I
nte
rna
t
io
na
l J
o
urna
l o
f
P
o
wer
E
lect
ro
nics
a
nd
Driv
e
S
y
s
t
em
s
(
I
J
P
E
DS
)
Vo
l.
1
2
,
No
.
1
,
Ma
r
2
0
2
1
,
p
p
.
356
~
3
6
3
I
SS
N:
2088
-
8
6
9
4
,
DOI
: 1
0
.
1
1
5
9
1
/
ijp
ed
s
.
v1
2
.i
1
.
pp
3
5
6
-
363
356
J
o
ur
na
l ho
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ep
a
g
e
:
h
ttp
:
//ij
p
e
d
s
.
ia
esco
r
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co
m
H
a
rmo
nics
elimi
n
a
tion
for DC
/DC
po
wer supply
bas
ed on
piezo
elect
ri
c f
i
lte
rs
H
a
s
a
n M
a
Alm
g
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ir
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E
na
a
m A.
K
ha
liq
Ali
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Wedia
n H
.
A
bd
a
l a
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ee
r
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M
us
t
a
f
a
A.
F
a
del A
l
-
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a
is
i
De
p
a
rt
m
e
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t
o
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El
e
c
tri
c
a
l
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n
g
i
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g
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Co
ll
e
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En
g
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rin
g
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M
u
sta
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siriy
a
h
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n
iv
e
rsit
y
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Ba
g
h
d
a
d
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Ira
q
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
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y:
R
ec
eiv
ed
Ap
r
3
,
2
0
20
R
ev
is
ed
J
an
6
,
2
0
2
1
Acc
ep
ted
J
an
26
,
2
0
2
1
Th
is
re
se
a
rc
h
p
re
se
n
ts
a
stu
d
y
,
m
o
d
e
ll
i
n
g
a
n
d
sim
u
latio
n
o
f
t
h
e
p
i
e
z
o
e
lec
tri
c
m
a
teria
l
wo
rk
a
s
fil
ters
(
p
iez
o
e
lec
tri
c
fil
ter)
u
se
d
to
e
l
imin
a
te
th
e
h
a
rm
o
n
ics
in
p
o
we
r
e
lec
tro
n
ic
c
ircu
it
s
,
h
ig
h
o
r
d
e
r
h
a
rm
o
n
ics
a
re
g
e
n
e
ra
ti
n
g
d
u
e
t
o
th
e
h
ig
h
sw
it
c
h
in
g
fre
q
u
e
n
c
ies
a
n
d
c
ircu
it
e
q
u
ip
m
e
n
t
,
d
e
tailed
si
m
u
latio
n
is
a
c
h
iev
e
d
f
o
r
th
e
p
iez
o
e
lec
tri
c
fi
lt
e
r
tes
ted
in
fu
l
l
-
b
ri
d
g
e
DC/DC
c
o
n
v
e
rter
c
ircu
it
wit
h
re
sistiv
e
lo
a
d
wo
r
k
s
a
s
d
c
p
o
we
r
su
p
p
ly
(1
2
t
o
4
8
v
o
lt
)
.
As
a
re
su
lt
,
t
h
e
u
se
s
o
f
p
iez
o
e
lec
tri
c
fil
ters
h
a
v
e
a
g
re
a
t
imp
a
c
t
o
n
h
a
rm
o
n
ics
e
li
m
in
a
ti
o
n
,
wh
ic
h
lea
d
s
t
o
re
d
u
c
e
th
e
o
v
e
ra
ll
to
tal
h
a
rm
o
n
ic
d
ist
o
rti
o
n
lea
d
s
to
in
c
re
a
se
th
e
e
fficie
n
c
y
,
a
s
we
ll
a
s
th
e
o
u
t
p
u
t
v
o
lt
a
g
e
fro
m
t
h
e
d
c
p
o
we
r
su
p
p
l
y
re
m
a
in
c
o
n
sta
n
t
b
y
v
a
ry
i
n
g
th
e
l
o
a
d
re
sista
n
c
e
o
v
e
r
a
wi
d
e
ra
n
g
e
.
Th
e
d
c
p
o
we
r
su
p
p
l
y
c
ircu
i
t
i
n
c
lu
d
in
g
t
h
e
p
iez
o
e
lec
tri
c
fil
ter
h
a
s
b
e
e
n
sim
u
late
d
u
sin
g
P
S
I
M
(V9
.
1
)
p
o
we
r
e
lec
tro
n
ic circ
u
it
sim
u
latio
n
so
ftwa
re
.
K
ey
w
o
r
d
s
:
DC
/D
C
p
o
wer
s
u
p
p
ly
Piezo
elec
tr
ic
m
ater
ial
Piezo
elec
tr
ic
f
ilter
s
Har
m
o
n
ics
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Mu
s
taf
a
A.
