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1.
I
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I
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N
P
o
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tr
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s
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t
s
in
th
e
c
u
r
r
en
t
s
an
d
v
o
lta
g
es
[
1
]
.
T
h
e
h
ig
h
f
r
eq
u
en
c
y
co
m
m
o
n
m
o
d
e
a
n
d
d
if
f
er
e
n
tial
m
o
d
e
cu
r
r
en
ts
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ca
b
le
s
p
r
o
d
u
ce
em
is
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io
n
s
t
h
at
ca
n
ca
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s
e
u
n
w
a
n
ted
elec
tr
o
m
a
g
n
etic
i
n
ter
f
er
en
ce
(
E
MI
)
[2
]
.
T
h
er
ef
o
r
e,
an
ac
cu
r
ate
m
o
d
el
o
f
th
e
ca
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les
th
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s
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h
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f
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eq
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n
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eh
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v
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s
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d
.
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p
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ar
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o
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te
n
m
o
d
elled
in
SP
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C
E
[3
]
.
T
h
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f
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n
c
y
b
eh
av
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m
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d
ict
th
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elec
tr
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m
ag
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ter
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[
4
]
.
Hen
ce
,
a
h
ig
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f
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eq
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en
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y
cir
cu
i
t
m
o
d
el
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f
ca
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l
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in
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s
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.
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g
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l
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e
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ch
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g
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als
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C
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le
m
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d
el
w
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e
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th
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ca
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m
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ated
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n
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x
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ti
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m
o
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els
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av
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ilab
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o
n
s
ta
n
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ar
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SP
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C
E
s
i
m
u
lato
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s
f
o
r
t
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o
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les
.
On
e
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ased
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n
tr
an
s
m
is
s
io
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lin
e
eq
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atio
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le
s
s
u
n
if
o
r
m
tr
an
s
m
i
s
s
io
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li
n
e.
T
h
is
m
o
d
el
d
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ib
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t
h
e
ca
b
le
b
y
it
s
c
h
ar
ac
ter
is
tic
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m
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ce
an
d
s
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g
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al
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r
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p
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g
ati
o
n
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ela
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.
Si
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ce
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m
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el
d
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o
t
in
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lu
d
e
t
h
e
ca
b
le
lo
s
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es,
it
is
n
o
t
s
u
itab
l
e
f
o
r
u
s
e
in
ap
p
licatio
n
s
to
p
r
ed
ict
E
MI
w
h
en
lo
n
g
ca
b
les
ar
e
u
s
ed
.
A
n
o
t
h
er
s
i
m
p
le
SP
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C
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m
o
d
el
is
b
as
ed
o
n
ca
s
ca
d
ed
s
ec
tio
n
s
o
f
p
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T
o
r
L
-
s
h
ap
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eq
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i
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ale
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t
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t
s
o
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er
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le
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g
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R
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n
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C
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ar
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m
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s
d
i
s
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alo
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g
t
h
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ca
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le.
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h
e
R
L
GC
m
o
d
el
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g
n
o
r
es
t
h
e
v
ar
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n
o
f
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e
p
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n
it
len
g
th
r
esis
tan
ce
a
n
d
i
n
d
u
cta
n
ce
w
it
h
f
r
eq
u
e
n
c
y
d
u
e
to
th
e
s
k
in
ef
f
ec
t
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n
d
p
r
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x
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m
it
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f
f
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.
Si
m
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,
t
h
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v
ar
iatio
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o
f
th
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p
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m
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tti
v
it
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d
lo
s
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tan
g
en
t
o
f
t
h
e
d
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tr
ic,
w
h
ic
h
r
esu
lts
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n
i
n
cr
ea
s
ed
lo
s
s
at
h
ig
h
er
f
r
eq
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en
c
ies,
is
n
o
t
ac
co
u
n
ted
f
o
r
in
t
h
is
m
o
d
el.
B
y
i
g
n
o
r
in
g
th
o
s
e
p
ar
a
m
etr
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v
ar
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n
s
,
in
ac
cu
r
ate
ti
m
e
a
n
d
f
r
eq
u
en
c
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d
o
m
ai
n
s
o
l
u
tio
n
s
ar
e
o
b
tain
ed
f
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m
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m
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latio
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Sev
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b
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p
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I
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S
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[5
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.
A
n
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et
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s
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m
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o
f
th
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ad
m
itta
n
ce
m
atr
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x
o
f
th
e
ca
b
le
[
6
-
12
]
.
T
h
ese
t
w
o
m
e
th
o
d
s
h
a
v
e
b
ee
n
p
r
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ted
an
d
co
m
p
ar
ed
in
th
i
s
p
ap
er
.
2.
T
H
E
O
RY
A
cc
u
r
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an
a
l
y
s
is
o
f
E
MI
in
p
o
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co
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v
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ter
s
y
s
te
m
s
f
o
r
d
r
iv
es
r
eq
u
ir
es
h
ig
h
f
r
eq
u
e
n
c
y
c
ir
cu
i
t
m
o
d
el
s
o
f
a
ll
t
h
e
co
m
p
o
n
e
n
t
s
in
t
h
e
s
y
s
te
m
.
A
c
o
m
m
er
cial
t
o
o
l,
A
NS
YS
-
Si
m
p
lo
r
er
th
at
in
te
g
r
ates
m
u
ltip
le
m
o
d
ell
in
g
tec
h
n
o
lo
g
ies
h
a
s
b
ee
n
u
s
ed
to
s
i
m
u
la
te
t
h
e
p
o
w
er
elec
tr
o
n
ic
co
n
v
er
ter
s
y
s
te
m
[
13
]
.
