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a
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24
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Feb
r
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20
26
:
3
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328
314
by
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s
s
ed
.
C
o
m
p
r
o
m
is
es
b
etwe
e
n
th
ese
f
ac
to
r
s
wer
e
an
aly
s
ed
in
o
r
d
e
r
to
o
b
tain
o
p
tim
al
p
a
r
a
m
eter
s
.
Or
o
s
z
[
9
]
p
r
esen
ted
a
f
ast
ap
p
r
o
x
im
atio
n
m
eth
o
d
u
s
ef
u
l
in
t
h
e
in
itial
d
esig
n
as
well
as
a
m
o
r
e
d
etail
ed
an
aly
s
is
o
f
in
d
u
cto
r
s
an
d
t
r
an
s
f
o
r
m
er
s
.
E
ig
h
ty
p
er
ce
n
t
o
f
a
lo
w
-
p
o
wer
co
n
v
er
ter
’
s
f
o
o
tp
r
in
t
is
o
cc
u
p
ied
b
y
p
ass
iv
e
co
m
p
o
n
en
ts
,
w
h
ich
s
er
v
e
a
v
a
r
iety
o
f
p
u
r
p
o
s
es,
in
clu
d
in
g
f
ilter
in
g
,
en
er
g
y
tr
an
s
f
er
,
g
alv
a
n
ic
i
s
o
latio
n
,
im
p
e
d
an
ce
m
atch
in
g
,
an
d
tem
p
o
r
a
r
y
elec
tr
ical
en
er
g
y
s
to
r
ag
e
.
L
i
u
et
a
l
.
[
1
0
]
p
r
esen
ted
in
h
is
ar
ti
cle
th
e
m
ain
d
ir
ec
tio
n
s
o
f
d
ev
elo
p
m
en
t a
n
d
tr
en
d
s
in
th
e
d
esig
n
o
f
p
o
wer
tr
an
s
f
o
r
m
er
s
.
T
h
e
m
a
i
n
r
e
s
e
a
r
c
h
d
i
r
e
ct
i
o
n
s
c
o
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d
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d
a
n
d
f
u
t
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r
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s
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r
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s
u
m
m
a
r
is
e
d
.
L
i
u
e
t
a
l
.
[
1
1
]
p
r
o
p
o
s
e
d
i
n
t
h
e
i
r
a
r
t
i
c
l
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c
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o
r
–
i
n
d
u
c
t
o
r
–
c
a
p
a
c
i
t
o
r
(
LLC
)
r
e
s
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n
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t
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v
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t
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it
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s
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it
c
h
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q
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y
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M
H
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p
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w
e
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d
e
v
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.
L
i
u
et
a
l
.
[
1
1
]
p
r
e
s
e
n
t
e
d
a
n
o
p
t
i
m
is
a
ti
o
n
d
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g
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m
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t
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w
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d
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f
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r
a
t
i
o
n
s
.
T
h
e
o
b
j
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c
t
i
v
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o
f
t
h
is
w
o
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k
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s
t
o
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t
u
d
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m
a
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n
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v
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v
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o
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p
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w
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r
a
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d
h
i
g
h
f
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q
u
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n
c
i
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s
.
T
h
e
tr
an
s
f
o
r
m
er
is
f
lat
in
s
h
ap
e,
with
s
q
u
ar
e
f
lat
s
p
ir
al
p
r
im
ar
y
a
n
d
s
ec
o
n
d
ar
y
m
icr
o
co
ils
.
T
h
e
d
esig
n
o
f
th
is
ty
p
e
o
f
m
icr
o
co
il
is
b
ased
o
n
th
e
s
p
ec
if
ic
atio
n
s
o
f
t
h
e
m
icr
o
co
n
v
er
ter
.
T
h
r
ee
p
o
in
ts
a
r
e
ess
en
tial
f
o
r
its
d
esig
n
:
th
e
c
h
o
ice
o
f
m
ater
ials
u
s
ed
in
its
co
n
s
tr
u
ctio
n
,
an
d
its
g
eo
m
etr
ic
an
d
elec
tr
ical
d
im
en
s
io
n
s
[
1
2
]
,
[
1
3
]
.
T
h
e
r
e
s
u
lts
o
f
th
e
d
im
en
s
io
n
in
g
will
b
e
u
s
ef
u
l
f
o
r
d
esig
n
in
g
th
e
m
ath
em
atica
l
m
o
d
e
l
an
d
p
er
f
o
r
m
i
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g
v
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r
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s
s
im
u
latio
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s
o
f
m
ag
n
eto
th
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m
al
b
eh
av
io
u
r
.
T
o
ascer
tain
t
h
e
id
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l
d
is
tr
ib
u
tio
n
o
f
cu
r
r
en
t
an
d
elec
tr
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p
o
te
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tial
in
th
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co
n
d
u
cto
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an
d
,
as
a
r
esu
lt,
to
g
et
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o
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d
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tr
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tio
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f
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es,
th
e
m
ag
n
etic
co
m
p
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en
t
en
tails
v
is
u
alizin
g
th
e
d
is
tr
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tio
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o
f
c
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r
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en
t
d
e
n
s
ity
,
m
ag
n
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f
ield
lin
es,
an
d
elec
tr
ical
p
o
ten
tial
.
Fo
r
th
e
th
er
m
al
p
ar
t
[
1
4
]
,
[
1
5
]
,
it
is
n
ec
ess
ar
y
to
v
is
u
alis
e
th
e
tem
p
er
atu
r
e
d
is
t
r
ib
u
tio
n
o
f
th
e
co
il
an
d
s
u
b
s
tr
ate.
T
h
e
n
o
v
e
l
t
y
o
f
t
h
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a
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ti
c
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n
t
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t
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d
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m
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b
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h
a
v
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r
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w
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f
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f
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w
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m
p
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l e
v
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t
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m
p
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at
u
r
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i
n
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d
i
f
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t
la
y
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o
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p
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t
.
C
o
n
d
u
c
t
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o
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t
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a
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k
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o
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c
c
o
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n
t
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te
a
d
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at
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.
I
t
s
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o
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l
d
b
e
n
o
t
e
d
t
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a
t
c
o
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tiv
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p
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c
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n
t
i
n
t
h
is
t
y
p
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o
f
s
i
t
u
a
ti
o
n
.
T
h
e
s
i
m
u
l
at
i
o
n
s
we
r
e
p
e
r
f
o
r
m
e
d
u
s
i
n
g
c
o
m
p
u
t
a
t
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o
n
s
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l
v
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r
(
C
O
MS
O
L
)
M
u
lt
i
p
h
y
s
ic
s
s
i
m
u
l
at
i
o
n
s
o
f
t
w
a
r
e
.
2.
F
L
YB
A
CK
M
I
CRO
-
CO
NV
E
RT
E
R
P
R
E
S
E
NT
AT
I
O
N
T
h
e
f
ly
b
ac
k
co
n
v
er
ter
[
1
6
]
,
[
1
7
]
,
F
ig
u
r
e
1
,
h
as
b
ee
n
c
h
o
s
e
n
b
ec
a
u
s
e
th
e
m
icr
o
-
tr
a
n
s
f
o
r
m
er
is
m
ad
e
u
p
o
f
f
ewe
r
p
ar
ts
an
d
a
s
in
g
le
wr
ap
p
ed
c
o
m
p
o
n
en
t
,
F
ig
u
r
e
2
,
a
n
d
o
f
a
s
in
g
le
s
witch
.
Mo
r
eo
v
er
,
it
is
f
r
eq
u
e
n
tly
u
s
ed
f
o
r
l
o
w
p
o
we
r
ap
p
licatio
n
s
(
<1
0
0
W
)
.
