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sa
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m
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s a
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g
).
K
ey
w
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d
s
:
C
ascad
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q
u
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t c
ir
cu
it
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lectr
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m
ac
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alien
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CC B
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m
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1
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7
]
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at
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m
i
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
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lec
&
C
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m
p
E
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g
,
Vo
l.
11
,
No
.
2
,
A
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r
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2
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2
1
:
1
1
2
3
-
1129
1124
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[
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f
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r
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tech
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g
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s
talla
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s
[
2
1
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2
7
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.
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th
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s
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alie
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m
-
L
io
u
v
ille
eig
en
f
u
n
ctio
n
s
(
in
t
h
e
zo
n
e
o
f
alter
n
atin
g
p
o
les
an
d
air
s
p
ac
es
b
et
w
ee
n
p
o
les)
an
d
m
a
n
y
s
in
u
s
o
id
al
f
u
n
c
tio
n
s
(
in
t
h
e
air
g
ap
)
.
Ne
v
er
th
ele
s
s
,
th
e
a
u
th
o
r
d
ev
elo
p
ed
th
e
ap
p
r
o
x
i
m
ate
m
e
th
o
d
f
o
r
m
o
d
elin
g
th
e
m
a
g
n
et
ic
f
ield
o
f
th
e
s
alie
n
t
-
p
o
le
elec
tr
ic
m
a
ch
in
e
s
w
h
en
o
n
l
y
o
n
e
p
iece
wis
e
co
n
ti
n
u
o
u
s
Stu
r
m
-
L
io
u
v
ill
e
eig
en
f
u
n
ctio
n
i
s
u
s
ed
(
i
n
t
h
e
zo
n
e
o
f
p
o
les)
a
n
d
m
an
y
s
i
n
u
s
o
id
al
f
u
n
ctio
n
s
(
in
t
h
e
air
g
ap
)
[
3
1
,
3
2
]
.
I
n
th
is
ca
s
e,
it
b
ec
o
m
es
p
o
s
s
ib
le
to
tr
an
s
f
o
r
m
th
e
g
e
n
er
al
s
o
l
u
tio
n
o
f
t
h
e
p
ar
tial
d
if
f
er
e
n
tial
eq
u
atio
n
in
to
f
o
u
r
-
ter
m
i
n
al
n
et
w
o
r
k
eq
u
atio
n
s
a
n
d
to
cr
ea
te
t
h
e
ca
s
ca
d
e
eq
u
iv
ale
n
t
cir
c
u
it
o
f
t
h
e
s
alien
t
-
p
o
le
ele
ctr
ic
m
ac
h
in
e
[
3
3
-
3
6
]
.
T
h
is
p
ap
e
r
de
als
w
it
h
t
h
e
s
a
m
e
s
u
b
j
ec
t
as
[
3
6
]
.
Ho
w
e
v
er
,
as
o
p
p
o
s
ed
t
o
[
3
6
]
,
th
e
A
-
H
-
cir
cu
it
o
f
t
h
e
elec
tr
ic
m
ac
h
i
n
e
is
cr
ea
ted
w
ith
o
u
t
u
s
i
n
g
p
iece
w
i
s
e
co
n
ti
n
u
o
u
s
S
tu
r
m
-
L
io
u
v
ille
ei
g
en
f
u
n
c
tio
n
s
(
b
u
t
als
o
w
it
h
o
u
t
p
r
o
p
er
ties
av
er
ag
i
n
g
)
.
2.
T
H
E
E
Q
U
I
VA
L
E
NT
A
-
H
-
CIRCUI
T
O
F
T
H
E
RO
T
O
R
T
h
e
o
b
j
ec
t
o
f
th
e
s
tu
d
y
is
t
h
e
s
y
n
ch
r
o
n
o
u
s
g
en
er
ato
r
w
it
h
th
e
s
alie
n
t
-
p
o
le
r
o
to
r
(
th
at
is
also
th
e
in
d
u
cto
r
)
.
B
o
th
t
h
e
r
o
to
r
y
o
k
e
an
d
th
e
s
tato
r
y
o
k
e
ar
e
p
er
f
ec
t
f
er
r
o
m
a
g
n
e
tic,
th
e
ir
m
a
g
n
etic
p
er
m
ea
b
ilit
y
is
in
f
i
n
ite.
T
h
e
m
ag
n
etic
p
er
m
e
ab
ilit
y
o
f
p
o
les
is
co
n
s
tan
t
an
d
f
i
n
ite.
P
o
les
a
n
d
air
s
p
ac
es
b
et
w
ee
n
p
o
les
ar
e
b
o
u
n
d
ed
b
y
co
o
r
d
in
ate
s
u
r
f
ac
es o
f
th
e
c
y
li
n
d
r
ical
co
o
r
d
in
ate
s
y
s
te
m
a
s
s
h
o
w
n
i
n
Fi
g
u
r
e
1
.
Fig
u
r
e
1
.
T
h
e
s
alien
t
-
p
o
le
s
y
n
ch
r
o
n
o
u
s
g
e
n
er
ato
r
T
h
e
cu
r
r
en
t
0
I
cr
ea
tes
th
e
e
x
cit
in
g
f
ield
.