Fu
r
t
h
er
t
h
i
s
w
o
r
k
u
s
ed
,
f
in
ite
ele
m
en
t
an
al
y
s
i
s
b
ase
d
A
NSY
S
-
Ma
x
w
e
ll
t
o
o
b
tain
th
e
h
ig
h
f
r
eq
u
e
n
c
y
b
eh
av
io
r
al
m
o
d
el
o
f
in
d
u
ctio
n
m
o
to
r
an
d
Ma
tlab
-
Si
m
u
li
n
k
to
s
i
m
u
late
it
s
co
n
t
r
o
l
an
d
s
t
u
d
y
f
a
u
lt
s
ca
u
s
ed
b
y
d
i
f
f
er
e
n
t
d
r
i
v
e’
s
co
m
p
o
n
e
n
t
s
.
T
h
e
h
ig
h
f
r
eq
u
e
n
c
y
b
eh
a
v
io
r
al
m
o
d
els
o
f
a
ll
th
e
co
m
p
o
n
en
t
s
i
n
t
h
e
p
o
w
er
el
ec
tr
o
n
ic
s
y
s
te
m
s
in
cl
u
d
in
g
t
h
e
ca
b
les
ca
n
al
s
o
b
e
o
b
tain
ed
f
r
o
m
d
if
f
er
en
t
s
o
f
t
w
ar
e
p
la
t
f
o
r
m
s
a
n
d
s
i
m
u
lated
in
SP
I
C
E
to
p
r
ed
ict
EMI
[
4
]
.
Fo
r
th
is
a
p
p
r
o
ac
h
,
t
w
o
m
et
h
o
d
s
to
o
b
tain
a
SP
I
C
E
ca
b
le
m
o
d
el
is
r
e
v
ie
w
ed
an
d
p
r
esen
ted
b
elo
w
.
T
h
e
elec
tr
ical
p
r
o
p
er
ties
o
f
a
tr
an
s
m
is
s
io
n
li
n
e
ar
e
ch
ar
ac
ter
ized
b
y
th
e
p
er
u
n
it
le
n
g
t
h
p
ar
am
eter
s
R
,
L
,
G
a
n
d
C
.
T
h
e
cir
cu
it
t
h
e
o
r
y
-
b
ased
d
ef
in
i
tio
n
s
o
f
t
h
e
p
ar
am
eter
s
ar
e
r
elate
d
to
th
e
s
to
r
ed
elec
tr
ic
a
n
d
m
ag
n
etic
en
er
g
ies,
a
s
w
ell
as
th
e
p
o
w
er
lo
s
s
a
n
d
o
b
tain
ed
f
r
o
m
a
f
ield
t
h
eo
r
y
-
b
as
ed
an
al
y
s
is
o
f
t
h
e
tr
an
s
m
is
s
io
n
li
n
e
[
1
4
]
.
T
h
e
tr
an
s
m
i
s
s
io
n
li
n
e
s
p
ar
a
m
eter
s
of
s
o
m
e
co
m
m
o
n
lin
e
s
s
u
ch
a
s
co
ax
ial,
t
w
o
w
ir
e
an
d
p
ar
allel
p
late
ar
e
d
eter
m
i
n
ed
at
lo
w
f
r
eq
u
en
c
y
u
s
in
g
an
a
l
y
tical
tech
n
iq
u
es
.
T
h
e
l
u
m
p
e
d
p
ar
am
eter
SP
I
C
E
m
o
d
el
o
f
th
e
tr
an
s
m
is
s
io
n
l
i
n
e
is
o
b
tai
n
ed
b
y
u
s
in
g
a
n
u
m
b
er
o
f
L
-
s
h
ap
ed
s
ec
tio
n
s
o
f
t
h
e
R
L
G
C
p
ar
a
m
eter
s
di
s
tr
ib
u
ted
alo
n
g
t
h
e
le
n
g
th
o
f
th
e
ca
b
le
.
I
f
n
s
ec
tio
n
s
(
L
-
s
h
a
p
ed
)
ar
e
u
s
ed
p
er
u
n
it
len
g
t
h
as
s
h
o
w
n
in
Fi
g
u
r
e
.
1
,
th
e
l
u
m
p
ed
ele
m
en
t
v
alu
e
s
in
ea
c
h
s
e
ct
io
n
ar
e
R
/
n
,
L
/n
.
G/n
a
n
d
C
/
n
.
T
h
e
f
ir
s
t
a
n
d
las
t
s
er
ies
b
r
an
c
h
es
ar
e
h
al
f
s
ec
tio
n
s
w
i
th
l
u
m
p
ed
elem
en
ts
R
/(
2
n
)
an
d
L
/(
2
n
)
to
k
ee
p
th
e
lin
e
s
y
m
m
etr
ic
.
T
h
er
e
s
h
o
u
ld
b
e
en
o
u
g
h
s
ec
tio
n
s
i
n
t
h
e
m
o
d
el
to
e
n
s
u
r
e
th
at
ea
ch
s
ec
t
io
n
r
ep
r
ese
n
ts
t
h
e
le
n
g
th
o
f
th
e
li
n
e
t
h
at
is
a
s
m
all
f
r
ac
tio
n
o
f
t
h
e
w
a
v
ele
n
g
t
h
(
λ
/2
0
)
at
t
h
e
h
i
g
h
est
f
r
eq
u
en
c
y
o
f
t
h
e
s
i
g
n
al
f
l
o
w
i
n
g
o
n
th
e
li
n
e
.
Dep
en
d
i
n
g
o
n
t
h
e
r
i
s
e
ti
m
e
of
th
e
ti
m
e
d
o
m
ai
n
s
i
g
n
al,
t
h
e
h
i
g
h
e
s
t
f
r
eq
u
en
c
y
co
m
p
o
n
en
t
o
n
th
e
lin
e
is
es
ti
m
ated
as
0
3
5
/(
r
is
e
ti
m
e)
.
So
m
e
d
esig
n
er
s
u
s
e
th
e
esti
m
ate
o
f
1
/(
r
is
e
ti
m
e)
f
o
r
th
e
h
i
g
h
est
f
r
eq
u
en
c
y
co
m
p
o
n
en
t.