W
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o
p
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d
f
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n
p
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v
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=
12
,
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5
,
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p
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=
5
,
o
p
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r
a
t
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y
=
100
.
Fig
u
r
e
1
.
E
lectr
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s
ch
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f
ly
b
ac
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co
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tain
i
n
g
th
e
m
icr
o
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f
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r
m
er
Evaluation Warning : The document was created with Spire.PDF for Python.
T
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KOM
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T
elec
o
m
m
u
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C
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Op
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(
Ta
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315
Fig
u
r
e
2
.
3
D
m
o
d
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o
f
th
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m
ic
r
o
-
tr
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s
f
o
r
m
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2
.
1
.
M
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a
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f
o
rm
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T
h
e
v
o
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m
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m
a
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Fro
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en
s
io
n
s
will
b
e
ass
ess
ed
wh
ile
ad
h
er
in
g
to
th
e
m
icr
o
-
co
n
v
er
ter
’
s
r
e
q
u
ir
em
e
n
t
s
f
o
r
m
ag
n
etic
en
er
g
y
s
to
r
ag
e
an
d
m
ater
ial
lo
s
s
es
[
1
8
]
,
[
1
9
]
.
2
.
2
.
G
eo
m
e
t
rica
l pa
ra
m
et
er
s
ca
lcula
t
io
n
Sq
u
ar
e
g
eo
m
etr
y
m
icr
o
co
ils
ar
e
d
ef
in
e
d
b
y
a
s
et
o
f
ess
en
tial
g
eo
m
etr
ic
p
ar
am
eter
s
th
at
d
ir
ec
tly
in
f
lu
en
ce
th
eir
elec
tr
o
m
ag
n
etic
p
er
f
o
r
m
an
ce
.
T
h
e
n
u
m
b
er
o
f
tu
r
n
s
d
eter
m
in
es
th
e
wi
n
d
in
g
d
en
s
ity
an
d
co
n
tr
ib
u
tes
to
th
e
in
cr
ea
s
e
i
n
i
n
d
u
ctan
ce
.
T
h
e
wid
t
h
o
f
th
e
c
o
n
d
u
ct
o
r
an
d
its
th
ick
n
ess
p
l
ay
a
m
ajo
r
r
o
le
in
th
e
elec
tr
ical
r
esi
s
tan
ce
a
n
d
h
ea
t
d
is
s
ip
atio
n
ca
p
ac
ity
o
f
th
e
m
icr
o
co
il.
W
in
d
in
g
s
p
ac
in
g
af
f
ec
ts
b
o
t
h
m
ag
n
etic
co
u
p
lin
g
an
d
p
r
o
x
i
m
ity
lo
s
s
es.
T
h
e
to
tal
len
g
th
o
f
th
e
c
o
n
d
u
cto
r
lt
m
ak
es
it
p
o
s
s
ib
le
to
ev
alu
ate
th
e
o
v
er
all
o
h
m
ic
r
esis
tan
ce
o
f
th
e
d
ev
ice.
Fin
ally
,
th
e
o
u
ter
d
i
am
eter
d
o
u
t
an
d
in
n
er
d
iam
et
er
d
in
ch
ar
ac
ter
ize
th
e
p
h
y
s
ical
s
ize
o
f
th
e
co
il
an
d
in
f
lu
e
n
ce
th
e
m
ag
n
etic
f
i
eld
p
r
o
d
u
ce
d
at
th
e
ce
n
ter
o
f
th
e
s
tr
u
ctu
r
e.
T
h
e
s
im
u
ltan
eo
u
s
o
p
tim
izatio
n
o
f
th
ese
p
ar
am
eter
s
is
th
er
ef
o
r
e
ess
en
tial
to
d
es
ig
n
ef
f
icien
t
m
icr
o
co
ils
ad
ap
ted
to
th
e
tar
g
eted
ap
p
licatio
n
s
,
s
u
ch
as m
icr
o
elec
tr
o
n
ics d
ev
ices o
r
in
teg
r
ated
s
en
s
o
r
s
,
F
ig
u
r
e
3
.
Fig
u
r
e
3
.
Mic
r
o
-
tr
an
s
f
o
r
m
er
p
r
im
ar
y
an
d
s
ec
o
n
d
a
r
y
c
o
ils
g
eo
m
etr
ical
p
ar
am
eter
s
2
.
3
.
E
lect
rica
l pa
ra
m
et
er
s
c
a
lcula
t
io
n
T
h
e
eq
u
iv
ale
n
t
elec
tr
ical
m
o
d
el,
d
er
iv
e
d
f
r
o
m
th
e
d
iag
r
a
m
p
r
esen
ted
in
Fig
u
r
e
2
,
is
u
s
ed
f
o
r
th
e
s
im
u
latio
n
o
f
th
e
elec
tr
o
m
ag
n
etic
b
eh
av
io
r
o
f
th
e
m
icr
o
-
tr
an
s
f
o
r
m
er
[
1
8
]
,
[
1
9
]
(
s
ee
Fig
u
r
e
4
)
.
T
h
is
m
o
d
el
in
teg
r
ates a
ll th
e
elec
tr
ical
p
ar
am
eter
s
r
ep
r
esen
tativ
e
o
f
th
e
d
ev
ice:
th
e
p
r
im
ar
y
a
n
d
s
ec
o
n
d
ar
y
in
d
u
cta
n
ce
s
an
d
,
ass
o
ciate
d
r
esp
ec
tiv
ely
with
th
e
two
win
d
in
g
s
;
t
h
e
s
er
ies
r
esis
tan
ce
s
an
d
,
r
ef
lec
tin
g
th
e
o
h
m
ic
lo
s
s
es;
th
e
an
d
o
x
id
e
ca
p
ac
ities
;
th
e
r
esis
tan
ce
s
o
f
th
e
m
a
g
n
etic
lay
er
an
d
;
as
well
as
th
e
r
esi
s
tan
ce
s
an
d
an
d
th
e
ca
p
ac
itan
ce
s
,
ass
o
ciate
d
with
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
TEL
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l
C
o
n
tr
o
l
,
V
o
l.
24
,
No
.
1
,
Feb
r
u
ar
y
20
26
:
3
1
3
-
328
316
s
ilico
n
s
u
b
s
tr
ate.
Fin
ally
,
th
e
co
u
p
lin
g
ca
p
ac
itan
ce
s
an
d
s
p
ec
if
ic
to
ea
ch
win
d
in
g
,
as
well
as
th
e
m
u
tu
al
ca
p
ac
itan
ce
b
etwe
e
n
th
e
two
win
d
i
n
g
s
,
e
n
s
u
r
e
th
e
p
r
ec
is
e
m
o
d
elin
g
o
f
t
h
e
elec
tr
o
s
tatic
in
ter
ac
tio
n
s
in
ter
n
al
to
t
h
e
m
ic
r
o
-
tr
an
s
f
o
r
m
er
.
Fig
u
r
e
4
.
E
q
u
iv
alen
t e
lectr
ical
cir
cu
it o
f
th
e
m
icr
o
-
t
r
an
s
f
o
r
m
er
2
.
4
.
M
a
g
net
ic
circ
uit
dim
en
s
io
nin
g
T
h
e
tr
an
s
f
o
r
m
atio
n
r
atio
m
is
o
n
e
o
f
th
e
m
ain
elec
tr
ical
p
ar
am
eter
s
o
f
th
e
m
icr
o
-
tr
an
s
f
o
r
m
er
,
it
is
g
iv
en
b
y
:
=
=
∝
V
o
u
t
∝
−
1
V
in
(
1
)
T
h
e
p
r
im
ar
y
in
d
u
ctan
ce
L
p
is
ca
lcu
lated
f
o
r
a
m
ax
im
u
m
cu
r
r
en
t r
ip
p
le:
0
.