L
et
u
s
s
u
b
s
tit
u
te
eq
u
iv
a
len
t
c
u
r
r
en
t
s
h
ee
t
s
(
th
at
w
il
l
b
e
lo
ca
ted
o
n
th
e
r
o
to
r
y
o
k
e
b
et
w
ee
n
p
o
les)
f
o
r
th
e
e
x
citi
n
g
c
u
r
r
en
t.
Fo
u
r
ier
’
s
ex
p
a
n
s
io
n
t
u
r
n
s
t
h
e
c
u
r
r
en
t
s
h
ee
t
in
to
0
0
1
,
3
,
5
1
si
n
c
os
k
I
k
p
H
k
p
r
k
p
(
1
)
w
h
er
e
2
p
is
th
e
n
u
m
b
er
o
f
p
o
les.
I
t
is
k
n
o
w
n
t
h
at
in
ca
s
e
o
f
b
o
th
th
e
e
x
citi
n
g
f
ield
a
n
d
th
e
lo
n
g
i
tu
d
i
n
al
ar
m
at
u
r
e
r
ea
ctio
n
,
f
ield
li
n
es
ar
e
d
ir
ec
ted
g
en
er
all
y
p
ar
allel
to
th
e
r
-
a
x
is
w
it
h
in
th
e
p
o
les
an
d
g
e
n
er
all
y
p
er
p
en
d
icu
lar
t
o
th
e
r
-
a
x
is
w
i
th
i
n
th
e
air
s
p
ac
es
b
et
w
ee
n
p
o
les.
T
h
er
ef
o
r
e,
w
e
ca
n
s
u
b
s
tit
u
te
th
e
an
i
s
o
tr
o
p
ic
zo
n
e
f
o
r
th
e
p
o
les
an
d
th
e
air
s
p
ac
es
w
h
er
e
t
h
e
co
m
p
o
n
e
n
ts
o
f
th
e
m
ag
n
etic
p
er
m
ea
b
il
it
y
m
u
s
t b
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8708
Th
e
ca
s
ca
d
e
eq
u
iva
len
t A
-
H
-
c
ir
cu
it o
f th
e
s
a
lien
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p
o
le
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era
to
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n
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b
a
s
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e
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..
(
A
lexe
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la
n
c)
1125
0
,
rf
(
2
)
w
h
er
e
f
is
t
h
e
m
a
g
n
e
tic
p
er
m
ea
b
ilit
y
o
f
p
o
les an
d
0
is
th
e
m
ag
n
etic
p
er
m
ea
b
ilit
y
o
f
air
.
I
n
ca
s
e
o
f
th
e
q
u
ad
r
at
u
r
e
-
a
x
i
s
ar
m
at
u
r
e
r
ea
ctio
n
,
f
ield
lin
es
ar
e
d
ir
ec
ted
g
en
er
all
y
p
ar
allel
to
th
e
r
-
a
x
is
w
it
h
i
n
t
h
e
air
s
p
ac
es b
et
w
ee
n
p
o
les a
n
d
g
e
n
er
all
y
p
er
p
en
d
icu
lar
to
t
h
e
r
-
a
x
i
s
w
it
h
i
n
t
h
e
p
o
les.
T
h
en
t
h
e
co
m
p
o
n
e
n
t
s
o
f
t
h
e
m
a
g
n
etic
p
er
m
ea
b
ilit
y
m
u
s
t b
e
0
,
.
r
f
(
3
)
I
n
th
e
a
n
is
o
tr
o
p
ic
zo
n
e,
Ma
x
well’
s
eq
u
atio
n
s
d
eter
m
i
n
e
elec
t
r
o
m
a
g
n
etic
f
ield
:
rot
0
,
rot
H
BA
(
4
)
I
n
ca
s
e
o
f
th
e
c
y
li
n
d
r
ical
co
o
r
d
in
ate
s
y
s
te
m
,
Ma
x
w
ell
’
s
eq
u
atio
n
s
(
4
)
ar
e
eq
u
iv
ale
n
t
to
th
e
p
ar
tial
d
if
f
er
e
n
tial e
q
u
at
io
n
f
o
r
th
e
v
e
cto
r
p
o
ten
tial:
22
2
2
2
1
1
1
0
r
A
A
A
r
r
r
r
(
5
)
w
h
er
e
A
is
t
h
e
z
-
co
m
p
o
n
e
n
t o
f
t
h
e
v
ec
to
r
p
o
ten
tial.
W
h
en
t
h
e
r
o
to
r
r
ev
o
lv
es,
w
e
ca
n
s
ee
th
e
tr
a
v
eli
n
g
w
a
v
es
o
f
th
e
f
ield
.
T
h
er
ef
o
r
e,
th
e
co
m
p
lex
p
la
n
e
r
ep
r
esen
tatio
n
o
f
t
h
e
v
ec
to
r
p
o
ten
tial c
a
n
b
e
u
s
ed
.
Fo
r
th
e
ea
ch
k
-
t
h
h
ar
m
o
n
ic,
th
e
(
5
)
tu
r
n
s
in
to
22
22
1
0
k
k
k
k
AA
A
r
r
r
r
(
6
)
w
h
er
e
k
r
kp
.
