The 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

Proceedings

APPLIED ELECTROMAGNETICS
AND MECHANICS

Edited by
Phuong Ho-Thanh, Ha Ta-Hong, Ngan Huynh-Kieu, Chi Dang-Kim

The 7th Asia Pacific Symposium on Applied Electromagnetics and Mechanics
July 25-27, 2012, Ho Chi Minh city, Vietnam

JAPAN SOCIETY OF APPLIED ELECTROMAGNETICS AND MECHANICS

The 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

JAPAN SOCIETY OF APPLIED ELECTROMAGNETICS AND
MECHANICS
All rights reserved. No part of this book maybe produced, stored in a retrieval system, ortransmitted, in any form or by any means without the prior written permission from thepublisher.
ISBN 978-4-931455-20-7
The 7th Asia Pacific Symposium on Applied Electromagnetics and Mechanics(2012, Ho Chi Minh city, Vietnam)

APPLIED ELECTROMAGNETICS AND MECHANICS
Proceedings of the 7th Asia Pacific Symposium on Applied Electromagnetics and Mechanics
July 25Ǧ27, 2012, Ho Chi Minh city, Vietnam

Organized by:Faculty of Electrical and Electronics Engineering, Ho Chi Minh City University ofTechnology

Editors:
Phuong Ho-Thanh, Ha Ta-Hong, Ngan Huynh-Kieu, Chi Dang-Kim
Publisher:
Japan Society of Applied Electromagnetics and Mechanics
1Ǧ4Ǧ6Ǧ401 Nezu, BunkyoǦku, Tokyo, 113Ǧ0031 Japan

Printed in Ho Chi Minh city, Vietnam.

The 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

CONFERENCE COMMITTEEHONORARY CHAIRMEN
Assoc.Prof. Vu Dinh Thanh
Prof. Junji Tani
Prof. M. Enokizono

Rector of Ho Chi Minh city University of Technology (HCMUT),
Vietnam
Former President of Japan Society of Applied Electromagnetics
and Mechanics (JSAEM), Japan
President of Japan Society of Applied Electromagnetics andMechanics (JSAEM), Oita University, JapanCHAIRMEN
Assoc. Prof. Nguyen Huu Phuc
Prof. Dang Luong Mo
Prof. Yoshifuru Saito
Prof. Yasuyoshi Horibata

HCMUT
Advisor to VNU-HCM
Hosei University
Hosei University

CO-CHAIRMEN IN ORGANIZING COMMITTEE ± TECHNICAL AND PUBLICATIONCOMMITTEE
Prof. Yoshifuru Saito
Hosei University
Prof. Yasuyoshi Horibata
Hosei University
Prof. Hiroyuki Wakiwaka
Shinshu University
Dr. Do Hong Tuan
HCMUT
Assoc.Prof. Duong Hoai Nghia
HCMUTDr. Huynh Thai Hoang
HCMUT
INTERNATIONAL STEERING COMMITTEE
Chairman:Prof. S. Yamada
Co-Chairman:
Prof. A. Nafalski
Member:M.M. Bayoumi
S. Chonan
K. Demachi
Prof. J. Faiz
E. Okada
Y. Saito
M. Sasaki
N. Takahashi
R. Tang
M. Uesaka
H.Wakiwaka
C. Xiang
M. Yamamoto
W.L. Yan
M. Norhisam
J.G. Zhu
K.ChamnongthaiAnuar Mohd Ramli
T. OhjiKanazawa University, Japan
University of South Australia, Australia
Al-Minia University, Egypt
Akita Prefectural University, Japan
University of Tokyo, Japan
University of Tehran, Iran
Ibaraki University, Japan
Hosei University, Japan
Gifu University, Japan
Okayama University, Japan
Shenyang University of Technology, China
University of Tokyo, Japan
Shinshu University, Japan
North China Electrical Power University
The University of Tokyo, Japan
Hebei University of Technology, China
Universiti Putra Malaysia, Malaysia
UTS, Australia
KMUTT, Thailand
Telekom Malaysia Berhad
Toyama University, Japan

The 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

H. Okazaki
T. Yuji
ORGANIZING COMMITTEE
Chairman:
Dr. Norhisam Misron
Co-Chairman:
Dr. Ismail MusirinMembers:
Wan Zuha Wan Hassan
Assoc. Prof. Dr. Mohammad Hamiruce Marhaban
Dr. Mohd Nizar Hamidon
PUBLICATION COMMITTEE
Chairman:T. Sawada
Co-Chairman:
Roslina Mohd Sidek
H. Ohsaki
CONTRIBUTORSJapan Society of Applied Electromagnetics and Mechanics
Ho Chi Minh City University of Technology, Vietnam
Hosei University, Japan
Kanazawa University, Japan

Gifu University, Japan
University of Miyazaki, Japan

UPM, Malaysia
UiTM, Malaysia
UPM, Malaysia
UPM, Malaysia
UPM, Malaysia

Keio University, Japan
UPM, Malaysia
University of Tokyo, Japan

The 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

Transformers for Contactless Power Suppliers
Tatsuya OHASHI1), Iliana MARINOVA2) and Yoshifuru SAITO1)
1)

Graduate School of Hosei University, Tokyo 184-8584, Japan
2)
Technical University of Sofia, Sofia 1756, Bulgaria

ABSTRACTContactless power supplier is composed of a transformer having the distinct primary and secondary coils
separated by air gap. Because of the electromagnetic compatibility problem, it is essential to keep the leakage
magnetic fields around the contactless power supplier as low as possible.
This paper carries out the wavelets multi-resolution analysis to the magnetic field distributions around contactless power supplier. As a result, we have succeeded in obtaining one of the reasonable core shapes by observing
the wavelets spectra of measured magnetic field vector distributions. Furthermore, it is revealed that a tested trial
transformer gives nearly 80 percent power transmission efficiency even though the primary and secondary coils are
separated by 10mm air gap.
Keywords:

contactless power suppliers, magnetic field visualization, discrete wavelets, multi-resolution analysis.

conventional U shape cores [2,3]. An extension of1

conventional inner core type transformer employing U

Introduction

shape cores spreads the magnetic fields around theDevelopment of modern semiconductor technology makes

transformer centered at the air gaps. On the other side, a flatit possible to realize

small and light weight electronictransformer employing dish shape ferrite cores and spirally

devices equipped with a large variety of smart functions

wound coils (called the "flat transformer" in short) confines

such as smart cellar phone as well as ultra mobile

the magnetic fields at the center of the flat transformer,

computers.

which

Although these electronics provide the highly efficient job

transformer.

minimizes

themagnetic

fields aroundtheenvironment, entertainments and convenient electronic

As a first stage, we have worked out the trial flat

consumer life, environments around human life are fillingtransformers. Experimental study utilizing secondary

up with the electromagnetic fields. Particularly, because ofresonant technique reveals that our flat transformer withthe many electric power suppliers to supply the electronic

1cm air gap and 0.69 coupling factor is capable to transmit

products, it is essentially accompanied the electric power

79 percent input power to the secondary circuits [4]. Further,lines jangle, which leads to SAR (specific absorption rate)

multi-resolution analysis of the discrete wavelets clarifies

problems.

the effect of secondary resonance circuits, i.e., the highest

One of the solutions of this electromagnetic compatibility

level the magnetic field vector distributions visualizes the

problem in the human life environment is to work out thedistinct difference of the magnetic field vector distributions

cordless contactless power suppliers [1].

between the secondary resonant and not resonant

This paper concerns with development of a transformer

conditions.

composed of the separated primary and secondary cores by

2 Visualization of the Magnetic Field Around the

air gap. This transformer having the open magnetic flux
paths between the primary and secondary core is of theparamount part to realize the contact-less power suppliers.

Transformers
2.1 Transformer employing U shape ferrite core

Apply the discrete wavelets transform to the magnetic field

Fig.1 shows the tested transformer employing two U

vector distributions around the transformer having open

shape ferrite cores. Table 1 lists specification of thismagnetic flux paths clarifies that the dish like ferrite corestransformer.

embedding spirally wound coils gives a far excellent

We have carried out the measurements of magnetic fieldmagnetic field vector distribution compared with those with

vector distributions around this transformer using a search

The 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

coil. The shape of this coil is a finite length solenoid andcurrent. The air gap between the heads of both primary anddimensions are the 1cm length, 14mm diameter, 30 turnsecondary U shape ferrite cores is of 1 cm.

wound coil using a 0.2mm diameter conducting wire. By

Fig.3 shows one of the measured magnetic field vectormeans of this search coil, we have measured the magnetic

distributions at some instance. It is obvious that thefield vector distributions.

magnetic field vectors distribute around the U shape cores.

38.7mm

9.1mm

22.0mm
Fig.1 Tested transformer employing U shape ferrite cores.

Table 1 Specification of the transformer
employing U shape cores.
U shape core
TDKPE22UU
Number of turns of primary coil
30turns
Number of turns of secondary coil 30turns
Diameter of primary coil
0.4mm
Diameter of secondary coil
0.4mm

Fig.3 Magnetic field vector distribution around thetransformer employing U shape ferrite cores.

2.2 Flat Transformer
The transformer employing U shape cores is essentially
one of the extensions of in-core type transformer. On theother side, the flat transformer is one of the extensions ofshell type transformer. Fig. 4 shows the tested flattransformer employing dish like ferrite cores. The dish likeFig.2 Scheme for measurement of the magnetic field
vector distribution.

Fig. 4 Tested transformer employing the dish like ferrite cores.

Fig. 2 shows a scheme for measurement of the magnetic

ferrite cores are composed of the Manganese and Zinc

field vector distribution. In this figure, the circular coils arecompound, and their customized products have been

the search coils. Two parallel surfaces illustrates theworked out by Tokin company.

magnetic field measurement surfaces in the direction ofExperimental measurement of the magnetic field vector

z-axis component. Number of measured points is 884

distributions is carried out by means of the same search coilwith respect to the x-, y-, z-directions. Secondary circuit isused to the transformer employing the U shape ferrite cores.

no load and primary is excited by a 10kHz sinusoidal 0.5A

Fig.5 shows a scheme of the magnetic field vector

The 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

distribution measurements for this flat transformer. In thisfigure, the primary and secondary coils are spirally wound.
Two parallel square surfaces illustrates the magnetic fieldmeasurement locations in the direction of z-axis component.
Number of measured points is 884 with respect to thex-, y-, z-directions. The secondary circuit is no load and theprimary circuit is excited by a 10kHz sinusoidal 0.5A
current. The air gap between the primary and secondary
core head surfaces is of 4 cm.
Fig.6 Magnetic field vector distribution between the flat shapecores.

3

The Wavelets Transform Analysis

3.1

Vector Wavelets Transform

The magnetic field vector distributions are generally three
dimensional vectors. Therefore, when we apply theFig.5 Scheme for measurement of the magnetic field vector
distribution for the flat shape transformer.

wavelets multi-resolution analysis to the three dimensional
vectors, it leads to the three-dimensional vector wavelets
transform [2,3].

Table 2 lists specification of the flat shape transformer
shown in Figs. 4 and 5.

When

we

T

P ri mar y core: Outer diameter
105mm
Primary core: inner diameter
99mm
Primary core: thickness
7mm
Primary core: diameter
105mm
Primary core: depth of the cylinder cut
1mm
Primary core: length of the spiral winding 506.3mm
P ri mar y core: dia meter o f the conductor
4 mmSecondar y core: Outer diamet er
105 mmSecondary core: inner diameter
99mm
S e c o nd a r y c o r e : t h i c kn e s s
7mmSecondary core: diameter
105mm
Secondary core: depth of the cylinder cut
1mmSecondary core: length of the spiral winding
506.3mm
Primary core: diameter of the conductor
4mm

Fig.6 shows one of the measured magnetic field vector
distributions at some instance. It is obvious that themagnetic field vectors spreads over primary winding like afountain, and also it is revealed that nature of the magnetic
field distributions is intrinsically different between thein-core type in Fig.3 and shell- core type in Fig.6 .

atranspose

operationofathree-dimensional (cubic) matrix Almn as> Almn @Table 2 Specification of the flat shape transformer.

denote(1)Amnl ,

the three-dimensional wavelets spectrum matrix Slmn isgiven byT

Slmn

ªW  ªW  W  A T ºT º .
«¬ n ¬ m > l lmn @ ¼ »¼(2)

where the matrix Smn is a three-dimensional wavelets
spectrum matrix with order l by m by n; and Wn, Wm and Wl
are the wavelets transform matrix with order n by n, m by mand l by l, respectively.
The measured magnetic field vectors distribute inthree-dimensionally so that the magnetic field vector
distribution matrix Hlmn is composed of the three
independent x-, y-, and z-vector component matrices X lmn,
Y lmn, Z lmn, respectively.
The matrix Hlmn is represented by

Hlmn

Xlmn  Ylmn  Zlmn .