I
n
p
r
ac
tice,
b
y
ch
o
o
s
i
n
g
t
h
e
n
u
m
b
er
o
f
s
ec
tio
n
s
to
b
e
lar
g
e
en
o
u
g
h
in
t
h
e
m
o
d
el
,
th
e
s
y
s
t
e
m
b
eh
av
io
r
w
it
h
a
lo
n
g
ca
b
le
is
p
r
ed
icted
in
th
e
ti
m
e
an
d
f
r
eq
u
e
n
c
y
d
o
m
ai
n
s
.
Ho
w
e
v
er
,
th
is
m
o
d
el
i
s
s
till
i
n
s
u
f
f
ic
ien
t
to
d
escr
ib
e
t
h
e
e
f
f
ec
ts
o
f
ca
b
le
le
n
g
th
o
n
s
ig
n
al
f
lo
w
,
as
t
h
e
p
er
u
n
i
t
len
g
t
h
p
ar
am
e
ter
s
ar
e
f
r
eq
u
en
c
y
d
ep
en
d
en
t.
I
n
o
r
d
er
to
d
eter
m
i
n
e
th
e
p
ar
am
eter
v
al
u
es
at
h
ig
h
f
r
eq
u
en
cies,
n
u
m
er
ical
tec
h
n
iq
u
es
,
s
u
c
h
as
t
h
e
f
in
i
te
ele
m
e
n
t
m
et
h
o
d
,
a
r
e
u
s
ed
[
15
]
.
T
h
eir
v
ar
iatio
n
s
w
it
h
f
r
eq
u
e
n
c
y
ar
e
later
ac
co
u
n
ted
in
t
h
e
SP
I
C
E
m
o
d
el.
O
n
e
m
et
h
o
d
to
ac
co
u
n
t
f
o
r
t
h
e
f
r
eq
u
en
c
y
d
ep
en
d
e
n
ce
o
f
th
e
p
ar
am
eter
s
is
th
e
u
s
e
o
f
a
lad
d
er
n
et
w
o
r
k
i
n
t
h
e
m
o
d
el
[
5
]
.
T
h
e
lo
s
s
es
d
u
e
t
o
s
k
i
n
ef
f
ec
t,
ca
u
s
i
n
g
t
h
e
ca
b
le
b
eh
a
v
io
r
to
b
e
f
r
eq
u
en
c
y
d
ep
en
d
en
t,
ar
e
m
o
d
elled
b
y
t
h
e
R
L
lad
d
er
n
et
w
o
r
k
.
T
h
is
lad
d
er
n
et
w
o
r
k
i
s
u
s
ed
i
n
p
lace
o
f
a
s
i
n
g
le
R
a
n
d
L
i
n
t
h
e
s
er
ie
s
b
r
an
c
h
o
f
Fi
g
u
r
e
1
.
T
h
e
f
r
eq
u
en
c
y
d
ep
en
d
en
t
v
ar
iatio
n
o
f
th
e
r
e
al
an
d
i
m
a
g
i
n
ar
y
co
m
p
o
n
e
n
t
s
o
f
p
er
m
itti
v
it
y
o
f
t
h
e
d
ielec
t
r
ic
m
ater
ial
o
f
t
h
e
ca
b
le
is
m
o
d
elled
w
it
h
a
n
R
C
lad
d
er
n
et
w
o
r
k
.
T
h
is
lad
d
er
n
et
w
o
r
k
is
u
s
ed
i
n
p
lace
o
f
a
s
i
n
g
le
G
an
d
C
i
n
th
e
s
h
u
n
t b
r
an
ch
o
f
Fig
u
r
e
1
.
Fig
u
r
e
1
.
T
r
an
s
m
i
s
s
io
n
L
in
e
Mo
d
el
w
it
h
n
Sect
io
n
s
o
f
P
er
Un
it L
e
n
g
th
P
ar
a
m
eter
s
R
,
L
,
G
an
d
C
Dis
tr
ib
u
ted
o
n
U
n
it
L
e
n
g
t
h
o
f
th
e
C
ab
le
Fig
u
r
e
2
.
C
r
o
s
s
-
s
ec
tio
n
o
f
th
e
T
w
o
W
ir
e
C
ab
le:
Dia
m
eter
o
f
t
h
e
W
ir
es D
2
=
1
.
3
8
m
m
,
Dia
m
eter
o
f
th
e
P
VC
C
o
v
er
in
g
o
f
W
ir
es D
1
=
2
.
88
m
m
,
Dia
m
eter
o
f
t
h
e
R
u
b
b
er
Sh
ield
Ov
er
th
e
t
w
o
W
ir
es D
3
=
8
.
7
m
m
,
R
elati
v
e
P
er
m
itti
v
it
y
o
f
R
u
b
b
er
=
2
.
3
,
C
o
n
d
u
ctiv
it
y
o
f
th
e
W
ir
es =
4
5
.
9
4
MS/
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
,
Vo
l.
9
,
No
.
2
,
J
u
n
e
2
0
1
8
:
744
–
749
746
An
o
th
er
m
et
h
o
d
to
ac
co
u
n
t
f
o
r
f
r
eq
u
en
c
y
d
ep
en
d
e
n
ce
o
f
p
er
u
n
it
le
n
g
t
h
p
ar
a
m
eter
s
is
b
y
d
ir
ec
tl
y
u
s
i
n
g
f
r
eq
u
e
n
c
y
d
ep
en
d
en
t
el
e
m
en
ts
i
n
t
h
e
SP
I
C
E
m
o
d
el.
T
o
d
o
th
is
,
L
ap
lace
SP
I
C
E
el
e
m
en
ts
ar
e
u
s
ed
to
r
ep
r
esen
t
th
e
f
r
eq
u
e
n
c
y
d
ep
en
d
en
t
ad
m
itta
n
ce
p
ar
a
m
e
ter
m
a
tr
ix
o
f
t
h
e
lo
n
g
ca
b
le.
