TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 16, No. 1, Octobe
r 201
5, pp. 38 ~ 4
5
DOI: 10.115
9
1
/telkomni
ka.
v
16i1.842
4
38
Re
cei
v
ed
Jun
e
26, 2015; Revi
sed
Jul
y
2
3
, 2015; Acce
pted Augu
st 15, 2015
Modeling and Analysis of Inductive Coil ELF Sensor
Rajendra Aparnathi*, Vedvy
as D
w
iv
edi
F
a
cult
y
of T
e
chno
log
y
and E
ngi
neer
in
g, C. U. Shah Un
iver
sit
y
, W
adh
w
a
n
c
it
y
,
Sure
ndra
n
agar, Gujar
a
t
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: rajen
d
raa
par
nathi
@liv
e.co
m
A
b
st
r
a
ct
Mathe
m
atic
al s
t
atistical a
naly
s
is of ind
u
ctive
l
oop c
o
il-s
ens
or is carri
ed o
u
t for its ma
gn
etic fie
l
d
effects operati
ng on extre
m
e
l
y low
frequen
cy (<30H
z
)
.
A system usi
ng r
e
sister, ind
u
ctor, and cap
a
ci
tor
effects finds reson
anc
e freq
uency for this
loop s
ens
or
and its se
nsiti
v
ity as ferro
magn
etic effect. T
h
e
desi
gn
meth
o
d
s for these
coils w
i
th ai
r and ferro
magn
etic cores
are technic
a
lly co
mp
ared
and
summari
z
e
d
,
w
h
ich
are
also
k
now
n a
nd
used
as se
arch
c
o
il
s or pick
up c
o
i
l
s
or
ma
gnetic
l
oop c
o
il
se
nsor
s.
T
he a
m
p
litu
d
e
and
b
andw
idt
h
of th
e freq
u
ency co
mpo
n
e
n
ts are c
o
mp
a
r
ed to th
e sta
ndar
di
z
e
d
n
o
r
m
a
l
spectru
m
. T
h
is
paper a
l
so pr
e
s
ents the ap
pli
c
at
ions of coi
l
sensor as
ma
g
netic coi
l
.
Ke
y
w
ords
: coi
l
sensor, mag
n
e
tic loo
p
coil, ferro
ma
gnetic c
o
re, extre
m
e lo
w
frequency.
Copy
right
©
2015 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Inductio
n
sen
s
or i
s
al
so
known a
s
se
a
r
ch
coil
be
ca
use
their me
asu
r
ing
p
r
in
ci
ples are
based o
n
varying magn
etic field m
e
a
s
u
r
eme
n
t. The
kno
w
le
dge
of physi
cal p
h
e
nomen
a relat
ed
to inductio
n
magnetom
e
t
ers (i
ndu
ctio
n, magneti
c
, and extrem
ely low noi
se amplificati
on)
con
s
titutes of
stron
g
ba
ckgrou
nd to ad
dre
ss
de
si
gn
of other types of mag
net
ometer a
nd their
appli
c
ation
s
[1]. The indu
ct
ion se
nsor p
r
i
n
cipl
e hel
p
s
d
e
rive directly
from Fa
rad
a
y’s law
equ
atio
n
(1) [1].
(1)
d
e
dt
Whe
r
e,
∅
∬
is magneti
c
flux throu
gh a coil
over a surfa
c
e (s) the vol
t
age is
prop
ortio
nal to the time derivative of the flux,
thus by principl
e, dc magn
etic field cannot
be
measure with
a static
coil, highe
r will b
e
the
freque
ncy higher
will
be the outp
u
t voltage (n
) coil
of sectio
n (s)
into an homo
geno
us in
du
cti
on magneti
c
field (B) equ
ation be
come
(2).
(
2
)
dB
en
S
dt
This
sign
al n
t
u
rns
coil
s,
is
desi
gn a
s
air
coil ind
u
ct
io
n
sen
s
o
r
.
A
s
i
n
cr
ea
se in
se
nsit
iv
it
y
of air coil in
crea
sing
nu
m
ber of tu
rn
s
(n)
or air
co
il
s
u
r
f
ac
e (
S
)
.
In
a
p
p
lica
t
io
ns
w
h
er
e th
e
s
i
ze
,
mass an
d pe
rforma
nce of
the se
nsor
are n
o
t t
oo stringent the
a
i
r-coil ind
u
cti
on sen
s
or i
s
an
efficient way to get mag
n
e
t
ic field vari
ation ar
e two o
t
her a
d
vanta
ges
of the ai
r coil indu
ctio
n
s
e
ns
or [2-3].