5
=
=
V
in
2
∝
2
2
.
.
(
2
)
T
h
e
s
ec
o
n
d
ar
y
in
d
u
ctan
ce
is
tak
en
f
r
o
m
(
2
)
.
=
2
(
3
)
T
h
u
s
,
th
e
to
tal
m
a
g
n
etic
en
er
g
y
th
at
h
as b
ee
n
s
to
r
ed
is
:
=
1
2
2
=
1
2
2
=
3
.
125
.
10
−
9
(
4
)
T
h
e
h
ig
h
est en
e
r
g
y
v
o
lu
m
e
d
e
n
s
ity
is
:
=
2
2
.
µ
=
25
.
59
/
3
(
5
)
T
h
e
v
o
lu
m
e
o
f
th
e
co
r
e
is
:
=
=
1
.
22
.
10
−
10
3
(
6
)
T
h
u
s
,
0
.
1
2
2
m
m
3
o
f
NiFe
is
r
eq
u
ir
ed
to
s
to
r
e
3
.
1
2
5
n
J
.
W
e
ch
o
s
e
th
e
s
q
u
ar
e
s
h
ap
e,
F
ig
u
r
e
3
,
f
o
r
win
d
in
g
s
with
o
u
ter
d
iam
eter
eq
u
al
to
1
5
0
0
μ
m
a
n
d
in
n
er
d
iam
eter
eq
u
al
to
7
5
0
μ
m
.
T
h
e
co
r
e
th
ic
k
n
ess
is
g
iv
en
b
y
(
7
)
:
=
2
(
7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
Op
timiz
in
g
p
la
n
a
r
micro
-
tr
a
n
s
fo
r
mer p
erfo
r
ma
n
ce
(
Ta
h
a
r
A
lili
)
317
2
.
5
.
Resul
t
s
o
f
t
he
g
e
o
m
et
ric
a
l a
nd
elec
t
rica
l sizin
g
T
ab
le
1
lis
ts
th
e
m
ain
g
eo
m
etr
ic
an
d
elec
tr
ical
p
ar
am
eter
s
o
f
th
e
s
tu
d
ied
m
icr
o
-
c
o
il.
T
h
ese
p
ar
am
eter
s
ar
e
u
s
ed
as
i
n
p
u
t
d
ata
f
o
r
th
e
elec
tr
o
m
ag
n
etic
a
n
d
th
e
r
m
al
s
im
u
latio
n
s
,
ca
r
r
ie
d
o
u
t
to
a
n
aly
ze
t
h
e
b
eh
av
io
r
o
f
th
e
m
icr
o
-
c
o
il
an
d
to
o
p
tim
ize
its
o
p
e
r
atin
g
p
er
f
o
r
m
an
ce
.
Du
e
t
o
th
e
ad
ap
tati
o
n
o
f
m
ath
e
m
atica
l
m
o
d
els
s
u
ch
as
Ma
x
well
’
s
e
q
u
atio
n
s
an
d
th
e
h
ea
t
eq
u
atio
n
to
s
im
u
late
th
e
m
ag
n
etic,
el
ec
tr
ic,
an
d
th
er
m
al
p
h
en
o
m
en
a,
a
s
et
o
f
s
im
p
lif
y
in
g
ass
u
m
p
tio
n
s
h
as
b
ee
n
in
tr
o
d
u
ce
d
in
o
r
d
er
to
r
ed
u
ce
th
e
co
m
p
lex
ity
an
d
th
e
in
h
er
en
t
m
ath
e
m
atica
l
n
o
n
lin
ea
r
ity
.
T
h
ese
ass
u
m
p
tio
n
s
ar
e
co
n
s
is
ten
t
with
th
o
s
e
co
m
m
o
n
ly
ad
o
p
ted
in
t
h
e
liter
atu
r
e
[
2
0
]
b
y
r
esear
ch
er
s
i
n
th
is
f
ield
.
−
T
h
e
is
o
tr
o
p
y
o
f
t
h
e
v
ar
io
u
s
m
ater
ials
u
n
d
er
in
v
esti
g
atio
n
.
−
T
h
e
tem
p
er
atu
r
e
af
f
ec
ts
th
e
th
er
m
al
co
n
d
u
ctiv
ity
co
e
f
f
icien
t
.
−
T
h
er
m
al
co
n
v
ec
tio
n
is
in
tr
o
d
u
ce
d
as a
b
o
u
n
d
ar
y
co
n
d
itio
n
f
o
r
th
e
s
u
b
s
tr
ate
-
m
icr
o
co
il a
s
s
em
b
ly
.
T
ab
le
1
.
Valu
es o
f
g
eo
m
et
r
ic
an
d
elec
tr
ical
p
ar
am
ete
r
s
G
e
o
me
t
r
i
c
p
a
r
a
m
e
t
e
r
s
El
e
c
t
r
i
c
a
l
p
a
r
a
m
e
t
e
r
s
d
out
=
1
5
0
0
μ
m
,
d
in
=
7
5
0
μ
m
,
e
=
5
4
.
2
7
μ
m
,
б
=
6
.
5
6
μ
m
,
n
p
=
5
,
n
s
=
2
,
w
p
=
4
6
.
3
9
μ
m
,
w
s
=
1
6
9
.
6
μ
m
,
t
p
=
1
3
.
1
3
μ
m
,
t
s
=
1
3
.
1
3
μ
m
,
s
p
=
3
5
.
7
5
μ
m
,
s
s
=
3
5
.
7
5
μ
m
,
l
p
=
2
.
2
5
c
m
,
l
ts
=
9
m
m
L
p
=
3
6
n
H
,
Rs
p
=
1
.
4
5
Ω
,
R
s
s
=
0
.
1
6
Ω
,
R
m
agp
=
1
0
3
.
9
8
K
Ω
,
R
m
ags
=
7
1
.
1
K
Ω
,
R
s
ubp
=
3
.
5
4
K
Ω
,
L
s=
6
.
2
5
N
h
,
R
s
ubs
=
2
.
4
2
K
Ω
,
C
ox
p
=
2
.
5
P
f
,
C
o
x
s
=
3
.
6
6
p
F,
C
kp
=
0
.
1
4
p
F,
C
k
=
1
0
.
7
9
p
F,
C
s
ubp
=
0
.
5
4
p
F,
C
s
ubs
=
0
.
7
9
p
F,
C
ks
=
0
.
0
5
7
p
F
.
T
h
e
ass
u
m
p
tio
n
o
f
h
o
m
o
g
en
eity
an
d
is
o
tr
o
p
y
is
b
ased
o
n
th
e
f
u
n
d
am
e
n
tal
p
r
i
n
cip
les
o
f
m
ater
ial
b
eh
av
io
r
.
I
n
g
e
n
er
al,
th
e
g
o
v
er
n
in
g
m
ath
e
m
atica
l
eq
u
atio
n
s
an
d
m
o
d
els
f
o
r
p
h
y
s
ical
p
h
en
o
m
en
a,
s
u
c
h
as
elec
tr
o
m
ag
n
etic
a
n
d
th
e
r
m
al
p
r
o
ce
s
s
es,
ar
e
f
o
r
m
u
lated
u
n
d
er
th
e
ass
u
m
p
tio
n
o
f
h
o
m
o
g
e
n
eo
u
s
an
d
is
o
tr
o
p
i
c
m
ater
ials
,
wh
er
e
th
e
s
p
atial
v
ar
iatio
n
o
f
th
e
r
m
o
p
h
y
s
ical
an
d
elec
tr
ical
p
r
o
p
e
r
ties
is
n
eg
le
cted
.