(3)Thus, the three-dimensional wavelets spectra of themagnetic field distribution are obtained by

The 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

T

Slmn

T
ª
ªW  ªW  X  Y  Z ºT º º . (4).
W

n
m
l
lmn
lmn
lmn
¬
¼ ¼ »
«¬
¬
¼

Generally, the wavelets spectrum Slmn is classified into themulti-level spectra according to the orthogonal property of
discrete wavelets transform. Number of levels p depends on
not only the number of data comprising spectrum Slmn but
also the wavelets base functions used for wavelets transform
matrices Wn, Wm. Wl.
Apply the inverse wavelets transform to each of the
(1)
(2)
( p)
decomposed wavelets spectra Slmn
yields the, Slmn, , Slmn

Fig.7 Wavelets spectra of the magnetic field vector distribution
measured around the transformer employing U shape cores..

wavelets multi-resolution result:
p

H lmn

¦H

( p)
lmn

i 1

T

(5)

T
ª T ª TT(i ) T º º
ª
º
W
W
W



S
¦
lmn ¼ » » ,« n «¬ m ¬ l
¼ ¼
i 1 ¬
p

where the levels 1,2, .. . p-th magnetic field vector
(1)
(2)
( p)
, respectively. Low anddistributions are Hlmn
, Hlmn, , Hlmn
higher level magnetic field vector distributions represent the
global and precise vector distributions, respectively. Sum of(a) Level p=1

the entire levels gives the original vector field distribution.
3.2 Wavelets analysis of the magnetic field vector
distribution around the transformer employing U
shape ferrite coresFig.7 shows the wavelets spectra of the magnetic field
vector distribution shown in Fig.3, where Daubechies
second order base function is employed. It must be notedthat wavelets transform to the vector fields gives the vector(b) Level p=2

fields even in the wavelets spectrum space. Further, themost dominant wavelets spectrum vectors are extracted as
observed in Fig. 7.
Because of the number of data in z-axis and also employed
Daubechies second order base function, it is possible toobtain the three levels multi-resolution magnetic field vector
distributions. These magnetic field vector distributions areshown in Fig. 8.
The results of the wavelets multi-resolution analysis to thetransformer employing U shape cores suggests that major
magnetic flux linking both of the primary and secondarycores is only the level 1 magnetic field vectors.

(c) Level p=3
Fig.8

Wavelets multi-resolution analysis results of the magnetic
field vector distribution measured around the transformer
employing U shape cores.

The 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

This means that the levels 2 and 3 magnetic fields vectors
are spreading around cores centering the air gap. This
spreading magnetic field vector distribution causes theelectromagnetic compatibility problem.

3.3 Wavelets analysis of the magnetic field vector
distribution around the flat transformer
Fig.9 shows the wavelets spectra of the magnetic field
vectors distribution shown in Fig.6, where Daubechies(a) Level p=1

second order base function is employed. The most dominant
wavelets spectrum vectors are extracted as observed in Fig.
9.

(b) Level p=2

Fig.9 Wavelets spectra of the magnetic field vector distribution
measured around the flat transformer.

Because of just the same reason as described in section
3.2, number of data in z-axis and also employed Daubechies
second order base function, it is possible to obtain the three(c) Level p=3

levels multi-resolution magnetic field vector distributions.

Fig.10Fig. 10 shows the magnetic field vector distributions in

Wavelets multi-resolution analysis results of themagnetic field vector distribution measured around air-gap

each level.

of the flat transformer.

The results of the wavelets multi-resolution analysis to theflat transformer suggest that major magnetic fluxes linking
both of the primary and secondary cores are the levels 1 and2 magnetic field vectors. Even though the level 3 magnetic
field vectors starts from primary core and return to the same
primary core, it is possible to reveal that they are regularly
distributing along with the surface of primal core as well as

Thus, the flat transformer has far excellent magnetic field
vector distribution characteristic from the viewpoint of theelectromagnetic compatibility.
4

Fundamental Characteristics of the Flat
Transformer

coil.
This means that the flat transformer minimizes the leakage

4.1 Coupling factor

magnetic fields from the air gap space between the primary

A coupling factor ț is one of the most importantand secondary core surfaces.

transformer characteristics , which indicates smallness of
the leakage magnetic field vectors between the primary andThe 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

secondary coils. Namely, as possible as large coupling
factor ț means as possible as small magnetic field vector
distribution around the transformer.
Let us consider a simplified circuit model of thewhich are respectively given by the following equations

La  Ls
,
4
M
.
L1 L2

M
k

transformer shown in Fig. 11 to evaluate the coupling factor
ț. The dots 'Â' shown over the primary and secondary coils in
Fig. 11 show the positive induced voltages at each of thecoil terminals.
aTable 3 shows the measured inductances La, Ls, L1, L2 andcoupling factor ț changing the air-gap length between the
primary and secondary core surfaces.

c
䖃

(8)

䖃

Table 3 Coupling factor of the transformer employing flat shapecores measured at 30kHz.
Gap[mm]

0

1

3

5

7

10

L1>ȝ+@

578.6

348.2

231.1

181.6

169.9

133.9

L2>ȝ+@

572.7

348.1

229.4

181.0

168.3

133.3

Ls>ȝ+@

2297.41358.2

881.8

669.4

617.6

450.8

When we connect each of the terminals in Fig. 11 to

Lo>ȝ+@

16.9

26.1

41.4

56.0

61.1

84.3

additive polarity as shown in Fig. 12(a), it is possible to

ț

0.99

0.96

0.91

0.84

0.82

0.69

b

d

Fig.11 Simplified circuit model of transformer to evaluate thecoupling factor ț.

obtain the following relationship:La

L1  L2  2M ,(6)

where La, L1, L2 and M are the additive-, primary self-,
secondary self- and mutual inductance, respectively.

The results listed in Table 3 suggests that the flattransformer is capable of keeping the good coupling factors
ț § 0.7 although the primary and secondary coils are
separated by air-gap of 1cm.
4.2

Power transmission rate

Powertransmission

rate

is

the

other

importantcharacteristic, which indicates the efficiency of thetransformer.
To improve the transformer efficiency, a secondary
resonance between the capacitor and secondary leakage
inductance is widely used and well known technique [4].
Fig.12 Series connection of the primary and secondary coils
shown in Fig. 11.

Fig. 13 shows a simplified circuit model attaching aresonant capacitor C.
L1

Also, when we connects each of the terminals in Fig. 11 to

䖃

L2
䖃

subtractive polarity as shown in Fig. 12(b), we haveLs

L1  L2  2M ,

(7)

C

R

where Ls is a subtractive-inductance.
Further, the primary and secondary self inductances can be

Fig. 13 Circuit diagram of a secondary resonant type transformer.

measured independently. Thereby, combination of (6) and(7) leads to the mutual inductance M and coupling factor,

Attaching 40ȝF resonant capacitor in parallel to theThe 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

secondary coil terminal of the flat transformer leads to a

p=2 as well as level p=3 demonstrate the dramatic reducing

nearly İ § 80% input power transmission rate defined byof the magnetic field vectors spreading to the outside

H

Secondary output power
u100 >%@ .
Pr imary input power

direction from the center of both primary and secondary(9)

coils.

4.3 Multi-resolution analysis of the flat transformer
under load condition
As described in Section 3.2, we have described about themagnetic field vector distribution and its wavelets
multi-resolution analysis results. To demonstrate theusefulness of the flat transformer, it must be demonstrated
that the transformer under loaded condition never stimulate(a) Level p=1

the magnetic field vectors around the transformer centeredat air gap.
Fig. 14 shows a measured magnetic field vector
distribution at some instance of the flat transformer underthe 1ȍ pure resistive load and secondary resonantconditions. Measurement conditions and method of themagnetic field vectors is just the same as that of Section 2.2.
Observe the magnetic field vector distribution in Fig. 14
reveals that the flat transformer under the loaded condition(b) Level p=2

reduces the entire magnetic field vectors due to thesecondary load current.

(c) Level p=3

Fig.14 Magnetic field vector distribution of the flat transformer
under the 1ȍ pure resistive load and secondary resonantconditions.

Fig.15Results of the wavelets multi-resolution analysis to theflat transformer under the 1ȍ pure resistive load andsecondary resonant conditions.

Further, a discrete wavelets multi-resolution analysis tothis magnetic field vector distribution shown in Fig. 15

To check the secondary resonance circuit effect, we havereveals that the magnetic field vectors at level p=3 focus on

carried out the discrete wavelets multi-resolution analysis tothe center of spirally wound primary coil. This means thatthe magnetic field vector distribution of flat transformer

the leakage magnetic flux is dramatically reduced compared

under the 1ȍ pure resistive load and secondarywith those of under no load condition shown in Fig. 10(c).

non-resonant conditions.

Also, comparison the wavelets multi-resolution results

Fig.16 show a level p=3 magnetic field vector distribution

shown in Fig. 11 with that of Fig. 15 suggests that the levelof the wavelets multi-resolution analysis results.

The 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

Second, by means of the multi-resolution analysis of thediscrete wavelets, the primary and secondary coils woundspirally focus on the magnetic field vectors to the center ofboth primary and secondary coils. Finally, even though the
air gap is relatively large and small coupling factor, it ispossible to transmit the electrical power from the primary to
the secondary circuits with relatively high efficiency.
Fig.16

Level p=3 magnetic field vector distribution of the flattransformer under the 1ȍ pure resistive load and secondary

One of the drawbacks of the exploited transformer is aweight compared with those of core type transformer.

non resonant conditions.

References
One of the big differences between the level p=3 field[1] S.Takada, Y.Saito and K.HoriiࠊVisualization of the magnetic

vector distributions shown in the Figs. 15(c) and 16 is thatfield vectors around the contact-less power suppliers, Japanthe most dominant vectors located at the center take theSociety of Visualization, Proceedings of the Visualization

opposite directions. Namely, the dominant vectors in Fig.

Symposium in 2000, Paper No. P01-001.

15(c) direct toward the center but that of Fig. 16 direct[2[

S.Matsuyama,

S.Matsuyama,

Y.Saito,Data

Handling

toward the outward from the center. Thus, it is clarified that

Methodology for Discrete Wavelets and Its Application to The

the resonance of secondary circuit increases the linkage flux

Dynamic Vector Fields, International Journal of Wavelets,

to the secondary coils. This leads to a highly efficient power

Multiresolution and Information Processing, Vol.4, No.2, Junetransmission rate.

(2006) pp.263-271. World Scientific Publishing Company.

5 Conclusion[3] S.Matsuyama, Y.Oguchi, Y.Saito, T.L.Kunii, HandlingTo develop the contactless power suppliers, this paper has

Technique of the Dynamic Color Computer Graphics by theworked out one of the reasonable transformers having open

Wavelets

magnetic flux path.

Proceedings of the Visualization Symposium in 1999, Paper

The reasons why the flat transformer is one of the mostNo. 206.

reasonable transformers are as follows.

transform,

Japan

Societyof

Visualization,[4] Harrison, J.L., A new resonance transformer, Electron Devices,

At first, our proposed transformer suppresses the leakage

IEEE Transactions on Issue Date: Oct 1979 Vol.26 Issue: 10,

magnetic fields around the core, because it is a natural

pp. 1545 - 1

extension of the shell type core structure.

