TELKOM
NIKA
, Vol. 11, No. 5, May 2013, pp. 2502 ~ 2507
ISSN: 2302-4
046
2502
Re
cei
v
ed
Jan
uary 22, 201
3
;
Revi
sed Ma
rch 1
0
, 2013;
Acce
pted Ma
rch 2
0
, 2013
Magnetoelectric Speed
Sensor to Detect Ultra-Low
Frequency Vibrations
Dong
Ke*, Qian Yuxia, Yuan Zhangy
i
Dep
a
rtment of Mecha
n
ica
l
an
d Electron
ic En
gin
eeri
ng, Sha
ndo
ng W
a
ter P
o
l
y
t
e
ch
nic
Rizha
o 27
68
26
, China
*Corres
pon
di
n
g
author, e-ma
i
l
: dongk
e_
199
8@1
63.com
A
b
st
r
a
ct
Ultra-low
fre
q
u
ency vi
brati
ons
are
ord
i
nary
p
h
ysical
p
hen
o
m
e
na,
and
a
b
s
olute
vibr
ant
sensor
s
are us
ua
lly
use
d
to d
e
tect the
m
. T
he
auth
o
r
prese
n
ts
a
met
hod t
hat us
ing
ma
gn
etoel
ectri
c
spee
d se
nsor
to
detect ultra-l
o
w
frequency vi
bratio
ns. W
i
th cascad
e
co
rre
cting circu
i
t, the low
e
st frequ
ency that can
be
m
e
asur
ed w
ill
be less than 0.5H
z
w
h
i
l
e the best dam
p
i
ng is m
a
intained. The author
has systematicall
y
ana
ly
z
e
d the c
o
rrectin
g circui
t, transfer function, t
heory of oper
ation, a
n
d
t
he difference
betw
een outp
u
t
character
i
stics before a
nd afte
r correcti
ng to the ultra-
low
freque
ncy sens
or.
Ke
y
w
ords
:
se
nsor, ultra-l
o
w
freque
ncy, vibr
ation,
correcti
n
g circuit, transfer function
Copy
right
©
2013 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
Ultra
-
lo
w freq
uen
cy vibrati
ons
are
ordin
a
ry
physi
cal
phen
omen
a, su
ch a
s
the v
i
bration
s
of well hea
dframes, hig
h
-ri
s
e buil
d
ing
s
, railway
and h
i
ghway bridg
e
s, dam
s an
d
the earthq
u
a
k
e
wave
s. Th
ese vibration
s
have
the
chara
c
te
ri
sti
c
s of hi
gh
a
m
plitude
(u
p
to 1
0
mm),
low
freque
ncy, ab
unda
nt of fre
quen
cie
s
that
lowe
r
than 1
H
z
and hi
gh
destroy po
we
r. They sel
d
o
m
affect people’
s everyday li
ves u
nder normal condition,
but will
l
e
ad to
huge destroy
once they
excee
d
allo
wable limits. T
herefo
r
e, the
measure and
research
of
ultra-l
o
w freq
uen
cy vibrati
ons
is impo
rtan
ce
in engi
nee
rin
g
. There a
r
e t
w
o typical se
nso
r
s i
n
en
gi
neeri
ng te
st, magneto
e
le
ctric
spe
ed
sen
s
o
r
an
d pie
z
o
e
l
e
ctri
c a
c
cele
rometer. T
he
piezoele
c
tri
c
accele
rom
e
te
rs
ca
n n
o
t b
e
use
d
in ultra
-
low fre
quen
cy vibration test becau
se
of
their low
sen
s
itivity to ultr
a-lo
w freq
uen
cy
sign
al, an
d p
i
ezo
e
le
ctric crystal
plate
d
oes not
ada
p
t
to qu
asi
s
tat
e
test. T
h
e
magneto
e
le
ctric
spe
ed sen
s
ors have the a
d
vantage
s
of anti interfere
n
ce a
nd resi
stance to imp
a
c
t, but their low
limit of test is all over
13
Hz be
ca
use of
their
hi
gh n
a
t
ural fre
que
n
c
y, so th
eir a
c
cura
cy of ult
r
a-
low frequ
en
cy test doe
s
n
o
t adapt to
the ne
ed
s of
engin
eeri
ng [
1
]. The a
u
th
or
system
atically
resea
r
ched
the meth
od
s that u
s
ing
co
rrectin
g
circuit to
re
duce the
te
st fre
que
ncy
of
magneto
e
le
ctric spee
d
se
n
s
ors.