I
n
th
e
p
r
esen
t
s
tu
d
y
,
ap
p
lied
to
th
e
m
icr
o
p
lan
ar
tr
an
s
f
o
r
m
er
,
th
e
m
ater
ia
l
p
r
o
p
er
ties
ar
e
c
o
n
s
id
er
ed
in
d
ep
en
d
e
n
t
o
f
b
o
th
d
ir
ec
tio
n
a
n
d
p
o
s
itio
n
,
wh
ich
en
ab
les
th
e
d
ir
ec
t
ap
p
licatio
n
o
f
th
e
g
o
v
er
n
in
g
eq
u
ati
o
n
s
w
h
ile
s
im
p
lify
in
g
th
e
o
v
er
all
m
o
d
el.
Fu
r
t
h
er
m
o
r
e,
c
o
n
v
ec
tiv
e
ef
f
ec
ts
ar
e
n
e
g
lecte
d
with
in
th
e
f
lu
id
m
ec
h
a
n
ics
f
r
am
ewo
r
k
,
as
th
e
m
icr
o
m
etr
ic
d
im
en
s
io
n
s
o
f
th
e
tr
an
s
f
o
r
m
er
e
n
s
u
r
e,
b
ased
o
n
th
e
R
ay
leig
h
n
u
m
b
er
esti
m
atio
n
,
th
at
n
atu
r
al
co
n
v
ec
tio
n
ar
o
u
n
d
t
h
e
co
ils
i
s
n
eg
lig
ib
le.
T
h
u
s
,
air
p
a
r
ticle
m
o
tio
n
s
u
r
r
o
u
n
d
in
g
th
e
c
o
ils
is
ig
n
o
r
ed
,
a
n
d
co
n
v
ec
tiv
e
h
ea
t tr
an
s
f
er
is
o
n
l
y
ac
co
u
n
ted
f
o
r
at
th
e
b
o
u
n
d
ar
ies th
r
o
u
g
h
R
o
b
in
-
ty
p
e
b
o
u
n
d
ar
y
co
n
d
itio
n
s
.
3.
M
I
CRO
T
RAN
SFO
RM
E
R
M
AG
NE
T
O
T
H
E
R
M
AL
B
E
H
AVIO
R
3
.
1
.
M
a
t
hema
t
ica
l
m
o
del
T
h
e
s
tu
d
ied
p
h
en
o
m
en
o
n
is
m
o
d
eled
b
y
a
s
et
o
f
c
o
u
p
led
eq
u
atio
n
s
co
m
b
i
n
in
g
Ma
x
well
’
s
eq
u
atio
n
s
with
th
e
h
ea
t
e
q
u
atio
n
,
f
o
llo
w
in
g
th
e
g
eo
m
etr
ical
d
esig
n
an
d
s
izin
g
o
f
th
e
tr
an
s
f
o
r
m
e
r
.
D
im
en
s
io
n
in
g
o
f
th
e
m
icr
o
-
co
ils
o
f
p
r
im
ar
y
an
d
s
ec
o
n
d
ar
y
:
t
h
e
eq
u
atio
n
s
s
h
o
w
t
h
at
th
e
p
r
im
a
r
y
an
d
s
ec
o
n
d
ar
y
in
d
u
ctan
ce
s
o
f
th
e
m
icr
o
-
tr
an
s
f
o
r
m
er
ar
e
d
i
r
ec
tly
co
n
n
ec
ted
to
th
e
e
n
er
g
y
s
to
r
ed
.
Fo
r
a
m
ax
im
u
m
cu
r
r
en
t,
th
at
is
to
s
ay
f
o
r
=
,
=
1
2
1
2
=
1
2
2
2
,
=
=
1
2
1
2
,
1
=
,
=
=
2
2
2
.
T
h
e
v
al
u
e
o
f
th
e
p
r
im
ar
y
in
d
u
ctan
ce
o
f
th
e
m
icr
o
-
tr
an
s
f
o
r
m
er
is
d
er
iv
ed
th
er
e
f
r
o
m
:
=
2
2
2
an
d
=
(
−
1
)
V
s
V
e
.
W
ith
0
.
5
=
th
en
m
eq
u
als 0
.
4
2
.
o
f
th
e
m
i
cr
o
-
tr
an
s
f
o
r
m
er
is
=
m
2
L
p
.
T
h
e
d
en
s
ity
o
f
en
er
g
y
is
g
iv
e
n
b
y
(
8
)
:
=
2
2
.
0
(
8
)
3
.
1
.
1
.
M
a
x
well
’
s
equa
t
io
ns
T
h
e
elec
tr
o
m
a
g
n
etic
p
h
en
o
m
e
n
o
n
is
g
o
v
er
n
ed
b
y
Ma
x
well
’
s
eq
u
atio
n
s
,
th
e
r
eso
l
u
tio
n
o
f
th
e
latter
will
allo
w
u
s
to
v
is
u
alize
th
e
m
ag
n
etic
b
eh
av
i
o
r
o
f
th
e
m
icr
o
tr
an
s
f
o
r
m
er
[
2
0
]
,
х
⃑
⃑
=
J
,
х
=
B
⃑
⃑
,
⃑
=
−
∇
⃑
⃑
V
−
,
=
⃑
+
⃑
⃑
,
=
0
,
⃑
=
µ
0
µ
⃑
⃑
,
⃑
⃑
=
0
⃑
.
3
.
2
.
P
hy
s
ica
l
m
o
del
B
ased
o
n
th
e
in
itial
s
p
ec
if
icatio
n
s
,
th
e
ch
ar
ac
ter
is
tics
o
f
th
e
m
icr
o
-
co
n
v
er
ter
ar
e
estab
lis
h
ed
,
th
u
s
f
o
r
m
in
g
th
e
s
tar
tin
g
p
o
in
t
f
o
r
th
e
m
icr
o
-
tr
an
s
f
o
r
m
er
’
s
d
esig
n
.
T
h
e
latter
co
n
s
is
ts
o
f
two
c
o
ils
d
ep
o
s
ited
o
n
a
m
ag
n
etic
m
ater
ial,
s
ep
ar
ate
d
b
y
a
d
ielec
tr
ic
lay
er
th
at
ac
ts
b
o
th
as
an
elec
tr
ical
in
s
u
lato
r
an
d
as
a
m
ag
n
etic
co
u
p
lin
g
s
u
p
p
o
r
t (
Fig
u
r
e
5
)
.
F
ig
u
r
e
6
illu
s
tr
ates th
e
s
tu
d
y
a
r
ea
an
d
its
b
o
u
n
d
ar
ies.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
TEL
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l
C
o
n
tr
o
l
,
V
o
l.
24
,
No
.
1
,
Feb
r
u
ar
y
20
26
:
3
1
3
-
328
318
Fig
u
r
e
5
.
Ph
y
s
ical
m
o
d
el
o
f
a
m
icr
o
-
p
lan
a
r
tr
an
s
f
o
r
m
er
Fig
u
r
e
6.
Do
m
ain
b
o
u
n
d
ar
ies s
tu
d
y
o
f
th
e
p
lan
ar
tr
an
s
f
o
r
m
er
3
.
3
.