Important
wa
ys to im
prov
e the
se
nsiti
v
ity
of an in
ductio
n
sen
s
or
co
nsi
s
t in
usi
ng
a
ferrom
agn
etic co
re. In
that
config
uratio
n, in that
config
uration,
the f
e
rrom
ag
netic co
re
a
c
ts
as a
magneti
c
am
plifier a
nd
co
il is
wou
nde
d
aro
und
t
he f
e
rromag
netic co
re i
n
ter-di
gital ele
c
tro
d
e
s
are a
m
ong t
he mo
st co
m
m
only used
perio
dic
ele
c
tr
ode
structu
r
es. Recent a
d
vances in
such
fields
as n
onde
stru
ctive
testing
(NDT),
micro
-ele
ctrome
cha
n
ical
system
s (MEMS),
telecom
m
uni
cation
s, che
m
ical
sen
s
in
g, piezo
a
co
u
s
tics, and bi
otech
nolo
g
y involve -nterd
igital
electrode
s in
very different
ways. At the
sam
e
time, a numb
e
r
of comm
on feat
ure
s
a
r
e
sha
r
ed
among th
ese
appli
c
ation
s
. The pu
rpo
s
e of this pa
p
e
r is to
outli
ne commo
n feature
s
an
d
to
highlight th
e
differen
c
e
s
o
f
sen
s
o
r
g
e
o
m
etry,
manuf
acturi
ng te
ch
nique
s, choi
ce of mate
rial
s,
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Modeling
and Anal
ysi
s
of Inductive Coil
ELF Sensor (Raje
ndra Aparn
a
thi)
39
analytical
and
nume
r
i
c
al m
odelin
g, de
si
gn o
p
timiza
ti
on, sy
stem in
tegration,
and
data
analysi
s
. It
is difficult a
n
d
pe
rhap
s
even excessive
to ma
intain equally
d
eep and com
p
re
h
ensive
t
r
eatm
ent
of all the
s
e
subje
c
ts. In
ste
ad, the f
r
ingi
ng el
ectr
i
c
fie
l
d sen
s
ors are given
the
d
eepe
st e
m
ph
asi
s
in this m
anu
script [4]. Significa
nt asp
e
cts
of
othe
r types of se
nso
r
s are di
scusse
d, whi
l
e
repetition i
s
avoided. Referen
c
e
s
a
r
e
provide
d
to
major
revie
w
pape
rs
and
boo
ks in
e
a
ch
se
ction
devot
ed to
a
parti
cula
r fiel
d of
inter digi
tal
electrode
ap
plicatio
ns, su
ch as
di
elect
r
ic
imaging, a
c
o
u
stic
sen
s
o
r
s,
and MEMS [1, 5].
One
way to
cla
ssify the v
a
riou
s m
agn
etic se
n
s
ors i
s
by the field
sen
s
in
g ra
n
ge. The
sen
s
o
r
can
b
e
arbitra
r
ily
divided into
three
catego
ri
es l
o
w fiel
d,
medium
field
and
high
fie
l
d
sen
s
in
g. The
tech
nology f
o
r
sen
s
in
g m
agneti
c
fi
eld
s
has al
so ev
olved d
r
iven
by the ne
ed
for
improve
d
se
n
s
itivity, smaller si
ze, and
compatib
ility with electro
n
ic
system
s men
t
ion Figure 1.
Figure 1. Filed Sense M
a
g
netic Field
se
nso
r
A typical single-coil variable
-reluctance noise sensor i
s
illustrated in Figure 1. The
sen
s
o
r
consi
s
ts of thre
e e
l
ements: a fe
rrom
agn
etic
core sen
s
or i
n
the sha
pe
of a semi
circular
ring, a variabl
e air gap, an
d a ferrom
a
g
netic plate.
T
he total relu
ctance of the magneti
c
circuit
is
the sum of t
he in
dividual
relu
ctan
ce
s:
in thi
s
rese
arch p
ape
r p
r
esented
Design in
ductive
coil
para
m
eter a
n
d
statical a
nal
ysis
an
d pre
a
m
plifier pa
ra
meters [6].