The 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

Enhance the Sensibility of the Eddy Current Testing
Hiroki KIKUCHIHARA1), Iliana MARINOVA2), Yoshifuru SAITO1),
Manabu OHUCH3), Hideo MOGI3) and Yoshiro OIKAWA3)
1)
Graduate School of Hosei University, Tokyo 184-8584, Japan
2)
Technical University of Sofia, Sofia 1756, Bulgaria
3)
Denshijiki Industry Co., Ltd, Tokyo 115-0051, Japan
Eddy current testing (ECT) is one of the most representative nondestructive testing methods for metallic
materials, parts, structures and so on. Operating principle of ECT is based on the two major properties of magnetic
field. One is that alternating magnetic field induces eddy current in all of the conducting materials. Thereby, an
input impedance of the magnetic field source, i.e., electric source, depends on the eddy current path. Second is thatthe magnetic field distribution depends only on the exciting but also the reactive magnetic fields caused by theeddy currents in targets. Former and latter are the impedance sensing and magnetic flux sensing types,
respectively.
This paper concerns with an improvement of sensibility of the impedance sensing method. Sensibility of the
ECT is improved by means of two steps. One is an optimum exciting frequency selection. We employ the naturalparallel resonant frequency of ECT coil. The other is to increase the sharpness of the resonance curve on
impedance versus frequency characteristic by changing the coil connection. Thus, we have succeeded indeveloping the ECT sensor having up to 4 times higher sensibility compared with those of conventional one.
Key words: Eddy current, Nondestructive testing, Resonant frequency

1

magnetic fields induces eddy current in all of the conducting

Introduction

materials. Thereby, the input impedance of the magnetic
Modernengineering

productssuchasair-plane,

automobile, smart building, high speed train and so on are
essentially composed of metallic materials for forming theshape of product, suspending the mechanical stress andconstructing the structural frames. In particular, the masstransportation vehicles, e.g. large air plane, hi-speed train,
express highway bus and so on, carrying a large number ofpeople are required ultimately high safety as well as
reliability.
To keep the safety of such vehicles, nondestructive testing
to the metallic materials is one of the most important
technologies because most of the structure materials arecomposed of the metallic materials.
Various nondestructive testing methods, such as eddy
current testing (ECT), electric potential method, ultrasonicimaging and x-ray tomography, are currently used. Amongthese methods, ECT does not require complex electronic
circuits and direct contact to target. Furthermore, target
whose major frame parts are composed of conductive
metallic materials can be selectively inspected by ECT[1,3].
Operating principle of ECT is very simple. The ECT isbased on the two major properties of magnetic field. One isthat exposing the conductive materials to the alternating

field source, i.e., electric source, can detect the change ofthe target impedance caused by defects blocking eddy
current flowing. The ECT based on this principle is called
impedance sensing type. The other type utilizes a separately
installed sensor coil to detect the leakage magnetic fluxchange. The magnetic field of ECT is composed of two
components: one is the exciting and the other is the reactive
magnetic fields. The reactive magnetic field is caused by theeddy currents in the target so that change of eddy current
paths changes the reactive magnetic fields. Thus, theindependently installed sensor detects this magnetic fieldchange. This type is called a separately sensing coil type.
This paper concerns with an improvement of sensibility of
the impedance sensing method. Improvement of thesensibility is carried out in the two major steps.
The first step is to select the optimum exciting frequency.
We select the natural parallel resonant frequency of the ECT
sensor coil when facing with a wholesome part of target. A
system comprising the ECT facing with the wholesome partof target takes the maximum pure resistive impedance.
When the ECT sensor coil meets with a defect of target, thisresonance condition is essentially not satisfied. This makes
it possible to maximize the deviation between the resonanceand not resonance impedances.

The 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

The second step is to increase the resonant impedance aswell as to sharpen the peaky impedance versus frequency
characteristic by changing the coil connection [4]. Since thenatural parallel resonance impedance become larger, thenthe deviation between the resonance and not resonance
impedances is essentially larger. This essentially enhances
the sensibility of ECT sensor.
2

Enhancement of ECT Sensibility

2.1 Operating principle of ECT
Let an arbitrary finite length solenoid coil shown in Fig.
1(a) be an eddy current sensor coil. When we put on this(a) Impedance |Z| vs. Frequency f.

sensor coil on a copper plate as shown in Fig. 1(b) andapply an alternating current to the sensor coil, because of the
Faraday¶s law, eddy current is induced as a reaction of thealternating magnetic fields. Measure the input impedance ofthe sensor coil is able to diagnose a difference of the target
copper plate condition between no defects (Fig. 1(b)) and
2mm crack defect(Fig. 1(c)). This is similar to thesecondary impedance change detection from primary input
terminal in a conventional single phase transformer.

E 3KDVHĳYV)UHTXHQF\I.

Thus, it is obvious that a simple finite length solenoid coilcan detect the defects of the target conducting materials.
This is the operating principle of ECT.

Fig.2 Frequency characteristics of the impedance and phase.

2.3 Optimum operation frequency
Decision of ECT operation frequency is of paramount
1 mm(a)Coil(a)Coil(b)Copper plate with 1mm
thickness

importance, because sensibility and searching depth of ECT
are greatly depending on the operation frequency.
Theoretically, the operation frequency of ECT can bedecided by taking the target conductivity and its skin-depth
into account. However, final selection of operation

1 mm
2mm

(c)1mm(c)2mm Air-gap
AirgapFig.1 Tested coil and the measurement conditions.

frequency is determined by the past experiences and thepractical tests.
In the present paper, we select the natural parallel resonant
frequency of the ECT sensor coil when facing with a

2.2 Natural resonant phenomena of ECT coilwholesome part of target. The ECT facing with the

Any of the coils always exhibit an inductive property

wholesome part of target takes the maximum pure resistive

because of the magnetic fields around them by applying a

impedance. When the ECT sensor coil meets with a defectcurrent into the coil. However, any of the coils have theof target, the resonance condition is essentially not

capacitances among the coils. Even though a simple finite

established. Therefore, the input impedance from sensor coillength solenoid coil shown in Fig. 1(a), it is possible toinput terminals is also reduced to small in value compared

observe its natural resonance phenomena as shown in Fig. 2.

with those of the resonant one. Namely, a deviation between

Figs 2(a) and 2(b) are the frequency f versus impedance |Z|

the resonance and not resonance impedances becomes

and the frequency f versus phase ȯ characteristics,

maximum value.

respectively.

A sensibility İ of ECT is defined by

The 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

parallelH

reference  measured
u100 > %@ ,reference(1)

conductors

and

their

resonant

connection,

respectively. Denoting R, L, M as the resistance,
self-inductance and, mutual inductance, it is possible todraw an equivalent circuit of the resonant connected two

where the reference and measured in (1) refer to the input

conductors as shown in Figs. 3(c), 3(d). Fig.4 shows a

impedances from the ECT coil terminals when facing thedifference between the normal and resonant coil connection

ECT coil with the wholesome and defect parts of target,[4]. Practically, the resonant connection is carried out by

respectively.

twisting the two coils to uniform the facing side of both

2.4 Enhancement of quality factor Q

conductors as shown in Fig. 5 [5].

The sensibility of (1) is greatly depended on the quality
factor Q of the parallel resonance defined by

Q

where

f0 ,
'f

(2)

f 0 and 'f are the resonant frequency and the(a) Normal(b) Resonance typeFig.4 Comparison of the normal with resonant coil connections.

bandwidth, respectively.
The quality factor Q represents a sharpness of the resonant
curve on the impedance versus frequency coordinate. So

Fig. 5 Example of a pair of twisted coils

that high Q in (2) means high sensibility in (1).
To increase the quality factor Q, we employ the resonant

3 Experimentconnection shown in Fig. 3. Figs. 3(a) and 3(b) are the two

3.1 Tested target peace and trial ECT coils
Fig. 6 shows a target peace which is composed of the twodifferent types ofmaterials (SUS304 and SUS316). A

vertical line shape artificial crack having 10mm length,
0.2mm width and 0.5mm depth had been made to thesandwiched SUS by the electrical discharge machining. Fig.
(a) Two conductors.

(b) Connection of the two
conductors.

6 shows a 20mm by 20mm target area. The ECT sensors
measured at the 9 by 9 sampling points with 2.5mm regularspacing on this 20mm by 20mm square area.

(c) Equivalent electric circuit of the connected conductors.

(d) Modified equivalent electric circuit of the connected
conductors.
Fig.3 Principle of a resonance coil connection.

Fig. 6 Target test piece and measured points.
The test peace is composed of the two different types of SUS
materials. A line shape artificial crack having 10mm length,
0.2mm width and 0.5mm depth had been made to the sandwiched
SUS by the electrical discharge machining. A 20mm by 20mm
square area is measured at the 9 by 9 points with 2.5mm regularspacing sampling

The 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

We have worked out a lots of ECT coils for comparison.

3.2 Conventional ECT operating at 256kHz

Table 1 lists the representative 6 tested ECT coils. Everytested coil is wound around the Manganese-Zinc type ferrite
bar used as an axial core material. No.1 is a normal ECT,
No. 2 is a resonance type not employing twisting of coil,No.3 is a resonance type employing 100/m twisting, No.4 isa resonance type employing 150/m twisting, No.5 is aresonance type employing 200/m twisting, and No.6 is aresonance type employing 400/m twisting.

No.1

No.2

No.3

Table 1. Specification of the trial ECT coils.
NormalConductor length
50cm
Diameter of conductor
0.1mm
Axis core
Ferrite bar (MnZn)
Coil outer diameter
2.4mm
Coil inner diameter
2mm
Coil length
6mm
Number of twisted turns
0
Number of coil layers
2Resonant
Conductor length
50cm
Diameter of conductor
0.1mm
Axis
Ferrite bar (MnZn)
Coil outer diameter
2.4mm
Coil inner diameter
2mm
Coil length
6mm
Number of twisted turns
0
Number of coil layers
2
Twisting

No.4

Twisting

No.5

Twisting

No.6

Twisting

Conductor length
50cm
Diameter of conductor
0.1mm
Axis
Ferrite bar (MnZn)
Coil outer diameter
3mm
Coil inner diameter
2mm
Coil length
5mm
Number of twisted turns
100/m
Number of coil layers
3
Conductor length
50cm
Diameter of conductor
0.1mm
Axis
Ferrite bar (MnZn)
Coil outer diameter
3mm
Coil inner diameter
2mm
Coil length
5mm
Number of twisted turns
150/m
Number of coil layers
3
Conductor length
50cm
Diameter of conductor
0.1mm
Axis
Ferrite bar (MnZn)
Coil outer diameter
3mm
Coil inner diameter
2mm
Coil length
5mm
Number of twisted turns
200/m
Number of coil layers
3
Conductor length
50cm
Diameter of conductor
0.1mm
Axis
Ferrite bar (MnZn)
Coil outer diameter
3mm
Coil inner diameter
2mm
Coil length
5mm
Number of twisted turns
400/m
Number of coil layers
3(a) No.1 Normal(b) No.2 Resonant(c) No.3 Twisting(d) No.4 Twisting(e) No.5 Twisting(f) No.6 TwistingFig. 7 Defect searching results. Any sensor coils can detect
the two different kinds of base metallic materials.

The 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

At first, we evaluated the line shape crack in Fig. 6 byconventional ECT employing 256kHz operating frequency.
Fig.7 shows the results of defect searching. Observe theresults in Fig. 7 suggests that any of the sensor coils arecapable of detecting the two different kinds of base metallic
materials. Further, it is difficult to decide which sensor is thehighest sensibility. In the other words, normal ECT defect(a) No.1 Normal

searching using a particular operating frequency neverreflects on the difference of the conductor connection andcoil twisting.
3.3 ECT operating at resonant frequency
Any types of ECT coils have their own natural resonant
frequency even if they are facing with the target without any
defect. No.1,2,3,4,5 and 6 ECT coils in Table 1 have the(b) No.2 Resonant

natural resonant frequencies, 4650, 4950, 3650, 3300, 3425
and 3475 kHz, respectively. Fig. 8 shows the typicalfrequency characteristics of the trial ECT coils.

(c) No.3 Twisting(a) No.1(d) No.4 Twisting(e) No.5 Twisting(b) No.2(f) No.6 Twisting(c) No.4
Fig. 8 Frequency f vs. impedance |Z| characteristics of the ECTFig. 9 The results of defect searching. Any sensor coils can detectcoils (a) No.1, (b) No.2 and (c) No.4, respectively.

two different kinds of base metallic materials.

The 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

Fig. 9 shows the defect searching result using each of the distinct

target, the resonance condition has not been established.

natural resonant frequencies. Comparison of the results in Fig. 7This has led that the impedance has reduced to small value

with that of Fig. 9 reveals that the resonant frequency operation iscompared with those at resonant condition. As a result, a

far superior sensibility in any ECT coils. In particular, No. 4 in Fig.

deviation between the resonant and9(d) exhibits nearly 10% deviation. This fact is verified that the

impedances has become the maximum. Thus, the sensibility

quality factor of No.4 in Fig. 9(b) is far excellent compared withof ECT sensor has been enhanced.

those of No.1 and of No.2.

Further, connection of the conductors to be applied a half

not resonantof the source voltage to adjacent conductors has made it
possible to enhance the capacitive effect among the
conductors. Practically, this connection has been carriedout by twisting the two coils to uniform the facing side ofboth conductors. Due to this enhancement of the capacitiveeffects, the resonant frequency has been reduced andsucceeded in increasing the sensibility.
(a) No. 1
References[1] I.Marinova, S.Hayano and Y.Saito, Ployphase eddy current
testing, Journal of Applied Physics, Vol. 75, No.10, pp.
5904-5906, 1994.
[2] N.Burais and A.Nicolas, Electromagnetic field analysis inremote field eddy current testing systems, IEEE Transactions on
Magnetics, Vol.25, No.4, pp.3010-3012, 1989.
(b) No.2[3] S.McFee and J.P.Webb, Automatic mesh generation for h-p
adaption, IEEE Transactions on Magnetics, Vol.29, No.2,
pp.1894-1897, 1993.
[4] Y.Midorikawa, S.Hayano and Y.Saito, A resonant phenomenon
between adjacent series connected coils and its application to aals, Advanced Computational and Design Techniques inApplied Electromagnetic Systems, Vol.6, pp. 633-639, 1995.
[5] S.Hayano, Y.Nakajima, H.Saotome and Y.Saito, A new typehigh frequency transformer, IEEE Transactions on Magnetics,(c) No.4
Fig. 10 Comparisons among the Quality Factor Q of the No.1,
No.2 and No,4 ECT coils.