Fad
el
Al
-
Qaisi
Dep
ar
tm
en
t o
f
E
lectr
ical
E
n
g
i
n
ee
r
in
g
Mu
s
tan
s
ir
iy
ah
Un
iv
er
s
ity
B
ab
Alm
u
ad
am
,
B
ag
h
d
a
d
,
I
r
a
q
E
m
ail: m
u
s
taf
a_
1
9
8
8
ab
b
as@
u
o
m
u
s
tan
s
ir
iy
ah
.
ed
u
.
iq
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
p
iezo
elec
tr
ic
m
ater
ials
(
PZ)
h
av
e
b
ee
n
wid
ely
u
s
ed
f
o
r
th
e
last
two
d
ec
a
d
es
in
elec
tr
o
n
ic
ap
p
licatio
n
s
,
th
e
p
o
s
s
ib
ilit
ies
o
f
p
iezo
’
s
u
s
ag
e
ar
e
alm
o
s
t
en
d
less
,
s
u
ch
in
th
e
co
m
m
u
n
ic
atio
n
f
ield
,
s
en
s
o
r
s
(
u
ltra
s
o
n
ic
s
en
s
o
r
s
,
k
n
o
ck
s
en
s
o
r
s
,
s
h
o
ck
s
en
s
o
r
s
,
a
cc
eler
ati
o
n
s
en
s
o
r
s
,
s
ca
n
n
in
g
p
r
o
b
e
m
icr
o
s
co
p
e
s
ca
n
n
er
s
)
,
p
o
wer
s
o
u
r
ce
s
(
elec
tr
ical
-
m
ec
h
an
ical
t
r
an
s
d
u
ce
r
s
)
,
s
tick
-
s
lip
m
o
to
r
s
,
u
ltra
s
o
n
ic
clea
n
er
s
p
iezo
elec
tr
ic
ac
tu
ato
r
s
,
p
iezo
elec
tr
ic
f
a
n
s
,
f
ilter
s
(
ce
r
am
ic
r
eso
n
ato
r
s
,
c
er
am
ic
f
ilter
s
,
m
icr
o
f
o
r
m
s
,
a
n
d
s
u
r
f
ac
e
ac
o
u
s
tic
wav
e
f
ilter
s
)
.
[
1
]
,
[
2
]
.
T
h
e
f
ir
s
t
em
p
ir
ical
m
an
if
estatio
n
o
f
a
r
elatio
n
s
h
ip
b
etwe
e
n
th
e
m
icr
o
s
co
p
ic
p
iezo
elec
tr
ic
p
h
en
o
m
e
n
o
n
an
d
th
e
cr
y
s
tallo
g
r
ap
h
ic
b
o
d
y
w
as
r
elea
s
ed
b
y
J
ac
q
u
es
C
u
r
ie
an
d
Pier
r
e
in
1
8
8
0
[
3
]
.
T
h
ey
p
r
ep
ar
ed
s
p
ec
ial
c
r
y
s
tals
u
s
in
g
(
q
u
ar
tz,
to
u
r
m
a
lin
e,
s
u
g
ar
-
ca
n
e
,
to
p
az
,
an
d
R
o
ch
elle
-
s
alt)
an
d
m
ea
s
u
r
e
th
e
ch
ar
g
es
o
n
th
e
s
u
r
f
ac
e
o
f
th
e
cr
y
s
tals
wh
en
m
ec
h
an
ical
s
tr
ess
s
u
b
jecte
d
t
o
it.
Ma
n
y
k
n
o
wn
m
ater
ials
o
wn
p
iezo
elec
tr
ic
f
e
atu
r
es,
s
u
ch
as
m
ater
ials
m
ad
e
o
f
ce
r
am
ic
(
e.
g
.
L
ea
d
-
zir
c
o
n
ate
-
titan
ate
(
PZT
)
)
an
d
cr
y
s
tal
(
e.
g
.
Qu
ar
tz)
an
d
[
4
]
-
[
6
]
.
T
h
e
ef
f
ec
t
o
f
p
iezo
elec
tr
ic
o
u
t
co
m
e
f
r
o
m
th
e
elec
tr
o
-
m
ec
h
a
n
ical
in
ter
ac
tio
n
in
th
e
cr
y
s
tal
m
ater
ials
,
wh
ich
h
a
p
p
en
e
d
b
etwe
en
th
e
elec
tr
ical
an
d
m
ec
h
an
ical
s
tates
o
f
t
h
e
cr
y
s
tal
[
7
]
.
T
h
e
p
iez
o
elec
tr
ic
m
ater
ials
ar
e
m
ater
ials
th
at
g
en
er
ate
a
ch
ar
g
e
wh
en
th
ey
ar
e
s
q
u
ee
ze
d
o
r
p
o
s
itio
n
ed
u
n
d
er
m
ec
h
an
is
tic
s
tr
ain
.
T
h
e
o
p
er
atio
n
o
f
PZ
m
ater
ials
is
also
r
ev
er
s
ib
le,
s
o
if
an
elec
tr
ic
f
ield
is
ap
p
lied
to
th
ese
m
ater
i
als,
th
ey
will
s
tar
t
v
ib
r
atin
g
an
d
th
eir
s
h
a
p
e
wi
ll
ch
an
g
e
s
lig
h
tly
(
m
ec
h
an
ic
al
s
tr
ain
)
,
PZ
m
ater
ials
also
k
n
o
w
n
as
elec
tr
o
-
m
ec
h
an
ical
m
ater
ials
,
wh
ich
ca
n
s
im
p
ly
d
ef
in
e
as
a
d
ev
ice
co
n
v
er
ts
m
ec
h
an
ical
en
e
r
g
y
to
elec
tr
ical
en
er
g
y
[8
]
,
[
9
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2
0
8
8
-
8
694
Ha
r
mo
n
ics elimin
a
tio
n
fo
r
DC
/D
C
p
o
w
er su
p
p
ly
b
a
s
ed
o
n
p
iezo
elec
tr
ic
filt
e
r
s
(
Ha
s
a
n
M
a
A
lmg
o
tir
)
357
Fig
u
r
e
1
s
h
o
ws
th
at
th
e
p
iez
o
elec
tr
ic
m
ater
ials
ar
e
co
m
p
o
s
ed
o
f
an
ar
r
an
g
em
en
t
o
f
a
p
o
lar
i
ze
d
m
ater
ial
th
at
is
in
a
n
eu
tr
al
s
tate
d
u
e
to
th
e
asy
m
m
etr
ical
d
is
tr
ib
u
tio
n
o
f
ch
ar
g
e.
