time domain response of transmission lines v3
TRANSCRIPT
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8/3/2019 Time Domain Response of Transmission Lines v3
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8/3/2019 Time Domain Response of Transmission Lines v3
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8/3/2019 Time Domain Response of Transmission Lines v3
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8/3/2019 Time Domain Response of Transmission Lines v3
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Andthe
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UsingO
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Andthe
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ing
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aves
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Eachse
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Simplifyi
Alsothe
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ment intro
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ucesadela
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sic The
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ry Not
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or(1.23)
(1.30)
(1.31)
(1.32)
s
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Asanex
d=1
c=1
T=d/c
Tau=T/2
VG=1ZG=50
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Forthe
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Thenat
amplethef
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Voltage(V)
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ametersare
% Distan
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mpiled
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he end o
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8/3/2019 Time Domain Response of Transmission Lines v3
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Voltage(V)
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mission Line S
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ry Not s
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8/3/2019 Time Domain Response of Transmission Lines v3
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First
Westar
voltages
In this
paramet
operatio
timean
The tot
respecti
At a po
usingth
Discardi
Thetim
differen
Thepoi
Convers
rderFDfromthe
andcurren
formulation
ers,which,
n.Inordert
spatialdo
al length a
ely.Onthe
ition n , th
forwarddi
nghighord
derivative
e.
tsaredraw
elyonemay
DCalculeavisideeq
s(, ):
F
F
V
I
we are n
eventuallyc
oapplythe
ains:
nd time o
figure,wed
t
nt
1nt
Nt
1t
1nt
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1Nt
e middle va
ferenceas
rtermsthe
tthemiddl
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tionofLuationsfor
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i zz t
z
eglecting th
anbebroug
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k
n
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t n
the trans
rawthecor
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lue of the s
1
n n
k kv v
dz
approximati
of , 1n n
viousfigure.
osentouse
ossyTra lineof len
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, )( ,
tR i z
tG v z
e possible
htintoplay
ssarytode
,1
,1
z k
t
mission lin
esponding
x
kz kz
z
1
x
1n
kv
n
kv v
Figure7patial deriv
2
2
n
kv z
d
onofthede
1
n n
k kv v
z z
onthe k po
1n n
k kv v
t t
thebackwa
smissio
thz with l
()
()
i zt L
t
vt C
frequency
tothetime
ineamesh
1K
N
e will be t
rid.
1 Kz
1
n
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ative betwe
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rivativethen
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sition,canb
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Linesossesand
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t
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ofdiscrete
hen (z z
z
t
1K
en , 1k k c
2
forwarddiff
eapproxima
sic The
ithaddition
of the di
eansofco
ointssampl
1)K and
an be appr
erencegets
tedwithth
ry Not
alforced
(1.33)
stributed
volution
edinthe
(1.34)
tK
ximated
(1.35)
(1.36)
forward
(1.37)
s
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Orthec
Naturall
denomi
versions
Inorder
inorder
andvolt
K+1poi
Thenfor
Finallyt
Thenfro
spatiali
Wecan
entraldiffer
,ifwetake
ators. But
,leadingto
torepresen
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agetestev
ntsandthe
thecurrent
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plugthesea
enceofthe
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our exampl
simplerupd
tthecurren
ntageofth
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currentvect
t
nt
1nt
Nt
1nt
1Nt
1t
2t
wetakeba
ativeisapp
we
see
th
from 1,k
pproximatio1
1
n
F
n
F
V
I
n n
k kv v
dz
patialderiv
1
2
n nk kv v
z z
erences,the
e is simpler
teequation
t,wemake
calculated
tsaredraw
orhasKdiv
kz1z 2z
kwarddiffe
roximatedi
tthe
time
i
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nsontheH
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iI
2
1
2
n
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n n
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tive(obtain
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1
6
nk z
schemewil
enough to
systems.
agrid(Yee
voltagesto
nonthen
isions.
kz kz
z
1
n
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Figure8rences
n n n
k k ki i i
z z
thesame
n n n
k k ki i i
dt t
ndicesfor
t
avisideequ
1
(
(
n
k
n
k
vR i
z
iG v z
2( )
n
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1
edusingTa
3
3(
nkv
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lconvergef
take only f
rid)onthe
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xtfigure.N
1 Kz
Kz
1
ay1
ecurrents
r
ationsandv
1
, )
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k
n
k
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lorseries)
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irst order f
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rents(orvi
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t
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angefrom
erifythat1n
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k
i
t
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t
sic The
eoftheord
orward or
evoltagep
eversa).Th
evoltagev
1,2,...,
ry Not
(1.38)
(1.39)
(1.40)
erofthe
ackward
ints,this
ecurrent
ctorhas
(1.41)
(1.42)
andthe
(1.43)
s
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Takinga
,k n . So
actualv
Plugging
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Andthe
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Thispro
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