Energy and Power Engineering, 2013, 5, 11-14
doi:10.4236/epe.2013.53B003 Published Online May 2013 (http://www.scirp.org/journal/epe)
Optical Design of OCT with Gapp ed Magnetic Ring*
Xiaoyi Su, Qifeng Xu
College of Electrical Engineering and Automation, Fuzhou University, Fuzhou, China
Received 2013
ABSTRACT
The mathematics and physics model of OCT (Optical Current Transformer) with a gapped magnetic ring is briefly dis-
cussed in the paper. And some proposals of how to select the magnetic materials and crystals and reduce the stress bire-
fringence of the crystal are also put forward in the paper. Based on the above, an OCT with 1000 A rated current is de-
signed by using the ANSOFT Maxwell tools.
Keywords: Ferromagnetic Collector Type; Optics Current Transformer; Magnetic Properties; Linear Birefringence
1. Introduction
Faraday magneto-optical effect is applied in optical cur-
rent transformer (OCT). Based on its sensing methodol-
ogy it can be divided into four types: fiber one, bulk
glass one, solenoid one, as well as gapped magnetic ring
one [1]. The one with a gapped magnetic ring utilizes a
small piece of magneto-optic crystal and other optical
elements to be placed in the gap of the magnetic ring
wounding around a current carrying conductor to form an
optical circuit. The gap magnetically induced by the cur-
rent flowing in the conductor and the crystal are the
“heart” of an optical current transformer head. Taken
together, the magnetic properties and the optical proper-
ties should be taken into consideration in the design. This
paper discusses the characteristics of the OCT with
gapped magnetic ring. Additionally, reasons and proce-
dures to select magnetic materials and crystals and miti-
gate stress birefringence are also represented specifically
in the paper. Depending on the analysis above and the
ANSOFT Maxwell tools, the optimized structure of an
OCT with 1000A has been achieved.
2. The Characteristics of OCT with Gapped
Magnetic Ring
When a linearly polarized light passes through a mag-
netic field paralleling to its propagation direction, a opti-
cal phase shift of the light called Faraday rotation angle
will created due to the Faraday effect
VHdl   (1)
where V is the Verdet constant. Once deemed if a gap of
magnetic ring is small enough, the gap magnetic can be
regarded as same as the ring inherent magnetic induced
by the current flowing in the conductor. Additionally,
based on the Ampere circuital theorem the gap magnetic
strength is given by ()
g
ggaa
H
Il ulu

 (2)
where l is the polarized light effective optical passing
path in the gap, I is the primary current, lg is the air-gap
length, ug is the air permeability, ua is the gapped mag-
netic ring permeability, la is the gapped magnetic ring
average loop length. As ug is far less than ua, Equation (1)
is simplified as
g
g
H
Il (3)
Combined Equation (1) with Equatio n (3), the Faraday
deflection angle θ and the primary current I are given by
g
cg
VHdluVIl l  
 (4)

g
gc
I
luVl   (5)
in which lc is the crystal length. Set Pi to be the polarizer
output light intensity and P0 to be the analyzer output
light intensity. According to the Malus law, the relation-
ship between Pi and P0 is expressed as
2
0cos () i
PaP



 (6)
where α is the optical attenuation coefficient intensity; φ
is the difference optical phase shift between the two out-
put light waves.
Desiring to obtain the maximum outpu t power, φ is set
to 45°. If θ is small enough, sin2θ will approximately
equal to 2θ. Equation (6) transforms into
0
2
(1 )
2
gc
iD
g
uVIl
a
PP PP
l
 
CAC
(7)
*Project supported by the National Natural Science Foundation of China
(51177016).