B
y
d
ef
o
r
m
in
g
th
e
m
ater
ial,
a
ch
ar
g
e
ca
n
b
e
cr
ea
ted
f
r
o
m
a
r
ea
lig
n
m
en
t
o
f
th
e
p
o
lar
iz
ed
s
tr
u
ctu
r
e.
T
h
is
p
r
o
d
u
ce
s
a
v
o
ltag
e
ac
r
o
s
s
a
s
ep
ar
atio
n
d
is
tan
ce
w
h
ich
ca
n
also
b
e
d
escr
ib
ed
as
an
elec
tr
i
c
f
ield
.
PZ
m
ater
ials
s
h
o
w
v
er
y
s
tr
o
n
g
f
r
eq
u
e
n
cy
r
elian
ce
wh
en
m
ec
h
an
ical
an
d
elec
tr
ical
en
er
g
y
a
r
e
co
u
p
led
[
10
]
-
[
1
2
]
.
Fig
u
r
e
1
.
Piezo
elec
tr
ic
ef
f
ec
t in
cr
y
s
tal
m
ater
ials
.
As
th
e
p
r
ev
io
u
s
s
tate
o
f
ar
t,
a
u
th
o
r
s
in
[
1
3
]
d
is
cu
s
s
th
e
ess
en
tial
b
o
u
n
d
ar
ies
o
f
elec
tr
o
-
m
ec
h
an
ical
en
er
g
y
tr
an
s
f
o
r
m
atio
n
ca
p
ab
i
lity
o
f
p
iez
o
elec
tr
ic
tr
an
s
f
o
r
m
er
s
(
PTs).
I
n
p
ap
er
[
1
4
]
a
u
th
o
r
s
p
r
o
p
o
s
ed
a
m
eth
o
d
to
r
aise
th
e
p
o
wer
d
e
n
s
ity
o
f
PTs
b
y
co
n
tact
h
ea
t
tr
an
s
f
er
s
tr
u
ctu
r
e
to
t
h
e
PTs.
T
h
e
au
th
o
r
in
[
1
5
]
s
h
o
ws
th
e
ap
p
licatio
n
s
o
f
p
iezo
elec
tr
ic
f
ilter
s
an
d
r
eso
n
ato
r
s
.
T
h
e
au
th
o
r
s
in
[
1
6
]
o
f
f
er
a
d
esig
n
o
f
a
PZ
fil
ter
m
o
d
u
le
u
s
ed
f
o
r
r
e
m
o
v
in
g
h
a
r
m
o
n
ic
f
r
eq
u
e
n
cies
in
PTs
an
d
co
m
p
ar
ed
th
e
d
esig
n
ed
f
ilter
wi
th
a
co
n
v
en
tio
n
al
in
d
u
cto
r
filt
er
.
I
n
[
1
7
]
a
u
th
o
r
s
u
s
e
m
u
ltip
le
-
co
n
n
ec
ted
Piezo
elec
tr
ic
T
r
an
s
f
o
r
m
e
r
s
to
ac
h
iev
e
h
ig
h
er
o
u
tp
u
t
p
o
wer
an
d
r
ed
u
ce
d
m
ec
h
an
ica
l lo
s
s
.
T
h
is
p
ap
er
is
o
r
g
an
ized
as
f
o
llo
ws.
Sectio
n
2
s
h
o
ws
th
e
b
asi
c
in
tr
o
d
u
ctio
n
a
n
d
m
o
d
eli
n
g
o
f
th
e
P
Fs
.
Sectio
n
3
p
r
esen
ts
th
e
an
aly
s
is
an
d
d
is
cu
s
s
io
n
f
o
r
t
h
e
d
ev
el
o
p
ed
p
o
wer
s
u
p
p
ly
a
n
d
el
im
i
n
a
te
h
ar
m
o
n
ics
u
s
in
g
PF
,
wh
ich
is
v
er
ified
th
r
o
u
g
h
s
im
u
latio
n
r
esu
lts
,
f
o
llo
wed
b
y
th
e
co
n
clu
s
io
n
s
an
d
f
u
t
u
r
e
wo
r
k
in
Sectio
n
4
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
2
.
1
.
P
iez
o
elec
t
ric
f
ilte
rs ba
s
ics
Ha
rm
o
ni
c
s
app
ear
s
o
n
th
e
elec
t
ri
c
s
y
stem
as
abru
p
t
sh
o
rt
p
u
lses
in
ele
c
t
ri
c
vo
l
t
a
g
es
and
c
u
rr
en
ts,
w
h
ic
h
c
rea
ted
b
y
t
h
e
elec
t
ro
n
ic
c
ir
c
u
it
e
quip
men
t
(
w
ir
es
,
tr
ansf
o
rme
rs,
and
indu
c
t
o
rs)
and
mac
h
ine
ry
c
a
n
malfu
nct
io
n
o
r
fail
in
the
p
resence
o
f
h
igh
h
ar
monic
v
o
lt
age
and/o
r
c
u
r
rent
lev
els
,
the
h
ar
mon
ic
d
isto
rt
i
o
n
th
at
app
e
a
rs
in
the
el
ec
t
ro
n
ic
c
ir
c
u
it
s
h
as
b
e
c
o
me
a
g
ro
w
ing
c
o
n
c
er
n
,
w
h
ic
h
deg
r
ade
s
the
l
evel
o
f
p
o
w
er
qua
li
t
y
and
it
s
ef
fic
ien
c
y
.