A
v
ec
to
r
f
itti
n
g
alg
o
r
it
h
m
ap
p
r
o
x
im
a
tes
t
h
e
ad
m
itta
n
ce
p
ar
am
eter
m
atr
ix
o
f
th
e
ca
b
l
e
as
a
f
u
n
ctio
n
o
f
f
r
eq
u
e
n
c
y
[
9
]
w
it
h
a
r
atio
n
al
f
u
n
ctio
n
i
n
th
e
L
ap
lace
d
o
m
a
in
.
A
L
ap
lace
SP
I
C
E
ele
m
en
t
is
t
h
en
u
s
ed
to
r
ep
r
esen
t
t
h
e
r
atio
n
al
f
u
n
ctio
n
ap
p
r
o
x
im
a
tio
n
.
A
m
o
d
el
th
at
ch
ar
ac
ter
izes
t
h
e
tr
an
s
m
is
s
io
n
lin
e
w
i
th
t
h
e
f
r
eq
u
e
n
c
y
d
ep
e
n
d
en
t
e
f
f
ec
ts
i
s
t
h
u
s
o
b
tain
ed
.
T
h
e
r
esu
lts
f
r
o
m
th
e
lad
d
er
n
et
w
o
r
k
SP
I
C
E
m
o
d
el
an
d
L
ap
lace
ele
m
en
t SP
I
C
E
m
o
d
el
ar
e
co
m
p
ar
ed
h
er
e.
T
h
e
lad
d
er
n
et
w
o
r
k
m
o
d
el
f
o
r
a
t
w
o
w
ir
e
ca
b
le,
as
p
r
esen
ted
i
n
[
5
]
,
h
as
b
ee
n
ca
lc
u
lated
h
er
e
f
o
r
t
h
e
p
u
r
p
o
s
e
o
f
co
m
p
ar
i
n
g
t
h
e
t
w
o
m
et
h
o
d
s
.
2.
1
.
L
a
dd
er
Net
wo
rk
M
o
del
f
o
r
a
T
w
o
Wire
Ca
ble
T
h
e
cr
o
s
s
s
ec
tio
n
o
f
a
1
m
t
w
o
w
ir
e
u
n
s
h
ield
ed
en
er
g
y
c
ab
le
is
s
h
o
w
n
i
n
Fi
g
u
r
e
2
.
Us
in
g
a
f
in
ite
ele
m
e
n
t
m
et
h
o
d
-
b
ased
elec
tr
o
m
ag
n
etic
s
o
l
v
er
to
o
l
(
A
NSY
S
-
HF
SS
)
,
th
e
R
L
G
C
p
ar
a
m
eter
s
o
f
th
i
s
ca
b
le
w
er
e
o
b
tain
ed
o
v
er
t
h
e
f
r
eq
u
e
n
c
y
r
an
g
e
1
0
KHz
-
1
0
0
MH
z.
T
h
es
e
p
a
r
a
m
eter
s
ca
n
b
e
also
d
eter
m
i
n
ed
w
it
h
a
v
ec
to
r
n
et
w
o
r
k
a
n
al
y
ze
r
.
T
h
e
1
m
lo
n
g
t
w
o
w
ir
e
ca
b
le
w
as
m
o
d
elled
w
ith
n
u
m
b
er
o
f
s
ec
tio
n
s
,
n
=
3
2
.
T
h
e
ti
m
e
d
o
m
ai
n
p
u
l
s
e
w
it
h
a
r
is
e
ti
m
e
o
f
1
0
n
s
w
a
s
u
s
ed
to
test
t
h
e
m
o
d
el
(
h
ig
h
e
s
t
f
r
eq
u
e
n
c
y
co
m
p
o
n
en
t
o
f
1
0
0
MH
z)
.
W
ith
3
2
s
ec
tio
n
p
er
m
eter
o
f
ca
b
le
,
th
e
len
g
t
h
o
f
ea
ch
s
ec
tio
n
w
as
m
u
c
h
lo
w
er
th
a
n
λ
/
2
0
at
1
0
0
MH
z.
T
h
e
v
ar
iatio
n
s
o
f
r
es
is
ta
n
ce
a
n
d
in
d
u
ctan
ce
w
i
th
f
r
eq
u
e
n
c
y
(
s
er
i
es
b
r
an
ch
o
f
Fi
g
u
r
e
1
)
ar
e
r
ep
r
esen
ted
b
y
a
n
R
L
lad
d
er
n
et
w
o
r
k
s
h
o
w
n
i
n
F
ig
u
r
e
3
.
A
least
s
q
u
ar
e
c
u
r
v
e
f
itti
n
g
alg
o
r
it
h
m
w
a
s
u
s
ed
to
d
ete
r
m
in
e
t
h
e
ele
m
en
ts
o
f
t
h
e
lad
d
er
n
et
w
o
r
k
.
T
h
i
s
alg
o
r
ith
m
m
i
n
i
m
ized
t
h
e
d
i
f
f
er
en
ce
in
eq
u
i
v
ale
n
t
i
m
p
ed
an
ce
s
o
f
t
h
e
la
d
d
er
n
et
w
o
r
k
an
d
th
e
s
er
ie
s
b
r
an
ch
o
f
th
e
ca
b
le
in
th
e
f
r
eq
u
en
c
y
r
an
g
e
.
T
h
e
v
ar
iatio
n
s
o
f
co
n
d
u
cta
n
ce
an
d
ca
p
ac
itan
ce
p
ar
a
m
eter
s
(
s
h
u
n
t
b
r
an
ch
o
f
Fi
g
u
r
e
1
)
w
i
th
f
r
eq
u
en
c
y
ar
e
r
ep
r
esen
ted
b
y
t
h
e
R
C
lad
d
er
n
et
w
o
r
k
s
h
o
w
n
i
n
Fi
g
u
r
e
4
.