4 Conclusion
New innovative idea to enhance the sensibility of ECT
sensor has been proposed in this work. Our idea needs not
any special tools but requires a consideration of natural
resonance phenomena-, i.e., utilization of the resonant
impedance, frequency and capacitive effect among the coils.
We have selected the natural parallel resonant frequency of
the ECT sensor coil when facing with a wholesome part oftarget. When the ECT sensor coil has met with a defect ofVol. 27, No.6, pp.5205-5207, 1991.

The 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

Fluctuation Frequency Analysis of the Barkhausen Signals
Jun KAWAZOE*1, Iliana Marinova*2 and Yoshifuru SAITO*1
Graduate School of Hosei University, Tokyo 184-8584, Japan*2
Technical University of Sofia, Sofia 1756, Bulgaria*1

Ferromagnetic materials are widely used for various artificial products such as cars, trains, ships and so on.
Because of its mechanical property, iron steel is most popular in use for the frame materials. Nondestructive
testing of iron steel is an extremely important way to maintain their mechanical reliability. As is well known factthat the Barkhausen signals are emitted from only the ferromagnetic materials having magnetic domain structures.
Also this signal varies depending upon their past mechanical as well as radioactive stress histories.
In the present paper, we have applied a generalized frequency fluctuation analysis to the Barkhausen signals
to detect the various mechanical stresses. Surprisingly, it has been succeeded in clarifying that application of ourfrequency fluctuation analysis to the Barkhausen signals makes it possible to detect the several kinds ofmechanical stress.
Key words: Barkhausen signal, Frequency fluctuation, Signal processing, Least squares

1. Introduction
Barkhausen signal is popularly observed in the
ferromagnetic materials composed of the magnetic domain
structures, e.g. iron, nickel, cobalt and garnet, when they aremagnetizing. Also, it is well known that the Barkhausen
signals are very sensitive to the physical external input, suchas mechanical stress and radioactive damage, to theferromagnetic materials.
The iron and its composite ferromagnetic materials arewidely used for main frame materials to support themechanical structures in many artificial products andconstructions. Because of their essential role, they arealways got mechanical stress and they keep their pastmechanical stress histories. Nondestructive detection of
their mechanical stress as well as residual stress is ofparamount importance for keeping the safety of themechanical structures, since it is possible to see ahead oftime what extent the mechanical structure will maintaintheir strength for further use.
According to the past researches concerning to a
relationship between the Barkhausen signal and appliedmechanical stress, it has been revealed that Barkhausen
signals are very sensitive to the mechanical stress andradioactive damage but any deterministic regularity has notbeen found [1,2].
Recently, only a macroscopic regularity has beenreported by means of a frequency fluctuation analysis
approach [3]. Principal purpose of this paper is thatconventional frequency fluctuation analysis employing only
1st order fluctuation is generalized to the frequency
fluctuation analysis employing the nth order fluctuations.
As a result, we succeed in extracting the distinct
difference between the stressed and not stressed Barkhausen
signals. Also, we succeed in visualizing in a most clear
manner on the four dimensional space, whose coordinates
are composed of the terms representing the higher orderfrequency fluctuation terms of Barkhausen signals.

One of the most famous frequency fluctuations is the 1/f
frequency fluctuation, which can be observed in most of thenatural phenomena such as natural wind, sea water waves,river flow sound and so on gives a healing effect to thementalities via human sensibilities[4].
Conventional 1/f frequency analysis is that applicationof the 1st order least squares to the both Fourier power
spectrum and frequency extracts the 1st order frequency
fluctuation, i.e., Log of Fourier power spectrum isapproximated by Log of a0 + a1f, yields a 1st orderfrequency fluctuation characteristic, where a0 and a1 are the0th and a 1st order frequency fluctuation terms, respectively.
If the frequency fluctuation term a1 takes a1=1, then we
have the 1/f frequency fluctuation.
On the other side, we generalize this conventional 1storder frequency fluctuation to the nth order frequency
fluctuation characteristics, i.e., Log of Fourier power
spectrum is approximated by a Log of a0 + a1f+a2f2+ ...+
anfn, where a0, a1, a2, ,..., an are the 0th, 1st 2nd, ... ,nth orderfrequency fluctuation terms, respectively. Careful
examination of the coefficients a0, a1, a2, ,..., an leads to theprecise frequency fluctuation characteristic of the
Barkhausen signal.
Second important key point of our approach is how tovisualize the dependency of the 0th, 1st, 2nd, ... ,nth orderfrequency fluctuation terms to the externally applied forces.
According to our experimental results on this research,most of the frequency fluctuation characteristics are
sufficiently represented up to the 4th order terms. So that let
the normalized 1st, 2nd, 3rd, 4th order frequency fluctuation
coefficients be respectively the coordinate values on the x-,y-, z-axes, and point color, then up to the 4th order frequency
fluctuation characteristics locate the three dimensional spacecoordinate position and point color. Thus, comparison
among the different specimens of this diagram visualizes aneach of the distinct characteristics depending on theirmechanical stress conditions.

The 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

2. Frequency Fluctuation Analysis
2.1 Basic equations
Let us consider an arbitrary signal g(t) and its Fourier
power spectrum G(f), and take the logarithm of both Fourier
Spectrum G(f) and frequency f. Plot the log G(t) on the log fcoordinate represents a frequency characteristic of the signal
g(t) on the frequency domain, i.e., the frequency
characteristic of the original signal is represented on a x-y
plane coordinate system whose horizontal x- and verticaly-axes are corresponding to the logarithms of Fourier power
spectrum G(f) and of frequency f, respectively.
In order to represent a global frequency characteristic of
the original signal g(t) in frequency domain, apply afollowing power series function:a0  a1 f  a2 f  ...  an f ,
n

2

h f

(1)

in this x-y plane makes it possible to evaluate the higher
order frequency fluctuation analysis.
The coefficients a0, a1 a2, ,..., an in (1) are determinedby least squares asA1ª¬C T C º¼ CT Y ,(2)

Fig.1. Barkhausen signal measurement devices.
The tested specimens are the silicon steels with the
0.35mm thickness, 30mm width and 100mm length. The
tested specimen is put on the upper two head surfaces of U
shape ferrite core wound the 300 turns exciting coil. The
specimen in Fig.1 is excited by flowing a 1A sinusoidal
alternating current through this exciting coil.
Fig. 2 shows a typical frequency characteristic of a
Barkhausen signal under no stress.

where a superscript T denotes a matrix transpose; thevectors A, Y and matrix C are respectively given by

A

Y

> a0

a1 . an @ ,ª¬h f0 h f1
ª1 f 0 f 02«
2
«1 f1 f1
C «1 f 2 f 22
«
.
«. .
«1 f
f m2
m
¬
m ! n.

T(3)
T. h f m º¼ ,
.
.
.
.
.

f 0n º»f1n »f 2n » ,». »f mn »¼(4)(5)

In (3)-(5), a number of equations m, i.e. number of thesampled frequencies f0, f1 f2, ,..., fn, always greater than thoseof unknowns n, i.e., number of the coefficients a0, a1 a2, ,...,
an. In most case, this condition is satisfied because of thenumber of sampled frequency m is much greater than thoseof the order n of the function h(f) in (1).
2.2 Classical 1st order frequency fluctuation
Fig. 1 shows a Barkhausen signal measurement devices.

Fig. 2. An example of typical frequency characteristicof a Barkhausen signal under no stress.
The frequency characteristic in Fig. 2 is obviously
divided into two frequency regions. One is lower frequency
region whose frequency fluctuation can be approximated by
f-2.26 derived from 1st order approximation in (1), and theother higher one is a dispersing signal whose frequency
fluctuation can be approximated by f 0, i.e. white noise.
On the other side, Fig. 3 show a typical frequency
characteristic of Barkhausen signal under 3kg stressed.

The 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

Log Power
1
1.0

1.5

2.0

2.5

3.0

Log f

3.5

1
2
3
4
5
6

Fig. 3. An example of typical frequency characteristicof a Barkhausen signal under 3kg stressed.
The frequency characteristic in Fig. 3 is also divided
into the two frequency regions. One is lower frequency
region whose 1st order frequency fluctuation can beapproximated by f-1.69, and the other higher one is adispersing signal whose frequency fluctuation can beapproximated by f 0.
Consideration to the difference between the first orderfrequency fluctuations f-2.26 and f-1.69 suggests that an
application of the 3kg stress to the tested silicon steel
changes the steep 1st order gradient -2.26 to the smoothly
gradient -1.68. This result had been verified by the 1st orderfrequency fluctuation analysis to the 30 distinct sample
specimens [3].
Thus, it is possible to detect the stress on the
ferromagnetic materials by the classical 1st order frequency
fluctuation analysis [3].
However, several difficulties are still remaining: One is
how to decide the frequency range to be computed thefrequency fluctuation characteristic. Second is that the 1storder frequency fluctuation analysis is only effective to a
relatively large stress, even though it is required to detect themuch more smaller stresses.
2.3 Generalized frequency fluctuation
Fig. 4 shows a frequency fluctuation characteristic
under no stress along with a curve obtained by up to the 4thorder power series function in (1), where the frequency
sampling points have been taken in a logarithmic order.
To check the reproducibility of the coefficients
a1 , a2 , a3 , a4 , we have 10~12 times independently
measured and computed these coefficients a1 , a2 , a3 , a4in (1) to the same specimen.

Fig. 4. Example of typical frequency characteristic ofa Barkhausen signal under no stress along withan up to 4th order power series curve in (1).
After normalizing all of the coefficients a1 , a2 , a3 , a4
to be the values between 1 and 0, let the normalized
coefficients a1 ' , a2 ' , a3 ' , a4 ' be respectively corresponded
to the x-, y-, z-axes values and point color, then this makes it
possible to visualize a dispersion characteristic of thecoefficients a1 ' , a2 ' , a3 ' , a4 ' . Fig. 5 shows a dispersion
characteristic of these coefficients a1 ' , a2 ' , a3 ' , a4 ' .
Combination of Figs. 5(a) with 5(b) reveals that thedispersion is limited along the vicinity of a hatched surface
in Fig. 6.
1.0

z 3rd order 0.5
1

1.0
y 2nd order 0.5
0.0
0.0

0.5
x 1st order

1.00(a) x-y plane

1.0

y 2nd order 0.5
1

0.0 0.0
0.0
0.5
1.0
0.5
z 3rd order x 1st order
1.00(b) x-z plane
Fig.5. Dispersion of the frequency fluctuation coefficients.

The 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

Comparison of the dispersion characteristics in Fig. 5(a)with that of Fig. 9(a) demonstrates a distinct effect of theapplied stress. Also, comparison of the dispersion
characteristics a1 ' , a2 ' , a3 ' , a4 ' in Fig. 5(b) with that of Fig.
9(b) suggests the same as before.
Combination of Figs. 9(a) and 9(b) yields the results
shown in Figs. 10 and 11.
1.0

z 3rd order 0.5

Fig.6. The normalized frequency fluctuation coefficientsa1 ' , a2 ' , a3 ' , a4 ' dispersing area (hatched surface).
Consideration to the hatched region in Fig. 6 suggeststhat an individual difference among the sound silicon steel
without any stresses could be limited along the vicinity of
the hatched surface in Fig. 6.

1

1.0
y 2nd order 0.5
0.0
0.0

0.5
x 1st order

1.00(a) x-y plane

2.4 Stress visualization
We have carried out the random stresses visualization inmuch the same as described in Section 2.3. These stresses
were applied to the specimen by hanging the random
weights by a string as shown Fig. 7.

1.0

y 2nd order 0.5
1

0.0 0.0
0.0
0.5
1.0
0.5
z 3rd order x 1st order
1.0
0

Fig.7. The stresses are applied by hanging the weights.
Fig. 8 shows one of the frequency fluctuation
characteristics under stress along with a curve obtained by
the 4th order power series function in (1).

(b) x-z plane
Fig.9. Dispersion of the frequency fluctuation coefficients.

