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s
[1
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4
]
.
W
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b
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av
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b
ec
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m
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ted
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[
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-
1
2
]
.
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n
d
co
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x
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if
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ti
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s
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a
[
1
3
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p
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e
ex
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s
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ce
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f
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Stra
u
b
[
1
4
]
s
h
o
wed
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at
ch
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tic
P
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L
c
ir
cu
it
s
s
o
m
eti
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f
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th
e
y
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ch
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to
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g
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.
Har
b
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d
Har
b
[
1
5
]
a
p
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n
o
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lin
ea
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t
h
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r
y
to
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ac
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k
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ab
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t
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[
1
6
]
s
tu
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s
elf
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cilla
tio
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s
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ch
ao
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e.
Fo
r
tu
n
a,
et
al
.
[
1
7
]
u
s
ed
ch
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tic
p
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l
s
e
p
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s
itio
n
m
o
d
u
latio
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to
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m
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y
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ar
s
en
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s
.
I
n
r
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en
t
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s
,
m
a
n
y
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s
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m
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d
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b
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m
s
d
u
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to
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ti
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d
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f
s
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n
als
[
1
8
-
2
0
]
.
T
h
is
d
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y
ef
f
ec
t
ca
u
s
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s
a
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b
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h
av
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r
w
h
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h
a
s
b
ee
n
r
ep
o
r
ted
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
11
,
No
.
2
,
A
p
r
il
2
0
2
1
:
1
4
3
1
-
1438
1432
in
n
o
n
li
n
ea
r
s
y
s
te
m
s
e
s
p
ec
ial
l
y
i
n
r
ad
io
en
g
i
n
ee
r
in
g
.
L
ater
,
n
u
m
er
o
u
s
e
x
p
er
i
m
e
n
tal
a
n
d
th
eo
r
etica
l
s
t
u
d
ies
h
a
v
e
d
em
o
n
s
t
r
a
t
e
d
t
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a
t
m
a
n
y
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o
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n
e
a
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d
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a
y
s
y
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t
e
m
s
e
x
p
e
r
i
e
n
c
e
d
a
c
h
a
o
t
i
c
b
e
h
a
v
i
o
r
a
s
a
r
e
s
u
l
t
o
f
d
y
n
a
m
ic
i
n
s
t
a
b
i
l
i
t
i
e
s
.
S
u
c
h
i
n
s
t
a
b
i
l
i
t
i
e
s
i
n
c
l
u
d
e
p
e
r
i
o
d
-
d
o
u
b
l
i
n
g
r
o
u
t
e
t
o
c
h
a
o
s
,
q
u
a
s
i
p
e
r
i
o
d
i
c
i
t
y
a
n
d
i
n
t
e
r
m
i
t
t
e
n
c
y
[
2
1
-
2
4
]
.
Mo
r
eo
v
er
,
s
tu
d
ies
h
a
v
e
s
h
o
wn
t
h
at
t
h
e
d
i
m
e
n
s
io
n
o
f
t
h
e
r
esu
lted
c
h
ao
tic
attr
ac
to
r
is
d
ir
e
ctl
y
p
r
o
p
o
r
tio
n
al
to
th
e
ti
m
e
d
ela
y
i
n
d
u
ce
d
in
t
h
e
s
y
s
te
m
in
d
ep
en
d
e
n
t
o
f
th
e
f
o
r
m
o
f
th
e
s
y
s
te
m
.
I
n
th
is
ca
s
e,
o
n
e
ca
n
o
b
tain
h
ig
h
-
d
i
m
en
s
io
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al
c
h
ao
tic
attr
ac
to
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s
b
y
i
n
cr
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s
i
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ti
m
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in
t
h
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s
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m
[
2
5
-
2
7
]
.
T
h
is
m
et
h
o
d
s
h
o
u
ld
b
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p
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f
o
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ed
w
i
th
ca
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t
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s
in
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s
tate
s
p
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r
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ese
n
tatio
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f
a
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Sch
a
n
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an
d
P
elst
er
[
2
8
]
w
h
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y
p
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th
e
ex
is
ten
ce
o
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a
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[
2
9
]
s
t
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d
e
l
a
y
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n
h
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G
r
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l
.
[
3
0
]
in
v
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s
ti
g
ate
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th
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o
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m
a
n
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tical
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[
1
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o
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o
r
ch
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T
h
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o
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s
:
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tai
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t
h
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ath
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atica
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tical
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.
2.
RE
S
E
ARCH
M
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H
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2
.
1
.