Ha
rm
o
ni
c
s
ar
e
es
p
ec
ia
l
ly
p
re
va
len
t
w
h
en
there
ar
e
many
p
ers
o
nal
c
o
mp
u
te
rs,
la
se
r
p
ri
n
ter
s,
fax
m
ac
h
in
es,
c
o
p
ier
s,
o
r
med
i
c
al
tes
t
equip
men
t
,
fluores
c
ent
l
igh
ti
ng
,
u
ninter
rup
ti
b
le
p
o
w
er
su
p
p
li
es
(
UP
S
s)
,
and
va
ri
ab
le
sp
eed
driv
es
al
l
o
n
the
same
ele
c
tr
ic
al
syst
em.
T
h
e
p
iez
o
ele
c
t
ri
c
i
nf
luen
c
e
is
quite
stu
di
ed
thes
e
d
ay
s
du
e
to
i
ts
h
u
g
e
app
li
c
at
i
o
ns
in
p
o
w
er
c
o
nv
ersi
o
n
c
ir
c
u
it
s
[
1
4
].
For
h
igh
frequen
c
ies
fil
ter
ing
it
’
s
more
diff
i
c
u
lt
to
make
mechan
ic
al
filt
ers
,
du
e
to
the
dim
ens
io
ns
o
f
the
me
c
h
ani
c
al
r
esonat
o
r
sh
ri
nks
in
ver
s
e
ly
to
the
reso
nan
t
frequen
c
y
[1
5
]
so
P
Fs
ar
e
ver
y
su
it
able
for
h
igh
-
fr
equen
c
y
filt
er
ing
app
l
ic
at
i
o
ns
.
T
h
e
P
Fs
ar
e
devic
es
that
tr
ansf
o
rm
ele
c
tr
ic
al
energ
y
b
y
the
mean
in
g
o
f
mechanic
al
vi
b
ra
ti
o
n.
T
h
ese
devic
es
ar
e
fab
ri
c
at
ed
u
sing
P
Z
ma
ter
i
al
s
that
ar
e
w
o
rki
ng
at
res
o
nance.
B
y
u
sing
su
it
able
de
sig
n
and
la
y
o
u
t
,
i
t
is
c
o
n
c
eiv
able
to
eli
m
inat
e
the
h
ar
moni
c
s
in
the
sig
nals
w
it
h
o
u
t
u
sing
any
elemen
ts
li
ke
indu
c
t
o
r
o
r
c
apa
c
it
o
r,
w
h
ic
h
lea
ds
to
g
ai
n
ver
y
h
igh
elec
t
ro
me
c
h
a
nic
a
l
tr
ansf
o
r
mati
o
n
effic
ie
ncy
,
h
igh
stabili
ty
,
h
igh
mac
h
inabil
it
y
[1
8
].
P
Fs
ar
e
the
b
est
c
h
o
ic
e
o
v
er
the
tr
adit
i
o
na
l
filt
ers
du
e
to
P
Fs
ar
e
lo
w
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
1
2
,
No
.
1
,
Ma
r
c
h
2
0
2
1
:
356
–
3
6
3
358
w
eig
h
t,
lo
w
c
o
s
t,
sm
al
l
size
and
not
a
ffect
ed
b
y
elec
tr
i
c
al
noi
se
[
1
6
].
T
h
ese
b
enef
it
s
make
P
F
ver
y
h
elpf
u
l
for
a
lo
t
o
f
app
li
c
at
i
o
ns
inc
lud
ing
the
D
C
and
AC
p
o
w
er
su
p
p
li
es
u
sed
in
elec
t
ro
ni
c
devi
c
e
s
[1
9
],
step
-
u
p
tr
ansf
o
rmers
,
p
la
sm
a
sourc
es
[2
0
],
and
in
inve
rt
ers
for
disp
la
y
b
ac
k
-
l
igh
ti
ng
,
du
st
c
lea
n
ing
c
o
ll
e
c
t
o
rs
,
p
ri
nt
in
g
mac
h
ines
and
im
age
ma
c
h
ines.
S
inc
e
then
,
the
de
v
elo
p
men
t
o
f
P
Fs
thro
u
g
h
h
isto
r
y
h
as
b
een
li
nked
to
the
p
ert
inent
w
o
rk
o
f
some
exc
e
ll
ent
inv
estiga
to
rs
as
w
el
l
as
to
the
g
ro
w
th
in
ma
ter
i
al
s,
ind
u
stri
al
iz
a
ti
o
n
p
ra
c
t
ic
abili
t
y
,
and
driv
ing
c
ir
c
u
it
mech
ani
sm
[
21]
.
Fig
u
r
e
2
s
h
o
ws
th
e
ty
p
e
o
f
ce
r
am
ic
PF
,
wh
ich
co
n
s
is
ts
o
f
t
wo
elec
tr
o
d
es
ar
e
m
o
u
n
ted
at
th
e
to
p
an
d
b
o
tto
m
o
f
th
e
PZ
ce
r
am
ics.