Log Power
1
1.0

1.5

2.0

2.5

3.0

3.5

Log f

1
2
3
4

1

5
6

Fig. 8. One of the frequency characteristic of the
Barkhausen signals under stress along withthe 4th order power series curve in (1).
Fig. 9 shows the dispersion characteristics ofcoefficients a1 ' , a2 ' , a3 ' , a4 ' .

0Fig. 10. The normalized frequency fluctuation coefficientsa1 ' , a2 ' , a3 ' , a4 ' difference between the stressed andno stressed groups on the x-y plane.

The 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

Log Power
1
1.0

1.5

2.0

2.5

3.0

3.5

Log f

1
2
3
4
1

5
6

0

Fig. 11. The normalized frequency fluctuation coefficientsa1 ' , a2 ' , a3 ' , a4 ' difference between the stressed andno stressed groups on the x-z plane.
Observation of the dispersion characteristics of thestressed specimens suggests that the normalized coefficientsa1 ' , a2 ' , a3 ' , a4 ' in (1) do not disperse but focus on arelatively small area. On the contrary, the normalized
coefficients a1 ' , a2 ' , a3 ' , a4 ' in (1) of the stress freespecimens disperse the vicinity of hatched area in Fig. 6.
This means that the externally applied stress suppresses thedispersion and confines them into the small space in Fig. 6.
2.5 Bending effect visualization

Fig. 13. One of the frequency characteristics of the
Barkhausen signal after bending a specimen along withthe 4th order power series curve in (1).
1.0

z 3rd order 0.5
1

1.0
y 2nd order 0.5
0.0
0.0

0.5
x 1st order

We have carried out the bending effect visualization inmuch the same as described in Section 2.4.
As shown the bended examples in Fig. 12, the 4
specimens were bended 0, 5, 15, and 45 degree. After thatthese 4 specimens were recovered to the original straight
form.

1.0

0

(a) x-y plane

1.0

y 2nd order 0.5
1

0.0 0.0
0.0
0.5
1.0
0.5
z 3rd order x 1st orderFig. 12. No bended and 5 degree bended.
Fig. 13 shows one of the frequency fluctuation
characteristics after bending along with a curve obtained by
the 4th order power series function in (1).

1.00(b) x-z plane
Fig.14. Dispersion of the frequency fluctuation
coefficients.
Fig. 14 shows the normalized dispersion characteristics
of coefficients a1 ' , a2 ' , a3 ' , a4 ' .
Comparison of the dispersion characteristics in Fig. 5(a)with that of Fig. 14(a) demonstrates a distinct effect of thebending. Also, comparison of the dispersion characteristics
in Fig. 5(b) with that of Fig. 14(b) suggests the same as
before.

The 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

1

frequency fluctuation characteristics could be visualized in athree dimensional space. This has clarified each of the
distinct differences among the specimen having the same
specifications, also clarified the measurement data
dispersions.
As the concrete examples, we have applied our method
to the stress visualization of the silicon steels, andsucceeded in extracting the characteristics of the stressed
specimens. Also, we have applied our method to the pastbended history detection. This has led to the similar results
obtained in the stress detection. Thereby, it has beenclarified that the distinct difference between the paststressed or bended histories is difficult.

0

Fig. 15. The normalized frequency fluctuation coefficientsa1 ' , a2 ' , a3 ' , a4 ' difference between the bending andnot bending groups on the x-y plane.

References
[1]
[2]

[3]

[4]
1

0

Fig. 16. The normalized frequency fluctuation coefficientsa1 ' , a2 ' , a3 ' , a4 ' difference between the bending andnot bending groups on the x-z plane.
Combination of Figs. 14(a) and 14(b) yields the results
shown in Figs. 15 and 16.
Observation of the dispersion characteristics of thebended specimens suggests that the normalized coefficientsa1 ' , a2 ' , a3 ' , a4 ' in (1) do not disperse but focus on arelatively small area. On the other side, the normalized
coefficients a1 ' , a2 ' , a3 ' , a4 ' in (1) of the bended freespecimens disperse the vicinity of the hatched surface in Fig.
6. Thereby, the externally applied bending stress suppresses
this dispersion and confines them into the small space in Fig.
6.
Thus, it is obvious that the distinction between the
stressed and bending effects is difficult from the Barkhausen
signal analysis.
3. conclusion
Previously, we have succeeded in detect the appliedstress on the silicon steel by means of the frequency
fluctuation method [3].
This paper has generalized this approach, i.e., 1st orderto the nth order frequency fluctuations. Further, the 4th order

R M. Bozorth: Ferromagnetism, p. 462 (IEEE PRESS)
M. Katsumata, S. Hayano and Y. Saito: A Study ofBarkhausen Phenomenon Visualization, The Visualization
Society of Japan, B203, July (2003).
S. Nojima and Y. Saito: Application of Frequency
Fluctuation to Barkhausen Signals and its Application, J.
Magn. Soc. Jpn., 35, 380-385 (2011).
M. Teranishi, K. Maruyama, S. Hayano, and Y. Saito:
Visualization of 1/f Frequency Component in Dynamic
Image of Natural Phenomena, The Visualization Society ofJapan, B108, July (2005).

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CEFC2012，Oita，Japan，Novemberll−14，2012

WP3−18

CoupledFieldModelingofFerrofluidHeatinginnImOrTissue

ValentinMateevl，IlianaMarinovalandYoshifuruSaito2
1TeclmicalUniversityofSo鮎，Sofia1756，Bulgaria
2GraduateSchoolofHoseiUniversity，Tokyo184−8584，Japan
VmateeV＠tu−SO負a．bg

thissamplebyprecisemeasurementsystem［3］・Accordingto
Ab如Taet −In 仙is work，metbod or magnetic 仙Iid
hyperthermiaisimpletnetLtedforbreastcancertherapy．Coupledfrequencydependentpropertiesofthedataset，ShowninFig・1，
fieldtnode］ingoffbrrofluidtraT）SpOrtandheatiJ）giJltumOrtissue
thermalconductivities，for alltisslleStypesincludedin theis preseTLted．A foT・Ward3D elcctromagnetic−thermal−ntlid modelarede負ned．
dynamics，伽iteelementmethodmodelisdeYeloped．TbemodeI
1∝脚t］SeSanatOmicalIyprecisemtlltilevelgeoTnetricalmodelofhumanbreastwithkJ）OWntissuese］ectricalproperties，bloodandliquor
100（伽fLowspeedsinit＄VeSSels．ThemodelpresetLtSthestruCtt］reOfreal
CanCer SatnPle acqllired by surgicalprocedure．CaTICer aTldl疇 Ul00∝I
norTnaltissueelectricalpropertiesaredirectlymeasuredfbrthisl∝氾
SamPle．TherTnalfield results are verified byiJ）h ared
仙ermograpllimagⅧg．
100
1000

1000001（l∝氾

Ⅰ．INTRODUCTION

1㈹000

10（泊∝I00†（H王I

Themethodofmagneticmlidhyperthermiaselectivelyheats
uptlSSueSbyinductedalternatingcurrenttotargetedmagnetic
飢Iid［1−2］．Magnetic8uid distribution determines thermal
丘eldinsidetissuesundertherapyprocess．Inverselymagnetic

nuid transportand distribution rearrangeS electromagnetic
負eld which candramatica11y change thermal負eldin that

SenSitivelivetissuedomain．OtherwiseanatOmyObjectsunderinvestlgation are particularly complex．structures，Which are
O董Iennonrigidandrandominshape，andexhibitconsiderable

Variabilityfrompersontoperson．Tissueselectromagneticand

Fig・1・Measuredrelativeelectricpemittivity−￡andelectric
COndtJCtivity，CrOfcan∝rtissuesamples．

I60

thermalpropertiesareanisotropic，丘equencyandtimevarylng

andingeneralarenotclear1ydeterminedforal1tissuesincase
underinvestlgation．Allofthisaswellasanabsenceofexplicit

ヰやShapemodelsthatcaptureanatomyspeci丘cs，makesmodelingtaskcha11englng．
Inthiswork，CO11Pled鎖eldmodelingofferronuidtranSpOrt

m M玉THOD

For determination of the thermal銭eld distributionin

】。。

（b）

and heatingintumOr tissueis presented．Aforward3D
electromagnetic−thermal−nuid dynamics丘nite element
method（FEM）modelisdeveloped．

T（Oc）

Fig．2．Sampleshape（a），laycrofcancermodel（b）andsurfhcethemalneld
distributioninbreastmodel（c）．

Fig．2showsthestruCtureOfrealcanCerSampleacquired
bysurgicalprocedure．The3DgeometrymodelofsameCanCer
StruCturereCOnStruCtedforthemodelisshowninFig．2（b）．

Calculated thermalfield distribution in the breastis
magnetichyperthermiatherapy，aCOupledelectromagnetic．
demonstratedinFig．2（C）．
thermaトfluid dynamics負eld modelis established．The
electromagnetic且elddistributioninsidetheconductivetissue
Ⅲ．REFERENCES

regiondependsonthetimevaryingmagneticfluxdensity．The
EDi侃ISionofmagneticnanoparticles
heat sourcesare detined by the electriclossesintissue， 【1］A．GolneshanaandM．Lahonian，
in a multi−SitelqeCtion processwithin a biologlCaltissl】e duringacquiredbythesollltionoftheelectromagnetic重eldproblem．

magnetic ＝餌Iid hyperthemia usinglattice Bolt2mann method ，肋亡んα扉e∫Re∫edrC力Co椚椚∽fcαJわ那，Vol．38，pp．425−430，2011．
TheanalysISWaSCarriedoutonathree−dimensionaltranSient［2］M．Liangruksa，R・Gangu】yandI．Puri， ？aJ7Lmetricinvestigation ofelectromagneticproblemaccordingFEMformulation．
heating due to magnetic fluid hyperthermia in a tumor with bloo
The FEM modelusesanatOmical1y precise multilevelper蝕5ion， ・ゐ〟用〃J〆A勾卯e舶用α〝d物e′fc肋′αfαれVol．323，
geometricalmodelof humanbreastwith known tissues
pp．708−716，2011・
electricalproperties，bloodandliquor now speedsinits［3］Ⅰ．Marinova and V．Mateev， Determination of Electromagnetic
vessels．Model contains information about real cancer

StruCtureSamPleacquiredbysurglCalprocedure．CanCerandnormaltissueelectricalproperties are directlymeasuredfor−409−

PropertiesofHumanTissues ，Proceedfngsqf．D7temationa］CoT殖T・e77Ce
O〝Co〝甲山α伽〃〃Jα〝d4pJfgdA血Jみg椚αJ如，2S−30June，Pads，Fr弧Cち2010，Vol．66，pp．1075−1079，2010．

白鼠Aれ眉○︵lU︶OHぉき○トS−SdO眉○︵NtON︵寸t・。

Inhren。eOnElectromagneticFieldComputation

http：／／www．cefヒ2012．org／．OITÅ＝品m UNIVERSITY

JU

㊥lEEE

︵︵NtONU﹄国U︶uOでd︸na∈OUP−U己じで告辞∈OJ︶U山一河口OUU□巴遭□OU山出出H罵睾2月芯二七め︻望七白FC要g］

CEFC2012，Oita，Japan，Novernl）er11−14，2012

TA3−2

FluctuationFrequencyAnalysisoftheBarkhausenSignals
underStaticandDynamicStresses
JunKAWAZOE＊，IlianaMARNOVA＊＊andYoshifuruSAITO＊＊GraduateSchoolofElectricalEngineering，HoseiUmiversity，3−7−2K毎inocho，Koganei，Tokyo184−8584，Japan＊＊TechnicalUniversityofSona，So丘a1756，Bulgaria
Jun．kawazoe．9s＠stu．hosei．ac．jp
Thus，itis revealed that our generalized 駐equency

Abstract− Most or tbe elec什omagnetic tompⅦta血ntechnologies fbr elcctricaltrLaChiJIeS design may be established

mlCtuationanalysismakesltpOSSibletovisualizethestaticas

ev℃n tIlOtlgh 仙e solid state physiealprope止ies or tbe

Wellasdymamicstressestothefb汀Omagneticmaterialsusedin

Ebrromagnetic materials used as main construC．ing materiaIs oftheelectricalmachines．
theelectrica）machiJleS血rCneVerfulIytakenintoaccotlnt．
This paper tries to compensate the current computational
II．VISUAuZATIONOFTHEBARKHAUSENSIGNALSe］ectricalmachines design probletn oTL theJbrromagnetic
Fig．1showsoneoftheexamplesof庁equencyfluctuationmateria］s．Namely，（hi＄paper tries toworkotJt the evalⅦating
methodology br which the e）ectric machines are optimally
CharacteristicundernostressalongwithacurveObtainedby
desigtled or not by meat）S Of the Barkhau＄en SlgtLalaTLalysi5．
up to the4th orderpower seriesfunction・Fig・2shows a
BarkI）auSen Slgnals．are intriJISica11y accompanylngwith the visualized result of the under no− and static−StreSSed
magnetizationproc￠5＄eSOr仙efbrromagneticmateria15．