G
ener
a
l c
o
nd
it
io
ns
o
f
s
im
ula
t
io
n
Fig
u
r
e
6
d
is
p
lay
s
th
e
b
o
u
n
d
ar
y
co
n
d
itio
n
s
o
n
th
e
s
tu
d
y
d
o
m
ain
’
s
b
o
r
d
e
r
s
,
wh
ich
ar
e
:
(
⃑
)
=
0
(
9
)
+
+
=
0
(
10
)
⃑
.
=
0
(
11
)
W
h
er
e:
⃑
=
+
+
⃑
is
th
e
n
o
r
m
al
v
ec
t
o
r
to
th
e
b
o
u
n
d
ar
y
f
r
o
m
wh
er
e:
.
+
.
+
.
=
0
(
12
)
I
n
o
u
r
s
tu
d
y
d
o
m
ain
,
th
e
s
im
u
latio
n
also
n
ee
d
s
in
itial
co
n
d
itio
n
s
.
Fig
u
r
e
s
7
(
a
)
an
d
(
b
)
p
r
esen
t
th
e
cu
r
r
en
t in
p
u
t a
n
d
o
u
tp
u
t,
r
esp
e
ctiv
ely
.
(
a)
(
b
)
Fig
u
r
e
7
.
I
n
itial o
p
er
atin
g
co
n
d
itio
n
s
o
f
th
e
p
lan
ar
tr
a
n
s
f
o
r
m
er
:
(
a)
i
n
p
u
t a
n
d
o
u
tp
u
t+
o
f
th
e
p
r
im
ar
y
cu
r
r
e
n
t
an
d
(
b
)
i
n
p
u
t a
n
d
o
u
tp
u
t o
f
t
h
e
s
ec
o
n
d
ar
y
cu
r
r
e
n
t
3
.
4
.
M
esh
ing
o
f
s
t
ud
y
do
m
a
i
n
T
h
e
C
OM
SOL
Mu
ltip
h
y
s
ics
f
in
ite
elem
en
t
m
eth
o
d
(
FEM
)
was
u
s
ed
f
o
r
th
e
n
u
m
e
r
ical
s
im
u
latio
n
,
wh
er
e
th
e
g
o
v
e
r
n
in
g
e
q
u
atio
n
s
o
f
th
e
s
tu
d
ied
p
h
en
o
m
en
o
n
h
av
e
b
ee
n
d
is
cr
etize
d
an
d
tr
an
s
f
o
r
m
ed
in
t
o
a
s
o
lv
ab
le
alg
eb
r
aic
s
y
s
tem
.
A
tetr
ah
ed
r
al
m
esh
h
as
b
ee
n
s
elec
ted
d
u
e
to
th
e
g
eo
m
etr
ical
co
m
p
lex
ity
o
f
th
e
d
o
m
ain
;
F
ig
u
r
e
8
,
p
ar
ticu
lar
l
y
th
e
in
tr
icate
co
il
s
tr
u
ctu
r
e
s
o
f
th
e
tr
an
s
f
o
r
m
er
,
w
h
ich
m
ak
es
tetr
ah
ed
r
al
elem
en
ts
m
o
r
e
s
u
itab
le
t
h
an
s
tr
u
ctu
r
ed
m
esh
es
s
u
ch
as
h
e
x
ah
ed
r
al
o
n
es.
A
r
ig
o
r
o
u
s
m
esh
co
n
v
er
g
e
n
ce
test
h
as
b
ee
n
p
er
f
o
r
m
ed
b
y
p
r
o
g
r
e
s
s
iv
ely
r
ef
in
in
g
th
e
m
esh
u
n
til
th
e
n
u
m
er
ical
r
esu
lts
b
ec
am
e
in
d
ep
en
d
en
t
o
f
th
e
elem
en
t
s
ize,
b
o
th
in
th
e
m
ag
n
eto
elec
tr
ic
an
d
th
e
r
m
al
d
o
m
ain
s
.
T
h
e
f
in
al
m
esh
en
s
u
r
ed
an
ac
ce
p
ta
b
le
co
m
p
r
o
m
is
e
b
etwe
en
ac
cu
r
ac
y
an
d
c
o
m
p
u
tatio
n
al
co
s
t,
with
th
e
r
elativ
e
er
r
o
r
c
o
n
s
tr
ain
ed
b
elo
w
1
0
-
5.
L
’e
n
t
r
é
e
d
u
c
o
u
r
a
n
t
I
=
0
,
5
A
L
a
so
r
t
i
e
d
u
c
o
u
r
a
n
t
V = 0
V
I
in
=
0
.
5
A
I
out
V
=
0
V
L
’e
n
t
r
é
e
d
u
c
o
u
r
a
n
t
i
n
d
u
i
t
I
=
1
,
2
5
A
L
a
so
r
t
i
e
d
u
c
o
u
r
a
n
t
i
n
d
u
i
t
V = 0
V
n
I
out
V=
0
V
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
Op
timiz
in
g
p
la
n
a
r
micro
-
tr
a
n
s
fo
r
mer p
erfo
r
ma
n
ce
(
Ta
h
a
r
A
lili
)
319
Fig
u
r
e
8
.
Me
s
h
o
f
m
icr
o
-
p
lan
a
r
tr
an
s
f
o
r
m
e
r
4.
SI
M
UL
A
T
I
O
N
R
E
S
UL
T
S
AND
DIS
CUSS
I
O
N
4
.
1
.
E
lect
ric
po
t
ent
ia
l
a
nd
m
a
g
net
ic
f
ield dis
t
ributio
n
Fig
u
r
e
9
s
h
o
ws
th
e
d
is
tr
ib
u
tio
n
o
f
elec
tr
ical
p
o
ten
tial
with
in
th
e
p
r
im
ar
y
an
d
s
ec
o
n
d
a
r
y
w
in
d
in
g
s
o
f
th
e
m
icr
o
tr
an
s
f
o
r
m
er
.
I
t
ca
n
b
e
s
ee
n
th
at
th
e
p
o
ten
tial
r
ea
ch
es
its
m
ax
im
u
m
v
alu
e
at
t
h
e
cu
r
r
e
n
t
in
jectio
n
p
o
in
t
an
d
th
en
g
r
ad
u
ally
d
ec
r
ea
s
es
alo
n
g
th
e
s
p
ir
al
d
u
e
t
o
th
e
in
tr
in
s
ic
r
esis
tiv
ity
o
f
t
h
e
co
n
d
u
cto
r
.
T
h
is
d
ec
r
ea
s
e
r
ef
lects
th
e
p
r
esen
ce
o
f
a
d
is
tr
ib
u
ted
o
h
m
ic
r
esis
tan
ce
,
r
esp
o
n
s
ib
le
f
o
r
e
n
er
g
y
d
is
s
ip
atio
n
th
r
o
u
g
h
J
o
u
le
h
ea
tin
g
.
T
h
u
s
,
th
e
r
eg
io
n
s
wh
er
e
th
e
v
o
ltag
e
d
r
o
p
is
m
o
r
e
p
r
o
n
o
u
n
ce
d
co
r
r
esp
o
n
d
to
th
e
ar
ea
s
o
f
m
o
s
t
s
ig
n
if
ican
t
p
o
wer
lo
s
s
,
r
ef
lec
tin
g
th
e
d
ir
ec
t
in
f
lu
en
ce
o
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t
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ater
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tr
ical
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r
o
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e
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er
all
b
eh
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io
r
o
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t
h
e
d
ev
ice.
Fig
u
r
e
1
0
s
h
o
w
th
e
d
is
tr
ib
u
tio
n
o
f
th
e
m
ag
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etic
f
ield
with
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e
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o
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c
o
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in
t
h
e
m
icr
o
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o
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er
.