Usi
n
g
t
h
e
s
a
m
e
least
s
q
u
a
r
e
cu
r
v
e
f
it
tin
g
al
g
o
r
ith
m
,
th
e
d
if
f
er
en
ce
i
n
ad
m
itta
n
ce
s
o
f
th
e
lad
d
er
n
et
w
o
r
k
an
d
th
e
s
h
u
n
t
b
r
an
ch
w
er
e
m
in
i
m
ized
.
A
SP
I
C
E
s
u
b
cir
cu
its
n
etli
s
t
f
o
r
Fig
u
r
e
3
an
d
Fig
u
r
e
4
ar
e
w
r
itte
n
w
it
h
t
h
e
d
eter
m
in
e
d
lad
d
er
n
et
w
o
r
k
ele
m
e
n
t
v
alu
es.
T
h
e
SP
I
C
E
m
o
d
el
f
o
r
t
h
e
ca
b
le
is
cr
ea
ted
b
y
in
cl
u
d
in
g
3
2
s
ec
tio
n
s
o
f
th
e
s
u
b
cir
cu
its
in
t
h
e
n
etli
s
t.
T
h
e
m
o
d
el
h
as
b
ee
n
v
al
id
ated
b
y
co
m
p
ar
in
g
th
e
i
n
p
u
t
i
m
p
e
d
an
ce
s
o
f
th
e
1
m
-
lo
n
g
ca
b
le
ter
m
in
a
ted
w
it
h
eith
er
a
s
h
o
r
t
o
r
o
p
en
c
ir
cu
it.
T
h
e
e
x
p
er
i
m
e
n
tal
r
es
u
lts
f
o
r
th
e
s
e
co
n
f
i
g
u
r
atio
n
s
f
r
o
m
[
5
]
h
a
v
e
b
ee
n
co
m
p
ar
ed
w
it
h
t
h
e
m
o
d
el
o
b
tain
ed
in
th
i
s
w
o
r
k
a
s
s
h
o
w
n
i
n
Fig
u
r
e
5
.
A
l
th
o
u
g
h
t
h
e
r
ec
alc
u
lated
v
al
u
e
s
o
f
t
h
e
ele
m
e
n
ts
o
f
th
e
lad
d
er
n
et
w
o
r
k
v
ar
y
s
li
g
h
tl
y
f
r
o
m
th
e
o
r
i
g
i
n
al
w
o
r
k
,
t
h
e
s
i
m
u
lated
i
m
p
e
d
an
ce
s
ar
e
in
g
o
o
d
ag
r
ee
m
e
n
t
w
it
h
t
h
e
m
ea
s
u
r
e
m
en
ts
.
T
h
e
ti
m
e
d
o
m
ai
n
r
esp
o
n
s
e
o
f
th
e
ca
b
le
to
a
4
0
V
p
u
ls
e
w
it
h
a
r
is
e
an
d
f
a
l
l
ti
m
e
o
f
1
0
n
s
is
s
h
o
w
n
in
Fig
u
r
e
6
.
T
h
e
ap
p
lied
in
p
u
t
4
0
V
p
u
ls
e
w
a
s
id
en
tical
to
th
e
p
u
ls
e
in
[
5
]
an
d
th
e
tr
an
s
ie
n
t
r
esp
o
n
s
e
s
i
m
u
latio
n
f
r
o
m
t
h
is
w
o
r
k
ag
r
ee
s
w
ell
w
i
t
h
m
ea
s
u
r
e
m
e
n
ts
[
5
]
.
T
h
is
s
o
l
u
tio
n
is
f
u
r
th
er
co
m
p
ar
ed
w
it
h
t
h
e
m
o
d
el
o
b
tain
ed
f
r
o
m
t
h
e
ad
m
itta
n
ce
p
ar
a
m
ete
r
m
a
tr
ix
o
f
t
h
e
ca
b
le.
Fig
u
r
e
3
.
R
L
lad
d
er
n
et
w
o
r
k
.
Fo
r
th
e
1
m
ca
b
le
o
f
Fig
u
r
e
.
2
w
it
h
3
2
s
ec
tio
n
s
,
R
1
=1
.
5
e
-
1
Ω
,
R
2
=9
.
9
0
2
1
e
-
2
Ω
,
R
3
=7
.
5
1
2
5
e
-
2
Ω
,
R
4
=4
.
2
5
e
-
2
Ω
,
R
5
=6
.
9
2
4
6
e
-
3
Ω
,
L
1
=5
.
0
0
0
2
e
-
1
3
H,
L
2
=6
.
0
7
3
3
e
-
1
1
H,
L
3
=6
.
0
7
3
3
e
-
1
1
H,
L
4
=3
.
4
3
9
2
e
-
1
0
H,
L
5
=1
.
7
1
5
8
e
-
0
8
H.
Fig
u
r
e
4
.
R
C
lad
d
er
n
et
w
o
r
k
.
Fo
r
th
e
1
m
ca
b
le
o
f
Fig
u
r
e.
2
w
it
h
3
2
s
ec
tio
n
s
,
R
1
=6
.
5
1
9
9
e8
Ω
,
2
=4
.
5
6
1
1
e6
Ω
,
R
3
=7
.
0
9
8
7
e
6
Ω
,
R
4
=1
.
3
7
9
7
e7
Ω
,
R
5
=4
.
2
3
5
7
e9
Ω
,
C
1
=0
.
5
4
0
1
8
e
-
1
5
F,
C
2
=1
.
3
4
7
5
e
-
1
5
F,
C
3
=2
.
9
3
4
2
e
-
1
5
F,
C
4
=1
.
9
0
2
6
e
-
1
5
F,
C
5
=1
.
6
5
e
-
1
2
F.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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&
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SPICE
ele
m
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T
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m
ittan
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atr
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a n
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ates
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r
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en
t
to
th
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v
o
ltag
es
at each
o
f
its
p
o
r
ts
[
1
4
]
.
A t
wo
wir
e
cab
le
o
f
an
y
len
g
th
f
o
r
m
s
a
tw
o
p
o
r
t
n
etwo
r
k
.
