elemen . Figu e 4
illus a es he me hods o calcula ions.
Fig. 4: Calcula ion o a enua ion and NEXT, FEXT a enua ion o
cascaded TCEPKPFLE and UTP cables.
The equa ions o calcula ing he a enua ion A( ),
NEXT a enua ion ANEXT( ) and FEXT a enua ion AFEXT( )
can be ma hema ically de ined:
[]
[]
[]
222
13
2
222
22
1 1 22
2
2 2222
1412
2
() () ()
() 10log ()
() () () () ()
() 10log ()
() () () () ()
() 10log ()
NEXT NEXT NEXT
NEXT NEXT
FEXT FEXT FEXT
FEXT FEXT
H H H
A H dB
H H H H H
A H dB
H H H H H
A H dB
=×
=-
=+××
=-
= × +×
=-
. (2)
The equa ions o es ima ions o a enua ion and
NEXT, FEXT c oss alk o cascaded TCEPKPFLE and
UTP cables we e implemen ed in o Ma lab and he esul s
o he calcula ions we e compa ed wi h he
measu emen s. Nex Fig. 5 p esen s an example o
a enua ion A( ).
Fig. 5: Compa ison o measu ed and calcula ed a enua ion o
TCEPKPFLE and UTP cascade.
I is e iden ha he a enua ion o he whole
cascade measu ed om he side o TCEPKPFLE cable
and om he side o UTP cable is p ac ically he same.
The calcula ion o he a enua ion based on he equa ion
(2) p o ides su icien and accu a e esul s. The
e lec ions and impedance misma ch do no signi ican ly
in luence he esul s.
The nex Fig. 6 and 7 ep esen s he esul s o
NEXT a enua ion measu ed and calcula ed acco ding o
he o mulas (2).
Fig. 6: Compa ison o measu ed and calcula ed NEXT a enua ion o
TCEPKPFLE and UTP cascade om he side o TCEPKPFLE
cable.
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Fig. 7: Compa ison o measu ed and calcula ed NEXT a enua ion o
TCEPKPFLE and UTP cascade om he side o UTP cable.
F om he compa ison be ween Fig. 6 and Fig. 7 is
ob ious ha he NEXT a enua ion is signi ican ly
di e en o he bo h side o cascaded cables. This is also
espec ed in model (2), because he i s pa o he
summa y NEXT a enua ion is gi en di ec ly by he
NEXT a enua ion o a nea elemen , while he second
pa o a summa y NEXT c oss alk depends on a
elemen , bu in addi ion i is a enua ed by he a enua ion
o a cable. I is also e iden ha he elemen wi h he
lowes NEXT a enua ion in he whole cascade
(TCEPKPFLE cable in his case) plays he dominan ole
in he summa y NEXT a enua ion. We can also obse e
ha he measu ed NEXT cha ac e is ic in Fig. 7 is
signi ican ly wa ie wi h in ensi e equency dips and
peaks. This is p obably caused by he e lec ions due o
impedance misma ch o bo h cables and hese
misma ches a e mo e dominan o UTP NEXT cha ac e .
A ce ain ole also plays c oss-FEXT c oss alk e ec ,
while he e lec ions on impedance misma ches may
p opaga e o he nea -end in o m o a FEXT c oss alk as
well as di ec e lec ions.
FEXT a enua ion measu ed om bo h side o a
cascade and calcula ed FEXT using o mulas (2) is
p esen ed in he ollowing Fig. 8.
Fig. 8: Compa ison o measu ed and calcula ed FEXT a enua ion o
TCEPKPFLE and UTP cascade.
The FEXT c oss alk a enua ion is iden ical om
bo h side o a cascade, as we can see om he measu ed
and calcula ed esul s in Fig. 8. The di e ences be ween
measu ed cha ac e is ics (blue and ed lines in Fig. 8) and
calcula ed esul s (g een line) a e p obably caused due o
he simpli ica ions o calcula ions, which we e p esen ed
a he beginning o his chap e .
3.2. TCEPKPFLE, UTP and SYKFY
Cascade
The p e ious models and me hods o calcula ing
a enua ion and NEXT, FEXT c oss alk o cascaded
TCEPKPFLE and UTP cable could be used also o
u he mul iple cascading o a ious me allic cables. Fo
ha eason, he cascade om TCEPKPFLE, UTP and
SYKFY cable was p epa ed, measu ed and modelled.
This cascade uses all h ee me allic cables wi h
pa ame e s p esen ed in chap e 2. The calcula ion o
summa y a enua ion and NEXT, FEXT c oss alk
a enua ion o he whole cascade is again based on he
cha ac e is ics o i s each elemen and hese calcula ions
a e p esen ed in he nex Fig. 9.