M
a
t
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m
a
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o
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hird o
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L
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ase
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Fi
g
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lled
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(
VC
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F
ig
u
r
e
1
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lo
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iag
r
a
m
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ase
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is
g
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b
y
[
1
5
]
:
))
t
(
s
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(
dt
d
1
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1
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d
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2
p
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(
1
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A
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(
1
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ca
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as:
(
2
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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p
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N:
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8708
C
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d
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b
a
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3
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1
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(
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t
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i
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:
(
3
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2
1
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)
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(
)
x
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ex
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dx
cx
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ax
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x
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x
x
1
1
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1
2
2
1
3
3
3
3
2
2
1
(
4
)
Har
b
an
d
Har
b
[
1
5
]
s
h
o
w
ed
t
h
at
th
e
s
y
s
te
m
h
ad
a
ch
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m
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as sh
o
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Fig
u
r
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m
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u
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m
alize
d
g
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in
k
=7
6
300
2
.
2
.
M
a
t
he
m
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del o
f
t
hird o
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w
it
h t
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Du
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l
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o
p
p
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r
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es:
))
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dt
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1
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1
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1
k
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d
dt
d
]
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(
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a
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7
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3
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
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&
C
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m
p
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n
g
,
Vo
l.
11
,
No
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2
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A
p
r
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2
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:
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4
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1
-
1438
1434
th
en
(
6
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b
ec
o
m
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s
:
(
7
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Def
i
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e
th
e
s
tate
v
ar
iab
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s
t
x
,
t
x
,
t
x
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x
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6
5
4
3
2
1
T
h
e
f
ir
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t
f
iv
e
s
tate
eq
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atio
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s
ar
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d
ir
ec
tly
d
er
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f
r
o
m
(
7
)
an
d
th
e
s
tate
v
ar
iab
les
d
ef
in
ed
a
b
o
v
e.
T
h
e
last
s
tate
eq
u
a
tio
n
w
il
l
b
e
d
er
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u
s
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n
g
P
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p
r
o
x
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m
ati
o
n
.
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g
t
h
e
s
tate
v
ar
iab
les
d
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in
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ab
o
v
e,
(
7
)
b
ec
o
m
e
s
:
(
8
)
T
o
d
er
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e
s
ix
th
s
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te
s
p
ac
e
eq
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w
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th
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y
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2
1
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tin
g
w
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h
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4
(
t)
=
(t
-
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d
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t
h
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lace
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=
(
s)
e
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s
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1
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s
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1
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I
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m
e
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o
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,
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h
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t to
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1
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1
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et:
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1
1
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f
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n
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(
1
1
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to
g
et:
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x
s
i
n
(
kA
x
)
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c
o
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kA
x
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x
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x
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4
2
6
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1
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6
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x
kA
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m
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1
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t
h
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th
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tial e
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2
x
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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
C
h
a
o
s
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B
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r
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)
1435
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3.
RE
SU
L
T
S
A
ND
D
I
SCU
SS
I
O
NS
I
n
th
is
s
ec
tio
n
,
t
h
e
eq
u
ilib
r
iu
m
an
d
d
y
n
am
ic
s
o
lu
tio
n
s
o
f
th
e
s
y
s
tem
ar
e
o
b
tain
ed
.
Firstl
y
,
b
y
s
ettin
g
th
e
r
ig
h
t
h
an
d
s
id
e
o
f
(
1
3
)
to
ze
r
o
,
th
e
eq
u
ilib
r
iu
m
s
o
lu
tio
n
(
t)
is
o
b
tain
ed
.
T
h
e
d
y
n
am
ic
s
o
lu
tio
n
is
f
o
u
n
d
b
y
v
ar
y
in
g
th
e
co
n
tr
o
l
p
ar
am
eter
s
(
k
is
u
s
ed
h
er
e)
an
d
u
s
in
g
th
e
co
n
tin
u
atio
n
s
ch
em
e
m
eth
o
d
.
T
h
e
s
tab
ilit
y
o
f
th
e
s
o
lu
tio
n
s
w
ill
b
e
s
tu
d
ied
u
s
in
g
th
e
J
ab
co
b
ian
m
atr
ix
.
T
h
e
eig
en
v
alu
es
o
f
th
e
J
ac
o
b
ian
m
atr
ix
ev
a
lu
ated
at
th
e
eq
u
ilib
r
iu
m
p
o
in
t
(
as
a
f
u
n
ctio
n
o
f
k
)
d
eter
m
in
e
th
e
s
tab
ilit
y
o
f
th
e
s
o
lu
tio
n
an
d
th
e
ty
p
e
o
f
b
if
u
r
ac
tio
n
s
o
cc
u
r
as
th
e
co
n
tr
o
l
lin
g
p
ar
am
eter
is
v
ar
ied
.