2. Rese
arch
Metho
d
2.1. Design Inductiv
e
Sensor Coil Paramete
r
The m
a
in
go
al of thi
s
revi
ew i
s
to
sum
m
ari
z
e th
e e
x
isting
kno
w
l
edge
ab
out i
ndu
ction
coil
sen
s
o
r
s,
inclu
d
ing ol
d, often forgott
en pu
b
licatio
ns a
s
well a
s
ne
w devel
o
p
ments. Fi
rst
l
y,
two m
a
in
de
signs of
coil
sensor (with ai
r
cores
an
d f
e
rromag
netic co
re
s) a
r
e
d
e
scrib
ed. T
h
en,
their freq
uen
cy respo
n
se is analyse
d
taki
ng into
acco
u
n
t the type of
sen
s
o
r
and th
eir asso
ciate
d
output ele
c
tro
n
ics. Seco
ndl
y, particula
r i
ndu
cti
on sen
s
ors a
r
e di
scussed a
nd thi
s
is follo
we
d by
a de
scri
ption
of the
mo
st
comm
on
app
lication
of
thi
s
type
of tra
n
sd
ucer: m
a
gnetic ante
n
nae.
The
relatively
low sensitivity of an
air
coil sens
or an
d proble
m
s
with its minia
t
urizatio
n
can
be
partially overcome
by the
inco
rpo
r
atio
n of a
ferro
m
agneti
c
core, whi
c
h a
c
ts a
s
a flux con
-
centrator in
si
de the coil. F
o
r a coil with
a ferrom
agn
etic co
re, Eq
uation (1
) ca
n be re
writte
n as
Mode
rn
soft magneti
c
mat
e
rial
s exhibit
a relative p
e
rmeability,
μ
r, large
r
tha
n
105, so this
can
result in a sig
n
ificant in
cre
a
se of the
se
nso
r
se
n
s
itivity. Howeve
r, it shoul
d be ta
ken into
acco
unt
that the re
sult
ant perm
eabil
i
ty of the core
,
μ
c, can b
e
much l
o
wer t
han the m
a
te
rial pe
rme
abil
i
ty
[6]. This is du
e to the demagneti
z
ing fiel
d effect
defin
ed by the demagneti
z
ing f
a
ctor
N, whi
c
h is
depe
ndent
o
n
the
geo
met
r
y of the
core If the
perm
eability
μ
r of
a m
a
terial
is rel
a
tively large
(whi
ch is
generally t
he case)
the resultant
per
m
eabilit
y of the core
μ
c d
epen
ds
mainly on th
e
demagnetizi
n
g factor
N. T
hus, i
n
the case of a
high permeability material,
the
sensitivity of the
sen
s
o
r
dep
en
ds mo
stly on the geomet
ry of the core [7].
The de
mag
n
e
tizing fa
ctor
N for a
n
ellip
-soi
dal
co
re
depe
nd
s on t
he core l
engt
h lc a
nd
core diam
eter Dc a
c
cordi
n
g
to an appro
-
ximate Equation (3
).
.
.
.
(
3
)
1.
(
1
)
or
r
c
r
dH
Vn
A
dt
N
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 16, No. 1, Octobe
r 2015 : 38 – 4
5
40
2
2
2
.(
l
n
1
)
(
4
)
cc
cc
Dl
N
lD
It can be d
e
rived from Eq
uation (4) th
at in ord
e
r to
obtain a
sm
all value of
N (a
nd a
large resultant perm
eability
μ
c
)
th
e
c
o
r
e
s
h
ou
ld
be
long
a
n
d
w
i
th
small diam
eter. Let u
s
con
s
i
d
er
the
dime
nsi
o
ns of
a se
arch
coil sen
s
o
r
optimize
d
fo
r
a large
se
nsit
ivity as de
scri
bed i
n
[8]. Th
e
core was
pre
pare
d
from
a
m
orp
hou
s ri
b
bon (Metgla
s
2714AF
)
with
dimen
s
ion
s
l
c
=
300 m
m
and
Dc
= 10 mm (aspe
c
t ratio equal to 30
). Substituting these values i
n
to equation
(4)
we obtain
N
∼
= 3.5
× 1
0
−
3 whi
c
h m
e
a
n
s that the
se
nsitivity is ab
out
300 time
s large
r
in
com
pari
s
on
with t
h
e
air-coil
sen
s
or. The
r
efo
r
e
,
the use
of a co
re
ma
d
e
of a soft magneti
c
ma
terial lea
d
s t
o
a
signifi
cant im
provem
ent of the se
n
s
or
sensitivity. However, this
e
nhan
cem
ent is achieved with
the sa
crifice of one of the most
import
ant advantag
es of the air
coil sen
s
or t
h
e linea
rity.