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t
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n
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e
o
b
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er
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ed
th
at
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e
m
ag
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etic
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ield
in
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en
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ity
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ig
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ter
o
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ar
ticu
lar
ly
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i
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er
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o
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s
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e
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c
u
r
r
e
n
t
d
e
n
s
ity
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o
r
e
co
n
ce
n
tr
ated
.
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h
is
s
tr
o
n
g
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lizatio
n
o
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th
e
f
ield
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a
d
ir
ec
t
co
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ce
o
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th
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il
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etr
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th
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p
r
o
x
i
m
ity
o
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th
e
cu
r
r
en
t
-
ca
r
r
y
in
g
co
n
d
u
cto
r
s
,
wh
ich
en
h
an
ce
th
e
m
ag
n
etic
f
lu
x
lin
k
a
g
e
in
th
e
ce
n
tr
al
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e
g
io
n
.
As
th
e
d
is
tan
ce
f
r
o
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t
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il
ce
n
ter
i
n
cr
ea
s
es
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war
d
th
e
o
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te
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ed
g
es,
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e
m
ag
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etic
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ield
g
r
ad
u
ally
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ec
r
ea
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es
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u
e
t
o
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er
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io
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th
e
s
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r
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o
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n
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g
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ed
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u
m
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I
n
th
e
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s
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o
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th
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lete
m
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o
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t
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s
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e
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u
p
er
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o
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itio
n
o
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f
ield
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g
en
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ated
b
y
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e
p
r
im
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y
a
n
d
s
ec
o
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d
ar
y
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d
in
g
s
lead
s
to
a
m
o
r
e
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o
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p
lex
d
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tr
ib
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tio
n
,
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r
e
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io
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o
f
h
ig
h
f
ield
in
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ity
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e
o
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er
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ed
i
n
th
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icin
ity
o
f
b
o
th
c
o
ils
,
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ile
th
e
f
ield
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tr
en
g
th
d
im
in
is
h
es
f
u
r
t
h
er
awa
y
f
r
o
m
th
e
ac
tiv
e
m
ag
n
etic
r
e
g
io
n
[
2
0
]
,
[
2
1
]
.
Fig
u
r
e
9
.
Po
ten
tial d
is
tr
ib
u
tio
n
in
th
e
co
ils
o
f
t
h
e
p
lan
ar
tr
an
s
f
o
r
m
er
Fig
u
r
e
1
0
.
Ma
g
n
etic
f
ield
d
is
tr
ib
u
tio
n
in
t
h
e
m
icr
o
-
tr
an
s
f
o
r
m
er
4
.
2
.
Curre
nt
dens
it
y
dis
t
rib
utio
n in t
he
co
nd
uct
o
rs
So
lv
in
g
Ma
x
well
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s
eq
u
atio
n
s
[
2
0
]
allo
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o
r
a
t
h
r
ee
-
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im
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r
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t
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en
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with
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s
p
r
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etailed
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er
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th
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u
ctu
r
e
’
s
elec
tr
o
m
ag
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b
eh
a
v
io
r
.
Fig
u
r
es
1
1
(
a)
an
d
(
b
)
illu
s
tr
ate
t
h
e
cu
r
r
en
t
d
en
s
ity
d
is
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ib
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tio
n
in
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e
p
r
im
a
r
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d
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o
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ar
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win
d
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g
s
o
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th
e
d
e
v
ice,
r
esp
ec
tiv
ely
.
I
t
ap
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ea
r
s
t
h
at
th
e
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r
r
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t
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en
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ity
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h
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a
m
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im
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o
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ted
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r
in
s
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esis
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o
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t
h
e
co
n
d
u
ctiv
e
m
ater
ial.
T
h
is
d
is
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ib
u
tio
n
is
n
o
n
-
u
n
if
o
r
m
a
lo
n
g
th
e
s
p
ir
al:
h
i
g
h
er
cu
r
r
e
n
t
co
n
ce
n
tr
atio
n
s
ar
e
o
b
s
er
v
ed
at
th
e
co
r
n
er
s
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
TEL
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l
C
o
n
tr
o
l
,
V
o
l.
24
,
No
.
1
,
Feb
r
u
ar
y
20
26
:
3
1
3
-
328
320
g
en
er
atin
g
ar
ea
s
o
f
lo
ca
lly
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cr
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ed
r
esis
tan
ce
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th
er
ef
o
r
e
g
r
ea
ter
o
h
m
ic
lo
s
s
es.
T
h
ese
d
is
tr
ib
u
tio
n
ir
r
eg
u
lar
ities
ar
e
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ir
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tly
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elat
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e
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eo
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et
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ig
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h
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ath
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r
th
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r
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,
s
k
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r
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f
ec
ts
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e
clea
r
ly
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m
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m
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n
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d
ly
b
etwe
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tu
r
n
s
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T
h
ese
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tr
o
m
ag
n
etic
p
h
en
o
m
en
a
co
n
tr
i
b
u
te
to
an
in
cr
ea
s
e
i
n
J
o
u
le
ef
f
ec
t
lo
s
s
es
an
d
s
ig
n
if
ican
tly
in
f
lu
e
n
ce
th
e
o
v
er
all
p
er
f
o
r
m
an
ce
o
f
th
e
m
icr
o
tr
an
s
f
o
r
m
e
r
,
p
a
r
ticu
lar
ly
in
ter
m
s
o
f
ef
f
icien
cy
an
d
th
er
m
al
b
eh
av
i
o
r
.
(
a)
(
b
)
Fig
u
r
e
1
1
.
C
u
r
r
en
t d
is
tr
ib
u
ti
o
n
in
th
e
m
icr
o
-
tr
an
s
f
o
r
m
er
:
(
a)
p
r
im
ar
y
a
n
d
(
b
)
s
ec
o
n
d
ar
y
4
.3
.
M
a
g
net
ic
f
ield dis
t
ributio
n v
s
t
he
g
a
p
Fig
u
r
e
1
2
s
h
o
ws
th
e
d
is
tr
ib
u
tio
n
o
f
m
ag
n
etic
f
ield
lin
es
wit
h
in
th
e
m
icr
o
tr
an
s
f
o
r
m
er
f
o
r
d
if
f
er
en
t
air
g
ap
v
alu
es,
c
o
r
r
esp
o
n
d
in
g
to
t
h
e
s
p
ac
e
s
ep
ar
atin
g
t
h
e
two
m
icr
o
co
ils
.
Fo
r
s
m
all
air
g
a
p
v
a
lu
es,
th
e
f
ield
lin
es
ar
e
m
o
s
tly
co
n
f
i
n
ed
to
t
h
e
ce
n
tr
al
m
ag
n
etic
r
e
g
io
n
,
t
h
u
s
en
s
u
r
in
g
o
p
tim
al
c
o
u
p
lin
g
b
etw
ee
n
th
e
p
r
im
a
r
y
an
d
s
ec
o
n
d
ar
y
win
d
in
g
s
.
C
o
n
v
e
r
s
ely
,
as
th
e
air
g
ap
in
cr
ea
s
es
,
a
p
r
o
g
r
ess
iv
e
d
is
p
er
s
io
n
o
f
th
e
f
ield
lin
es
is
o
b
s
er
v
ed
,
i
n
d
icatin
g
g
r
ea
ter
m
ag
n
etic
leak
ag
e.
T
h
is
d
is
p
er
s
io
n
r
ed
u
ce
s
th
e
ef
f
icien
c
y
o
f
th
e
m
ag
n
etic
co
u
p
lin
g
an
d
r
esu
lts
in
a
s
ig
n
if
ican
t d
ec
r
ea
s
e
in
th
e
in
d
u
cta
n
ce
o
f
b
o
th
win
d
in
g
s
.