I
n
th
is
p
ap
er
,
w
e
w
r
o
te
o
u
r
o
w
n
p
r
o
g
r
am
f
o
r
ca
lcu
latin
g
th
e
eq
u
ilib
r
iu
m
p
o
in
ts
an
d
th
e
ty
p
e
o
f
b
if
u
r
ca
tio
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s
o
cc
u
r
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ed
as th
e
co
n
tr
o
llin
g
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ar
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eter
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ar
ied
.
Sim
u
latio
n
is
p
r
f
o
r
m
ed
w
ith
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e
d
elay
o
f
0
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1
5
μ
s
ec
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d
d
if
f
er
en
t
v
alu
es
o
f
n
o
r
m
alize
d
co
n
tr
o
l
p
ap
r
am
eter
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k
.
f
o
r
k
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5
,
th
e
eq
u
lib
r
iu
m
s
o
lu
tio
n
(
co
n
s
tan
t
s
o
lu
tio
n
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o
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tain
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as
s
h
o
w
n
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Fig
u
r
e
3
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a)
b
elo
w
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s
k
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ea
s
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th
e
s
y
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tem
w
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lo
s
e
its
s
tab
ilit
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ia
a
Ho
p
f
b
if
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r
ca
tio
n
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in
t
H
at
=
3
.
28
,
an
d
a
p
er
io
d
ic
s
o
lu
tio
n
is
b
o
r
n
as
s
h
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w
n
in
Fig
u
r
e
3
(
b
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.
T
h
is
Ho
p
f
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if
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r
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is
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o
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n
d
to
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s
u
p
er
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itical
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o
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t
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ased
o
n
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e
eig
en
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alu
s
o
f
th
e
J
ac
o
b
iam
m
atr
ix
.
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r
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2
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en
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o
f
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m
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s
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s
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Fig
u
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es
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ea
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ilit
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ase
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elay
o
f
0
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5
μ
s
ec
.
(
a)
(
b
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(
c)
(
d
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Fig
u
r
e
3
.
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h
ase
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lan
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f
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e
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f
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d
if
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n
t n
o
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lized
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(
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it
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0
.
15
s
ec
,
=
1
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=
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,
(
a)
Stab
le
s
o
lu
tio
n
f
o
r
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2
.
5
,
(
b
)
Oscill
ato
r
y
s
o
l
u
tio
n
f
o
r
=
3
.
28
,
(
c)
P
e
r
io
d
-
2
b
if
u
r
ca
tio
n
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o
r
=
6
,
(
d
)
P
er
io
d
-
4
b
if
u
r
ca
tio
n
f
o
r
=
9
.
6
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
11
,
No
.
2
,
A
p
r
il
2
0
2
1
:
1
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3
1
-
1438
1436
Fig
u
r
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4
.
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h
ase
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lan
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t f
o
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ch
ao
tic
b
eh
av
io
r
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r
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alize
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=
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ab
le
1
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ilit
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f
o
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o
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er
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L
L
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h
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n
s
ta
n
t
ti
m
e
d
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y
(
0
.
1
5
μ
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ec
)
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o
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mal
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z
e
d
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p
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n
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o
o
p
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a
i
n
(
k
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n
st
a
b
i
l
i
t
y
<
3
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8
D
c
o
u
t
p
u
t
3
.
2
8
O
sci
l
l
a
t
o
r
y
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n
st
a
b
i
l
i
t
y
6
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e
r
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2
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t
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n
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6
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4
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r
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t
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n
1
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7
3
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r
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8
b
i
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r
c
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t
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23
C
h
a
o
s
T
ab
les
2
s
h
o
w
s
t
h
e
ef
f
ec
t
o
f
ti
m
e
d
ela
y
o
n
th
e
in
s
tab
ilit
i
es
o
f
th
e
s
o
lu
t
io
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d
its
ef
f
ec
t
o
n
th
e
ch
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tic
r
eg
io
n
.
W
ith
o
u
t
d
ela
y
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th
e
o
s
cilla
to
r
y
b
eh
a
v
io
r
o
f
t
h
e
s
y
s
te
m
s
tar
ts
a
t
o
p
en
lo
o
p
g
ain
o
f
7
.
3
4
1
an
d
th
e
ch
ao
tic
b
eh
a
v
io
r
b
eg
in
s
to
a
p
p
ea
r
at
o
p
en
lo
o
p
g
ai
n
eq
u
al
o
f
7
6
.
3
an
d
r
e
m
ai
n
s
at
th
is
f
o
r
v
a
lu
e
s
u
p
to
k
=
100
.
On
t
h
e
o
th
er
h
an
d
,
f
o
r
ti
m
e
d
elay
=
0
.