2. Magnetoel
ectric Spe
e
d
Sensor
Magneto
e
le
ctric spee
d
se
nso
r
s (sp
eed
ometer
s) h
a
ve the
adva
n
tage
s of
high
outpu
t
sign
al, sim
p
le
su
bsequ
ent
circuit a
nd
go
od a
n
ti
interfe
r
en
ce
ca
pabil
i
ty, and a
r
e
e
x
tensively u
s
ed
in low frequ
e
n
cy test. The
y
belong to inertia se
n
s
ors [2], and the mecha
n
ical model of inertia
sen
s
o
r
s i
s
sh
own in Fig
u
r
e
1.
Speed se
nso
r
s are
si
ngle
-
degree
-of-fre
edom sy
stem
s, and
their freque
ncy d
o
m
a
in ha
s
the cha
r
a
c
teristic of seco
n
d
ord
e
r hig
h
-pass.
The n
o
r
mali
zation transfe
r fun
c
tio
n
betwe
en th
e
output voltag
e and the inp
u
t vibration velocity is sho
w
n a
s
follows:
Gs
s
ss
0
2
2
00
0
2
2
()
(1)
whe
r
e
0
is damping ratio, and
0
is inhe
ren
t
angular freq
uen
cy.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NIKA
Vol. 11, No
. 5, May 2013 : 2502 – 250
7
2503
Figure 1. Mechani
cal mod
e
l
of inertia se
nso
r
In gen
eral, th
e freq
uen
cy t
hat can b
e
te
sted i
s
hi
ghe
r than n
a
tural f
r
equ
e
n
c
y of
Speed
sen
s
o
r
s. At
pre
s
ent, the
natural f
r
e
quen
cie
s
of
magneto
ele
c
tri
c
speed
sen
s
o
r
s
phy
s
ical
con
s
tru
c
tion
are g
ene
rally
not lowe
r th
an 4
H
z, an
d
the frequ
en
ci
es that
can
b
e
tested
by them
are u
s
ually hi
gher tha
n
13
Hz, so they do
not adapt to
the ultra-lo
w
freque
n
cy test.
3. Design an
d analy
s
is of
sensor
3.1. Theor
y
of Oper
ation
and Trans
fe
r Function.
In order to expand the
freque
ncy re
spo
n
se
of magneto
e
le
ctric spee
d se
nso
r
s,
corre
c
ting ci
rcuit is introd
uce
d
. Corre
c
ting met
hod
s can be divided into two
forms, feed
back
corre
c
ting
an
d casca
de
co
rre
cting
[3]. T
o
second
o
r
d
e
r
high
-pa
s
s
segm
ent, fee
dba
ck corre
c
ting
redu
ce
s the
natural
fre
q
u
ency
whil
e th
e da
mp i
s
al
so
cut
do
wn.
In o
r
de
r to
kee
p
a
p
p
r
op
riate
damp
for corrected
sy
stem
output
chara
c
teri
stic, th
e
damp
of o
r
igi
nal dyn
a
mic
cha
r
a
c
teri
stic is
often increa
sed in
adva
n
ce [4]. For example a
resi
stan
ce
is co
nne
c
ted
in parall
e
l
to
magneto
e
le
ctric
spe
ed se
nso
r
, and th
e sen
s
o
r
da
mp ca
n increased by th
e adju
s
tment
of
magneto
e
le
ctric d
a
mp. Bu
t to a ce
rtain
degree, this
correctin
g
is a
nother de
cayi
ng
to
fre
q
uen
c
y
comp
one
nt that has
alre
ad
y been atten
u
a
ted a
s
a resu
lt of sen
s
o
r
’
s
freq
uen
cy chara
c
te
risti
c
. So
an
a
m
plificati
on seg
m
ent sho
u
ld be ad
ded
i
n
follo
w-
up
circuit, a
n
d
this will
aff
e
ct
sign
al-n
oi
se
ratio. In additi
on, for the
se
con
d
order
hi
gh pa
ss
se
g
m
ent, the pha
se of lo
w fre
q
u
en
cy sig
nal
will
distort, ph
ase differen
c
e
nearby
ze
ro
-frequ
en
cy is
approximatel
y 180º. This will lead to
low
freque
ncy n
e
gative feedba
ck tu
rnin
g int
o
po
sitive feedba
ck, an
d b
e
pro
ne to ch
attering [5]. T
h
e
author u
s
e
s
ca
scade
correcting
ci
rcuit
for ma
gnet
o
e
l
ectri
c
spe
ed sen
s
o
r
,
an
d has
de
sig
ned
a
comp
en
satio
n
segm
ent C(s) which ca
n be impleme
n
ted in phys
ic
s
.