Fig
u
r
e
1
3
illu
s
tr
ates
th
is
ev
o
lu
tio
n
b
y
s
h
o
win
g
th
e
v
a
r
iatio
n
o
f
in
d
u
ctan
ce
as
a
f
u
n
ctio
n
o
f
th
e
air
g
ap
f
o
r
th
e
p
r
im
a
r
y
an
d
s
ec
o
n
d
ar
y
co
ils
.
T
h
e
r
esu
lts
s
h
o
w
t
h
at
th
e
in
d
u
ctan
ce
v
alu
es
ar
e
m
ax
im
u
m
wh
en
th
e
air
g
ap
is
s
m
all,
a
co
n
d
itio
n
th
at
f
av
o
r
s
th
e
co
n
ce
n
tr
atio
n
o
f
m
ag
n
etic
f
lu
x
in
t
h
e
m
ag
n
etic
m
ater
ial.
As th
e
air
g
ap
wid
en
s
,
th
e
p
r
o
p
o
r
tio
n
o
f
f
lu
x
escap
in
g
in
to
th
e
air
i
n
cr
ea
s
es,
lead
in
g
to
a
p
r
o
g
r
e
s
s
iv
e
r
ed
u
ctio
n
in
in
d
u
ctan
ce
.
T
h
is
b
e
h
av
io
r
h
ig
h
lig
h
ts
th
e
d
ir
ec
t
d
e
p
en
d
e
n
ce
o
f
th
e
m
icr
o
tr
a
n
s
f
o
r
m
er
’
s
elec
tr
o
m
ag
n
eti
c
p
er
f
o
r
m
an
ce
o
n
th
e
air
g
ap
g
e
o
m
etr
y
.
Fin
ally
,
Fig
u
r
e
1
4
illu
s
tr
ates
th
e
o
v
er
all
p
h
y
s
ical
m
o
d
el
o
f
th
e
m
icr
o
tr
an
s
f
o
r
m
er
,
in
teg
r
atin
g
th
e
v
ar
io
u
s
elec
tr
o
m
a
g
n
etic
an
d
g
eo
m
etr
ic
co
m
p
o
n
e
n
ts
o
f
th
e
d
ev
ice.
T
h
is
m
o
d
el
p
r
o
v
id
es
an
ess
en
tial
b
asis
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o
r
u
n
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er
s
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d
i
n
g
t
h
e
c
o
u
p
lin
g
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etwe
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o
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an
d
f
o
r
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ti
m
izin
g
th
e
co
m
p
o
n
e
n
t
’
s
ef
f
icien
cy
in
m
icr
o
s
co
p
ic
p
o
wer
co
n
v
er
s
io
n
a
p
p
licatio
n
s
.
Fig
u
r
e
1
2
.
L
in
es d
is
tr
ib
u
tio
n
m
ag
n
etic
f
ield
f
o
r
d
i
f
f
er
en
t
g
a
p
s
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
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Op
timiz
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mer p
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(
Ta
h
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r
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lili
)
321
Fig
u
r
e
1
3
.
Var
iatio
n
o
f
th
e
in
d
u
ctan
ce
o
f
t
h
e
co
il
ac
co
r
d
in
g
to
th
e
g
ap
Fig
u
r
e
1
4
.
L
o
n
g
itu
d
in
al
s
ec
tio
n
o
f
a
m
icr
o
-
tr
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f
o
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er
5.
M
I
CRO
-
T
RAN
SFO
RM
E
R
T
H
E
R
M
A
L
B
E
H
AVIO
UR
5.
1
.
P
hy
s
ica
l
m
o
del
Fo
r
th
e
s
tu
d
y
o
f
th
e
s
tead
y
-
s
tate
th
er
m
al
b
eh
a
v
io
r
,
we
s
elec
ted
a
m
o
d
el
d
escr
ib
ed
b
y
th
e
h
ea
t
eq
u
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n
in
wh
ich
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co
n
d
u
ct
o
r
is
f
o
r
m
ed
o
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c
o
n
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cto
r
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,
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e
in
s
u
latin
g
lay
er
is
Kap
to
n
,
th
e
m
ag
n
etic
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r
e
is
NiFe
an
d
th
e
s
u
b
s
tr
ate
is
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ilic
o
n
,
s
ee
F
ig
u
r
e
1
4
.
5
.
2
.
M
a
t
hema
t
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l
m
o
del
I
s
u
s
ed
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e
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e
r
atu
r
e
d
is
tr
ib
u
tio
n
in
a
s
p
ec
if
ic
ar
ea
wh
ile
ac
co
u
n
tin
g
f
o
r
t
h
e
v
ar
io
u
s
tr
an
s
m
is
s
io
n
m
o
d
es in
(
1
3
)
[
2
2
]
,
[
2
3
]
.
[
+
⃑
]
=
(
)
+
(
13
)
:
s
o
u
r
ce
ter
m
i
f
it
is
an
in
t
er
n
al
h
ea
t
g
en
er
atio
n
.
E
ac
h
ter
m
o
f
t
h
is
eq
u
atio
n
h
as
a
p
h
y
s
ical
m
ea
n
in
g
tr
an
s
latin
g
th
e
th
er
m
al
p
h
e
n
o
m
en
o
n
in
to
m
ath
em
atica
l
liter
atu
r
e.
T
h
e
in
d
ex
i
co
r
r
esp
o
n
d
s
to
th
e
n
at
u
r
e
o
f
th
e
m
ater
ial:
c
o
p
p
e
r
,
p
r
in
ted
cir
cu
it
b
o
ar
d
(
PC
B
)
o
r
air
.
T
h
e
n
at
u
r
e
o
f
t
h
e
m
ater
ial
is
r
ep
r
esen
ted
b
y
th
e
in
d
e
x
:
co
p
p
er
,
PC
B
,
o
r
air
,
tem
p
er
at
u
r
e
[
K]
,
air
v
elo
city
(
m
/s
)
if
i
n
m
o
tio
n
(
c
o
n
v
ec
tio
n
)
,
d
u
r
atio
n
[
s
]
,
s
o
u
r
ce
ter
m
th
at
g
en
er
ates
an
in
ter
n
al
h
ea
t
f
lo
w
[
W
/m
3
]
,
m
ater
ial
d
en
s
ity
[
Kg
/m
3
]
,
m
ater
ial
h
ea
t
ca
p
a
city
[
J
/Kg
.
K]
,
an
d
m
ater
ial
th
er
m
al
co
n
d
u
ctiv
ity
[
W
/m
.
K]
.
E
ac
h
ter
m
o
f
th
is
eq
u
atio
n
h
as
a
p
h
y
s
ical
m
ea
n
in
g
tr
an
s
latin
g
th
e
th
er
m
al
p
h
e
n
o
m
en
o
n
in
t
o
m
a
th
em
atica
l
liter
atu
r
e.
T
h
e
f
o
llo
win
g
ter
m
s
ar
e
u
s
ed
ac
c
u
m
u
lativ
e
ter
m
wh
ich
m
ea
n
s
th
e
s
to
r
ag
e
o
f
h
ea
t
d
u
r
in
g
tim
e
,
co
n
v
ec
tiv
e
te
r
m
(
ad
v
ec
tiv
e
)
if
th
er
e
is
a
m
o
v
em
en
t
o
f
a
s
elf
-
s
u
p
p
o
r
tin
g
f
lu
id
,
d
if
f
u
s
iv
e
ter
m
(
co
n
d
u
ctiv
e)
tr
a
n
s
lates
th
e
way
o
f
p
r
o
p
ag
atio
n
ac
co
r
d
in
g
to
th
e
n
atu
r
e
o
f
th
e
m
ater
ial,
s
o
u
r
ce
ter
m
i
f
it is
an
in
ter
n
al
g
en
e
r
atio
n
o
f
h
ea
t.