X. Y. SU, Q. F. XU
12
where PAC, the alternate current signal, is expressed as
PAC = (aPiugVIlc)/lg, while PDC, the direct current signal,
is expressed as PDC = (aPi)/lg. Eliminating the fluctua-
tions of optical power by introducing the operation
U=PAC/PDC. The relationship between U and I is given
by
2
g
cg
UIuVIll (8)
3. The Optimal Design of OCT
3.1. The Selection of Magnetic Material
The cold-rolled silicon steel, the permalloy alloy and the
amorphous alloy are commonly made on gapped mag-
netic rings. Their characteristics differences are reflected
in the magnetic permeability, the remanence density, the
saturation magnetization, the coercive force, the iron loss,
the Curie temperature, as well as the magnetostriction
coefficient. Considering that the OCT actual operation
environment temperature is less than the Curie tempera-
ture of magnetic materials, the iron loss and the magne-
tostriction coefficient are negligible under the 1000A
power frequency system, so these three factors, the iron
loss, the Curie temperature and the magnetostriction co-
efficient can be ignored. Table 1 shows the remainder
typical parameters.
Table 1. The comparison of typical parameters of the three
materials.
Typical Parameters
Materials Saturation
Mag-
netiz-ation
(T)
Magnetic
permeability
(*104)
Remanence
density
（T）
Co-
erci-ve
force
(A/m)
amorphous
alloy 1.5 0.25 1 2.0
permalloy
alloy 0.6 5.8 0.4 4.3
cold-rolled
silicon
steel 1.7 0.12 1.56 7
Permalloy alloy has the highest initial permeability,
the amorphous alloy has a lower one and the cold-rolled
silicon steel has a lowest one. Additionally, for closed
cores, a higher initial permeability is good for measure-
ment sensitivity. But the gapped magnetic rings are dif-
ferent. As the gap magnetic induction Bg is
()
g
aag g
I
Blu lu  (9)
Once the air permeability is 104 to 105 times bigger
than magnetic rings’. Then la is 102 times larger than lg,
so la/ua is far less than lg/ug. Equation (9) is simplified as
g
gg
BuIl (10)
In this case, the magnetic indu
pr
ction Bg depends on the
imary current I, the gap length lg and the air permeabil-
ity ug . That is to say, the permeability ua is an unimpor-
tant factor to the magnetic properties of gapped magnetic
rings.
Static field simulations on three magnetic materials
shown in Table 1 are done respectively by using the
ANSOFT Maxwell tool. The simulation gapped magnetic
ring parameters as follow: the inner radius is 30 mm, the
outer radius is 70 mm, the height is 40 mm and, the gap
length is 20 mm. Their basic magnetization curve are
illustrated in Figure 1. When the primary current is less
than 4 KA, these three curves are overlapped and the
cold-rolled silicon steel one has the lo ngest current linear
region. Since normal load current flowing on the con-
ductor is usually under 1 kA level, associating with the
linear region length shown in Figure 1, cold-rolled sili-
con steel and amorphous alloy have better magnetic per-
formance compared to permalloy alloy.
The remanence of magnetic concentrator ring is given
by[2]:
()( 0)
g
ag
r
a
g
g
ul ul
BfH fH
ll
   (11)
where f(B) is a closed core magnetization curve function.
to select a suitable magnetic
The remanence in the Gapped magnetic ring are de-
pended on the average magnetic path length and the air
gap length. These dependencies make the necessity to
design a r ight ring overall size. A smaller remanence has
certain distinct advantages to maintain the response
characteristics of magnetization, decrease coercive force
and reduce hysteresis loss.
Taken together, the norm
material is the one having a small remanence, a small
coercive force and a large saturation magnetic flux den-
sity. Thereby, amorphous alloy is the most suitable mate-
rial.
Figure 1. The basic magnetization curve of the three gap
magnetic rin gs.

X. Y. SU, Q. F. XU 13
3.2. The Selection of Magneto-Optical Crystal
Since the Verdet constant varies with the dynamic tem-
perature, the temperature coefficient should be consid-
ered during the selection of magneto-optical crystal.
When the te mperatu re change s from -2 5℃ to +80℃, the
Verdet constant of FR-5, a paramagnetic material, is re-
duced by 30% throughout the mutative temperature and
YIG that is a ferromagnetic material has 25% irregular
variation, while ZF-7 that is an anti-magnetic material
only changes 0.79% [3]. Similarly, an anti-magnetic ma-
terial called MR1 almost has no effect on the Verdet
constant in the temperature ranging from -55 to +135℃.
Additionally, its Verdet constant is as high as 0.065 -
0.092 min/Oe.cm (@ 632.8 nm) which is helpful to
shorten the crystal length and reduce the line birefrin-
gence. Therefore, the MR1 is employed in this design.
As the OCT using light to measure the magnetic field
surrounding a current carrying conductor has a transfer
function with a sine wave characteristics which made the
OCT polarization interference be a non-linear portion.
An approximate linear relationship between sin2θ and 2θ
introduced in the section 2 can fix th is problem when θ is
small enough. Ultimately, the OCT accuracy level will
determine the maximum Faraday deflection angle and the
crystal length. Set X is the difference between lg and lc ,
Equations (5) could be transformed as
c
X
l