The
core, eve
n
if
made
from
th
e be
st fe
rrom
agneti
c
m
a
te
rial, introdu
c
e
s
to
the t
r
an
sfer fun
c
tion
of
the se
nsor
some no
nline
a
r
facto
r
s
whi
c
h depe
nd
o
n
temperature,
freque
ncy, flux den
sity, etc.
Additional m
agneti
c
noi
se [8] also d
e
crea
se
s
the
resolution o
f
the sensor.
Moreove
r
, the
ferrom
agn
etic core alte
rs the di
stri
butio
n of the investigated m
a
g
netic field (o
r flux density),
whi
c
h can have important
conse
quences. High perm
eability core coil
sensor i
s
most of used in
high
sen
s
itivity or dimen
s
ion limitation
is impo
rtant
. It is typical geomet
ry or air
sen
s
o
r
is
pre
s
ente
d
in indu
ctive coil
Figure 2 and i
ndu
ct
ive ante
n
na coil pre
s
ented in Figu
re 3.
Figure 2. Inductive Coil
with Paramete
r
Figu
re 3. De
sign Indu
ctive Coil in Simula
tor
We will sta
r
t with
the
de
scription of
ma
gnetic
amplifi
c
ation
provid
ed by
a fe
rro
magneti
c
core. Our description
wi
ll rely
on
a si
mplif
ied modelling
of dem
agnetizing field [
9
].
Dema
gneti
z
in
g field
ene
rgy
modelli
ng i
s
still of g
r
eat i
m
porta
nce fo
r mi
cro
ma
gn
etism
studie
s
of
magneti
c
sen
s
ors.
Th
e se
arch coil
d
e
m
agneti
z
ing
fie
l
d effect
stud
y has th
e ad
vantage to
b
e
a
peda
gogi
c a
pplication an
d to give magnitud
e
sca
l
es to the d
e
sig
ner th
rou
g
h the app
a
r
ent
perm
eability con
c
e
p
t whi
c
h is at the source of
the
magneti
c
am
plification of
a ferro
mag
n
e
t
ic
core [10]. This last poi
nt remain
s a co
mmon de
no
minator of m
any magneti
c
sen
s
o
r
s. Wh
en a
magneti
c
fiel
d is ap
plied
on a
ferrom
agneti
c
mat
e
rial, thi
s
o
n
e
be
com
e
s m
agneti
z
ed.
T
h
is
magneti
z
atio
n, linked to
t
he m
agneti
c
field a
s
exp
r
e
s
sed, im
plies an i
n
cre
a
se
of flux den
sit
y
in
Equation (5).
0
(
)
(
5
)
Mx
H
BH
M
A way to
in
crease ma
gneti
c
a
m
plificatio
n is to
u
s
e
m
a
gneti
c
con
c
entrato
rs at t
he e
n
d
s
of the ferrom
agneti
c
co
re (3).
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Modeling
and Anal
ysi
s
of Inductive Coil
ELF Sensor (Raje
ndra Aparn
a
thi)
41
Let us
con
s
i
der a fe
rroma
gnetic
co
re u
s
ing
m
agn
etic con
c
entrato
rs of le
ngth (L), ce
nter
diamete
r
(d
)
and e
n
d
s
dia
m
eter
(D). Hi
gh-p
e
rm
eab
ili
ty core
coil
sensors a
r
e of
ten used in t
h
e
ca
se when hi
gh se
nsitivity
or dime
nsio
n limitat
ions are importa
nt. The mentio
n bello
w equati
o
n
is pre
s
e
n
ted
appa
rent pe
rmeability.
'2
2
(
6
)
1(
/
)
(
1
)
n
r
ap
pa
r
e
nt
ex
t
zr
B
d
B
NL
D
D
For a
given
set len
g
th,
diamete
r
an
d
magneti
c
m
a
terial, an
in
cre
a
se of m
agneti
c
con
c
e
n
trato
r
s diameter will
lead to a significa
nt increase of appa
rent pe
rmea
b
ility higher than
50%. Thu
s
the ma
ss
of windi
ng of coil and a
s
a
con
s
e
quen
ce the therm
a
l noi
se du
e
to
resi
stan
ce
of the windi
ng.