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o
r
a
two
p
o
r
t
n
etwo
r
k
,
th
e
eq
u
ati
o
n
b
elo
w
s
h
o
ws
th
e
r
elatio
n
s
h
ip
b
etween
cu
r
r
en
t
an
d
v
o
ltag
e at
t
h
e in
p
u
t
(
p
o
r
t
1
)
an
d
o
u
t
p
u
t
(
p
o
r
t
2
)
.
Sin
ce
th
e
ca
b
le
is
a
r
ec
ip
r
o
ca
l
n
et
w
o
r
k
,
.
T
h
e
ad
m
itta
n
ce
p
ar
a
m
eter
s
m
atr
i
x
o
f
th
e
ca
b
le
ca
n
b
e
m
ea
s
u
r
ed
u
s
i
n
g
a
v
e
cto
r
n
et
w
o
r
k
an
a
l
y
ze
r
o
v
er
a
d
esire
d
f
r
eq
u
en
c
y
r
an
g
e.
T
h
is
r
eq
u
ir
es
p
laci
n
g
ap
p
r
o
p
r
iate
co
n
n
ec
to
r
s
b
et
w
ee
n
th
e
ca
b
le
an
d
th
e
n
et
w
o
r
k
an
al
y
ze
r
an
d
i
m
p
ed
an
ce
ter
m
i
n
a
tio
n
o
f
5
0
Ω
at
th
e
en
d
o
f
ca
b
le
.
T
h
e
ad
m
itta
n
ce
p
ar
am
eter
s
m
atr
ix
o
f
t
h
e
t
wo
w
ir
e
ca
b
le
ca
n
also
b
e
o
b
t
ain
ed
f
r
o
m
a
f
i
n
ite
ele
m
e
n
t
an
al
y
s
is
s
o
f
t
w
ar
e.
F
o
r
a
1
m
lo
n
g
ca
b
le
w
it
h
th
e
cr
o
s
s
-
s
ec
tio
n
s
h
o
w
n
i
n
Fi
g
u
r
e
2
,
th
e
ad
m
itta
n
ce
p
ar
am
eter
m
atr
ix
h
as
b
ee
n
o
b
tain
ed
f
r
o
m
a
f
in
i
te
ele
m
e
n
t
s
o
lv
er
(
A
NS
YS
-
HF
SS
)
o
v
er
a
f
r
eq
u
en
c
y
r
an
g
e
o
f
1
0
KHz
-
1
0
0
MH
z.
Fig
u
r
e
5
.
I
n
p
u
t I
m
p
ed
an
ce
o
f
1
m
C
ab
le
T
er
m
i
n
ated
in
S
h
o
r
t Ci
r
cu
i
t (
SC
)
an
d
Op
e
n
C
ir
c
u
it (
OC
)
Fig
u
r
e
6
.
T
r
an
s
ien
t
R
esp
o
n
s
e
o
f
1
m
C
ab
le
T
er
m
in
ated
i
n
a
7
5
0
Ω
L
o
ad
,
C
o
n
n
ec
ted
to
5
0
Ω
So
u
r
ce
an
d
an
I
n
p
u
t P
u
ls
e
o
f
4
0
V
(
Star
ts
at
t =
3
0
n
s
w
it
h
R
is
e
T
i
m
e
o
f
1
0
n
s
,
D
u
r
atio
n
1
5
0
n
s
,
Fall T
im
e
o
f
1
0
n
s
)
T
h
e
ad
m
it
tan
ce
p
ar
a
m
e
ter
s
o
b
tain
ed
ar
e
a
f
u
n
c
tio
n
o
f
f
r
eq
u
e
n
c
y
a
n
d
th
er
e
f
o
r
e
ca
n
b
e
ex
p
r
ess
ed
as
a
f
u
n
ctio
n
in
th
e
L
ap
lace
d
o
m
a
in
(
.
A
r
atio
n
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f
u
n
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n
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p
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m
at
io
n
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]
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T
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itta
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as:
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d
D
is
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l.
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h
e
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m
ex
p
r
ess
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all
th
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p
ar
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s
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n
t
h
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m
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ce
m
atr
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x
w
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h
t
h
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m
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t
o
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p
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d
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t
w
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p
ar
am
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s
in
t
h
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ad
m
it
tan
ce
m
atr
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x
ar
e
eq
u
al.
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r
a
cir
cu
it
s
i
m
u
latio
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,
th
e
r
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al
f
u
n
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ap
p
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m
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s
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ili
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T
h
e
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m
[
9
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cr
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ap
p
r
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m
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t
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le
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T
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e
alg
o
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ith
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[
1
6
]
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n
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[
1
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A
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e
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a
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s
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m
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[
5
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p
ed
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ce
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h
e
n
ter
m
in
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in
s
h
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o
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it
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as
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u
r
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2
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r
ee
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h
m
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m
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[
5
]
an
d
th
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lad
d
er
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et
w
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k
r
ep
r
esen
tatio
n
.
T
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w
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Fi
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r
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.
T
w
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t N
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Mo
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u
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I
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t J
P
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&
Dr
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to
p
er
f
o
r
m
a
ti
m
e
d
o
m
ai
n
s
i
m
u
latio
n
u
s
i
n
g
t
h
e
L
ap
lace
SP
I
C
E
ele
m
e
n
t
m
o
d
el
ar
e
lo
n
g
er
t
h
an
t
h
o
s
e
o
f
t
h
e
lad
d
er
n
et
w
o
r
k
m
o
d
el.
T
h
i
s
i
s
d
u
e
to
th
e
f
ac
t
th
a
t
w
h
ile
p
er
f
o
r
m
in
g
tr
an
s
ien
t
a
n
al
y
s
i
s
in
SP
I
C
E
,
th
e
i
m
p
u
l
s
e
r
esp
o
n
s
e
o
f
th
e
L
ap
lace
ele
m
e
n
ts
ar
e
ca
lcu
lated
an
d
co
n
v
o
lv
ed
w
it
h
i
n
p
u
t
s
ig
n
al.