Barkhausensignalcharacteristics．

Ⅰ．TIIEBARKHAUSENSIGNALANALYSIS

l．喝R闘r1,,

Barkhausen Slgnalis popularly observedin the
fbrromagnetic materials composed of the magnetic domain
StruCtureS，e．g．1rOn，nickel，CObaltandgarnet，Whentheyare
magnetizlng．AIso，itis wellkn0wnthat the Barkhausen

Slgnalsareverysensitivetothephysicalexternalinput，SuChas
mechanicalstressandradioactivedamagetOthefbrromagnetic
materials．

A11ofsuchferromagnetic materials construCt the m句Or
丘amepartsofelectricalmachines，eVenthoughthesolidstatemagnetizationpropertiesoffbrromagneticmaterialsareneverfu11y taken the computationaldesign oftheminto account．
Because oftheir essentialrole，fbrromagnetic materials arealways got mechanical stress and they keep their past

Fig．1．Exampleoftypical丘equencycharacteristicofaBarkhausenslgnalundernostressalongwith
ampto4thorderpowerseriescurve・

mechanicalstress histories．NondestruCtive detection oftheirmechanicalstress as wellasresidualstressisofparamountimportance for checking the properness of the mechanical
StruCtureS，Sinceitispossibletoseeal1eadoftimewhatextent
themechanicalstruCturewi11maintaintheirstrengthforfurther
uSe．

According to the past researches concermng tO a
relationship between the Barkhausen slgnaland appliedmechanicalstress，ithasbeenrevealedthatBarkhausenslgnals
are very sensitive to the mechanicalstressand radioactive
damage butany deterministic regularityhas notbeenfoundFig．2．nenormalized丘equency仙1Ctuationcoe餌cientsrl，2］．

Recently，0nlyamacroscopicregularityhasbeenreporteddi飴rencebetween仇es仕essedandnoshessd脚pS．

bymeanS Ofafreqt）enCy nuCtuationanalysis approach［3］．

PrincIPalpurposeofthispaperisthatconventionalfrequency
nuctuationanalysis employlng OnlylSt orderfluctuationis
generalized to the丘equency飢ICtuation analysIS employlng

thenthorderfluctuations．

Ⅲ．REFERENCES【l】RM・Bozo止h：Fe汀Oma卯etism，p．462（旺EEPRESS）【2］M・Katsumata，S，Hayanoand Y．Saito：A Study of B訂khausen
PhenomenonVisualization，TheVisuali2ntionSocietyofJapan，B203，

Asaresult，WeSuCCeedinextractingandvisuali2：ingtheJuly（2003）・
distinct di飴rence between the stressed and not stressed

Barkhausenslgnalsforthenrsttimeintheworld．

【3］S．Nqjima and Y．Saito：Application ofFreqt］enCy Fluctuation to
BarkhauscnSignalsanditsApplication，J．Magn．Soc．Jpn．，35，380−
3S5（2011）．

−304−

白鼠Aれ眉○︵lU︶OHぉき○トS−SdO眉○︵NtON︵寸t・。

Inhren。eOnElectromagneticFieldComputation

http：／／www．cefヒ2012．org／．OITÅ＝品m UNIVERSITY

JU

㊥lEEE

︵︵NtONU﹄国U︶uOでd︸na∈OUP−U己じで告辞∈OJ︶U山一河口OUU□巴遭□OU山出出H罵睾2月芯二七め︻望七白FC要g］

CEFC2012，Oita，Japan，Novemberll−14，2012

WC4−4

OptimizationoftheEddyCurrentTesting

HirokiKIKUCHmARAl，IlianaMANNOVA2，YoshifuruSAITOl，
ManabuOHUCH3，HideoMOGI3andYoshiroOⅨAWA3
1GraduateSchoolofHoseiUniversity．Tokyo184−8584，Japan
2TechnlcalUniversityofSona・So鮎1756，Bulgaria
3DenshiiikiIndustryCo．，Ltd．Tokyol15−0051，Japan
Abstmct−Eddy current testing（ECT）is one of the mo＄t
repre＄entative tLOndestruCtive testing methods fbr metallic
Ⅱ．DEVELOPMENTOFASEPÅRATELYSENSINGCOnTYPE
matedals，pa河5，StrⅦCtⅦreSandsoon．
Figure2showsourdevelopedseparatelysensingcoiltype
ThispapercoTLCemSwithanimprovementofsetlSibilityoftwo
SenSOrthatiscomposedofcoshapeexcltlngCOilsandsmall
typesofECT．OJ）eisconvetLtionalatLdtheotherisaseparately
SearChing coilwound around aferrite bar．We named thisSemSingeoilけpeECT．Enbancetbe5en5ibi出けOrtheconYendomal
SensOr aS‖∞COil一一．This∝・COilwasinnovated by afu11y
ECT are mainlycarried olltby acIassicalanalyticalapproach・Ontheotherside，theotherseparatelysetLSiJlgCOiltyT）eisfu11y COmPutationalapproachusingthefimiteelementsmethod．
exploitedbyacomputational且pPrOaCh．
Asaresult，SenSibilityofthecotLVentionalECTwasetIdlanted
to the4th times higherthatL thoseoforigiJlaloJle．AIso afulIy
COmp11terOrienteddesigtLedtype，i．e．，theseparatelysen血gcoil
type，displayed a remarkBLble sensibility with highliftofr岳
althotIghith＄directiotlality．
I．ENHANCEMENTOFTHECoNVmONALECTsENSIBmmY

The Grst step ofthe conventionalECTis to selectthe
OPtlmum eXCltlng frequency．Decision of ECT operation
frequencyisofparamountimportanCe，becausesensibilityand
SearChingdepthofECTaregreatlydependingontheoperation
frequency．Weselectedthenaturalparallelresonant危・equenCy

OftheECTsensorcoilwhenfhcingwithawholesomepartOf

Fig．3Magneticnuxdensityvectordistributionwhensensingaline
target・WhentheECTsensorcoilmeetswithadefectoftarget，
defbct．
thisresonanCeCOnditionisessentiallynotsatis負ed．Thismakes

itpossibletomaximizethedeviationbetweentheresonanCe
andnotresonanceimpedanCeS．
′「−−＼
＼＼、＿、

「￣、、−

Fig・4Measuredvoltageofthesensorcoil．

（a）256kHzoperating録equency（b）naturalresonant丘・equenCy
Fig．1nlereSultsofdeftctsearching

Figures3and4showthecomplltedmagnetic幻uxdensity

VeCtOrSdistributionandthemeasuredvoltagesofthesearch

ThesecondstepoftheconventionalECTistoincreasea
qualityfactorQbychangingthecoilconnection．Thequality COil，reSpeCtively．AbluelineinFig．4istheinducedvoltage
fhctorQrepresentsasharpnessoftheresonantCurVe．Thereby Whensenslngalinedefect．Theothercoloredlinesaretheno
defbctornotdirectedangles．Themostimportantkeyofthe∝〉thesensibilityoftheECTisgreatlydependedonthequality
coilisthatwesetthesensorcoilwoundaroundaftrritebarat
factorQ．ToincreasethisqualityfhctorQ，WeemPloyedthe
thenoorqultelowmagnetic fklds space causedbythe∝）resonantCOnneCtiontl］．Duetothesetwosteps，SenSibilityof

Shapecoilstodetectonlythemagneticfluxesduetothedefbct．
This keylocation has been determined by anintensive
SearChingresultsinFig．1（a）withthoseofFig．1（b）revealsthat computational approach using FEMTET by MURATA

theconventionalETCwasenchantedtothe4thtimeshigher
thanthose oforiginalone．Comparison oftheline deftct

So氏wareCO・LTD．Japan．

thesensibilityofresonantfreqenCyOPeration（Fig・1（b））isfhr

SuPeriorthanthoseofconvent10nalECToperatingat256KHz

Ⅲ．REFERENCES

丘equency（Fig．1（a））．

【l］Y．Midorikawa，S．HayanoandY．Saito，AresonantPhenomenonbetwecn
aqjacentseriesconnectedcoilsanditsapplicationtoanals，Advanced
Computationaland Design Teclmiquesin Applied Electromagnetic
Systems，Vol・6，Ppr633−639，1995．

−495−

第21回MAGDAコンファレンスin仙台
一電磁現象及び電磁力に関するコンファレンスー

講演論文集

会期：

2012年11月21日（水）−22日（木）会場：

仙台市戦災復興記念館

主催：

日本AEM学会

協賛：

日本機械学会，電気学会，日本磁気学会，日本シミュレーション学会，日本生体磁気学会，計測自動制御学会，システム制御情報学会，日本原子力学会，日本保全学会，日本
非破壊検査協会，IEEEMagnetic8Society（JapanChapted，プラズマ・核融合学会，
日本ばね学会，ライフサポート学会，財団法人青葉工学振興会

第21回MAGDA⊃ンファレンスin仙台

OS6−8

新∞型渦電流センサの開発
Developmentofanew∝）COiltypeeddycurrentsensor
菊地原弘基＊1、膏藤兆古＊1（正員）

大内学＊2、茂木秀夫＊2、及川芳朗＊2
HirokiKIKUCHIHARA（Stu．Mem．），YoshifuruSAITO（Mem．）
ManabuOUCHI（NoMem．），HideoMOGI（NoMem．），YoshiroOIKAWA（NoMem．）
Eddycurrenttesting（ECT）isoneofthenlOStrePreSentativenondestruCtivetestingmethodsformeta11ic

materials，PartS，StruCtureSandsoon．OperatingprlnCipleofECTisbasedonthetwom句OrPrOpertiesofmagnetic
貢eld．Oneisthatalternatingmagneticneldinduceseddycurrentinalloftheconductingmaterials．Thereby，an
1nputimpedanCeOfthemagneticfieldsourcedependsontheeddycurrentpath・Secondisthatthemagneticfield
distributiondependsnotonlyontheexcitingbutalsothereactivemagnetic坑eldscausedbytheeddycurrentsin
targets．Formerandlatteraretheimpedancesensingandmagneticfluxsensingtypes，reSpeCtively．

ThispaperconcernSwithadevelopmentofanewmagneticnuxsensingtypesensornamedl一00COil whose
excitingandsensingcoilsareCOmpOSedofthe（刀Shapeexcitingcoilandnnitelengthsolenoidcoilwoundaround
ftrritebar；reSpeCtively．Developmentofthis（カCOilhasbeencarriedoutbymeanSOffu11y2Dand3Dfinite
elementscomputationalscheme．Accordingtothesimulationresults，Wehaveworkedoutaprototypeof∝）COils．
Practicalexperimentsreflectonthevalidityofourkeyideaaswe11ascomputationalresultsquitewell．
Kbwords：Eddycurrenttesting，NondestruCtivetesting

ダクトではフレームの健全性に高度な信頼性、安全性

1緒言の確保が要求される。

現代の文明社会を支えるのは人類の叡智が創造し金属の健全性を確保する手段として最も基幹的で重た多くの文明の利器である。例えば、高速な移動手段

要な技術が、金属材料に対する非破壊検査技術である、を提供する高速鉄道、自動車、航空機、そして、電力

金属の非破壊検査法として、渦電流探査法￠ddy

生成・系統システム、照明システム、セキュリティシ

CurrentTbsting、以後ECTと略記）、電気ポテンシャル

ステムなど、いわゆる産業プロダクトから鉄橋、大型法、超音波影像法およびⅩ線断層撮影法のような様々ビルや高速道路などの社会的インフラストラクチャまな方法がある。この中で、ECTによる方法は、検査で広汎で多岐に渡る文明の利器が存在する。

対象と直接接触の必要がなく、比較的簡単な装置で高これら文明の利器の多くは何らかの形で機械的構造

速な検査が可能である。このため、ECTは自動車の部を持ち、強度や形状維持のフレームが存在する。これ品検査から橋梁の劣化検査など極めて多くの分野で広らの多くは金属材料からなり、それぞれの産業プロダ

汎に使われている。これは、人類の創造する文明の利クトの機能を維持するため、機械的ストレスを受け続器の力学的強度維持は、大部分が導電性を有する金属けている。産業プロダクトの中で、大量輸送に関わる材料からなるためであり、特にECTは選択的に非接触