g
uV
I



(12)
Assuming the OCT accuracy
pr
Reduce Stress Birefringence
tion
ilar expansion coefficient with
th
mization Structure of Gapped
Magnetic Rings
eter-
mineurrent carrying conductor which
ner and outer radius N, the more uniform gap
m
is a 0.2 class and the
imary current is 1000 A, its measurement error is less
than 0.2%. Then the maximum Faraday deflection angle
θmax is 0.877°. Set the maximum X is 20 mm, (As the
prism and polarizer product class size are 7 mm and 2
mm respectively. The other 2mm space is reserved for
installation). Putting these data into Equation (12), l is
calculated to 16.72 mm. Therefore, the crystal maximum
length is 16 mm.
3.3. Methods to
During the process of magneto-optic crystal produc
and processing or the in teract ion between the sensor head
and the adjacent structure, residual stress will occur and
stress birefringence will created simultaneously.
Since expansion coefficient has a function with the
temperature when the temperature ch anges the di fferenc e
on the materials expansion coefficient will cause tem-
perature gradients owing to the uneven temperature dis-
tribution of the sens ing head. Then thermal stress is gen-
erated within the sensing head and a linear birefringence
appears. Line birefringence aliasing on the Faraday po-
larization angle can undermine the reliability and stabil-
ity of the OCT [4]. For example, an OCT sensing head
has a structure of 70 mm outer diameter, 30 mm inner
diameter, 40 mm height and 30 mm air gap length and
ZF-7 as the sensing element which is 10 mm long, con-
ducted by a 1000 A primary current, its Faraday rotation
angle is 4.81° and its line birefringence angle is about
0.560 and it introduces 11.64% measurement error. The
method to reduce the linear birefring ence is to reduce the
magneto-optical material length. For example, using a
200 um thick magneto-optical film that dopes with Ce3+
by using the technology of liquid phase epitaxial (LPE)
as the sensing element instead of ZF-7 [5], then the
Faraday deflection angle is turned to 28.60 and its line
birefringence angle is 0.0112° only and the corre-
sponding error drops to 0.039%. It turns that the influ-
ence of linear birefringence on Faraday deflection angle
is effectively weakened.
Further, filling asbestos in sensor head or utilizing
materials having the sim
e magneto-optical material can also free from the tem-
perature variation gradient and weaken the thermal stress
birefringence.
3.4. The Opti
Since the gapped magnetic ring’s inner radius r is d
d by the size of a c
is determined by the primary current. Depending on the
analysis, the rated current of an OCT designed in this
paper is 1000 A, so conductive rod radius is set to 18 mm.
Additionally, leaving a 10mm margin sp ace to fill asbes-
tos, the gapped magnetic ring inner radius r is 28 mm.
Assuming N is the difference between th e inne r and ou ter
radius of the gapped magnetic ring. So the outer radius R
can be expressed as the sum of r and N. Combing Equa-
tion (3) with Equation (11), the gap length not only de-
termines the gap induction, but also affects the remanent
density. when the magnetic material is certain, the
smaller the gap length, the greater the gap induction and
remanence. Since the crystal length is described in selec-
tion 3.2, the air gap has a length ranging from 20 mm to
36 mm. Depending on the ANSOFT Maxwell tool, mak-
ing simulations on three gapped magnetic rings with 25
mm, 30 mm and 35 mm penning gap length under the
1000 A system respectively. The result are illustrated in
Figure 2 and Figure 3 which show the effect of the dif-
ference between a gapped magnetic ring inner and outer
radius on the gap induction Bg , as well as on the rema-
nent Br.
The larger the difference between a gapped magnetic
ring’s in
agnetic field distribution and the smaller the magnetic
flux leakage [6]. When N exceeds the length 30 mm, the
gap magnetic distribution is completely uniform. Con-
sidering to decrease the volume of material and achieve

X. Y. SU, Q. F. XU
14
4. Conclusions
This paper discusses the characteristics of OCT with
gapped magnetic ring, and some considerations to select
the magnetic material and the magneto-optical crystal,
and reduce the stress birefringence. Depending on the
analysis in the paper, the optimized design of an OCT
with 1000 A rated primary current is designed by using
the ANSOFT Maxwell tools. This optimized sensing
head has a structure as follows: 28 mm inner radius, 58
mm outer radius, 15 mm height and 25 mm length gap.
Additionally, the magneto-optical crystal choose MR1
with the length of 5 mm. In a temperature range from -40
℃ to +80℃, the OCT designed can be employed suc-
cessfully.
Figure 2. The effect of the difference between a gapped mag-
netic ring’s inner and outer radius on th e gap induction.
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doi：10.1109/61.156982