15
,
th
e
o
s
c
illato
r
y
b
eh
a
v
io
r
s
tar
ts
at
k
=3
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2
8
an
d
ch
ao
s
s
tar
ts
a
t
2
3
a
n
d
r
e
m
ai
n
s
i
n
t
h
is
s
tate
f
o
r
v
alu
e
s
o
f
k
u
p
to
1
1
8
.
2
.
I
t
is
clea
r
th
a
t
t
h
e
s
tab
le
r
eg
io
n
b
ec
o
m
e
s
n
ar
r
o
w
er
an
d
t
h
e
ch
ao
tic
r
eg
io
n
b
ec
o
m
es
w
id
er
as ti
m
e
d
ela
y
in
cr
ea
s
e
s
.
T
ab
le
2
.
I
n
s
tab
ilit
y
o
f
p
h
a
s
e
er
r
o
r
f
o
r
d
if
f
er
en
t v
a
lu
e
s
o
f
t
h
e
o
p
en
lo
o
p
g
ain
f
o
r
th
ir
d
o
r
d
er
P
L
L
w
it
h
d
i
f
f
er
e
n
t
ti
m
e
d
ela
y
O
p
e
n
l
o
o
p
g
a
i
n
(
k
)
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e
l
a
y
(
1
.
3
μs)
O
p
e
n
l
o
o
p
g
a
i
n
(
k
)
d
e
l
a
y
(
0
.5
μs)
O
p
e
n
l
o
o
p
g
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i
n
(
k)
d
e
l
a
y
(
0
.
1
5
μs)
O
p
e
n
l
o
o
p
g
a
i
n
(
k
)
(
n
o
d
e
l
a
y
)
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n
st
a
b
i
l
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t
y
<
0
.
5
7
<
1
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1
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<
3
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c
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t
p
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5
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1
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2
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3
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5
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2
9
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6
40
P
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r
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4
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3
0
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h
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s
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0
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C
h
a
o
t
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c
r
e
g
i
o
n
4.
CO
NCLU
SI
O
N
I
n
th
i
s
p
ap
er
,
n
e
w
r
es
u
lt
s
o
n
n
o
n
li
n
ea
r
an
al
y
s
i
s
o
f
t
h
ir
d
o
r
d
er
p
h
ase
lo
ck
ed
lo
o
p
(
PLL
)
w
it
h
f
ee
d
b
ac
k
ti
m
e
d
ela
y
ar
e
r
ep
o
r
ted
.
W
e
u
s
ed
th
e
m
o
d
er
n
n
o
n
lin
ea
r
th
eo
r
y
to
s
t
u
d
y
th
e
e
f
f
e
ct
o
f
ti
m
e
d
ela
y
o
n
th
e
s
tab
ilit
y
o
f
t
h
e
s
o
lu
tio
n
an
d
c
h
ao
tic
b
e
h
av
io
r
o
f
t
h
e
P
L
L
u
n
d
er
i
n
v
est
ig
atio
n
A
f
ir
s
t
o
r
d
er
P
ad
e
ap
p
r
o
x
i
m
a
tio
n
w
a
s
u
s
ed
to
d
e
r
iv
e
t
h
e
s
ta
te
s
p
ac
e
r
ep
r
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ta
tio
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o
f
th
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d
o
r
d
er
P
L
L
.
Dif
f
e
r
en
t
b
eh
a
v
io
r
w
er
e
id
en
ti
f
ied
f
o
r
t
h
is
cla
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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&
C
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I
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N:
2088
-
8708
C
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r
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in
time
d
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lo
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(
B
a
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s
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m
Ha
r
b
)
1437
RE
F
E
R
E
NC
E
S
[1
]
F. G
a
rd
n
e
r,
“
P
h
a
se
lo
c
k
T
e
c
h
n
iq
u
e
s,”
W
il
e
y
-
In
ter
sc
ien
c
e
,
Ne
w
J
e
rs
e
y
,
USA
,
2
0
0
5
.
[2
]
R.
Be
st,
“
P
h
a
se
-
L
o
c
k
e
d
L
o
o
p
s: De
sig
n
,
S
im
u
latio
n
,
a
n
d
A
p
p
l
ica
ti
o
n
s,”
M
c
Gr
a
w
-
Hill
,
2
0
0
7
.
[3
]
D.
S
tep
h
e
n
s,
“
P
h
a
se
-
L
o
c
k
e
d
L
o
o
p
s
f
o
r
W
irele
ss
Co
m
m
u
n
ica
ti
o
n
s:
Dig
it
a
l,
A
n
a
lo
g
a
n
d
O
p
ti
c
a
l
Im
p
lem
e
n
tatio
n
s,”
S
p
rin
g
e
r
,
2
0
0
7
.