大型バス、高速列車、大型旅客機のみならず、原子力

で金属部分のみ検査可能である1，2）。

発電所で代表される大規模エネルギー変換システムな

本稿は∞文字形状の励磁コイルと有限長ソレノイド

どのプラントや社会的インフラストラクチャ設備では、型の検出コイルからなる渦電流センサ（以後∞コイル）

機械的ストレスだけでなく熱応力、中性子による劣化を提案する。
この∞コイルの動作は、励磁コイルの生成する磁束などが発生する。当然ではあるが、これらの産業プロがゼロとなる領域へ検出コイルを配置し、被検査対象

連絡先：菊地原弘基、〒184−85S4小金井市梶野町3−7−2，
法政大学大学院工学研究科電気工学専攻脅膝兆古研究室，中の欠損に起因する磁束分布の乱れを検出コイルが感知する原理に基づく。

e−mai1：hiroki．kikuchihara．6e＠stu．hosei．acjp ＊1法政大学大学院工学研究科電気工学専攻＊2電子磁気工業株式会社−181一

象の欠損を通した場合のみとする。これが回路的な観

2 ∞コイル点から見た∞コイルの動作原理である。

2．ノECTセンサの動作原理

2．j∞コイルの解析モデル
ECTの動作原理は、大別して二方法がある。一方は∞コイルは三次元有限要素法によるシミュレーショ

交番磁界を被検査対象に照射することで被検査対象中ンを用いての開発した3）。

に渦電流を発生させ、被検査対象中の欠損の有無による渦電流分布の相違を電源から見た入力インピーダン

Fig．1は∞文字に対応する二個の隣接する励磁コイ

スの変化で感知する方法である。ここでは、このECTルを示し、Fig．2（わはこれら二個の励磁コイルに互いに法をインピーダンス感知型と呼ぶ。このインピーダン

逆位相の電流を流した場合の磁束密度強度分布を示す。
コイル内の磁束密度強度に比較して極めて小さい磁束

ス感知型ECTの特徴は励磁コイルがセンサも兼ねる点にあり、構造が簡単で安価である。他方は励磁コイ

密度強度を持つ領域が二個の励磁コイル間に存在する。

ルの他に独立した検出コイルを備えた励磁・検出コイ

Fig．2（b）は二個の励磁コイル間にフェライト棒に巻い

ル分離型である。この励磁・検出コイル分離型は被検た検出コイルを挿入したシミュレーション結果である。
検出コイルを磁束密度の強度が極めて小さい領域に配

査対象中の欠損の有無に起因する渦電流分布の相違が置したため、励磁コイルが生成する磁束密度強度分布
はFig．2（わと変わらない。

喚起する磁束の変化を感知する検出コイルの配置に自由度を持つ。このため、励磁・検出コイル分離型は、インピーダンス感知型に比較して高感度とされているが、検出コイルの構造や設置場所などに多くの経験的習熟度を必要とする。本稿で述べる∞コイルの動作原
理は励磁・検出コイル分離型に属する。
2，2∞コイルの動作原理∞コイル開発の原点は、∞文字状に巻かれた二個のFig．1Twoexcitingcoils．

励磁コイルに通電すると、左右の励磁コイル下端ではN極とS極の磁極が形成される。N極とS極の磁極の中間にはゼロ磁界領域が必ず存在する。このゼロ磁界領域へ磁性体コアに巻いた検出コイルを配置しても、被検査対象が存在しない、もしくは被検査対象に欠損が存在しない場合は励磁コイルが生成する磁界強度分

布に対象性が保たれるから、ゼロ磁界領域も維持され検出コイルには電圧は誘起しない。

換言すれば、N極とS極間には必ずゼロ磁界領域が（a）Withoutfbrritebar

存在する。励磁コイルが生成するN極とS極の磁界強度分布が対象である限り、励磁コイル間の磁界がゼロ領域は維持される。しかし、被検査対象に欠損があれば、欠損に起因する渦電流分布の非対称性に起因する磁界は検出コイルへ鎖交する。結果として検出コイルに電圧が誘起し欠損が探知される。
実際は、磁界がゼロ領域は限られた微小範囲である
ため、検出コイルの軸は磁界がゼロ領域を取り囲むよO））Withfen・itebar

うにゼロ領域へ平行に配置する。すなわち、∞文字状

Fig．2Magnetic負eldsintensitydis什ibution．

の励磁コイル軸へ直交する方向へ検出コイルの軸を配置し、励磁コイルと検出コイル間の相互インダクタン

Figs．2（わと2（b）が殆んど同じ磁束密度強度分布となスをゼロにする。両者に相互結合が起こるのは検査対

ることは、極めて小さい磁束密度強度を持つ領域に磁−182−

性体が存在しても、全体の磁束密度強度分布に殆んど流れるが、渦電流が流れる方向は欠損が無い場合と同影響しないことを意味する。換言すれば、検出コイル

じであるためフェライトコア内の磁束密度ベクトルは

を棒状磁性体へ巻いて構成でき、仮に検出コイルが存

Fig．5（b）に示す方向となる。このため、検出コイルの面

在する部分が非ゼロ磁界になった場合、磁界は検出コに垂直方向磁束密度ベクトルが存在せず検出コイルにイルへ集中することを意味する。

誘起電圧は発生しない。すなわち、欠損が検知できな

2．4シミュレーション

い。

Fig．3に示す∞コイルの動作原理を検証するために三次元の有限要素法によるシミュレーション行う。
恥blelに励磁コイルと検出コイルの諸定数を示す。

∞コイルが厚さ1mmの被検査対象とする銅板上に配置され、欠損が無い場合、検出コイルに対し欠損が0度、90度、45度の場合に関してシミュレーション行う。

（a）Node伝ct

Fig．33Dsimulationmodelofthe∝）COil

ThblelvariousconstantSuSedinthe3DFEMsimulation．
Coilouterdiameter
Coilinnerdiameter
Coil length
Number oftum
hputcurrent（peak）

22．4mm
20mm
lOmm
75
250mA
256kHzO））Odegreedefbcttothetwoaqjacentexcitingcoils

Sensing coil
Coilouterdiameter
Coil血1erdiameter
Coil length
Number oftum
Axis core

1．4mmx2．4mm

lmmx2mmbnln1
100
JFEfelTit叫偲1H｝3℃

Figs．4、5はそれぞれ被検査対象とする銅板上に流（C）90degreedefecttothetwoaqjacentexcitingcoils

れる渦電流と検出コイルのフェライトコア内の磁束密度ベクトル分布を示している。
被検査対象とする銅板中に欠損が存在しない場合、Fig．4（わに示す渦電流分布となる。渦電流よって生じる
磁束密度ベクトルは検出コイルの面に対し平行方向のみであるためFig．5（わに示す方向となり、検出コイルに誘起電圧は発生しない。
Fig．4（b）は被検査対象とする銅版中に存在する2m
幅の直線状欠損を検出コイルに対し0度に配置された（d）45degreedefヒcttothetwoaqjacentexcitingcoils

場合の渦電流分布である。渦電流は欠損に沿う方向に

Fig．4Eddycurrentsinaplanemetallictarget．

ー183一

磁コイルそれぞれに起因する渦電流は互いに逆方向であるため、両者の生成する磁束密度ベクトルは欠損の両端で互いに打ち消し合い、フェライトコア内の磁束密度ベクトルはFig．5（C）に示すようにフェライトの断面方向へ平行となり、検出コイルに誘起電圧は発生せず、欠損を検知できない。
Fig．4（のは被検査対象とする銅版中に存在する2mm
幅の直線状欠損が検出コイルに対し45度に配置された場合の渦電流分布を示す。渦電流は欠損に沿って流（わNode飴ct

れ、Fig．5（のに示すように検出コイル断面に垂直成分を含む磁束密度ベクトルが生ずる。この結果、検出コイ
ルに誘起電圧が発生し欠損が検知される。
Figs．5（わー（d）における検出コイルの誘起電圧をFig．6に示す。Fig．6は被検査対象とする銅版中に存在する
2mm幅の直線状欠損が検出コイルに対し45度の場合、高い誘起電圧が発生し欠損の有無が明確に識別されることを示す。
O））Odegreedefecttothetwoa4jacentexcitingcoils

Fig・6Inducedvoltagesinthesensorcoi1（c）90degreedefecttothetwoa嘩acentexcitingcoils

3 実験

ユノ試作∞コイル

Thble2Ⅵ血ousconstantsoftheprototypecocoil．

（d）45degreede良cttothetwoa嘩acentexcitingcoils
Fig▲5Magneticfluxdensityvectordis廿ibutionsinthe飴rritebar

Fig．4（c）に被検査対象とする銅版中に存在する2mm
幅の直線状欠損を検出コイルに対し90度に配置された場合の渦電流分布を示す。銅板中の渦電流は欠損によって妨げられ検出コイル面に垂直な方向の磁束密度

Conductor length
DiameterOfconductor
Coilouterdiameter
Coili皿erdiameter
Coil length
Numberofturn
Numberofcoillayers
Numberofcoils
Inputcurrentbeak）

4．7m
O．4mm
23mm
20mm
lOmm
75
3

2

250mA
256kHzConductorlength
60cm
DianleterOfconductor
O．1mm
Axis core
Feniteba叩血Zn）
Coilouterdiameter 2．4mmx2．4mm
Coilinnerdiameter l．4mmxl．4mm
Coi11ength
6mm
Numberofturn100
2
Numberofcoillayers
Numberofcoilsl

ベクトルを生成する方向に流れる。しかし、二個の励−184−

被検査材料として厚さ1mm、長さ10cmm、幅10cm

文字状に巻かれた励磁コイルの作る磁束密度分布は必の銅板二枚を使用する。一方は欠損が無く、他方は幅が2mm長さ5cmの直線状貫通欠損を持つ。

ず二個の励磁コイル間にゼロ磁束密度領域が存在することに着目し、ゼロ磁束密度領域へ検出コイル配置しT油1e2は∞コイル試作に使用した励磁コイルと検た着想を反映した結果と考えられる。

出コイルの諸定数を示す。

4 結論

Fig．7に示すように試作…コイルは二個の励磁コイ
ルと一個の検出コイルからなる。この∞コイルの諸定

本稿は「∞コイル」と称する新しいECTセンサを提数は三次元有限要素法によるシミュレーションで使用案し、その着想の妥当性を有限要素法によるシミュレ

したFig．3のそれらと同一である。

ーションと実際の実験結果で検証した。
∞コイルは、人間の着想を有限要素法によるシミュ
レーションで可視化し、励磁コイル間のゼロ磁界領域の存在を確認し、さらにゼロ磁界領域に磁性体を配置した場合の磁界分布を吟味して開発された。
∞コイルの基幹的着想は、励磁コイルが作る磁束密度強度分布が変化しない限り励磁コイル間に存在するゼロ磁界領域も維持される。しかし、被検査対象中の渦電流分布が欠損によって乱され、全体の磁束密度強度分布が変化した場合、ゼロ磁界領域が非ゼロ磁界領Fig．7PictureOftheprototypeのCOil．

域となる現象を利用した点に尽きる。この基幹的着想

j．2実験結果

はシミュレーションと実験で裏付けられた。

Fig．7に示す∞コイルを被検査対象上に配置し、欠損

本稿の三次元有限要素法解析はムラタソフトウェが無い場合、検出コイルに対し欠損が0度、45度、90ア株式会社の「Femtet」で行われた。

度の場合に対する検出コイルに誘起する電圧を測定す

る。
参考文献

Fig．Sは検出コイルに誘起する電圧の実測値である。

Fig．8からシミュレーション結果と同様に欠損が検出【l］Ⅰ．Marinova，S・HayanO and YSaito，Ployphase eddy current

コイルに対し45度の場合に高い誘起電圧が発生する

testing，Joumalof Applied Physics，Ⅵ）1．75，No．10，PP．

ことが判る。また、Fig．6のシミュレーション結果と比5904−5906，1994．

較して実測値は約半分程度の振幅となるが、欠損に対【2］N．Burais and A．Nicolas，Electromagnetic負eld analysisin

する検出電圧の傾向は一致する。

remotefieldeddycurrenttestingsystems，IEEEThsactionson
Magnetics，Ⅵ）1・25，No．4，Pp．3010−3012，1989．

［3］S．McFeeandJ・PIWebb，Antomaticmeshgenerationforh−P
adaption，IEEE Transactions on Magnetics，Ⅵ）1．29，No．2，
pp．1S94−1897，1993．

Fig．8MeasuredvoltagesofthepracticalsenslngCOil．
以上の結果から、∞コイルの動作原理が検証され、提案した∞コイルは欠損検知感度に指向性を有するが、比較的高いS／N比を持つことが判明した。これは、∞−185一