T
h
e
g
en
er
al
s
o
lu
tio
n
o
f
t
h
e
eq
u
atio
n
(
6
)
is
12
kk
k
A
C
r
C
r
.
(
7
)
T
h
e
tan
g
e
n
tial c
o
m
p
o
n
e
n
t o
f
t
h
e
m
a
g
n
etic
i
n
ten
s
it
y
(
ex
cl
u
d
i
n
g
t
h
e
ex
c
iti
n
g
f
ield
s
o
u
r
ce
)
is
12
1
kk
kk
k
A
H
C
r
C
r
rr
.
(
8
)
Su
p
p
o
s
e
th
at
at
th
e
b
o
u
n
d
ar
ies
o
f
t
h
e
an
i
s
o
tr
o
p
ic
zo
n
e,
th
e
v
ec
to
r
p
o
ten
tial
an
d
t
h
e
tan
g
e
n
tia
l
co
m
p
o
n
e
n
t o
f
th
e
m
a
g
n
et
ic
in
t
en
s
it
y
v
ec
to
r
ar
e
k
n
o
w
n
.
As in
Fig
u
r
e
1
f
o
r
th
e
f
ir
s
t f
ie
ld
h
ar
m
o
n
ic
,
if
1
rr
,
1
1
1
2
1
kk
k
A
C
r
C
r
,
(
9)
11
1
1
1
2
kk
k
k
H
r
C
r
C
r
.
(
1
0
)
I
f
2
rr
(
s
ee
Fig
u
r
e
1
)
,
2
1
2
2
2
kk
k
A
C
r
C
r
,
(
1
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
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&
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Vo
l.
11
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No
.
2
,
A
p
r
il
2
0
2
1
:
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2
3
-
1129
1126
22
2
2
1
2
kk
k
k
H
r
C
r
C
r
.
(
1
2
)
Su
p
p
o
s
e
th
at,
f
o
r
th
e
f
ir
s
t
f
i
eld
h
ar
m
o
n
ic
,
t
h
e
eq
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i
v
ale
n
t
A
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H
-
cir
cu
it
(
in
w
h
ic
h
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ec
to
r
m
a
g
n
eti
c
p
o
ten
tial
i
s
co
n
s
id
er
ed
eq
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i
v
alen
t
to
th
e
v
o
ltag
e
an
d
th
e
tan
g
e
n
tia
l
co
m
p
o
n
en
t
o
f
th
e
m
ag
n
etic
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te
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it
y
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ec
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m
u
ltip
lied
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y
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ad
iu
s
is
co
n
s
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er
ed
eq
u
i
v
ale
n
t
to
t
h
e
cu
r
r
en
t)
co
r
r
esp
o
n
d
s
to
th
e
r
o
to
r
as
s
h
o
w
n
i
n
Fig
u
r
e
2
.
Fig
u
r
e
2
.
T
h
e
eq
u
iv
alen
t
A
-
H
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cir
cu
it o
f
t
h
e
r
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to
r
T
h
e
id
ea
l c
u
r
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en
t so
u
r
ce
01
Hr
co
r
r
e
s
p
o
n
d
s
to
th
e
f
ir
s
t h
ar
m
o
n
ic
o
f
th
e
cu
r
r
en
t e
x
p
r
ess
io
n
(
1
)
:
0
01
sin
Ip
H
r
j
p
.
(
1
3
)
T
h
e
ex
p
r
ess
io
n
s
(
9
)
-
(
1
2
)
d
es
cr
ib
e
th
e
o
p
er
atio
n
co
n
d
itio
n
s
o
f
t
h
e
eq
u
i
v
ale
n
t
A
-
H
-
cir
cu
it.
O
n
t
h
e
o
th
er
h
a
n
d
,
w
h
e
n
o
p
er
atio
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co
n
d
itio
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s
c
h
a
n
g
e,
t
h
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n
s
t
an
ts
o
f
th
e
eq
u
i
v
alen
t
A
-
H
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ci
r
cu
it
(
in
cl
u
d
i
n
g
t
h
e
i
m
p
ed
an
ce
s
11
Z
,
12
Z
,
13
Z
)
s
h
all
n
o
t
ch
a
n
g
e.
T
h
er
ef
o
r
e,
w
e
ca
n
d
eter
m
i
n
e
th
e
i
m
p
ed
an
ce
s
11
Z
,
12
Z
,
13
Z
b
y
an
al
y
z
in
g
t
h
e
ex
p
r
ess
io
n
s
(
9
)
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I
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th
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ield
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ad
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atu
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ax
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: th
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t
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eq
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t
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ir
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(
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LC
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.
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o
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e
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t
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n
in
to
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cr
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.
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m
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m
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lead
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s
a
m
e
r
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lt.
I
t is ev
id
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n
ce
o
f
th
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co
r
r
ec
tn
es
s
o
f
m
o
d
eli
n
g
.
RE
F
E
R
E
NC
E
S
[1
]
E.