5
.
3
.
Sim
pli
f
ica
t
i
o
n o
f
t
he
he
a
t
equa
t
io
n a
cc
o
rding
t
o
t
he
co
ns
idered
a
s
s
um
ptio
ns
I
n
th
is
s
ec
tio
n
,
th
e
g
en
e
r
al
h
e
at
eq
u
atio
n
is
s
im
p
lifie
d
b
y
ta
k
in
g
in
to
ac
c
o
u
n
t
th
e
ass
u
m
p
tio
n
s
m
ad
e
f
o
r
th
e
m
icr
o
tr
a
n
s
f
o
r
m
er
s
tu
d
y
.
T
h
ese
ass
u
m
p
tio
n
s
m
a
in
ly
co
n
ce
r
n
s
tead
y
-
s
tate
c
o
n
d
itio
n
s
,
m
ater
ial
h
o
m
o
g
en
eity
,
an
d
th
e
g
eo
m
et
r
ic
s
y
m
m
etr
y
o
f
th
e
s
tr
u
ctu
r
e.
T
h
ey
allo
w
u
s
to
n
e
g
lect
ce
r
t
ain
co
n
d
u
ctio
n
an
d
co
n
v
ec
tio
n
te
r
m
s
,
th
u
s
r
ed
u
ci
n
g
th
e
co
m
p
lete
eq
u
atio
n
to
a
f
o
r
m
m
o
r
e
u
s
ab
le
f
o
r
th
e
th
e
r
m
al
an
aly
s
is
o
f
th
e
d
ev
ice.
T
h
is
s
im
p
lific
atio
n
is
an
ess
en
tial
s
tep
in
estab
lis
h
in
g
a
th
er
m
al
m
o
d
el
co
n
s
is
ten
t
with
th
e
ac
tu
al
o
p
er
atin
g
c
o
n
d
itio
n
s
.
W
e
ca
n
tr
an
s
cr
ib
e
(
2
3
)
in
g
en
er
al
wr
itin
g
,
s
in
ce
o
u
r
t
h
er
m
al
s
tu
d
y
is
co
n
d
u
cte
d
in
th
r
ee
d
im
en
s
io
n
s
,
b
y
s
u
p
p
o
s
in
g
:
⃑
=
(
u
,
v
,
w
)
an
d
=
(
λ
ix
,
λ
iy
,
λ
iz
)
I
(
+
+
+
)
=
∂
∂
x
(
λ
ix
∂
T
∂
x
)
+
∂
∂
y
(
λ
iy
∂
T
∂
y
)
+
∂
∂
z
(
λ
iz
∂
T
∂
z
)
+
p
(
1
4
)
−
Neg
lig
ib
le
co
n
v
ec
tio
n
:
=
=
=
0
=
∂
∂
x
(
λ
ix
∂
T
∂
x
)
+
∂
∂
y
(
λ
iy
∂
T
∂
y
)
+
∂
∂
z
(
λ
iz
∂
T
∂
z
)
+
p
(
1
5
)
K
K
N
i
F
e
N
i
F
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
TEL
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l
C
o
n
tr
o
l
,
V
o
l.
24
,
No
.
1
,
Feb
r
u
ar
y
20
26
:
3
1
3
-
328
322
−
Ma
ter
ials
h
o
m
o
g
en
eity
T
o
=
=
an
d
ar
e
co
n
s
tan
ts
,
=
(
2
2
+
2
2
+
2
2
)
+
(
1
6
)
−
I
n
th
e
s
tatio
n
ar
y
ca
s
e
T
h
e
s
o
u
r
ce
ter
m
r
ep
r
esen
ts
th
e
h
ea
t f
lu
x
g
en
er
ate
d
b
y
th
e
J
o
u
le
ef
f
ec
t in
th
e
c
o
n
d
u
cto
r
:
(
2
2
+
2
2
+
2
2
)
+
=
0
(
1
7
)
Po
wer
lo
s
t b
y
J
o
u
le
lo
s
s
:
=
2
(
1
8
)
B
y
r
ep
lacin
g
th
e
r
esis
tan
ce
f
o
r
m
u
la:
=
0
2
(
1
9
)
B
y
ex
p
an
d
in
g
th
e
s
o
u
r
ce
ter
m
:
=
(
2
0
)
: c
o
n
d
u
ct
o
r
v
o
lu
m
e
3
p
=
ρ
0
L
VS
m
o
y
I
2
(
2
1
)
=
0
.
2
=
0
2
2
(
2
2
)
=
0
2
(
2
3
)
T
h
e
cu
r
r
e
n
t d
en
s
ity
v
ec
to
r
is
:
=
⃑
+
⃑
⃑
+
⃑
⃑
⃑
‖
‖
2
=
2
=
2
+
2
+
2
(
2
4
)
W
e
r
ep
lace
it in
(
2
5
)
:
=
0
(
2
+
2
+
2
)
(
2
5
)
Fin
ally
,
o
u
r
e
q
u
atio
n
t
o
s
o
lv
e
i
s
:
(
2
2
+
2
2
+
2
2
)
+
0
(
2
+
2
+
2
)
=
0
(
2
6
)
5
.
4
.
G
ener
a
l c
o
nd
it
io
ns
o
f
s
im
ula
t
io
n
a
nd
b
o
un
da
ry
co
nd
it
io
ns
T
h
e
tem
p
e
r
atu
r
e
a
n
d
th
er
m
al
co
n
v
ec
ti
o
n
im
p
o
s
ed
as
c
o
n
d
itio
n
s
at
th
e
b
o
u
n
d
ar
ies
o
f
th
e
p
lan
ar
s
u
b
s
tr
ate
-
co
il
ass
em
b
ly
d
eter
m
in
e
th
e
th
er
m
al
co
n
d
u
ctiv
i
ty
co
ef
f
icien
t
an
d
t
h
e
is
o
tr
o
p
y
o
f
th
e
v
ar
io
u
s
m
ater
ials
in
th
e
s
tu
d
y
d
o
m
ain
.
T
h
e
ter
m
“
m
icr
o
-
co
il,
”
wh
ic
h
is
a
h
ea
t
s
o
u
r
ce
,
is
in
tr
o
d
u
c
ed
in
d
etail
in
(
2
6
)
.
T
h
e
co
il,
s
u
b
s
tr
ate,
an
d
air
ar
e
all
ass
u
m
ed
to
b
e
at
r
o
o
m
t
em
p
er
atu
r
e
(
2
0
°C
)
at
tim
e
=
0
.
A
co
n
v
ec
tiv
e
f
lo
w
is
s
u
p
p
lied
to
th
e
ai
r
b
o
x
’
s
b
o
u
n
d
a
r
ies,
g
iv
en
b
y
(
2
7
)
[
2
4
]
,
[
2
5
]
:
−
〉
=
ℎ
0
(
−
∞
)
(2
7
)
:
air
co
n
d
u
ctiv
ity
[
W
/m
.
°K],
:
d
ir
ec
tio
n
n
o
r
m
al
t
o
th
e
b
o
r
d
er
[
m
]
,
ℎ
0
:
air
co
n
v
ec
tio
n
co
ef
f
icien
t
[
W
/m
2
.
°K],
∞
: a
m
b
ien
t te
m
p
e
r
a
tu
r
e.
Evaluation Warning : The document was created with Spire.PDF for Python.