第21回MAGDAコンファレンスin仙台

PS29

最適化手法に基づく非接触給電用変圧器の開発
DevelopmentofContactlessTransfbrmersbrContactlessPowerSuppliers
BasedonOptimizatioTIMethodology
大橋竜也■1（学生員）、賓藤兆古＊1（正員）TbtsuyaOHASHI（Stu．Mem．），YoshifuruSAITO（Mem．）
ContactlesspowersupplieriscomposedofatranSfbrmerhavingthedistinctprlmaryand secondary cores
SeParatedbyairgap．Becauseoftheelectromagneticcompatibilityproblem，itisessentialtokeeptheleakage
magnetic鎖eldsaroundthecontactlesspowersupplieraspossibleaslow
Previouslywehaveclarifiedthatthewaveletsmulti−reSOlutionanalysistothemagnetic且eld distributions

aroundcontactlesstransformerleadstoobtainoneofthereasonablecoreshapesbyobservingthewaveletsspectra
Ofmeasuredmagneticfieldvectordistributions．FurthermOre，ithasbeenrevealedthatatestedtrialtranSformer
givesnearly80percentpowertranSmissione餌ciencyeventhoughtheprimaryand secondarycoils coresare
SeparatedbylOmmalrgaP．

Thispaperisoneofthesuccessresearchsolutionstoovercomethespecificabsorptionrate（SAR）problem
basedonthefiniteelementsandoptimizationmethodologies．Namely，aCOntaCtlessflatshapedtranSformerWhose
primalandsecondaryftrritecoresareSeParatedhasbeensuccessfu11yoptimizedbycombiningthe丘niteelements
WithlinearprogrammlngOPtimizationapproaches．
Kb7WOTdg：COntaCtlesstransformer，magneticfieldvisualization，SAR，OPtimization．

ば人類の文明生活が維持できない。換言すれば、あら1緒言

ゆる周波数の電磁界で満たされた空間の中で人類は生半導体技術の発展は、電気・電子機器の小型軽量化

活を強いられている状況である。電気・電子機器に対のみならず、インテリジェント化を可能とし、爆発的してだけでなく人類に対しても可能な限り、電磁界がな電気・電子機器の普及をもたらした。その結果、高分布しない自然な空間が望ましいことは言うまでもな

周波で駆動される電気・電子機器は生産設備のみならい。

ず家電機器まで広汎に普及し、家庭、事務所、工場、生活環境中における電磁環境（ElectroMagnetic
Compatibility）問題の解決策の一つは、低SARレベル

その他あらゆる場所でパソコン、ファックス、携帯電
話、空調設備、照明機器等の多くの電気・電子機器がの非接触給電システム開発にある。この非接触給電シ設置され、必要不可欠な文明の利器として活用されてステムの最基幹部品が一次・二次コア分離型変圧器でいる。それらの電気・電子機器が空間を占める密度は、ある。
本稿は、エアギャップによって分離された一次・従来想定不可能な密度である。この意味で二現代の人
工空間はあらゆる周波数の電磁界で満たされている。

二次分離型変圧器開発に関するものである。すなわち、

これはSAR（SpeCiBcAbsorptionRate）問題を喚起する

本稿では、先行研究で明らかにされたスープ皿形状のことに他ならない。

外鉄型磁性コアを用いた一次・二次コア分離型変圧器

この過酷な電磁環境中でも、電気・電子機暑削ま誤作の設計定数を有限要素法で求め、さらに、有限要素法

動をすることなく円滑にそれらの機能を発揮しなけれで求められた設計定数を用いて二次共振型変圧器の動作周波数と共振用キャパシタンスを最適化手法によっ

連絡先：大橋竜也、〒1糾−85糾小金井市梶野町3−7−2，
法政大学大学院工学研究科電気工学専攻賓膝兆古研究室，て決定する1￣3）。その結果、1cmのエアギャップが存在

e−mail：tatSuya．Ohashi．6z＠stu．hosei．acjp ＊1法政大学大学院工学研究科電気工学専攻

しても一次・二次電力伝送効率SO％近くが得られるこ−435−

とが判明し、この結果は実験によって検証された。
2 一次・二次コア分離型変圧器の基礎特性
2．Jコア形状
非接触給電システムではエアギャップを介して電力電送を行う。このため、一次・二次コア分離型変圧器は最も重要な基幹部品である。
一般に変圧器のコア材である磁性体は重量が重いた
め、コア材の量を可能な限り削減することが望まれる。

加

これは通常動作周波数の高周波化でなされる。高周波］鴨卵

特性のよい磁性材料はフェライトである。
ギャップを介して行われるため、変圧器周辺の漏れ磁Fig．2 0neofthemagnetic丘eldvectordis扇butionsof
thetested仕ansformerunderthelnpurereSistiveloadand

界が最小であることが必須である。離散値系ウェーブ

SeCOndaryresonantconditions．

一次・二次コア分離型変圧器では、電力伝送がエアレット変換の多重解像度解析を用いた変圧器周辺の磁2．j結合係数界ベクトル分布解析から、磁性体コアの形状は外鉄型
一次・二次コイル間の漏洩磁束の過多を表す指標での一種であるスープ皿型が最適であることが判明している1，2）。

ある結合係数Kは変圧器の最も重要な性能指標の一つである。すなわち、結合係数Kが大きいことは変圧器

この結果を踏まえ、各種のスープ皿形状のフェライ

周辺の漏洩磁束が小さいことを意味する。

トコア形状と一次・二次巻線形式に関して有限要素法

変圧器の一次・二次コイルをFig．3に示す回路モデに拠る数値シミュレーションを行った。その結果、既存のスープ皿形状のフェライトコアの中からFig．1にルで考える。Fig．3の端子a，b，C，dをFig．4に示すように示す同一形状のスープ皿型フェライトコアを一次・二結線し、インダクタンスを測定することで式（1）から結合係数Kが求まる。

次コア分離型変圧器として採用した。

1「Fig．1 Atestedflatshape臨rritecoretranSformer．

Fig．3 Circuitmodelof血IISformer．

2．2磁界ベクトル分布。」m−Jm。 a b c d

Fig．1に示すスープ皿型フェライトコアを有する変圧器で、二次側へ1nの負荷抵抗と共振用キャパシタ

糎方向 Lsンスを接続し、二次側共振状態下の磁界ベクトル分布の測定例をFig．2に示す。Fig．2は一次・二次コア間の。」m＿。脚L a b d c

磁界ベクトルの町Z三成分を、コアに平行なⅩ−y平面とコア面に垂直な高さ方向をz方向とした測定結果で逆方向Loある。Fig．2から、主要な磁束は一次・二次コア中心部

Fig．4 Seriescomectionoftheprimaryandsecondaryに集中し、コア端部から漏れる磁束密度ベクトルが殆んど無いことが判る。

inductanCeS．

−436−

エ∫＝ち＋ち＋2〟，
ち＝ち＋ち−2〟，〟＝ 主二左

（1）

4

∴た＝

l

Fi肌碑

八丁
戸イヱ

Tablelにスープ皿型フェライトコアを使用した変止む1S允Imer．

圧器の結合係数Kを示す。T地1elの結果から、スープ
皿型フェライトコアを使用した変圧器は5mm程度の3有限要素シミュレーションと最適化手法

エアギャップが存在しても結合係数が80％を越える
よJ有限要素シミュレーション

十分な磁気結合を維持することがわかる。

有限個のスープ皿型フェライトコアの中から、漏洩
ThblelCoupling払ctorofthetestedtransformer

磁束を最小化するフェライトコア形状と一次・二次巻

employmgSOuPPlatelikeshapecoresmeasuredat30kHz．

線形式を有限要素法に拠る数値シミュレーションで選叩［mm］ 03

択した。Fig．6にシミュレーションに用いたモデルを示

10

7

5

す。なお、数値シミュレーションは、汎用有限要素法

Ll【いH］ 578．6 348．2 231．1 181．6 169．9 133．9

パッケージFemtet（MmTAソフトウェア）で行った。

L2［岬］ 572．7 348．1 229．4 1Sl．0 16S．3 133．3
Ls【l止Ⅰ】 2297．4 135S．2 881．8 669．4 617．6 450．8
L血叫 16．9 26．1 41．4 5（；．0 61．1 S4．3
0．99

K

0．96

0．91

0．S4

0．S2

0．69

2．4一次・二次電力伝送効率

一次側から二次側へ伝送される電力の伝送効率もLT

また変圧器の重要な性能指標の一つである。本稿では、Fig．5に示すように二次側にコンデンサを接続し、二次Fig・6SimulationmodelofthetransformeremPloyingthesoup

側漏れインダクタンスとコンデンサ間に共振回路を形成し伝送効率の改善を図る3）。

Platelike危mitecores．

一次・二次コア間のギャップを10mm、二次側に純抵抗負荷1n、共振用コンデンサ40岬、動作周波数

Fig．7は一次・二次コア間のギャップ長に対するイ

30虹七に設定し、式（2）より算出した伝送効率の実験値
は約80％となり、一次・二次コア間のギャップが10mm

ンダクタンス値を実験値と共に示す。Fig．7の結果から、
シミュレーションと実験、いずれの場合もインダクタ

である一次・二次コア分離型変圧器の電力伝送効率とンスはギャップ長に反比例して減少する傾向を示し、しては良好と言える。

両者の値が殆んど一致することが判る。

また、後述する線形計画法による最適化理論によるしたがって、Fig．6に示したシミュレーションモデ

結果から、この比較的良好な伝送効率を維持するコンルの妥当性が検証された。

デンサと周波数の選択幅は十分に広い。
g＝Fig．8は、シミュレーションによる一次・二次コア分

Secondaryoutputpower
×100【％】
PrimarylnputPOWer

離型変圧器の磁束密度ベクトル分布の一例を示す。
（2）

ー437−

るコンデンサ容量と動作周波数の組み合わせが複数存

lndu⊂tan亡 l山1l

在することを示す。この結果は2．4節で実験的に得られた結果を裏付けている。

￠

2

4

6

8

1（I6ap【憫】

Fig．7ThecomputedselfこinductancesversusaillgaPlength・
1000◆■．コく丁ウさ8■−003

Fig．9Powertransmissionratebythelinearprogrammmg
Optimization．

以上の結果から、有限要素法による磁界分布解析や線形計画法による伝送効率の最適化など、現代の計算
す1、G2087加−00S機を用いた解析手法を駆使して非接触給電用一次・二次分離型変圧器設計の一手法を確立した。

◆2．SOウ■11●−00く

Fig．80neofthesimulatedmagneticfieldvectorsdistributionsof
thetranSformer．UnitofcolorbarisTbsla．

4結言
低SARを実現する非接触給電用一次・二次分離型

変圧器を設計するために、有限要素法を用いて一次・よg共振用コンデンサと動作周波数の最適化

二次磁性体コア形状や巻線形式を選定し、変圧器の回式（2）で与えられる一側から二次側へ伝送される電

路定数、抵抗、インダクタンスを算出した。さらに、

力の伝送効率gは、一次コイルの抵抗r八 白己インダ

それらの回路定数を用いて、特定の負荷時における二クタンスエハー次・二次間の相互インダクタンス〟、次共振型変圧器の最適なコンデンサ容量と動作周波数

二次コイルの抵抗り、二次負荷抵抗r、二次共振用コを線形計画法で決定し、非接触給電用一次・二次分離

ンデンサC、さらに動作周波数′の関数であるから、型変圧器設計の一手法を確立した。

g＝′（1，ち，r，ち，ち，〟，C，′）（3）

参考文献

で表される。

【1］S．Thkada，YSaitoandKHorii、Ⅵsualizationofthem4gnetic

一次コイルの抵抗rハ 自己インダクタンスん、一Geldvectorsaroundthecontact−1esspowersuppliers，Japan次・二次間の相互インダクタンス肱二次コイルの抵

SocietyofⅥsualization，Proceedings oftheⅥsualization

抗りは一次・二次コアや巻線の幾何学的寸法と媒質のSymPOSiumin2000，PaperNo．POl，001．

パラメタで決まる。さらに、二次負荷抵抗rは1nと【2［S．Matsuyama，YOguchi，YSaito，TL．Kunii，Handlingする。このため、式（3）の伝送効率gが最大となるコンTechniqueoftheDymamicColorComputerGraphicsbythe

デンサCと動作周波数′を線形計画法仕血甜

Wavelets tranSfom，Japan Society of Visualization，

mo餅肌m血g）で求める。

ProceedingsoftheVisualizationSymPOSiumin1999，Paper

すなわち、

No．206．

g→maX［3］J．L．Harrison，AnewresonancetransfbrmeIちElectronT）evices，（4）となるコンデンサ容量Cと動作周波数′求める。F短．9

lEEE甘ansactionson TssueDate：Oct1979Ⅵ）l．261ssue：10，

が結果である。

pp．1545−1．

Fig．9の結果は比較的大きい10mのエアギャップを有する場合の伝送効率であり、80％以上の効率を得−438−