M
ish
k
in
,
“
T
h
e
o
ry
o
f
th
e
sq
u
irrel
-
c
a
g
e
in
d
u
c
ti
o
n
m
o
to
r
d
e
ri
v
e
d
d
irec
tl
y
f
ro
m
M
a
x
we
ll
’s
f
ield
e
q
u
a
ti
o
n
s,”
Qu
a
rte
rly
J
o
u
rn
a
l
o
f
M
e
c
h
a
n
ics
a
n
d
Ap
p
l
ied
M
a
th
e
m
a
ti
c
s
,
v
o
l.
7
,
no
.
4
,
p
p
.
4
7
2
-
4
8
7
,
1
9
5
4
.
[2
]
S
.
A
.
Na
sa
r
,
“
El
e
c
tro
m
a
g
n
e
ti
c
th
e
o
ry
o
f
e
lec
tri
c
a
l
m
a
c
h
in
e
s
,
”
Pro
c
e
e
d
in
g
s
o
f
t
h
e
In
st
it
u
t
io
n
o
f
El
e
c
trica
l
En
g
i
n
e
e
rs
,
v
o
l.
1
1
1
,
no
.
6
,
p
p
.
1
1
2
3
-
1
1
3
1
,
1
9
6
4
.
[3
]
J.
G
re
i
g
a
n
d
E.
M
.
F
re
e
m
a
n
,
“
Trav
e
li
n
g
w
a
v
e
p
ro
b
lem
in
e
lec
tri
c
a
l
m
a
c
h
in
e
,
”
Pro
c
e
e
d
in
g
s
o
f
th
e
In
stit
u
ti
o
n
o
f
El
e
c
trica
l
En
g
in
e
e
rs
,
v
o
l.
1
1
4
,
no
.
1
1
,
p
p
.
1
6
8
1
-
1
6
8
3
,
1
9
6
7
.
[4
]
S.
W
il
li
a
m
so
n
,
“
T
h
e
a
n
iso
tro
p
ic
la
y
e
r
th
e
o
ry
o
f
in
d
u
c
ti
o
n
m
a
c
h
in
e
s
a
n
d
in
d
u
c
ti
o
n
d
e
v
ice
s
,
”
I
M
A
J
o
u
rn
a
l
o
f
Ap
p
li
e
d
M
a
t
h
e
ma
ti
c
s
,
v
o
l.
1
7
,
no
.
1
,
p
p
.
69
-
84
,
1
9
7
6
.
[5
]
V
.
M
.
Ka
z
a
n
sk
y
a
n
d
A
.
I.
In
k
in
,
“
A
n
e
le
c
tro
m
a
g
n
e
ti
c
m
o
d
e
l
a
n
d
e
le
m
e
n
ts
o
f
th
e
in
d
u
c
ti
o
n
m
a
c
h
in
e
’s
th
e
o
ry
(in
Ru
ss
ian
)
,
”
In
d
u
c
ti
o
n
M
icr
o
-
M
a
c
h
in
e
s.
T
h
e
In
ter
-
Un
ive
rs
it
y
Co
n
f
e
re
n
c
e
o
n
In
d
u
c
ti
o
n
M
a
c
h
in
e
s:
Pro
c
.
(
Ka
u
n
a
s)
,
1
9
6
9
,
pp
.
2
1
7
-
2
2
9
.
[6
]
V
.
M
.
Ka
z
a
n
sk
y
,
e
t
a
l.
,
“
T
h
e
a
n
a
ly
ti
c
a
l
stu
d
y
o
f
e
lec
tro
m
a
g
n
e
ti
c
f
ield
in
a
n
a
c
ti
v
e
v
o
lu
m
e
o
f
th
e
n
-
p
h
a
se
a
s
y
n
c
h
ro
n
o
u
s m
a
c
h
in
e
w
it
h
a
n
o
n
-
slo
t
sta
to
r
(i
n
R
u
ss
ian
)
,
”
In
d
u
c
ti
o
n
e
lec
tric mo
to
rs
wit
h
a
n
a
ll
o
c
a
te
d
a
c
ti
v
e
sta
t
o
r
la
y
e
r: P
ro
c
.
,
No
v
o
si
b
irsk
:
NET
I,
no
.
2
,
p
p
.
41
-
57
,
1
9
7
2
.
[7
]
A
.
I.
In
k
in
a
n
d
V.
M
.
Ka
z
a
n
sk
y
,
“
Eq
u
iv
a
len
t
tran
sf
o
r
m
a
ti
o
n
s
o
f
a
c
ti
v
e
z
o
n
e
s
in
ro
tati
n
g
e
lec
tri
c
m
a
c
h
in
e
s
(in
Ru
ss
ian
)
,
”
El
e
c
tricity,
v
o
l.
1,
p
p
.
42
-
45
,
1
9
7
5
.
[8
]
E.
M
.
F
re
e
m
a
n
,
“
T
ra
v
e
ll
in
g
w
a
v
e
s in
in
d
u
c
ti
o
n
m
a
c
h
in
e
s: i
n
p
u
t
im
p
e
d
a
n
c
e
a
n
d
e
q
u
iv
a
len
t
c
ircu
it
s
,
”
Pro
c
e
e
d
in
g
s o
f
th
e
In
stit
u
ti
o
n
o
f
El
e
c
trica
l
E
n
g
i
n
e
e
rs
,
v
o
l.
1
1
5
,
no
.
1
2
,
p
p
.
1
7
7
2
-
1
7
7
6
,
1
9
6
8
.