A typi
cal ge
ometry of su
ch a
sen
s
o
r
is re
se
nted i
n
Figure 5.
The
optimal val
u
e
of
core
diam
eter
Di
ha
s
b
een
dete
r
min
ed a
s
Di
= 0.
3 D [11]. T
h
e
coil
exhibit
s
a
resi
stan
ce
wh
ich can be
m
ention Equati
on (7
).
2
2
(1
)
(
)
(7
)
dN
d
L
RN
d
Whe
r
e
ρ
is the elect
r
ical resi
stivity, d
ɷ
is the wire d
i
ameter, t is the thickne
ss
of wire
insul
a
tion, d is the diamete
r
on whi
c
h
coi
l
is wou
nde
d and L
ɷ
is the
length of the coil [10].
The
coil
exhi
bits a
self-ind
uctan
c
e
which can
be
expresse
d 1
0
in
ca
se
of an
in
ductio
n
sen
s
o
r
usi
ng
ferrom
agn
etic core a
nd u
s
i
ng equ
ation.
2
(8)
o
apper
e
n
t
NS
L
l
Whe
r
e
(S) i
s
the fe
rrom
agneti
c
core
se
ction,
μ
o natural vacuum perm
eability,
λ
=
(l/l
ɷ
)2/5 i
s
co
rre
ction
facto
r
. The
differe
nt ele
c
tric
al n
o
ise
si
gnal
p
o
tential b
e
tween
ea
ch tu
rn of
the coil
co
nse
quen
ce
a ca
p
a
citan
c
e
be
cause of the
store e
n
e
r
gy b
e
twee
n the tu
rns
of the coil
in
mention bell
o
w Equation
(9
) [11].
0
(
2
(
)
)
(9)
(1
)
r
l
l
l
Cd
n
d
t
tn
Whe
r
e
ε
o
ε
r
are
re
spe
c
tively the vacu
u
m
permittivity and the
rel
a
tive permittivity of the
nl is the num
ber of layers and othe
r parameter
a
r
e prese
n
t and given sen
s
o
r
, the element of the
indu
ctive coil
sen
s
o
r
ele
c
tro modelin
g can be dete
r
mi
ne in Figu
re 4
.
Figure 4. Rep
r
esentation In
ductio
n
Coil
Senso
r
Flux
meter
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046
TELKOM
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KA
Vol. 16, No. 1, Octobe
r 2015 : 38 – 4
5
42
The tra
n
sfe
r
function b
e
tween the o
u
tp
ut of
the ind
u
ctive coil
se
nso
r
voltage
and flux
den
sity can b
e
pre
s
ent in
Equation (10) [11].
2
(
)
(1
0
)
(1
)
appar
e
n
t
e
r
out
jN
S
V
BL
C
j
R
C
3. Results a
nd Analy
s
is
De
sign Fe
rro
m
agneti
c
Co
re inductive Coil Senso
r
Hi
gh permeabil
i
ty ferrite core coil
sen
s
o
r
s are o
ften use
d
in
case
wh
en hi
g
h
se
nsitiv
ity or diam
eter lim
itati
on. The le
ngth of the
co
il
l is recomme
nded to be a
b
out 0.7–0.9 lc. For su
ch
coi
l
dimensi
o
n
s
, the output sig
nal V and SNR
ratio at room
temperatu
r
e
can b
e
descri
bed a
s
It can be con
c
lud
e
d from relatio
n
shi
p
s (9) an
d
(10
)
that in t
he case of a
coil
sen
s
o
r
with a fe
rro
m
agneti
c
core
the mo
st efficient met
hod
of
improvin
g the
sen
s
o
r
p
e
rfo
r
man
c
e i
s
to
make
the le
n
g
th of the
co
re (o
r
rathe
r
t
he ratio l/Di
)
as
large
a
s
po
ssible, sin
c
e
th
e sensitivity is p
r
op
or
tion
al
to l3. Figu
re
5 presents th
e dep
end
en
ce of
the resultant perm
eability. The choice of the as
pect ratio of the core
is very important.