W
h
en
th
er
e
is
a
s
tr
ess
o
n
th
e
PZ,
it
p
r
o
d
u
ce
s
p
o
lar
izatio
n
wh
ich
is
a
lin
ea
r
f
u
n
ctio
n
o
f
t
h
e
s
tr
ess
(
p
iezo
el
ec
tr
ic
ef
f
ec
t
)
,
a
n
d
wh
e
n
a
p
ie
zo
elec
tr
ic
s
u
b
s
tan
c
e
h
as
an
elec
tr
ic
f
ield
ap
p
lie
d
ac
r
o
s
s
its
elec
tr
o
d
es,
it
p
r
o
d
u
ce
s
d
is
to
r
tio
n
wh
ich
is
a
lin
ea
r
f
u
n
ctio
n
o
f
th
e
elec
tr
ic
f
ield
(
r
ev
e
r
s
e
p
iezo
elec
tr
ic
ef
f
ec
t
)
an
AC
v
o
ltag
e
s
ig
n
al
with
ce
r
tain
f
r
eq
u
en
cy
is
s
u
b
m
itted
o
n
th
e
ter
m
in
als
o
f
th
e
PF
,
a
p
o
wer
f
u
l
m
ec
h
a
n
ical
v
ib
r
atio
n
is
p
r
o
d
u
ce
d
b
y
in
v
er
s
e
PZ
e
f
f
ec
t
[
1
3
]
,
[
2
2
]
.
T
h
e
elec
tr
ical
e
q
u
iv
alen
t
cir
c
u
it
o
f
th
e
PF
is
s
h
o
wn
b
elo
w
in
Fig
u
r
e
3
,
wh
ich
it
ca
n
b
e
s
ee
n
th
at
it
co
n
s
is
ts
o
f
an
R
L
C
s
er
ies
b
r
an
c
h
(
R
1
,
L
1
,
an
d
C
1
)
r
ep
r
esen
ts
th
e
in
er
tia,
f
r
ic
tio
n
,
an
d
s
tiff
n
ess
o
f
th
e
cr
y
s
t
al
co
n
n
ec
te
d
in
p
ar
allel
to
ca
p
ac
itan
ce
C
0
,
wh
ich
r
ep
r
esen
t th
e
s
elf
-
ca
p
ac
ito
r
o
f
th
e
cr
y
s
tal
[
2
3
]
.
Fig
u
r
e
2
.
C
er
am
ic
ty
p
e
PF
.
Fig
u
r
e
3
.
PF
s
eq
u
iv
alen
t c
ir
c
u
it
.
2.
2.
P
iezo
elec
t
ric
f
ilte
r
m
o
de
llin
g
As
m
e
n
tio
n
b
ef
o
r
e
th
e
PF
ch
ar
ac
ter
is
tics
f
o
r
th
e
p
iezo
elec
tr
i
c
ef
f
ec
t
an
d
r
ev
e
r
s
e
p
iezo
elec
tr
ic
ef
f
ec
t
ca
n
b
e
illu
s
tr
ated
in
th
e
(
1
)
(
2
)
[
2
0
]
:
=
(
1
)
=
(
2
)
wh
er
e
(
P
)
is
th
e
p
o
lar
izatio
n
,
(
T
)
is
th
e
s
tr
ess
m
ea
s
u
r
ed
i
n
[
N/m
2
]
,
(
S
)
d
is
to
r
tio
n
,
(
E
)
elec
tr
ic
f
ield
m
ea
s
u
r
e
d
in
[
V/m
]
an
d
(
d)
p
iezo
elec
tr
ic
s
tr
ain
co
n
s
tan
t.
Fo
r
a
n
elastic
m
ater
ial,
th
e
r
elatio
n
s
h
ip
o
f
d
is
to
r
tio
n
S
t
o
th
e
s
tr
ess
T
i
s
g
iv
en
b
y
(
3
)
an
d
f
o
r
a
d
ielec
tr
ic
s
u
b
s
tan
ce
,
th
e
r
elatio
n
s
h
ip
o
f
elec
tr
ical
d
is
p
lace
m
en
t
D
with
elec
tr
ic
f
ield
s
tr
en
g
th
E
is
g
iv
e
n
b
y
(
4
)
[
2
4
]
:
=
(
3
)
=
(
4
)
wh
er
e
(
s
E
)
is
th
e
co
m
p
lian
ce
,
(
ε
)
is
th
e
PZ
p
er
m
itti
v
ity
at
co
n
s
tan
t
s
tr
ain
an
d
(
D)
is
th
e
e
lectr
ic
d
is
p
lace
m
en
t
m
ea
s
u
r
ed
in
[
C
/m
2
].
T
h
e
PZ
m
ain
eq
u
atio
n
s
in
s
tr
ess
ch
ar
g
e
f
o
r
m
ar
e
s
h
o
wn
b
y
(
5
)
an
d
(
6
)
.
T
h
ese
e
q
u
atio
n
s
ca
lled
th
e
b
asic
p
iezo
elec
tr
ic
eq
u
ati
o
n
s
,
wh
ic
h
c
h
ar
ac
ter
ize
th
e
c
o
n
n
ec
tio
n
b
etwe
en
th
e
m
ec
h
an
ical
an
d
t
h
e
elec
tr
ical
s
tates.
Alth
o
u
g
h
v
ar
i
o
u
s
v
ib
r
atio
n
m
o
d
e
an
d
m
ec
h
a
n
ical
s
tr
u
ctu
r
e
[
3
]
:
=
∙
+
∙
(
5
)
=
∙
+
∙
(
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2
0
8
8
-
8
694
Ha
r
mo
n
ics elimin
a
tio
n
fo
r
DC
/D
C
p
o
w
er su
p
p
ly
b
a
s
ed
o
n
p
iezo
elec
tr
ic
filt
e
r
s
(
Ha
s
a
n
M
a
A
lmg
o
tir
)
359
All
ce
r
am
ic
f
ilter
s
d
er
iv
e
th
e
ir
b
asic
f
r
eq
u
e
n
cy
s
elec
tiv
ity
f
r
o
m
a
m
ec
h
an
ical
v
i
b
r
atio
n
r
esu
ltin
g
f
r
o
m
a
p
iezo
elec
tr
ic
ef
f
ec
t,
th
e
r
eso
n
an
t
a
n
d
a
n
ti
-
r
eso
n
an
t
f
r
eq
u
e
n
cies
o
f
PF
s
h
o
wn
i
n
F
ig
u
r
e
4
ca
n
b
e
ca
lcu
lated
b
y
u
s
in
g
(
7
)
an
d
(
8
)
r
esp
ec
tiv
ely
;
=
1
2
√
1
1
(
7
)
f
a
=
1
2π
√
L
1
C
1
C
0
C
1
+
C
0
(
8
)
Fig
u
r
e
4
.