Its
trans
fer func
tion is
s
h
own
as
follows
:
2
1
1
1
2
2
0
0
0
2
2
2
)
(
s
s
s
s
s
C
(2)
After the correcting by thi
s
compensation segment, the inpu
t
still has the
characteri
stic
of second o
r
d
e
r high
-p
ass, and the no
rm
alizatio
n tran
sfer fun
c
tion i
s
sh
own as fo
llows:
2
1
1
1
2
2
0
1
2
)
(
)
(
)
(
s
s
s
s
C
s
G
s
G
(3)
The comp
en
sation se
gm
ent
C(s)
ma
ke
10
and
1
the best da
mp. T
he natu
r
al
freque
ncy
of
sy
stem o
u
tput cha
r
a
c
teristic th
at
h
a
v
e bee
n
co
rrecte
d i
s
de
cre
a
sed. So
the
obje
c
tive that expandi
ng t
he lo
we
st fre
quen
cy
that
ca
n be
test
ed by
sen
s
o
r
s a
n
d
co
rre
ct
ing
s
e
ns
or
’s d
y
na
mic
c
h
a
r
ac
te
r
i
s
t
ic
s
is ach
i
eved. Rel
a
tively highe
r m
e
cha
n
ical natu
r
al fre
q
ue
ncy
of
origin
al sen
s
or mai
n
tain
s
unchan
geabl
ely, physical
con
s
tru
c
tion
i
s
sta
b
le, a
nd
sen
s
o
r
h
a
s
g
ood
perfo
rman
ce
on a
n
ti interf
eren
ce
an
d resi
stan
ce to
i
m
pact.
Natu
ral freq
uen
cy
of syste
m
out
put
cha
r
a
c
teri
stic that ha
s be
e
n
co
rrecte
d
comple
tely
d
e
p
end on
th
e corre
c
ting ci
rcuit conn
ecte
d
in
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Magneto
e
le
ctric Spe
ed Se
nso
r
to Dete
ct Ultra-L
o
w F
r
eque
ncy Vibrations (Do
ng
Ke)
2504
seri
es. So th
e co
rre
cted
sensor mai
n
tai
n
s the adv
a
n
tage
s of orgin
a
l sen
o
r a
s
well as imp
r
ov
es
low freq
uen
cy output characteri
stic.
The tran
sfer functio
n
of
the
com
pen
sa
tion
segm
ent exp
r
e
s
se
d by Eq.
(1
) ca
n
be
expand
ed a
s
follows:
2
1
1
1
2
1
2
2
1
1
1
2
2
1
1
2
2
1
)
(
s
s
s
K
s
s
K
s
C
(4)
whe
r
e
KK
1
0
2
1
2
2
00
1
1
1
1
2
,
()
whe
n
10
and
11
0
0
,
K1 and K2
wi
ll all be g
r
eat
er than
zero.
So co
rre
cting
segm
ent ca
n
be realized
by parallelin
g
low pass se
gment, band
pass seg
m
e
n
t and all pa
ss
segm
ent. By adjustin
g
proportio
nal rel
a
tion betwe
e
n
three
seg
m
ents’ g
a
in, the ze
ro poi
nt of
corre
c
ting
se
gment will counteract wit
h
the pol
e of
original sensor,
and system
o
u
tp
ut
characteri
stic will
be t
he f
o
rm
of
second order
hi
gh-pass express
ed by E
q
. (3). The functional
block dia
g
ra
m is sh
own in
Figure 2.