Figure 5 Indu
ctive Coil Out
put
Voltage Resp
ective Fre
quen
cy
The length
should be
suf
f
iciently large
to
benefit from the perm
eability of th
e core
material. O
n
t
he othe
r h
a
n
d
, if the aspe
ct rati
o i
s
la
rg
e the resultan
t perme
ability depe
nd
s on
the
material permeability. Thi
s
may cause
error
result
ing from the instability of
material perm
eability
due to the chang
es of te
mperature o
r
applied fi
eld
frequen
cy. For large val
ues of mate
ria
l
perm
eability t
he resultant
perm
eability
μ
c p
r
a
c
tically
doe
s
not d
e
pend
on
mat
e
rial
ha
ra
cteri
s
tics
becau
se rel
a
tion (3
) is then
:
1
(
1
1)
c
N
High
er val
u
e
s
of m
a
terial
perm
eability
allow th
e u
s
e
of long
er
co
res
without th
e ri
sk of
the re
sulta
n
t perm
eability
depe
nding
on
the mag
netic
cha
r
a
c
teri
sti
c
of the
mate
rial u
s
ed. A
s
an
example, let us con
s
ide
r
a
low-n
o
ise ind
u
ction ma
gne
tometer that is de
scribe
d in [10]. Here, the
core wa
s p
r
e
pare
d
from a
m
orp
hou
s rib
bon (M
etgla
s
2714AF)
wit
h
temperatu
r
e-i
nde
pend
e
n
t
prop
ertie
s
an
d dimen
s
ion
s
: length 150
mm, cro
s
s-
se
ction of the o
r
de
r 5 × 5 m
m
2 (a
spe
c
t ratio
of aro
und
27
). A coil of
1
0
00
0 turns
wa
s
wou
nd
with a
0.15
mm diam
eter wire. Th
e n
o
ise
cha
r
a
c
teri
stic of this
sen
s
o
r
is
pre
s
e
n
te
d in Fig
u
re
7. The o
b
taine
d
noi
se level
arou
nd 0.0
5
pT
Hz
−
1/2
wa
s found to be
co
mparable
with the
values reporte
d for SQUID
sen
s
o
r
s.
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TELKOM
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ISSN:
2302-4
046
Modeling
and Anal
ysi
s
of Inductive Coil
ELF Sensor (Raje
ndra Aparn
a
thi)
43
The
same
a
u
thors
comp
ared
the infl
uen
ce of th
e
co
re m
a
teri
al. For
an
a
m
orp
hou
s
Metglas co
re
the noi
se
was fou
nd to
be 0.05
pT
Hz
−
1/2,
whil
st for the
sa
me sen
s
or
with a
perm
a
lloy Su
perm
u
metal
core
it exhibite
d la
rge
r
n
o
ise
of 2
pT
Hz
−
1/2
.
Als
o
, a
c
o
mp
a
r
is
on
o
f
air
coil a
nd fe
rro
m
agneti
c
core sen
s
ors
ha
s b
een
re
por
t
ed [13, 1
4
]. Experime
n
tal result
s
sho
w
t
hat
well-de
sign
ed
ferrom
agn
etic co
re in
du
ction se
nsors
exhibited a li
nearity comp
arabl
e with a
i
r-
cor
e
se
ns
or
s.
Senso
r
s with
ferro
mag
netic cores
are
o
ften use
d
for magneti
c
inv
e
stigatio
ns i
n
spa
c
e
resea
r
ch [11
,
14]. Devices with a core len
g
th o
f
51 cm an
d weight of
75 g (incl
u
ding
prea
mplifier)
exhibited a
resol
u
tion (noi
se level
)
of 2
fT Hz
−
1/2 [1
4]. In an ana
lysis of Ea
rth
’
s
magneti
c
fiel
d (O
GO
sea
r
ch
coil exp
e
ri
ments) t
he fol
l
owin
g thre
e-axis sen
s
ors
have be
en u
s
ed:
coil 1
00 00
0
turns
of 0.03
6 mm in dia
m
eter, co
re
made from ni
ckel–iron all
o
y 27 cm lo
ng
and
squ
a
re
(0.
6
×
0.
6 cm2
)
cr
o
s
s
-
sect
io
n.
E
a
ch
se
n
s
o
r
weighted 1
50
g (with h
a
lf the wei
ght bei
ng
the co
re
). Th
e se
nsitivit
y
in t
h
is
ca
se
wa
s 10
μ
V (nT
Hz
)
−
1
[1
0]. The detai
led de
sig
n
a
nd
optimizatio
n
of an extre
m
ely sen
s
itive
three
-
axis
se
arch coil
ma
g
netomete
r
for
spa
c
e
re
se
a
r
ch
is de
scribe
d in [14].