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Fig. 9: Calcula ion o a enua ion and NEXT, FEXT a enua ion o
cascaded TCEPKPFLE, UTP and SYKFY cables.
The cascade models a e based only on simple
di ec c oss alk couplings be ween all cables. I would be
possible o u he imp o e he accu acy o modelling by
implemen ing in luence o c oss-NEXT and FEXT
c oss alk, e lec ions in cables joining and o he e ec s,
bu acco ding o he esul s p esen ed in nex g aphs,
hese simple di ec calcula ions p o ide su icien ly
accu a e esul s. The calcula ion o a enua ion A( ),
NEXT a enua ion ANEXT( ) and FEXT a enua ion AFEXT( )
is de ined as:
(
)
(
)
(
)
(
)
() ()
][log10 2
2
5
2
3
2
1
2
dB H A
H H H H
NEXTNEXT -=
××= ,(3)
() () () () () () () () () ()
2
2
2
4
2
3
2
3
2
1
2
2
2
2
2
1
2
1
2 H H H H H H H H H H NEXTNEXTNEXTNEXT ××××++×+=
() ()
][log10 2dB H A NEXTNEXT -= ,(4)
() () () () () () () () () ()
2
3
2
3
2
1
2
6
2
2
2
1
2
6
2
4
2
1
2 H H H H H H H H H H FEXTFEXTFEXTFEXT ×××××+×+=
() ()
][log10 2dB H A FEXTFEXT -= .(5)
These models we e again implemen ed in o
Ma lab simula ion p og am. The nex Fig. 10 illus a es
he compa ison be ween measu ed and calcula ed
a enua ion o he en i e cascade.
Fig. 10: The measu ed and calcula ed a enua ion o he whole cascade
om TCEPKPFLE, UTP and SYKFY cables.
The a enua ion o he en i e cascade om
TCEPKPFLE, UTP and SYKFY cables wi h he leng h o
300 m is in luenced mainly by he a enua ion o SYKFY
cable. This causes he equency dips and peaks and he
wa y cha ac e . Howe e , he model shows he same
beha iou and i p o ides ealis ic esul , which is e y
close o he eal measu ed cha ac e is ic. The NEXT
a enua ion measu ed and calcula ed om bo h side o he
en i e cascade is p esen ed in nex Fig. 11 and 12.
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Fig. 11: Compa ison o measu ed and calcula ed NEXT a enua ion o
TCEPKPFLE, UTP and SYKFY cascade om he side o
TCEPKPFLE cable.
Fig. 12: Compa ison o measu ed and calcula ed NEXT a enua ion o
TCEPKPFLE, UTP and SYKFY cascade om he side o
SYKFY cable.
The NEXT a enua ion measu ed and calcula ed
om he side o TCEPKPFLE cable is again p ac ically
he same, because he NEXT c oss alk o TCEPKPFLE
cable is dominan and he es o he NEXT a enua ions
in equa ion (4) ha e only a mino e ec . On he o he
hand, he NEXT a enua ion om he side o SYKFY
cable is in luenced by all NEXT a enua ions (and also by
e lec ions and c oss-FEXT e ec s), so he calcula ed
model is no as accu a e as in he p e ious si ua ion.
Howe e , he accu acy o he calcula ion is s ill su icien
and i equally es ima es he eal NEXT cha ac e is ic. The
FEXT a enua ion o he whole cascade measu ed om
bo h side and calcula ed om FEXT cha ac e is ics o all
elemen s is p esen ed in ollowing Fig. 13.
Fig. 13: Compa ison o measu ed and calcula ed FEXT a enua ion o
TCEPKPFLE, UTP and SYKFY cascade.
The compa ison in Fig. 13 clea ly illus a es ha
he model o FEXT c oss alk due o he se e al
simpli ica ions p o ides app oxima e cha ac e is ics,
which can be used o es ima ions o FEXT o cascaded
me allic cables. On he o he hand, he FEXT wa y
equency cha ac e depends on he a io gi en by he
leng h o he cable and wa eleng h o a p opaga ing
signal [10]. The e o e i is no possible o simula e he
exac equency cha ac e o FEXT a enua ion o he
whole cascade om FEXT cha ac e is ics measu ed o
all sepa a e elemen s.