[9
]
E.
M
.
F
re
e
m
a
n
,
“
Eq
u
iv
a
len
t
c
ircu
it
s f
ro
m
e
lec
tro
m
a
g
n
e
ti
c
th
e
o
ry
lo
w
-
f
re
q
u
e
n
c
y
in
d
u
c
ti
o
n
d
e
v
ice
s
,
”
Pro
c
e
e
d
in
g
s
o
f
th
e
In
stit
u
ti
o
n
o
f
El
e
c
trica
l
E
n
g
i
n
e
e
rs
,
v
o
l.
1
2
1
,
no
.
1
0
,
p
p
.
1
1
1
7
-
1
1
2
1
,
1
9
7
4
.
[1
0
]
E.
M
.
F
re
e
m
a
n
a
n
d
T
.
G
.
Blan
d
,
“
Eq
u
iv
a
len
t
c
ircu
it
o
f
c
o
n
c
e
n
tr
ic
c
y
li
n
d
rica
l
c
o
n
d
u
c
to
rs
i
n
a
n
a
x
ial
a
lt
e
rn
a
ti
n
g
m
a
g
n
e
ti
c
f
ield
,
”
Pro
c
e
e
d
in
g
s
o
f
t
h
e
In
stit
u
ti
o
n
o
f
E
lec
trica
l
En
g
i
n
e
e
rs
,
v
o
l.
1
2
3
,
no
. 2
,
p
p
.
1
4
9
-
1
5
2
,
1
9
7
6
.
[1
1
]
A
.
I.
In
k
in
,
“
T
h
e
c
ircu
it
a
p
p
ro
x
im
a
ti
o
n
o
f
li
n
e
a
r
m
e
d
iu
m
s
in
f
lu
e
n
c
e
d
b
y
e
lec
tro
m
a
g
n
e
ti
c
f
ield
(in
R
u
ss
ian
)
,
”
El
e
c
tricity,
no
.
4,
p
p
.
6
4
-
67
,
1
9
7
5
.
[1
2
]
A
.
I.
In
k
in
a
n
d
B.
V
.
L
it
v
in
o
v
,
“
T
h
e
s
y
n
th
e
sis
o
f
c
a
sc
a
d
e
e
q
u
iv
a
l
e
n
t
c
ircu
it
s
o
f
in
d
u
c
ti
o
n
e
lec
tri
c
m
a
c
h
in
e
s
o
n
t
h
e
b
a
sis o
f
sta
n
d
a
rd
E
-
H
-
f
o
u
r
-
term
in
a
l
n
e
tw
o
rk
s
(in
Ru
ss
ian
)
,
”
El
e
c
tro
tec
h
n
ics
,
v
o
l.
1,
p
p
.
2
9
-
3
3
,
1
9
7
7
.
[1
3
]
A
.
I.
In
k
in
a
n
d
Yu
.
G
.
Bu
c
h
h
o
lz,
“
F
o
u
n
d
a
ti
o
n
s
o
f
th
e
sy
n
th
e
siz
in
g
o
f
n
o
n
-
li
n
e
a
r
c
a
sc
a
d
e
e
q
u
iv
a
le
n
t
c
ircu
it
s
o
f
a
n
e
lec
tri
c
m
a
c
h
in
e
(in
Ru
ss
ian
)
,
”
El
e
c
tricity,
v
o
l.
6,
p
p
.
3
3
-
3
7
,
1
9
7
9
.
[1
4
]
A
.
I.
In
k
in
,
“
El
e
c
tro
m
a
g
n
e
ti
c
f
i
e
ld
s
a
n
d
p
a
ra
m
e
ters
o
f
e
l
e
c
tri
c
m
a
c
h
in
e
s:
tu
to
rial
(in
Ru
ss
ian
)
,
”
No
v
o
sib
irsk
:
UK
EA
,
p
p
.
1
-
4
6
4
,
20
02.
[1
5
]
B.
V
.
L
it
v
in
o
v
a
n
d
O.
B.
Da
v
id
e
n
k
o
,
“
S
tan
d
a
rd
c
e
ll
s
a
n
d
c
a
sc
a
d
e
e
q
u
iv
a
len
t
c
ircu
it
s
o
f
e
lec
tri
c
m
a
c
h
in
e
s:
m
o
n
o
g
ra
p
h
(in
Ru
ss
ian
)
,
”
N
o
v
o
si
b
irsk
:
NST
U,
p
p
.
1
-
2
1
5
,
2
0
0
8
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
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&
C
o
m
p
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n
g
I
SS
N:
2088
-
8708
Th
e
ca
s
ca
d
e
eq
u
iva
len
t A
-
H
-
c
ir
cu
it o
f th
e
s
a
lien
t
-
p
o
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era
to
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s
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o
f th
e
.
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(
A
lexe
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la
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c)
1129
[1
6
]
B.
V.
L
it
v
in
o
v
a
n
d
O.
B.