1
2
s
2
+
2
1
1
s
+
1
2
1
s
2
+
2
1
1
s
+
1
2
s
U
(
s
)
K
3
K
1
K
2
+
+
+
Y
(
s
)
Figure 2. Fun
c
tional bl
ock
di
agram of co
rre
cting
segm
ent
After corre
c
ting, the natural frequ
en
cy
decre
ases,
and the normali
zatio
n
transfe
r
function
bet
ween vib
r
ation
velocity inp
u
t
and
sy
stem
voltage o
u
tp
ut ca
n
still expre
s
sed
by Eq.
(1).
The vibration
displ
a
ceme
n
t
is often i
n
te
reste
d
in
eng
ineeri
ng
ultra
-
low freq
uen
cy test.
The voltag
e
output shoul
d
be integ
r
ate
d
on
ce. But simple integ
r
al
will lea
d
to t
he a
c
cumulat
i
on
of ze
ro
shifti
ng, therefore
it is
difficult t
o
re
alize. So
the integ
r
al segment
i
s
re
placed by
a
f
i
rst
orde
r
i
nertia
segm
ent.
In addition, stop
ping dire
ct
cu
rre
nt segm
en
t is al
so
ad
de
d in
ci
rcuit. T
he
function
al
bl
o
c
k
dia
g
ra
m whi
c
h usi
ng output
Y(s)
t
o
exp
r
e
s
s co
rre
cted
am
plitude i
s
sho
w
n in
Figure 3.
Figure 3. Fun
c
tional bl
ock
diagram of
ultra-l
o
w fre
que
ncy displa
ce
ment
G(s)
magn
eto
electric sp
eed
sensor
integr
al
segme
n
t
freque
n
c
y
c
har
a
c
teristic
correcting segment
stoppi
ng d
i
rect
current segm
ent
X(s
)
Y(s)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NIKA
Vol. 11, No
. 5, May 2013 : 2502 – 250
7
2505
3.2. Correc
t
i
ng Circuit an
d Trans
f
er F
unction.
The sig
nal a
d
justme
nt circuit of ultra-l
o
w fr
eq
uen
cy
displa
cem
e
n
t
sensor that has b
een
corre
c
ted
in
cl
ude
s inte
gral,
low fre
que
ncy com
pen
sati
on a
n
d
stop
pi
ng di
re
ct
cu
rrent segm
ents.
It is shown in Figure 4.
Figure 4. Signal adju
s
tme
n
t circuit of correcte
d displ
a
cem
ent se
n
s
or
In figure 4, the low p
a
ss
amplifying ci
rcuit
is con
s
tituted by IC2, C21, etc. a
nd its
trans
fer func
tion is
shown as
follows
:
RR
RR
R
C
C
s
RC
R
C
R
RR
C
s
RRC
C
23
24
21
22
23
21
22
2
21
21
22
21
24
22
23
22
21
22
21
22
11
1
()
(5)
IC3 co
nstitut
e
a band
pa
ss a
m
plifying
circuit, and i
t
s tran
sfer fu
nction i
s
sh
o
w
n a
s
follows
:
RR
RRC
s
s
RC
R
C
R
C
R
RR
C
s
RR
RR
R
C
C
34
35
31
34
31
2
31
31
33
31
33
32
35
32
34
31
31
32
31
32
33
31
32
11
1
()
(6)
The expe
cte
d
ratio of natural fre
quen
cy to damping
depend
s on
the denomi
n
ator of
above two tra
n
sfer fu
nction
s, i.e. co
rresp
ondin
g
re
sist
ances in
circu
i
t.
The summing
amplifier ci
rcuit is con
s
tituted
by IC4, R44, etc. The
adju
s
tment of R41,
R42
an
d
R4
2 will
chan
ge
the e
n
large
m
ent fa
ctor
o
f
circuit to
th
e outp
u
t si
gn
als
of lo
w-p
a
ss,
band
-pa
s
s a
nd all-p
a
ss
segment
s. Th
erefo
r
e, the
cou
n
tera
ction
of corre
c
ting
segm
ent’s
zero
point to origin
al sen
s
o
r
’s pole is realized.