I
f
th
e
m
o
d
el
ar
r
iv
ed
at
u
s
i
n
g
L
ap
lace
ele
m
en
t
s
is
n
o
t
p
ass
iv
e,
n
u
m
er
ical
in
ac
cu
r
ac
y
r
es
u
lts
.
I
f
s
tep
s
ar
e
tak
en
to
av
o
id
t
h
is
p
r
o
b
le
m
w
h
en
s
y
n
t
h
esiz
in
g
t
h
e
m
o
d
el
,
ac
cu
r
ate
tr
an
s
ie
n
t
an
al
y
s
is
ca
n
,
h
o
w
e
v
er
,
b
e
r
ea
lized
.
A
l
th
o
u
g
h
eit
h
er
o
f
th
e
m
et
h
o
d
s
u
s
ed
to
o
b
tain
a
SP
I
C
E
m
o
d
el
f
o
r
th
e
ca
b
le
is
ap
p
r
o
p
r
iate
in
ter
m
s
o
f
ac
cu
r
ac
y
,
t
h
e
u
s
e
o
f
v
ec
to
r
f
itti
n
g
al
g
o
r
ith
m
to
o
b
tai
n
a
m
o
d
el
is
f
o
u
n
d
to
b
e
eleg
an
t
an
d
li
k
el
y
to
b
e
m
o
r
e
s
u
itab
le
f
o
r
m
u
lt
ico
n
d
u
cto
r
ca
b
les.
RE
F
E
R
E
NC
E
S
[1
]
W
e
i
Z.
,
“
T
h
e
El
e
c
tro
m
a
g
n
e
ti
c
In
terf
e
re
n
c
e
M
o
d
e
l
A
n
a
l
y
sis
o
f
t
h
e
P
o
w
e
r
S
w
it
c
h
in
g
De
v
i
c
e
s”
,
T
EL
KOM
NIKA
In
d
o
n
e
sia
n
J
o
u
rn
a
l
o
f
El
e
c
trica
l
En
g
i
n
e
e
rin
g
,
V
o
l.
1
1
,
N
o
.
1
,
p
p
.
1
6
7
–
72
,
2
0
1
3
.
[2
]
Cla
y
to
n
R.
P
a
u
l,
“
I
n
tro
d
u
c
ti
o
n
to
El
e
c
tro
m
a
g
n
e
ti
c
Co
m
p
a
ti
b
il
it
y
”
,
Jo
h
n
W
il
e
y
&
S
o
n
s,
2
0
0
6
.
[3
]
G
ian
lu
c
a
S
e
n
a
,
Ro
b
e
rto
M
a
ra
n
i,
G
e
n
n
a
ro
G
e
lao
,
A
n
n
a
G
in
a
P
e
rri,
“
A
Co
m
p
a
ra
ti
v
e
S
tu
d
y
o
f
P
o
w
e
r
S
e
m
ico
n
d
u
c
t
o
r
De
v
ice
s
f
o
r
In
d
u
strial
P
W
M
In
v
e
rters
”
,
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Po
we
r
E
lec
tro
n
ics
a
n
d
Dr
ive
S
y
ste
m
(
IJ
PE
DS
)
,
V
o
l.
7
,
No
.
4
,
p
p
.
1
4
2
0
-
1
4
2
8
,
De
c
e
m
b
e
r
2
0
1
6
.
[4
]
N.
Id
ir
a
n
d
Y.
W
e
e
n
s
a
n
d
M
.
M
o
re
a
u
a
n
d
J.
J.
F
ra
n
c
h
a
u
d
,
“
Hig
h
-
F
re
q
u
e
n
c
y
Be
h
a
v
io
r
M
o
d
e
ls
o
f
A
C
M
o
t
o
rs”
,
IEE
E
T
ra
n
.
O
n
M
a
g
n
e
ti
c
s
,
Vo
l:
4
5
,
No
.
1
,
p
p
.
1
3
3
–
13
,
Ja
n
.
2
0
0
9
.
[5
]
Y.W
e
e
n
s,
N.
Id
ir,
R.
Ba
u
iere
,
a
n
d
J
.
J.
F
ra
n
c
h
a
u
d
,
“
M
o
d
e
li
n
g
a
n
d
sim
u
latio
n
o
f
u
n
s
h
ield
e
d
a
n
d
sh
ield
e
d
e
n
e
rg
y
c
a
b
les
in
F
re
q
u
e
n
c
y
a
n
d
T
i
m
e
d
o
m
a
in
s”
,
IEE
E
T
ra
n
s
.
On
M
a
g
n
e
ti
c
s
,
V
o
l.
4
2
,
N
o
.
7
,
p
p
.
1
8
7
6
-
1
8
8
2
,
De
c
e
m
b
e
r
2
0
1
6
.
[6
]
B.
G
u
sta
v
se
n
a
n
d
A
.
S
e
m
l
y
e
n
,
“
Ra
ti
o
n
a
l
a
p
p
r
o
x
im
a
ti
o
n
o
f
f
re
q
u
e
n
c
y
d
o
m
a
in
re
sp
o
n
se
b
y
V
e
c
to
r
F
it
ti
n
g
”
,
IEE
E
T
ra
n
s.
Po
we
r De
li
v
e
ry
,
V
o
l.
1
4
,
No
.
3
,
p
p
.
1
0
5
2
-
1
0
6
,
,
Ju
ly
1
9
9
9
.
[7
]
B.
G
u
sta
v
s
e
n
,
“
Im
p
ro
v
in
g
th
e
p
o
le
re
lo
c
a
ti
n
g
p
r
o
p
e
rti
e
s
o
f
v
e
c
t
o
r
f
it
ti
n
g
”
,
IEE
E
T
ra
n
s.
Po
we
r
De
li
v
e
ry
,
V
o
l
.