T
h
e
t
y
p
ical
r
esp
o
n
s
e
f
o
r
PF
.
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
I
n
th
is
r
esear
ch
,
th
e
p
iezo
ele
ctr
ic
ce
r
am
ic
m
ater
ials
ar
e
test
ed
as
a
f
ilter
in
D
C
/D
C
f
u
ll
-
b
r
id
g
e
co
n
v
er
ter
cir
cu
it
p
r
esen
ted
b
y
1
2
to
4
8
DC
/DC
p
o
wer
s
u
p
p
ly
,
th
e
m
o
d
elin
g
o
f
PF
b
y
u
s
i
n
g
ce
r
am
ic
ty
p
e
as
s
h
o
wn
in
Fig
u
r
e
5
.
T
h
e
p
ar
a
m
eter
s
o
f
th
e
PF
r
ep
r
esen
ted
in
T
ab
le
1
.
T
h
e
p
ar
am
eter
s
ar
e
tak
en
f
r
o
m
th
e
Sp
ec
if
icatio
n
s
o
f
th
e
ce
r
a
m
ic
PF
m
o
d
el
C
H
-
S4
2
,
wh
ich
u
s
e
d
to
f
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I
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
694
I
n
t J
Po
w
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lec
&
Dr
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Sy
s
t,
Vo
l.
1
2
,
No
.
1
,
Ma
r
c
h
2
0
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1
:
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6
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362
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CO
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I
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&
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c
De
v
ice
s.
”
4
th
IEE
E
Utta
r
Pr
a
d
e
sh
S
e
c
ti
o
n
I
n
t
e
rn
a
ti
o
n
a
l
Co
n
f
e
re
n
c
e
o
n
El
e
c
tr
ica
l,
Co
m
p
u
ter
a
n
d
El
e
c
tro
n
ics
(UPCON)
GLA
Un
ive
rs
it
y
.
M
a
th
u
ra
.
2
0
1
7
:
2
6
-
28.
[4
]
F
e
i
C.
,
e
t
a
l
.
,
“
Hig
h
P
e
rf
o
rm
a
n
c
e
P
iez
o
e
lec
tri
c
Cry
sta
l
Alp
h
a
-
Bib
o
f
o
r
P
h
o
to
a
c
o
u
stic
G
a
s
De
tec
ti
o
n
,
”
IE
EE
Co
n
fer
e
n
c
e
s S
y
mp
o
si
u
m o
n
Pi
e
z
o
e
lec
tricity A
c
o
u
stic W
a
v
e
s
a
n
d
De
v
ice
Ap
p
li
c
a
ti
o
n
s (
S
PA
W
DA)
,
2
0
1
9
,
p
p
.
1
-
4.
[5
]
To
u
fi
k
M
,
A
b
d
e
lh
a
fi
d
C.
,
“
S
t
u
d
y
a
n
d
S
imu
lati
o
n
wit
h
VH
DL
-
AM
S
o
f
th
e
El
e
c
tri
c
a
l
Im
p
e
d
a
n
c
e
o
f
a
P
iez
o
e
lec
tri
c
Ultras
o
n
ic
Tran
s
d
u
c
e
r
,”
I
n
ter
n
a
t
i
o
n
a
l
J
o
u
rn
a
l
o
f
P
o
we
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
m
(IJ
PE
DS
)
,
v
o
l.
10
,
n
o
.
2
,
p
p
.
1
0
6
4
-
1
0
7
1
,
2
0
1
9
.
[6
]
S
h
u
a
i
P
.
,
Wen
b
in
L.
,
Jia
n
g
m
in
g
K.
,
“
S
imu
lati
o
n
An
a
ly
sis
o
f
In
ter
fa
c
e
Circu
it
s
fo
r
P
iez
o
e
lec
tri
c
En
e
rg
y
Ha
rv
e
sti
n
g
with
Da
m
p
e
d
S
i
n
u
so
i
d
a
l
S
i
g
n
a
ls
a
n
d
Ra
n
d
o
m
S
i
g
n
a
ls
,
”
T
EL
KO
M
NIKA
T
e
lec
o
mm
u
n
ica
t
io
n
Co
mp
u
ti
n
g
El
e
c
tro
n
ic
a
n
d
Co
n
tro
l
,
v
o
l.
13
,
n
o
.
3
,
p
p
.
767
-
7
7
5
,
2
0
1
5
.
[7
]
G
a
u
tsc
h
i
G
.
,
“
P
iez
o
e
lec
tri
c
S
e
n
so
rics
:
F
o
rc
e
S
train
P
re
ss
u
re
Ac
c
e
le
ra
ti
o
n
a
n
d
Ac
o
u
stic E
m
issio
n
S
e
n
so
rs M
a
teria
ls
a
n
d
Am
p
li
fiers
,
”
Be
rli
n
,
He
id
e
l
b
e
rg
.
S
p
rin
g
e
r.
2
0
0
2
.
[8
]
M
a
S
.
,
e
t
a
l.