[4
]
E.
Ra
d
w
a
n
,
e
t
a
l.
,
“
M
o
d
if
ied
P
h
a
se
L
o
c
k
e
d
L
o
o
p
f
o
r
G
rid
Co
n
n
e
c
t
e
d
S
i
n
g
le
P
h
a
se
In
v
e
rter,”
I
n
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.
9
,
n
o
.
5
,
p
p
.
3
9
3
4
-
3
9
4
3
,
2
0
1
9.
[5
]
J.
S
ten
sb
y
a
n
d
B.
Ha
rb
,
“
Co
m
p
u
ti
n
g
th
e
Ha
l
f
-
P
lan
e
P
u
ll
-
in
R
a
n
g
e
in
a
S
e
c
o
n
d
-
Ord
e
r
P
h
a
se
L
o
c
k
e
d
L
o
o
p
,
”
El
e
c
tro
n
ics
L
e
tt
e
rs
,
v
o
l.
3
1
,
n
o
.
1
1
,
p
p
.
8
4
5
-
8
4
6
,
1
9
9
5
.
[6
]
J.
P
i
q
u
e
ira,
e
t
a
l.
,
“
A
n
a
ly
z
in
g
th
e
Eff
e
c
t
o
f
th
e
P
h
a
se
-
Jitt
e
r
in
t
h
e
Op
e
ra
ti
o
n
o
f
S
e
c
o
n
d
Or
d
e
r
P
h
a
se
-
L
o
c
k
e
d
L
o
o
p
s,”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Circ
u
it
s
a
n
d
S
y
ste
ms
II
-
Exp
re
ss
Briefs
,
v
o
l.
5
2
,
n
o
.
6
,
p
p
.
3
3
1
-
3
3
5
,
2
0
0
5
.
[7
]
J.
P
i
q
u
e
ira
a
n
d
L
.
M
o
n
teiro
,
“
C
o
n
sid
e
ri
n
g
S
e
c
o
n
d
-
Ha
rm
o
n
ic
T
e
rm
s
in
th
e
Op
e
ra
ti
o
n
o
f
th
e
P
h
a
se
De
te
c
to
r
f
o
r
S
e
c
o
n
d
-
Or
d
e
r
P
h
a
se
-
L
o
c
k
e
d
L
o
o
p
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Circ
u
it
s
a
n
d
S
y
ste
ms
I:
Fu
n
d
a
me
n
ta
l
T
h
e
o
ry
a
n
d
Ap
p
li
c
a
ti
o
n
s
,
v
o
l
.
5
0
,
n
o
.
6
,
p
p
.
8
0
5
-
8
0
9
,
2
0
0
3
.
[8
]
L
.
M
o
n
teir
o
,
e
t
a
l.
,
“
Bi
f
u
rc
a
ti
o
n
A
n
a
l
y
si
s
f
o
r
T
h
ird
-
Ord
e
r
P
h
a
se
-
L
o
c
k
e
d
L
o
o
p
s,”
IEE
E
S
i
g
n
a
l
Pr
o
c
e
ss
in
g
L
e
tt
e
rs
,
v
o
l.
1
1
,
no.
5
,
p
p
.
4
9
4
-
4
9
6
,
2
0
0
4
.
[9
]
J.
P
iq
u
e
ira,
“
Us
in
g
Bif
u
rc
a
ti
o
n
s
in
t
h
e
De
term
in
a
ti
o
n
o
f
L
o
c
k
in
Ra
n
g
e
s
f
o
r
T
h
ird
-
Ord
e
r
P
h
a
se
-
L
o
c
k
e
d
L
o
o
p
s,”
Co
mm
u
n
ica
ti
o
n
s i
n
No
n
li
n
e
a
r S
c
i
e
n
c
e
a
n
d
Nu
me
ric
a
l
S
imu
l
a
ti
o
n
,
v
o
l.
1
4
,
n
o
.
5
,
p
p
.
2
3
2
8
-
2
3
3
5
,
2
0
0
9
.
[1
0
]
A
.
Ha
q
u
e
,
“
A
c
h
iev
in
g
P
u
ll
-
in
A
v
o
id
i
n
g
Cy
c
le
S
li
p
u
sin
g
S
e
c
o
n
d
-
Ord
e
r
P
L
L
s,”
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
a
n
d
Co
m
p
u
ter
E
n
g
i
n
e
e
rin
g
(
IJ
ECE
)
,
v
o
l.
4
,
n
o
.
2
,
p
p
.
2
4
3
-
2
5
6
,
2
0
1
4
.