The
coil
ma
g
netomete
r
d
e
v
eloped
for the
sci
entific had a noi
se
l
e
vel
of 4
fT Hz
−
1/2
at
30 Hz. Appro
x
imation ferrit
e
core effect
are p
r
e
s
ent in
Table 1.
Table 1. Approximate Maximum Permeabilities
Material
μ
/(H m-1
)
μ
r
A
ppl
i
c
a
t
i
on
Ferrite
U 60
1.00E-05
8
UHF chokes
Ferrite M3
3
9.42E-04
750
Resonant circuit RM cores
Nickel (99% pure
)
7.54E-04
600
-
Ferrite N41
3.77E-03
3000
Power
circuits
Iron (99
.
8% p
u
re
)
6.28E-03
5000
-
Ferrite T38
1.26E-02
10000
Broadband
t
r
ansf
o
rmers
Silicon GO steel
5.03E-02
40000
D
y
namos, mains
transforme
r
s
supermallo
y 1.26
1000000
Recording
heads
Table 2. Perf
orma
nce of Inductive Coil Sensor an
d Pa
ramete
r
Sr.No
Rin
Ro
L
C
Zin
Zo
f
B/W
Dc
lc D
Di
Dm
1 10
11.4
0.15
147
10.000
096
47
10.05
29.35
7.958
11
330
180
156.6
168.3
2 10
11.4
0.20
147
10.000
143
79
10.06
26.25
6.36
12
360
186.2
161.99
4
174.09
7
3 10
11.4
0.25
147
10.000
241
77
10.05
23.96
5.3
13
390
175.3
152.51
1
163.90
55
4 10
11.4
0.30
147
10.000
376
41
10.04
22.18
4.541
12.5
375
167.2
145.46
4
156.33
2
5 10
11.4
0.35
147
10.000
239
54
9.99
26.9
4.547
11.5
345
168.4
146.50
8
157.45
4
6 10
11.4
0.35
100
10.000
266
78
10.34
21.
96
4.547
9.5
285
162.5
141.37
5
151.93
75
7 10
11.4
0.35
150
10.000
146
34
10.23
19.02
4.547
8.5
255
156
135.72
145.86
8 10
11.4
0.35
200
10.000
163
65
10.25
17.01
4.547
12.8
384
152.6
132.76
2
142.68
1
9 10
11.4
0.35
250
10.000
093
05
10.09
15.53
4.547
9.8
294
153.4
133.45
8
143.42
9
10
10
11.4
0.35
300
10.000
281
83
10.17
14.37
4.547
11.4
342
157.3
136.85
1
147.07
55
11
10
11.4
0.35
350
10.000
078
22
10.06
13.45
3.978
12.1
356.
9
158.2
137.63
4
147.91
7
12
10
11.4
0.40
350
10.271
416
11
10.02
12.68
3.536
13.3
29.
1
149.2
129.80
4
139.50
2
13
10
11.4
0.45
375
10.090
633
31
10.08
11.62
3.183
10.6
324
161
140.07
150.53
5
14
10
11.4
0.50
390
10.000
369
2
10.08
10.86
2.89
14.2
426
157
136.59
146.79
5
15
10
11.4
0.55
390
11.720
212
58
11.78
9.63
2.44
9.6
288
148.6
129.28
2
138.94
1
16
6
6.7
0.98
670
5.0030
900
7
5.12
6.2 3.824
16
480
153.2
133.28
4
143.24
2
17
5
6.1
0.98
670
15.009
964
11
15.1
6.
17
2.436
14.2
426
162.3
141.20
1
151.75
05
18
15
16.7
0.98
670
10.000
080
82
9.89
5.58
1.81
17.1
513
148.5
129.19
5
138.84
75
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 16, No. 1, Octobe
r 2015 : 38 – 4
5
44
To obtain the desi
r
e
d
resona
nce freque
nc
y an
d a resi
stan
ce noi
se ab
ove the
prea
mplifier voltage n
o
ise t
he dia
m
eter
of cop
p
e
r
wi
re of 71
μ
m an
d
n
u
mb
er
o
f
tu
r
n
s
o
f
12
20
0
were sele
cte
d
. The core
wa
s built fro
m
170 mm l
o
ng 50
μ
m
thi
ck ann
ealed FeNiM
o
15
–8
0–5
perm
a
lloy stri
ps, with
a cro
ss
se
ction
of 4.2 mm
×
4.2
mm. The ma
ss
of the who
l
e three
-
axis
sen
s
o
r
an
d t
he b
r
acket
was o
n
ly 430
g. There a
r
e comm
ercially
available se
arch coil sen
s
ors.