,
“
E
x
p
e
rime
n
tal
I
n
v
e
stig
a
ti
o
n
o
f
P
iez
o
e
lec
tri
c
it
y
o
f
Ne
a
r
F
ield
El
e
c
tro
sp
u
n
P
VD
F
Na
n
o
fi
b
e
rs
”
T
EL
KOM
NIKA
T
e
lec
o
mm
u
n
ic
a
ti
o
n
C
o
mp
u
ti
n
g
El
e
c
tro
n
ic a
n
d
Co
n
tro
l
,
v
o
l.
14
,
n
o
.
2A
,
p
p
.
1
4
5
-
1
5
1
,
2
0
1
6
.
[9
]
N.
H.
M
.
Ha
n
i
f,
e
t
a
l.
,
“
P
o
w
e
r
Esti
m
a
ti
o
n
f
o
r
Wea
ra
b
le
P
i
e
z
o
e
lec
tri
c
En
e
rg
y
Ha
rv
e
ste
r
,
”
T
EL
KOM
NIK
A
T
e
lec
o
mm
u
n
ica
ti
o
n
Co
mp
u
ti
n
g
E
lec
tro
n
ic a
n
d
C
o
n
tro
l
,
v
o
l.
16
,
n
o
.
3
,
p
p
.
9
8
3
-
9
8
8
,
2
0
1
8
.
[1
0
]
Kra
u
tk
rä
m
e
r,
J.
&
Kra
u
tk
rä
m
e
r,
H.
“
Ultras
o
n
ic T
e
stin
g
o
f
M
a
teria
ls
,”
S
p
ri
n
g
e
r.
1
9
9
0
.
[1
1
]
S
a
leh
G
.
e
t
a
l.
,
“
Ev
a
l
u
a
ti
o
n
o
f
P
iez
o
e
lec
tri
c
En
e
rg
y
Ha
r
v
e
ste
r
Ou
tco
m
e
s
in
R
o
a
d
T
ra
ffic
Ap
p
l
ica
ti
o
n
s
,
”
4
t
h
IET
Clea
n
E
n
e
rg
y
a
n
d
T
e
c
h
n
o
lo
g
y
Co
n
fer
e
n
c
e
(CEA
T
)
,
K
u
a
la L
u
m
p
u
r,
M
a
lay
sia
.
2
0
1
6
,
p
p
.
1
-
5
.
[1
2
]
An
is
A.,
e
t
a
l.
,
“
P
o
we
r
G
e
n
e
r
a
ti
o
n
b
y
Us
i
n
g
P
iez
o
e
lec
tri
c
Tran
sd
u
c
e
r
with
Be
n
d
i
n
g
M
e
c
h
a
n
ism
S
u
p
p
o
rt.
”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
P
o
we
r E
lec
tro
n
ics
a
n
d
Dr
ive
S
y
ste
m (
IJ
P
EDS
),
Vo
l.
10
,
n
o
.
1
,
p
p
.
5
6
2
-
567
,
2
0
1
9
.
[1
3
]
An
it
a
M
.
,
a
n
d
S
e
t
h
R.
,
“
F
u
n
d
a
m
e
n
tal
Li
m
it
s
o
n
E
n
e
rg
y
Tra
n
sfe
r
a
n
d
Circu
it
C
o
n
si
d
e
ra
ti
o
n
s
fo
r
P
iez
o
e
lec
tri
c
Tran
sfo
rm
e
rs
,
”
IEE
E
T
r
a
n
sa
c
ti
o
n
s o
n
P
o
we
r E
lec
tro
n
ics
,
v
o
l.
17
,
n
o
.
1
,
p
p
.
8
-
14
,
2
0
0
2
.
[1
4
]
Wei
W.
e
t
a
l.
,
“
P
o
we
r
De
n
sity
o
f
P
iez
o
e
lec
tri
c
Tran
sfo
rm
e
rs
Im
p
ro
v
e
d
Us
i
n
g
a
C
o
n
tac
t
He
a
t
Tran
s
fe
r
S
tru
c
tu
re
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
on
Ultra
so
n
ic
s,
Fer
ro
e
lec
trics
,
An
d
Fre
q
u
e
n
c
y
c
o
n
tro
l
,
v
o
l.
59
,
n
o
.
1
,
p
p
.
73
-
81
,
2
0
1
2
.
[1
5
]
Ba
sh
ir
B.
M
.
,
Ha
b
i
b
u
r
R.
,
a
n
d
M
o
h
d
R.
,
“
M
o
d
e
ll
i
n
g
a
n
d
S
imu
latio
n
o
f
P
iez
o
e
lec
tri
c
Ac
tu
a
to
r
fo
r
Vib
ra
ti
o
n
Co
n
tr
o
l
,
”
IEE
E
1
0
th
Asia
n
C
o
n
tr
o
l
Co
n
fer
e
n
c
e
(AS
CC)
,
Ko
ta Ki
n
a
b
a
lu
,
M
a
lay
sia
.
2
0
1
5
.
[1
6
]
Bin
J.
,
Weiwe
i
S
.
,
a
n
d
Z
h
ih
u
a
F
.
,
“
P
iez
o
e
lec
tri
c
F
il
ter
M
o
d
u
le
Us
e
d
i
n
Ha
rm
o
n
ics
E
li
m
in
a
ti
o
n
fo
r
H
ig
h
-
Ef
fi
c
ien
c
y
P
iez
o
e
lec
tri
c
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
on
P
o
we
r E
lec
tro
n
ics
,
v
o
l.
31
,
n
o
.
1
,
p
p
.
5
2
4
-
5
3
2
,
2
0
1
6
.
[1
7
]
J.