[1
1
]
B
.
Ha
rb
a
n
d
J.
S
ten
sb
y
,
“
T
h
e
H
a
lf
-
P
lan
e
P
u
ll
-
In
Ra
n
g
e
o
f
a
S
e
c
o
n
d
-
Ord
e
r
P
h
a
se
-
L
o
c
k
e
d
L
o
o
p
,
”
J
o
u
rn
a
l
o
f
t
h
e
Fra
n
k
li
n
In
sti
tu
te
,
v
o
l.
3
3
3
,
no.
2
,
p
p
.
1
9
1
-
1
9
9
,
1
9
9
6
.
[1
2
]
B.
Ha
rb
,
e
t
a
l.
,
"
A
Co
ll
o
c
a
ti
o
n
-
B
a
se
d
A
lg
o
rit
h
m
F
o
r
A
n
a
l
y
z
in
g
Bi
f
u
rc
a
ti
o
n
s
in
P
h
a
se
L
o
c
k
e
d
L
o
o
p
s
w
it
h
T
a
n
lo
c
k
a
n
d
S
a
w
to
o
t
h
P
h
a
se
De
tec
to
rs
,
"
M
a
th
e
ma
ti
c
a
l
Pro
b
lem
s in
E
n
g
in
e
e
rin
g
,
v
o
l.
2
0
1
8
,
p
p
1
-
7
,
2
0
1
8
.
[1
3
]
T
.
En
d
o
a
n
d
L
.
C
h
u
a
,
“
Ch
a
o
s
f
ro
m
P
h
a
se
-
L
o
c
k
e
d
L
o
o
p
s
,
”
I
E
E
E
T
r
a
n
s
a
c
t
i
o
n
s
o
n
C
i
r
c
u
i
t
s
a
n
d
S
y
s
t
e
m
s
,
v
o
l
.
3
5
,
n
o
.
8
,
p
p
.
9
8
7
-
1
0
0
3
,
1
9
8
8
.
[1
4
]
E.
Bra
d
ley
a
n
d
E.
S
trau
b
,
“
Us
in
g
Ch
a
o
s
t
o
Bro
a
d
e
n
t
h
e
Ca
p
tu
re
Ra
n
g
e
o
f
P
h
a
se
-
L
o
c
k
e
d
L
o
o
p
:
Ex
p
e
rim
e
n
tal
V
e
rif
ica
ti
o
n
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Circ
u
it
s
a
n
d
S
y
ste
ms
I:
F
u
n
d
a
m
e
n
t
a
l
T
h
e
o
r
y
a
n
d
A
p
p
l
i
c
a
t
i
o
n
s
,
v
o
l
.
4
3
,
n
o
.
1
1
,
p
p
.
9
1
4
-
9
2
2
,
1
9
9
6
.
[1
5
]
A
.
Ha
rb
a
n
d
B.
Ha
rb
,
“
Ch
a
o
s
a
n
d
Bif
u
rc
a
ti
o
n
in
T
h
ird
Ord
e
r
P
h
a
se
-
L
o
c
k
e
d
L
o
o
p
s,”
Ch
a
o
s,
S
o
l
it
o
n
s
a
n
d
Fra
c
t
a
ls
,
v
o
l.
1
9
,
no.
3
,
p
p
.
6
6
7
-
6
7
2
,
2
0
0
4
.
[1
6
]
B.
C.
S
a
rk
a
r
a
n
d
S
.
Ch
a
k
ra
b
o
rty
,
“
S
e
lf
-
O
sc
il
latio
n
s
o
f
a
T
h
ird
Ord
e
r
P
L
L
in
P
e
rio
d
ic
a
n
d
Ch
a
o
ti
c
M
o
d
e
a
n
d
it
s
T
ra
c
k
in
g
in
a
S
lav
e
P
L
L
,
”
Co
mm
u
n
ica
ti
o
n
s
i
n
No
n
li
n
e
a
r
S
c
ie
n
c
e
a
n
d
Nu
me
ric
a
l
S
imu
l
a
ti
o
n
,
v
o
l.
1
9
,
n
o
.
3
,
pp.
7
3
8
-
7
4
9
,
2
0
1
4
.
[1
7
]
L
.
F
o
rtu
n
a
,
e
t
a
l.
,
“
Ch
a
o
ti
c
P
u
lse
P
o
sit
io
n
M
o
d
u
lati
o
n
to
Im
p
ro
v
e
th
e
Eff
icie
n
c
y
o
f
S
o
n
a
r
S
e
n
so
rs
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
In
str
u
me
n
ta
t
io
n
a
n
d
M
e
a
su
re
me
n
t
,
v
o
l.