The frequ
en
cy cha
r
a
c
teri
stics of
this se
nsor
a
r
e
sh
own in
F
i
gure.6
a
nd
the summa
ry
of
perfo
rman
ce
and
re
si
sta
n
ce
indu
ctan
ce
and fin
d
all pa
ramete
r are
sho
w
n
in Tabl
e 2
a
l
so
pre
s
ent
in i
n
put po
we
r V
s
output volta
ge of
pream
plifier in
sho
w
n
Figu
re
7
In the Fi
gure
8 i
s
pre
s
ent the
value of ban
d weig
h, Sensitivity,
alpha and b
e
ta gain facto
r
vs extreme l
o
w
freque
ncy
5 to 41.51
Hz g
r
aph
rel
a
tion
ship. al
so
prese
n
t ferrom
agneti
c effect
in Indu
ctive
coil
Senso
r
sho
w
n in Figure 9.
Figure 6. Inductive Coil Se
nso
r
Pre
-
amp
lifier
Figure 7. Inductive Coil Se
nso
r
Output
Voltage
vs
Input Power Charac
teris
t
ic
Figure 8. Gra
ph with (B/W,
S, Alpha and
Betta)
Figure 9. Ferromagn
etic Effect for Sen
s
o
r
4. Conclusio
n
The indu
cto
r
sen
s
o
r
u
s
ed f
o
r mag
netic fi
eld mea
s
u
r
e
m
ents h
a
ve b
een kno
w
n e
x
tremely
low f
r
eq
uen
cy sign
al o
r
n
o
ise. It
ca
n b
e
p
r
e
c
isely calcul
ation
of tran
sfer fun
c
tion a
nd li
mitation
(Boun
dary
)
o
f
elf sen
s
or.
The ind
u
cti
on coil se
nsor with fe
rro
m
agneti
c core pre
p
a
r
ed f
r
om
moden
amo
r
phou
s mate
ri
al exhibit sen
s
itivity. But e
x
tremely low
freque
ncy fo
r magneti
c
fie
l
d
appli
c
ation
s
can be better
served by usi
n
g SQUID
met
h
od
s the most of extremely low frequ
en
cy
sen
s
o
r
, the practi
cal limit of the resolut
i
on
depe
nde
d on the possibility of ach
i
eving the no
ise
and
level of freque
ncy.
T
he
de
sig
ned system allo
ws to e
nhan
ce
the SNR so
to improve the
minimal
re
sol
u
tion of the
front-en
d
sen
s
or. Any shap
e and
si
ze
of
indu
ctive coil
sen
s
o
r
that
h
a
s
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Modeling
and Anal
ysi
s
of Inductive Coil
ELF Sensor (Raje
ndra Aparn
a
thi)
45
this impe
dan
ce
can
be u
s
ed with th
e same p
r
eam
pli
f
ier, allowi
ng
for a vari
ety of sen
s
itivity and
conve
n
ien
c
e
operation wit
hout having t
o
make a
n
y chang
es.
Referen
ces
[1]
Raje
ndr
a Apar
nathi, Dr Ve
d
V
y
as
D
w
iv
edi.
Desig
n
L
oop I
nductor C
o
i
l
Sensor for ELF
Noise S
i
g
nals
.
Europ
e
a
n
Jour
nal of Acad
e
m
i
c
Essays.
2014
; 2(1): 21-26.
[2]
Raje
ndr
a Apar
nathi, Dr Ve
d
V
y
as
D
w
iv
edi.
Electro Ma
gnet
ic Biose
n
sor F
o
r Extrem
el
y L
o
w
F
r
eqe
nc
y
Brain Waves.
In
te
rn
a
t
io
na
l Jo
u
r
n
a
l
o
f
Ad
van
c
ed
R
e
sea
r
ch
i
n
El
e
c
tri
c
a
l
,
El
e
c
tro
n
i
cs and
Instrume
ntatio
n Engi
ne
erin
g.
201
3; 2(9).
[3]
S T
u
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