H.
P
a
rk
e
t
a
l.
,
“
An
a
ly
sis
o
f
Th
e
T
h
e
rm
a
l
Ba
lan
c
e
Ch
a
ra
c
teristics
fo
r
M
u
l
ti
p
le
-
C
o
n
n
e
c
ted
P
iez
o
e
lec
tri
c
Tran
sfo
rm
e
rs
,
”
1
6
th
IE
EE
In
ter
n
a
ti
o
n
a
l
S
y
mp
o
si
u
m
o
n
t
h
e
Ap
p
li
c
a
ti
o
n
s
o
f
Fer
ro
e
lec
trics
.
Na
ra
,
Ja
p
a
n
.
2
0
0
7
;
p
p
.
801
-
8
0
4
[1
8
]
Alfre
d
o
V.
C
.
,
“
P
iez
o
e
lec
tri
c
Tr
a
n
sfo
rm
e
rs:
An
Histo
r
ica
l
Re
v
iew
,
”
M
DPI
Act
u
a
t
o
rs
,
v
o
l.
5
,
n
o
.
12
,
p
p
.
1
-
22
,
2
0
1
6
.
[1
9
]
Do
n
g
F
.
W.
e
t
a
l.
,
“
A
Ba
ll
-
Im
p
a
c
t
P
iez
o
e
lec
tri
c
Co
n
v
e
rter
Wr
a
p
p
e
d
b
y
Co
p
p
e
r
Co
i
l
,
”
IEE
E
T
r
a
n
sa
c
ti
o
n
s
o
n
Na
n
o
tec
h
n
o
lo
g
y
,
v
o
l.
17
,
n
o
.
4
,
p
p
.
7
2
3
-
7
2
6
,
2
0
1
8
.
[2
0
]
KWOK
K.
F
.
e
t
a
l
.
,
“
G
e
n
e
ra
l
S
tu
d
y
o
n
P
iez
o
e
lec
tri
c
Tran
sfo
rm
e
r
,
”
IEE
E
Fi
rs
t
I
n
ter
n
a
t
io
n
a
l
Co
n
fe
re
n
c
e
o
n
Po
we
r
El
e
c
tro
n
ics
S
y
ste
ms
a
n
d
A
p
p
li
c
a
ti
o
n
s
,
H
o
n
g
Ko
n
g
,
Ch
i
n
a
.
2
0
0
4
.
[2
1
]
P
ra
sa
d
A.,
a
n
d
Ch
a
ll
a
B
.
,
“
M
o
d
e
li
n
g
a
n
d
S
imu
latio
n
o
f
Th
re
e
Lev
e
l
P
iez
o
e
lec
tri
c
Tran
sf
o
rm
e
r
Co
n
v
e
rters
,
”
Ad
v
a
n
c
e
s i
n
Ro
b
o
ti
c
s &
Au
t
o
ma
ti
o
n
,
v
o
l.
3
,
n
o
.
2
,
2
0
1
3
.
[2
2
]
M
a
rti
n
S
.
R
.
,
M
ich
a
e
l
W.
a
n
d
M
ich
a
e
l
A.
E
.
,
“
F
o
rwa
rd
C
o
n
d
u
c
ti
o
n
M
o
d
e
C
o
n
tr
o
ll
e
d
P
iez
o
e
lec
tri
c
Tran
sfo
rm
e
r
-
Ba
se
d
P
F
C
Led
Dri
v
e
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s o
n
P
o
we
r E
lec
tro
n
ics
,
v
o
l.
28
,
n
o
.
10
,
p
p
.
4
8
4
1
-
4
8
4
9
,
2
0
1
3
.
[2
3
]
M
o
h
a
m
m
a
d
G
.
,
S
.
,
M
o
tak
a
b
b
e
r
a
n
d
M
u
h
a
m
m
a
d
I.
,
“
De
sig
n
a
n
d
An
a
ly
sis
o
f
a
Bu
c
k
-
Bo
o
st
C
o
n
v
e
rter
Circu
it
f
o
r
P
iez
o
e
lec
tri
c
En
e
rg
y
Ha
rv
e
stin
g
S
y
ste
m
,
”
IEE
E
I
n
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
Co
m
p
u
ter
a
n
d
Co
mm
u
n
ica
ti
o
n
En
g
i
n
e
e
rin
g
(
ICCCE)
,
Ku
a
la L
u
m
p
u
r,
M
a
la
y
sia
.
2
0
1
7
.
[2
4
]
T.
An
d
e
rse
n
,
M
.
A.
E.
An
d
e
rse
n
,
O.
C
.
T
h
o
m
se
n
.
,
“
S
imu
lati
o
n
o
f
P
iez
o
e
lec
tri
c
Tran
sf
o
rm
e
rs
with
COMS
OL
,
”
COMS
OL
Co
n
fe
re
n
c
e
.
M
il
a
n
.
2
0
1
2
.
[2
5
]
Wed
ian
H.,
M
u
sta
fa
Al
-
Qa
isi,
a
n
d
Am
m
a
r
Al
-
G
izi
,
“
Co
m
p
a
riso
n
b
e
twe
e
n
p
iez
o
e
lec
tri
c
tr
a
n
sfo
rm
e
r
a
n
d
e
lec
tro
m
a
g
n
e
ti
c
tran
sfo
rm
e
r
u
se
d
in
e
lec
tro
n
ic
c
ircu
it
s
,”
T
EL
KO
M
NIKA
T
e
lec
o
mm
u
n
ic
a
ti
o
n
C
o
mp
u
ti
n
g
El
e
c
tro
n
ic
a
n
d
Co
n
tro
l
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