Da
v
id
e
n
k
o
,
“
T
h
e
e
q
u
iv
a
len
t
c
ircu
i
t
o
f
t
h
e
sy
n
c
h
ro
n
o
u
s
re
a
c
ti
v
e
m
o
to
r
su
b
jec
t
t
o
h
ig
h
e
r
sp
a
ti
a
l
h
a
rm
o
n
ic o
f
m
a
g
n
e
to
m
o
ti
v
e
f
o
rc
e
(in
Ru
ss
ian
)
,
”
E
lec
tricity,
v
o
l.
5,
p
p
.
48
-
52
,
2
0
1
0
.
[1
7
]
B.
V.
L
it
v
in
o
v
a
n
d
O.
B.
Da
v
i
d
e
n
k
o
,
“
S
y
n
c
h
ro
n
o
u
s
re
a
c
ti
v
e
m
o
to
r
w
it
h
re
d
u
c
e
d
m
a
g
n
e
ti
c
c
o
n
d
u
c
tan
c
e
a
lo
n
g
tran
sv
e
rse
a
x
is
(in
Ru
ss
ian
)
,
”
E
lec
tro
tec
h
n
ics
,
v
o
l.
3,
p
p
.
15
-
20
,
2
0
1
0
.
[1
8
]
L
.
Qa
s
e
e
r,
e
t
a
l.
,
“
Co
m
b
in
e
d
f
iel
d
a
n
d
c
ircu
it
t
h
e
o
ries
in
sq
u
irrel
-
c
a
g
e
in
d
u
c
ti
o
n
m
o
to
rs
b
a
se
d
o
n
m
icro
-
T
c
ircu
it
m
o
d
e
l
,
”
Ace
s J
o
u
rn
a
l
,
v
o
l.
2
6
,
n
o
.
7
,
p
p
.
5
5
1
-
5
6
0
,
2
0
1
1
.
[1
9
]
L
.
Qa
s
e
e
r,
e
t
a
l.
,
“
Clo
se
d
-
f
o
r
m
a
n
a
ly
sis
o
f
sq
u
irrel
-
c
a
g
e
in
d
u
c
ti
o
n
m
o
to
rs
w
it
h
a
n
iso
tr
o
p
ic
m
o
d
e
li
n
g
o
f
sta
to
r
a
n
d
ro
to
r
,
”
I
EE
E
T
ra
n
s
a
c
ti
o
n
s
o
n
E
n
e
rg
y
Co
n
v
e
rs
io
n
,
v
o
l.
2
7
,
n
o
.
3
,
p
p
.
5
5
3
-
5
6
0
,
2
0
1
2
.
[2
0
]
V
.
V
.
Ko
rn
e
e
v
,
“
De
sig
n
c
o
e
ff
ic
ien
ts
a
n
d
a
d
d
e
d
l
o
ss
e
s
o
f
s
y
n
c
h
ro
n
o
u
s
m
a
c
h
in
e
s
w
it
h
p
e
r
m
a
n
e
n
t
m
a
g
n
e
ts
a
n
d
f
ra
c
ti
o
n
a
l
to
o
th
w
in
d
i
n
g
s:
c
a
n
d
id
a
te'
s
d
is
se
rtatio
n
:
s
p
e
c
ialit
y
0
5
.
0
9
.
0
1
(
in
Ru
ss
ian
)
,
”
No
v
o
sib
irsk
:
NST
U,
p
p
.
1
-
1
4
4
,
2
0
1
8
.
[2
1
]
A
.
I.
In
k
in
,
e
t
a
l.
,
“
T
h
e
c
a
lcu
latio
n
o
f
tran
sf
o
rm
e
r
in
d
u
c
ti
o
n
h
e
a
ti
n
g
s
y
ste
m
(in
Ru
ss
ian
)
,
”
El
e
c
tro
te
c
h
n
ics
,
v
o
l.
1
1
,
p
p
.
3
4
-
3
7
,
2
0
0
0
.
[2
2
]
F
.
N.
S
a
ra
p
u
lo
v
,
e
t
a
l.
,
“
M
a
th
e
m
a
ti
c
m
o
d
e
ls
o
f
li
n
e
a
r
in
d
u
c
ti
o
n
m
a
c
h
in
e
s
o
n
th
e
b
a
sis
o
f
e
q
u
iv
a
l
e
n
t
c
ircu
it
s
2
n
d
e
d
it
io
n
(i
n
Ru
ss
ian
)
,
”
Ye
k
a
terin
b
u
rg
:
UG
T
U
-
UP
I,
p
p
.
1
-
4
3
1
,
2
0
0
5
.
[2
3
]
L
.
Qa
se
e
r,
“
A
n
a
l
y
sis
o
f
d
o
u
b
le
a
n
d
si
n
g
le
sid
e
d
i
n
d
u
c
ti
o
n
h
e
a
ti
n
g
sy
st
e
m
s
b
y
la
y
e
r
th
e
o
ry
a
p
p
ro
a
c
h
,
”
J
o
u
rn
a
l
o
f
e
lec
tro
ma
g
n
e
ti
c
a
n
a
lys
is a
n
d
a
p
p
li
c
a
ti
o
n
s
,
v
o
l
.
2
,
no
.
7
,
p
p
.
4
0
3
-
4
1
0
,
2
0
1
0
.
[2
4
]
L
.