The inte
gral
segm
ent i
s
re
alize
d
by inte
gr
ating
amplif
ying ci
rcuit which
co
nstitut
ed by
IC1 a
nd
R11,
R1
2, R13, C11. Becau
s
e
the integ
r
al
segment i
s
critical i
n
stabl
e, i
t
is repla
c
e
d
by
an in
ertia
seg
m
ent in
p
r
acti
ce. T
he t
r
an
sf
er fu
nctio
n
of
this
seg
m
ent
is
s
C
R
R
R
11
12
11
12
1
1
, and
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Magneto
e
le
ctric Spe
ed Se
nso
r
to Dete
ct Ultra-L
o
w F
r
eque
ncy Vibrations (Do
ng
Ke)
2506
the integral time co
nsta
nt is
i
RC
12
11
. In addition, two first orde
r sto
ppi
ng direct
current
segm
ents a
r
e
added to re
st
rain the affect
of low freque
ncy noi
se an
d deviation.
The no
rmali
z
ation tran
sfer fun
c
tion
betwe
en out
put Y(s) of corre
c
ted ult
r
a-l
o
w
freque
ncy se
nso
r
and vib
r
ation displa
ce
ment is shown as follo
ws:
2
2
1
1
1
2
2
1
1
2
)
(
)
(
)
(
s
s
s
s
s
s
s
s
X
s
Y
s
H
d
d
i
i
(7)
4. Outpu
t
Ch
arac
teris
t
ic Comparis
on Before an
d After Corre
c
t
ing
The
curve
s
o
f
amplitude
-freque
ncy
cha
r
acte
ri
stic and
pha
se-f
req
u
ency
cha
r
a
c
t
e
risti
c
(no
r
mali
zatio
n
) befo
r
e an
d
after corre
c
ti
ng that pl
otting in acco
rdan
ce with Eq. (7) are sh
own
in
Fig.5. Cu
rves named 1
are norm
a
lization amplitu
d
e
-
freq
uen
cy c
hara
c
te
risti
c
curve
and p
h
a
se
-
freque
ncy ch
ara
c
teri
stic
curve of low freque
ncy di
sp
lacem
ent se
n
s
or b
e
fore
co
rre
cting. Cu
rv
e
s
named 2
are norm
a
lization amplitud
e
-
freq
uen
cy
chara
c
te
risti
c
curve
and p
hase-frequ
en
cy
cha
r
a
c
teri
stic cu
rve
of u
l
tra-lo
w f
r
eq
uen
cy di
spla
ceme
nt sen
s
or after co
rrecting
(natural
freque
ncy of output cha
r
a
c
teri
stic after corre
c
ting
is 0.5Hz, dam
ping ratio is
0.65, integral
and
stoppi
ng dire
ct cu
rre
nt time con
s
t
ant is
2.2s).
We ca
n find from
Fi
g.5 that the lowe
st freq
ue
ncy
before
co
rre
cting is gre
a
ter than 15Hz, a
nd the lowe
st
frequen
cy after co
rrectin
g
is abo
ut 0.6Hz.
0.
1
1
10
-
180
-9
0
0
90
180
)
.
F
r
e
q
uen
cy
f
/Hz
0.
1
1
10
0.
0
0.
3
0.
6
0.
9
Ph
as
e
spe
c
t
ru
m
p
/
deg
).F
re
q
u
enc
y
f
/Hz
3
2
1
1
2
3
b
(
a
(
A
m
pl
i
t
ude
s
p
e
c
t
r
um
(
a
). am
plitude
-freq
uen
cy ch
ara
c
teri
stic (
b
). ph
ase-fre
quen
cy ch
ara
c
teri
stic
Figure 5. Amplitude-f
r
eq
ue
ncy ch
ara
c
te
ristic
an
d pha
se-fre
que
ncy chara
c
te
risti
c
of spee
d
sen
s
o
r
befo
r
e
and after correctin
g
Curve
s
n
a
me
d 3 a
r
e am
pli
t
ude-frequ
en
cy ch
aracte
ri
stic
cu
rve an
d pha
se
-fre
q
uen
cy
cha
r
a
c
teri
stic curve of second
orde
r hig
h
pass segm
ent whi
c
h co
ntains
stoppi
ng dire
ct current
segm
ent.
Comp
ari
ng
curve
2 a
nd
cu
rve 3
in
Figu
re 5
(a
),
we
ca
n find
that b
e
c
au
se
of th
e
affect
of time con
s
tant of first
orde
r in
ertia
se
gment a
nd stoppin
g
dire
ct curre
n
t
se
gment,
the
amplitude
of
curve
2
de
ca
ys a little g
r
e
a
ter th
a
n
curve 3 at the
freque
ncy
ran
g
e
nea
r
0.5Hz
and
lowe
r than 0
.