The s anda d NEXT and FEXT a enua ion models
desc ibed in [5] can be used o p o ide he compa ison o
accu acy be ween measu ed NEXT, FEXT a enua ion
and modelled cha ac e is ics o cascaded cables based on
o mulas (4), (5). The s anda d NEXT model can be
ma hema ically de ined as:
[
]
( ) 15log ; ,
NEXT NEXT
A k dB dB MHz
=- , (6)
whe e ANEXT( ) is an a enua ion o NEXT c oss alk, kNEXT
is a c oss alk pa ame e and is a equency. I we apply
his s anda d NEXT model (6) on measu ed and modelled
esul s p esen ed in Fig. 12 we can pe o m di ec
compa ison o he model’s (4) accu acy, which is
p esen ed in he ollowing Fig. 14. The kNEXT c oss alk
pa ame e s we e calcula ed indi idually o bo h
cha ac e is ics.
INFORMATION AND COMMUNICATION TECHNOLOGIES AND SERVICES VOLUME: 9 | NUMBER: 3 | 2011 |SEPTEMBER
© 2011 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 134
Fig. 14: S anda d NEXT model o measu ed esul s and NEXT model
o calcula ed NEXT o TCEPKPFLE, UTP and SYKFY
cascade.
The compa ison be ween s anda d NEXT model
o measu ed esul s and NEXT model o calcula ed
NEXT a enua ion o a cascade illus a es ha he
accu acy o NEXT calcula ion using o mula (4) is
su icien . The di e ence is app ox. 1-2 dB, which is
p obably caused by he simpli ica ions and o he
condi ions, which we e discussed a he beginning o
chap e 3.1.
The s anda d FEXT model comes om he
de i a ion o capaci i e and induc i e unbalances
be ween wo symme ical pai s and acco ding o [5] can
be de ined as:
[ ]
( ) ( ) 10log 20log
;,,,
FEXT FEXT
A kA l
dBdBdBkmMHz
=+-- , (7)
whe e AFEXT( ) ep esen s an a enua ion o FEXT
c oss alk, kFEXT is a c oss alk pa ame e , A( ) is an
a enua ion o pai , l is a leng h o pai and is a
equency.
Fig. 15: S anda d FEXT model o measu ed esul s and FEXT model
o calcula ed FEXT o TCEPKPFLE, UTP and SYKFY
cascade.
The Fig. 15 p esen s he compa ison be ween
s anda d FEXT model o measu ed esul s and s anda d
FEXT model o calcula ed esul s p esen ed in p e ious
Fig. 13.
In his case we can see ha he accu acy o FEXT
calcula ion using equa ion (5) is accep able, while he
di e ence be ween measu ed FEXT cha ac e is ic o
cascaded TCEPKPFLE, UTP and SYKFY cables and he
FEXT calcula ed using (5) is less han 1 dB.
4. Conclusion
This pape p esen ed a possibili y o calcula ing and
es ima ing ansmission pa ame e s (a enua ion, NEXT
and FEXT c oss alk) o mul iple cascaded me allic
cables. These calcula ions a e based on he ansmission
cha ac e is ics o each elemen in a gi en cascade.
Se e al simpli ica ions and condi ions (especially o
neglec ing some in luences) we e applied and he
accu acy o his me hod was discussed and compa ed
using s anda d c oss alk models. These esul s we e
compa ed wi h measu ed cha ac e is ics o a cascade
ealized om TCEPKPFLE, UTP and SYKFY cables.
These esul s clea ly con i m ha p oposed me hods o
calcula ing cascaded ansmission lines can be applied
and used in p ac ical applica ions o es ima e
ansmission cha ac e is ic o mul iple cascaded
ansmission lines and me allic cables wi h di e en
pa ame e s.
Acknowledgemen s
This wo k was suppo ed by he G an Agency o he
Czech Technical Uni e si y in P ague, g an No. SGS
10/275/OHK3/3T/13.
Re e ences
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Abou Au ho s
Pa el LAFATA was bo n in Ceske Budejo ice, Czech
Republic in 1982. He ecei ed his Mas e (Ing.) deg ee in
Feb ua y 2007 and Ph.D. in June 2011 a FEE, Czech
Technical Uni e si y (CTU) in P ague, specializing in
Telecommunica ion Enginee ing. Cu en ly he is an
assis an p o esso and esea ch assis an a he
Depa men o Telecommunica ion Enginee ing o he
CTU in P ague. He is a membe o he T ansmission
Media and Sys ems scien i ic g oup a he Depa men .
His esea ch ac i i ies a e ocused mainly on p oblems o
dis u bance and c oss alk in me allic cables used o
digi al subsc ibe lines and his esea ch also co e s
se e al opics abou op ical access ne wo ks.