Qa
se
e
r,
“
M
icro
-
T
c
ircu
it
m
o
d
e
l
f
o
r
d
o
u
b
le
a
n
d
sin
g
le
si
d
e
d
in
d
u
c
ti
o
n
h
e
a
ti
n
g
sy
ste
m
s,”
Ap
p
li
e
d
c
o
m
p
u
t
a
ti
o
n
a
l
e
lec
tro
ma
g
n
e
ti
c
s so
c
i
e
ty j
o
u
rn
a
l
,
v
o
l.
2
5
,
no
.
8
,
p
p
.
7
1
3
-
7
2
1
,
2
0
1
0
.
[2
5
]
L
.
Qa
s
e
e
r,
“
M
icro
-
T
c
ircu
it
m
o
d
e
l
f
o
r
th
e
a
n
a
ly
sis
o
f
c
y
li
n
d
rica
l
in
d
u
c
ti
o
n
h
e
a
ti
n
g
sy
ste
m
s,”
IEE
E
T
ra
n
s
a
c
ti
o
n
s
o
n
e
n
e
rg
y
c
o
n
v
e
rs
io
n
,
v
o
l.
2
5
,
no
.
4
,
p
p
.
1
0
2
1
-
1
0
2
7
,
2
0
1
0
.
[2
6
]
A
.
V
.
Blan
c
,
“
El
e
c
tro
m
a
g
n
e
ti
c
f
i
e
ld
a
n
d
e
d
d
y
c
u
rre
n
ts
in
th
e
m
a
n
tl
e
o
f
th
e
o
re
-
s
m
e
lt
in
g
f
u
rn
a
c
e
,
”
I
OP
Co
n
f
e
re
n
c
e
S
e
rie
s: M
a
ter
ia
ls E
n
g
in
e
e
rin
g
,
v
o
l.
5
6
0
,
n
o
.
1
,
20
19
,
p
p
.
1
-
7.
[2
7
]
A
.
V
.
Blan
c
,
“
T
h
e
c
a
sc
a
d
e
e
q
u
iv
a
len
t
A
-
H
-
c
ircu
it
o
f
th
e
in
d
u
c
ti
o
n
h
e
a
ti
n
g
s
y
st
e
m
w
it
h
a
su
p
e
rc
o
n
d
u
c
ti
n
g
in
d
u
c
to
r
(in
Ru
ss
ian
)
,
”
El
e
c
tro
tec
h
n
ics
,
v
o
l.
2,
p
p
.
4
3
-
4
9
,
2
0
2
0
.
[2
8
]
A
.
I.
In
k
in
,
“
T
h
e
a
n
a
l
y
ti
c
a
l
trea
t
m
e
n
t
o
f
m
a
g
n
e
ti
c
f
ield
in
th
e
a
c
ti
v
e
v
o
lu
m
e
o
f
th
e
e
lec
tri
c
m
a
c
h
in
e
w
it
h
p
e
r
m
a
n
e
n
t
m
a
g
n
e
ts
(in
Ru
ss
ian
)
,
”
El
e
c
tricity
,
v
o
l.
5,
p
p
.
3
0
-
3
3
,
1
9
7
9
.
[2
9
]
A
.
I.
In
k
in
,
“
A
n
a
li
t
ica
l
so
lu
ti
o
n
o
f
m
a
g
n
e
ti
c
f
i
e
ld
’s
e
q
u
a
ti
o
n
s
i
n
d
i
sc
re
te
stru
c
tu
re
s
o
f
sa
li
e
n
t
-
p
o
le
e
lec
tri
c
m
a
c
h
in
e
s
(in
Ru
ss
ian
)
,
”
El
e
c
tricity,
v
o
l.
8,
p
p
.
1
8
-
2
1
,
1
9
7
9
.
[3
0
]
A
.
I.
In
k
in
,
“
T
h
e
m
a
th
e
m
a
ti
c
a
l
f
o
rm
u
latio
n
o
f
m
a
g
n
e
ti
c
f
ield
in
th
e
v
o
lu
m
e
s
o
f
sa
li
e
n
t
-
p
o
le
t
h
e
e
lec
tr
ic
m
a
c
h
in
e
s,”
El
e
c
tricity
(in
Ru
ss
ian
)
,
v
o
l.
2,
p
p
.
3
0
-
3
5
,
1
9
9
7
.
[3
1
]
A
.
V
.
Blan
c
,
“
T
h
e
a
n
a
ly
ti
c
a
l
c
a
lcu
latio
n
o
f
e
x
c
it
in
g
f
ield
o
f
sy
n
c
h
ro
n
o
u
s
m
a
c
h
in
e
o
n
t
h
e
b
a
se
o
f
th
e
sin
g
le
p
iec
e
w
is
e
c
o
n
ti
n
u
o
u
s
e
ig
e
n
f
u
n
c
ti
o
n
(i
n
R
u
ss
ian
)
,
”
Co
l
lec
ted
sc
ien
ti
fi
c
p
a
p
e
rs
o
f
th
e
N
S
T
U,
v
o
l
.
4
,
n
o
.
3
8
,
p
p
.
3
-
8
,
2
0
0
4
.
[3
2
]
A
.
I.
In
k
in
a
n
d
A
.
V
.