5Hz. In co
rresp
ondi
ng p
hase freq
u
e
n
cy cu
rve, the pha
se
a
ngle of wo
rking
freque
ncy ra
n
ge whi
c
h nat
ural freq
uen
cy is greater
th
an 0.5Hz is -180º, the 0.5
H
z p
hase shif
t o
f
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NIKA
Vol. 11, No
. 5, May 2013 : 2502 – 250
7
2507
curve
3 is
-9
0
º
, and the 0.5
H
z
pha
se
shif
t of curve
2 re
ach
e
s
-65
º
(A
fter 180º
reve
rse
pha
se, th
e
pha
se an
gle
of working fre
quen
cy ran
g
e
of correcte
d sen
s
o
r
is 0º.).
If the require
ment of mea
s
ureme
n
t sig
nal to
pha
se
is not hig
h
, the affect by i
n
tegral
and stop
ping
dire
ct
current
se
gment
s wil
l
be not
o
b
vio
u
s. But if th
e
sign
al
with hi
gh requi
rem
e
n
t
on pha
se
distortion is te
st
ed, for exam
ple ultra
-
lo
w
freque
ncy tra
n
sie
n
t sign
al, wave
shap
e
will
be disto
r
ted
becau
se of the affect
by integral a
nd stopping di
re
ct
current se
g
m
ents. The
r
e
f
ore,
time con
s
tant
of integral an
d stoppi
ng direct
cu
rrent se
gments
sho
u
l
d
be sel
e
cte
d
a little bigger.
5. Conclusio
n
(1) Ma
gneto
e
lectri
c vibration sp
eed se
nso
r
ha
s the
characte
ri
stic of se
con
d
orde
r
high p
a
ss, a
nd ha
s th
e a
d
vantage
s of
stable
phy
si
cal
con
s
tructi
on, goo
d p
e
rf
orma
nce on
anti
interferen
ce a
nd re
si
stan
ce
to impact. But the lo
we
st freque
ncy tha
t
can be te
ste
d
by it depen
ds
on the physi
cal natural freq
uen
cy of sen
s
or, an
d it
is often several times to natural freque
ncy.
(2) Ba
sed
on the
simi
larity of el
e
c
trom
echani
cal sy
stem,
we
ca
n
de
sign
comp
en
satio
n
network
with anal
og
circuit to co
rre
ct the
output ch
ara
c
teri
stic of
magneto
e
le
ctric
vibration
spe
ed sen
s
or. T
he corre
c
ted
magneto
e
le
ctric
vib
r
ation speed se
nso
r
become
s
second
orde
r hig
h
p
a
ss syste
m
whi
c
h ha
s th
e sam
e
type transfe
r fun
c
tion of origi
n
a
l
sen
s
o
r
, and
its
natural frequ
ency of outp
u
t characte
ri
stic is u
s
u
a
ll
y reduced to
1/20-1/50 of
original
sen
s
or’
s
physi
cal natu
r
al freq
uen
cy.
Referen
ces
[1]
B T
ang,
HL
La
ng.
Deve
lo
pme
n
t & Innovatio
n
of Machinery
& Electrical
. 20
08; 21(3): 3
9
-4
1.
[2]
Y Fan, XH Sui.
Measuri
ng T
e
chn
i
qu
es &
Data Proc
essi
ng
. Ch
ina M
e
trolo
g
y
Pub
licat
ions, C
h
in
a.
200
6.
[3]
Y F
an, H Liu,
N W
ang, G Z
h
ou.
Journ
a
l of Shan
do
ng Un
i
v
ersity of Science an
d T
e
ch
nol
ogy
. 200
1;
20(3): 41-
43.
[4]
S
Yu.
Journal
of Electronic M
easur
e
m
ent a
n
d
Instrument
. 1998; 12(
2): 7-1
2
.
[5]
J Niu, Y Liu, R Huo, K Song.
Journ
a
l of Sha
n
don
g Univ
ersit
y
of T
e
chnolo
g
y
. 2000; 30(
2): 111-
115.
Evaluation Warning : The document was created with Spire.PDF for Python.