5
2
,
n
o
.
6
,
p
p
.
1
8
0
9
-
1
8
1
4
,
2
0
0
3
.
[1
8
]
A
.
Ga
rb
o
,
e
t
a
l.
,
“
De
l
a
y
e
d
D
y
n
a
m
ics
in
a
n
El
e
c
tro
n
ic
Re
la
x
a
ti
o
n
Os
c
il
lato
r,
”
Ph
y
sic
a
l
Rev
iew
E
,
v
o
l.
1
0
0
,
p
.
0
3
2
2
2
4
,
2
0
1
9
.
[1
9
]
R.
S
u
re
sh
a
n
d
V
.
K.
C
h
a
n
d
ra
se
k
a
r,
“
In
f
lu
e
n
c
e
o
f
T
i
m
e
-
D
e
la
y
F
e
e
d
b
a
c
k
o
n
Ex
trem
e
E
v
e
n
ts
in
a
F
o
rc
e
d
L
ién
a
rd
S
y
st
e
m
,
”
Ph
y
sic
a
l
Rev
iew E
,
v
o
l.
9
8
,
p
.
0
5
2
2
1
1
,
2
0
1
8
.
[2
0
]
O.
M
.
K
w
o
n
,
e
t
a
l.
,
“
S
e
c
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re
Co
m
m
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ica
ti
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n
Ba
se
d
o
n
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a
o
ti
c
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ro
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iza
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ia
In
terv
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l
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m
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y
in
g
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l
a
y
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e
e
d
b
a
c
k
Co
n
tr
o
l,
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No
n
li
n
e
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r Dy
n
a
mic
s
,
v
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l.
6
3
,
p
p
,
2
3
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-
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5
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0
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1
.
[2
1
]
R.
V
a
ll
e
e
a
n
d
C.
De
li
sle
,
“
Ro
u
t
e
to
Ch
a
o
s
ia
a
n
Ac
u
sto
-
Op
ti
c
Bistab
le
De
v
ice
,
”
Ph
y
sic
a
l
Rev
iew
.
A
,
v
o
l.
3
1
,
p
.
2
3
9
0
,
1
9
8
5
.
[2
2
]
M
.
L
e
Be
rre
,
e
t
a
l.
,
“
Ty
p
e
-
I
In
term
it
ten
c
y
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u
te
to
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h
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o
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in
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le
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it
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tard
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d
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fe
re
n
ti
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l
Diff
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r
e
n
c
e
S
y
ste
m
,
”
J
o
u
rn
a
l
o
f
th
e
Op
ti
c
a
l
S
o
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iety
o
f
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ric
a
B
,
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l.
5
,
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o
.
5
,
p
p
.
1
0
5
1
-
1
0
6
2
,
1
9
8
8
.
[2
3
]
Y.
S
o
n
g
,
e
t
a
l.
,
“
S
tab
il
it
y
a
n
d
Ho
p
f
Bif
u
rc
a
ti
o
n
i
n
a
M
o
d
e
l
o
f
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n
e
Ex
p
re
ss
io
n
w
it
h
Distri
b
u
ted
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i
m
e
De
l
a
y
s,”
Ap
p
li
e
d
M
a
t
h
e
ma
ti
c
s a
n
d
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o
mp
u
ta
ti
o
n
,
v
o
l.
2
4
3
,
p
p
.
3
9
8
-
4
1
2
,
2
0
1
4
.
[2
4
]
Y.
F
e
n
g
a
n
d
Z.
W
e
i.
,
“
De
lay
e
d
F
e
e
d
b
a
c
k
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n
tr
o
l
a
n
d
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u
rc
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ti
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n
A
n
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l
y
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o
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th
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e
n
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ra
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d
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p
ro
tt
B
S
y
ste
m
w
it
h
Hid
d
e
n
A
tt
ra
c
to
rs,”
T
h
e
Eu
r
o
p
e
a
n
P
h
y
sic
a
l
J
o
u
rn
a
l
S
p
e
c
ia
l
T
o
p
ics
,
v
o
l
.
2
2
4
,
p
p
.
1
6
1
9
-
1
6
3
6
,
2
0
1
5
.
[2
5
]
K.
Ik
e
a
d
a
a
n
d
K.
M
a
tsu
m
o
to
,
“
S
tu
d
y
o
f
a
Hi
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h
-
Dim
e
n
sio
n
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l
Ch
a
o
ti
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tt
ra
c
to
r
,
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J
o
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rn
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l
o
f
S
t
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stica
l
Ph
y
sic
s
,
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l.
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4
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p
p
.
9
5
5
-
9
8
3
,
1
9
8
6
.