Blan
c
,
“
T
h
e
a
p
p
ro
x
im
a
te
a
n
a
l
y
ti
c
a
l
c
a
lcu
lat
io
n
o
f
e
x
c
it
in
g
f
ield
o
f
e
lec
tri
c
m
a
c
h
in
e
s
o
n
th
e
b
a
se
o
f
th
e
p
iec
e
w
ise
c
o
n
ti
n
u
o
u
s
e
ig
e
n
f
u
n
c
ti
o
n
(i
n
Ru
ss
ian
)
,
”
El
e
c
tricity,
v
o
l.
6,
p
p
.
5
2
-
5
6
,
2
0
0
8
.
[3
3
]
A
.
V
.
Blan
c
,
“
T
h
e
A
-
H
-
e
q
u
iv
a
le
n
t
c
ircu
it
o
f
a
s
y
n
c
h
ro
n
o
u
s
e
lec
tr
ic
m
a
c
h
in
e
w
it
h
tan
g
e
n
ti
a
l
p
e
rm
a
n
e
n
t
m
a
g
n
e
ts,”
Pro
c
e
e
d
in
g
s
o
f
th
e
2
0
1
8
1
4
t
h
in
ter
n
a
t
io
n
a
l
sc
ien
ti
fi
c
-
tec
h
n
ica
l
c
o
n
fer
e
n
c
e
o
n
a
c
tu
a
l
p
r
o
b
lem
s
o
f
e
lec
tro
n
ic
in
stru
me
n
t
e
n
g
i
n
e
e
rin
g
(
AP
EIE
-
4
4
8
9
4
)
,
v
o
l.
1
,
no.
5,
2
0
1
8
,
p
p
.
6
2
-
65
.
[3
4
]
A
.
V
.
Blan
c
,
“
A
c
a
sc
a
d
e
e
q
u
iv
a
l
e
n
t
A
-
H
-
c
ircu
it
o
f
a
p
e
rm
a
n
e
n
t
m
a
g
n
e
t
e
x
c
it
e
d
e
lec
tri
c
a
l
m
a
c
h
in
e
(in
Ru
ss
ian
)
,
”
El
e
c
tricity,
v
o
l.
1
0
,
p
p
.
4
2
-
4
7
,
2
0
1
9
.
[3
5
]
A
.
V
.
Blan
c
,
“
A
c
a
sc
a
d
e
e
q
u
iv
a
len
t
A
-
H
-
c
ircu
it
o
f
a
s
y
n
c
h
ro
n
o
u
s
sa
li
e
n
t
-
p
o
le
e
lec
tri
c
m
a
c
h
in
e
,
”
I
OP
Co
n
f
e
re
n
c
e
S
e
rie
s: M
a
ter
ia
ls E
n
g
in
e
e
rin
g
,
v
o
l.
5
6
0
,
n
o
.
1
,
2
0
1
9
,
p
p
.
1
-
7
.
[3
6
]
A
.
Blan
c
,
“
Ex
c
it
in
g
f
i
e
ld
a
n
d
q
u
a
d
ra
tu
re
-
a
x
is
a
r
m
a
tu
re
re
a
c
ti
o
n
in
a
c
a
sc
a
d
e
e
q
u
iv
a
len
t
A
-
H
-
c
ir
c
u
it
o
f
a
sa
li
e
n
t
-
p
o
le
g
e
n
e
ra
to
r,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
(
IJ
ECE
),
v
o
l.
1
0
,
n
o
.
2
,
p
p
.
1
6
7
4
-
1
6
8
1
,
2
0
2
0
.
B
I
O
G
RAP
H
Y
O
F
AUTHO
R
Ale
x
e
y
V
a
ler
iev
i
c
h
B
la
n
c
w
a
s
b
o
rn
i
n
1
9
7
1
.
He
re
c
e
iv
e
d
th
e
M
a
ste
r'
s
d
e
g
r
e
e
in
M
e
c
h
a
n
ica
l
&
E
lec
tri
c
a
l
En
g
in
e
e
rin
g
(
in
1
9
9
9
)
a
n
d
th
e
C
a
n
d
i
d
a
te
’s
d
e
g
re
e
in
En
g
in
e
e
rin
g
(in
2
0
0
5
)
f
ro
m
th
e
No
v
o
sib
irsk
S
tate
T
e
c
h
n
ica
l
Un
iv
e
rsity
.
S
in
c
e
2
0
0
5
,
h
e
is
th
e
a
ss
o
c
iate
p
ro
f
e
ss
o
r
in
th
e
D
e
p
a
rtme
n
t
o
f
th
e
T
h
e
o
re
ti
c
a
l
E
lec
tri
c
a
l
E
n
g
in
e
e
ri
n
g
in
th
e
No
v
o
sib
irsk
S
tate
T
e
c
h
n
ica
l
Un
iv
e
rsit
y
.
He
h
a
s
6
0
sc
ien
ti
fic
p
u
b
li
c
a
ti
o
n
s.
His
sc
ien
ti
f
ic
w
o
rk
s
h
a
v
e
to
d
o
w
it
h
th
e
e
n
g
in
e
e
rin
g
e
lec
tro
d
y
n
a
m
ics
a
n
d
th
e
h
e
a
t
-
tran
sf
e
r
th
e
o
ry
.
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