2
1
,
N
o
.
3
,
p
p
.
1
5
8
7
-
1
5
9
2
,
Ju
ly
2
0
0
6
.
[8
]
D.
De
sc
h
rij
v
e
r,
M
.
M
ro
z
o
w
s
k
i,
T
.
Dh
a
e
n
e
,
a
n
d
D.
De
Zu
tt
e
r,
“
M
a
c
ro
m
o
d
e
li
n
g
o
f
M
u
lt
ip
o
rt
sy
s
tem
s
u
sin
g
a
F
a
st
im
p
le
m
e
n
tatio
n
o
f
V
e
c
to
r
F
it
ti
n
g
M
e
th
o
d
”
,
IEE
E
M
icr
o
wa
v
e
a
n
d
W
ire
les
s
Co
mp
o
n
e
n
ts
L
e
tt
e
rs
,
V
o
l
.
1
8
,
N
o
.
6
,
p
p
.
3
8
3
-
3
8
5
,
J
u
n
e
2
0
0
8
.
[9
]
T
h
e
V
e
c
to
r
f
it
ti
n
g
w
e
b
site
-
h
tt
p
s:
//
ww
w
.
sin
te
f
.
n
o
/p
r
o
jec
tw
e
b
/v
e
c
t
fit
/
M
a
y
1
5
th
2
0
1
7
.
[1
0
]
Iv
ica
S
tev
a
n
o
v
ic,
Be
rn
a
rd
W
u
n
sc
h
,
G
ian
L
u
ig
i
M
a
d
o
n
n
a
,
S
tan
islav
S
k
ib
in
,
“
Hig
h
-
F
re
q
u
e
n
c
y
B
e
h
a
v
io
ra
l
M
u
lt
ico
n
d
u
c
to
r
Ca
b
le M
o
d
e
li
n
g
f
o
r
EM
I
S
im
u
latio
n
s in
P
o
w
e
r
El
e
c
tro
n
ics
”
,
IEE
E
T
r
a
n
s.
On
I
n
d
u
st
ria
l
In
f
o
rm
a
ti
c
s
,
V
o
l
.
1
0
,
N
o
.
2
,
p
p
.
1
3
9
2
-
1
4
0
0
,
M
a
y
2
0
1
4
.
[1
1
]
El
i
S
tee
n
p
u
t,
“
A
S
p
ice
c
ircu
it
c
a
n
b
e
s
y
n
th
e
siz
e
d
w
it
h
a
sp
e
c
i
f
ied
se
t
o
f
S
-
p
a
ra
m
e
ter
s”
,
V
rij
e
Un
iv
e
rsiteit
Bru
ss
e
l,
p
p
1
-
1
2
.
[1
2
]
A
n
to
n
i
je
R.
Djo
rd
jev
ic,
“
S
P
ICE
-
Co
m
p
a
ti
b
le
M
o
d
e
ls
f
o
r
M
u
lt
ic
o
n
d
u
c
to
r
T
ra
n
sm
issio
n
L
in
e
s
in
L
a
p
lac
e
-
T
ra
n
s
f
o
r
m
Do
m
a
in
”
,
IEE
E
T
ra
n
s
.
o
n
M
icr
o
wa
v
e
T
h
e
o
ry
a
n
d
T
e
c
h
n
i
q
u
e
s
,
Vo
l.
4
5
,
N
o
.
5
,
p
p
.
5
6
9
-
5
7
9
,
M
a
y
1
9
9
7
.
[1
3
]
Ye
m
n
a
Be
n
sa
le
m
a
n
d
M
o
h
a
m
e
d
Na
c
e
u
r
A
b
d
e
lk
rim
,
“
M
o
d
e
li
n
g
a
n
d
S
im
u
latio
n
o
f
In
d
u
c
ti
o
n
M
o
to
r
b
a
se
d
o
n
F
in
it
e
El
e
m
e
n
t
A
n
a
l
y
sis”
,
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Po
we
r
E
lec
tro
n
ics
a
n
d
Dr
ive
S
y
ste
m
(
IJ
PE
DS
)
,
Vo
l.
7
,
No
.
4
,
p
p
.
1
1
0
0
-
1
1
0
9
,
De
c
e
m
b
e
r
2
0
1
6
.
[1
4
]
Da
v
id
M
.
P
o
z
a
r,
“
M
icro
w
a
v
e
En
g
in
e
e
rin
g
”
,
Jo
h
n
W
il
e
y
&
S
o
n
s,
1
9
9
8
.
[1
5
]
S
a
rh
a
n
M
.
M
u
sa
a
n
d
M
a
tt
h
e
w
N
.
O.
S
a
d
ik
u
,
“
F
i
n
it
e
El
e
m
e
n
t
A
n
a
l
y
sis
f
o
r
F
iv
e
T
ra
n
s
m
issio
n
L
in
e
s
in
M
u
lt
i
lay
e
r
Die
lec
tri
c
M
e
d
ia”
,
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Ad
v
a
n
c
e
s
in
Ap
p
li
e
d
S
c
ien
c
e
s
(
IJ
AA
S
)
,
V
o
l
.
1
,
N
o
.
4
,
p
p
.
1
8
1
-
1
9
0
,
De
c
e
m
b
e
r
2
0
1
2
.
[1
6
]
B.
G
u
sta
v
se
n
a
n
d
A
.
S
e
m
l
y
e
n
,
“
En
f
o
rc
in
g
p
a
ss
iv
it
y
f
o
r
A
d
m
it
tan
c
e
M
a
tri
c
e
s
a
p
p
ro
x
im
a
ted
b
y
ra
ti
o
n
a
l
f
u
n
c
ti
o
n
s”
,
IEE
E
T
ra
n
s.
P
o
we
r sy
ste
ms
,
V
o
l
.
1
6
,
N
o
.
1
,
p
p
.
9
7
-
1
0
4
,
Ja
n
2
0
0
1
.
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