[2
6
]
F
.
A
ta
y
a
n
d
H.
Ru
a
n
,
“
S
y
m
m
e
tr
y
A
n
a
l
y
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f
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p
led
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lar
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ste
m
s
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n
d
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r
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m
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rity
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l.
2
8
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.
3
,
p
p
.
7
9
5
-
8
2
4
,
2
0
1
5
.
[2
7
]
R.
Ye
n
ice
ri
a
n
d
M
.
Ya
lcin
,
“
M
u
lt
i
-
S
c
ro
ll
Ch
a
o
t
ic
A
tt
ra
c
to
rs
f
ro
m
a
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n
e
ra
li
z
e
d
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i
m
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-
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la
y
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a
m
p
led
-
Da
ta
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st
e
m
,
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In
ter
n
a
ti
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n
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l
J
o
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r
n
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l
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Circ
u
it
T
h
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ry
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n
d
Ap
p
li
c
a
ti
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n
s
,
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l.
4
4
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o
.
6
,
p
p
.
1
2
6
3
-
1
2
7
6
,
2
0
1
6
.
[2
8
]
M
.
S
c
h
a
n
z
a
n
d
A
.
P
e
lster,
“
A
n
a
ly
ti
c
a
l
a
n
d
Nu
m
e
r
ica
l
In
v
e
stig
a
ti
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o
f
th
e
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h
a
se
-
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c
k
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L
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o
p
w
it
h
T
ime
De
la
y
,
”
Ph
y
sic
a
l
Rev
iew E
,
v
o
l.
6
7
,
n
o
.
5
,
p
.
0
5
6
2
0
5
,
2
0
0
3
.
[2
9
]
J.
Bu
c
k
w
a
lt
e
r
a
n
d
R.
Y
o
rk
,
“
T
ime
De
la
y
Co
n
sid
e
ra
ti
o
n
s
in
Hig
h
-
F
re
q
u
e
n
c
y
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h
a
se
-
L
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c
k
e
d
L
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o
p
,
”
2
0
0
2
I
EE
E
Ra
d
i
o
Fre
q
u
e
n
c
y
In
teg
r
a
ted
Cir
c
u
it
s
(
RF
IC)
S
y
mp
o
siu
m.
Dig
e
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f
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p
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rs
(
Ca
t.
No
.
0
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CH3
7
2
8
0
)
,
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USA
,
2
0
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p
p
.
1
8
1
-
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.
[3
0
]
M
.
G
ra
n
t,
e
t
a
l,
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T
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rf
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rm
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n
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li
g
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lay
,
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.
4
,
p
p
.
5
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1
9
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7
.
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(JEA
).
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s
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m
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S
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.
(8
5
),
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.
S
c
.
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8
8
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n
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h
D
(9
5
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S
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),
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n
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Un
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w
a
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n
a
d
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e
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ti
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t
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1
9
8
8
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n
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1
9
9
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in
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w
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t
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0
0
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)
.
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re
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r
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r
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m
m
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n
s,
m
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lt
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le
a
c
c
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h
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m
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tru
m
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n
d
M
IM
O
c
o
m
m
u
n
ica
ti
o
n
sy
st
e
m
s.
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e
is a m
e
m
b
e
r
o
f
IEE
E
a
n
d
JEA
.
Ahm
a
d
M
.
H
a
r
b
(M
'
9
8
-
S
M
'
0
6
)
w
a
s
b
o
rn
in
Irb
i
d
,
J
o
rd
a
n
,
i
n
1
9
6
3
.
He
re
c
e
iv
e
d
th
e
P
h
.
D
.
d
e
g
re
e
f
ro
m
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irg
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ia
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o
ly
tec
h
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ic
In
stit
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te
a
n
d
S
tate
Un
iv
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y
,
Blac
k
sb
u
rg
,
V
A
,
in
1
9
9
6
,
t
h
e
M
.
S
.
d
e
g
re
e
f
ro
m
th
e
Jo
rd
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n
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i
v
e
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y
o
f
S
c
ien
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e
a
n
d
T
e
c
h
n
o
lo
g
y
,
Irb
id
,
Jo
rd
a
n
,
in
1
9
9
0
,
a
n
d
th
e
B.
S
.
d
e
g
re
e
f
ro
m
Y
a
r
m
o
u
k
Un
iv
e
rsity
,
Irb
id
,
Jo
r
d
a
n
,
in
1
9
8
7
,
a
ll
in
e
lec
tri
c
a
l
e
n
g
in
e
e
rin
g
.
,
Cu
rre
n
tl
y
,
A
h
m
a
d
i
s
a
P
ro
f
e
ss
o
r
a
t
G
e
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