MLIS - Universiti Putra Malaysia Institutional Repository

UNIVERSITI PUTRA MALAYSIA
FABRICATION AND CHARACTERIZATION
OF SOME NiZn-BASED
FERRITE MULTILAYER INDUCTORS
(MLIS)
LUCIA LIEW WOAN SHYAN
FSAS 2000 45

FABRICATION AND CHARACTERIZATION
OF SOME NiZn-BASED
FERRITE MULTILAYER INDUCTORS
(MLIS)
LUCIA LIEW WOAN SHYAN
MASTER OF SCIENCE
UNIVERSITI PUTRA MALAYSIA
2000

FABRICATION AND CHARACTERIZATION OF SOME NiZn-BASED
FERRITE MULTILAYER INDUCTORS (MLIS)
By
LUCIA LIEW WOAN SHYAN
Thesis Submitted in Fulfilment of the Requirements for the
Degree of Master of Science in the Faculty of Science
U niversiti Putra malaysia
September 2000

DEDICATIONS
To
Dear Mom and Dad, brothers and sisters
11

Abstract of thesis presented to the Senate of Universiti Putra Malaysia in
fulfilment of the requirement for the degree of Master of Science
FABRICATION AND CHARACTERIZATION OF SOME NiZn-BASED
FERRITE MUL Tll,A YER INDUCTORS (MLIS)
By
LUCIA LIEW WOAN SHY AN
September 2000
Chairman: Associate Professor Mansor Hashim, Ph.D.
Faculty: Institute of Advanced Technology
The multilayer inductor is particularly important as a highly stable, easy to use
and miniaturised component in electronic systems, such as radios, VCRs and
computers. There were two main tasks in this research project, one was to
make a proper preparation set-up, and the other was to measure the inductance
and the reciprocal of the Q factor of the multilayer inductors produced. Layers
of ferrite sheets were stacked together with silver layers in between by means
of tape casting method. End metallization was applied to make contact with
the inner conductors. Bulk and multilayered components of the same
dimension were made to undergo parallel conventional sintering. The
experimental work resulted in the complete construction of a tape-casting set­
up. The measured L values were in the range of 10-1 to lOS Henries and L fell
rapidly with frequency from 1kHz to 30MHz. The energy was represented by
111

lIQ ranged from 10- 3 to 10 and also fell rapidly within the same frequel\cy
range.
IV

Abstrak tesis yang dikemukakan kepada Senat Universiti Putra Malaysia
sebagai memenuhi keperluan untuk ijazah Master Sains.
PEMBENTUKAN DAN PENCIRIAN INDUKTOR PELBAGAI
LAPISAN (MLIS) }'ERIT NiZn
Oleh
LUCIA LIE\V \VOAN SHYAN
September 2000
Pengerusi: Profesor Madya Mansor Hashim, Ph.D.
Fakulti: lnstitut Teknologi Maju
lnduktor multi lapisan adalah penting terutamanya sebagai komponen
berkestabilan tinggi, mudah digunakan dan bersaiz amat kecil dalam sistem
elektronik seperti radio, VCR dan komputer. Ada dua objektif utama dalam
kerja peyelidikan ini. Salah satu daripadanya ialah penyediaan satu set alat
yang sesuai untuk pengeluaran komponen pelbagai Iapisan, manakala yang satu
lagi ialah mengukur induktans dan salingan faktor Q induktor pelbagai lapisan
yang dihasilkan. Lapisan ferit diletakkan berselang-seli dengan lapisan perak
Hujung susunan ini dikemaskan dengan meletakkan lapisan perak untuk
dijadikan konduktor. Toroid dan komponen pelbagai lapisan disinter bawah
keadaan pembakaran selari. Kerja ujikaji ini menghasilkan suatu binaan
lengkap peralatan tuangan-pita. Nilai L yang diukur berada dalam julat 10-1 ke
10 ) henry dan L menyusut cepat dengan frckucnsi daripada 1 kHz to 30MHz.
v

Kehilangan tenaga yang diwakili oleh l/Q berada dalam julat 10- 3 ke 10; ia
juga menyusut cepat dengan frekuensi dalam julat yang sarna.
VI

ACKNO\VLEDGEMENTS
First of all, I would like to extend my deepest gratitude to God the Almighty,
for giving me the strength, the faith, the wisdom, the confidence, the courage,
and the helps needed to complete my thesis.
Secondly, I would like to give my greatest appreciation to my dear supportive
supervisor, PM Dr. Mansor Hashim, for his superb supervision, generosity,
patience, endurance, and dedication throughout the whole of this project. Also
not forgetting my supervisory committee members: Dr. Jumiah Bt Hassan and
PM Dr. Salleh Bin Hj. Hamn, and Prof. Dr. Abdul Halim Shaari, the
chairperson of the Examination Committee.
I would also like to thank Dr. M. K Vidyadaran, Mr. Ho Oi Kuan, Miss Azilah
Bt. Abdul Jalil,
during my SEM session.
Many thanks also for Khoon, San, Kak Ana, lab mates, and friends, especially
Fanny, for their generous assistance and encouragement, and also the
technicians, Mr. Nordin and Mr. Roslim, and the lab assistants Pak Mat Rasa.
Finally, special thanks to my parents, brothers and sisters, especially Nancy
who has helped a lot, and brothers and sisters in Christ, for praying earnestly
forme.
VII

I certify that an Examination Committee met on 28 September 2000 to conduct
the final examination of Lucia Liew Woan Shyan on her Master of Science
thesis entitled "Fabrication And Characterization Of Some NiZn-based Ferrite
Multilayer Inductors (MLIs)" in accordance with Universiti Pertanian Malaysia
(Higher Degree) Act 1980 and Universiti Pertanian Malaysia (Higher Degree)
Regulations 1981 . The Committee recommends that the candidate be awarded
the relevant degree. Members of the Examination Committee are as follows:
Abdul Halim Shaari, Ph. D
Professor
Faculty of Science and Environmental Studies
Universiti Putra Malaysia
(Chairman)
Mansor Bin Hashim, Ph.D
Associate Professor
Institute of Advanced Technology
Universiti Putra Malaysia
(Member)
Jumiah Bt Hassan, Ph. D
Lecturer
Faculty of Science and Environmental Studies
Universiti Putra Malaysia
(Member)
Salleh Bin Hj. Harun, Ph. D
Associate Professor
Faculty of Science and Environmental Studies
Universiti Putra Malaysia
(Member)
HAZALI-MOHA YIDIN, Ph. D
Professor/Deputy Dean of Graduate School,
Universiti Putra Malaysia
Date: 2 8 NOV 2000
viii

This thesis submitted to the Senate of Universiti Putra Malaysia has been accepted as
fulfilment of the requirement for the degree of Master of Science.
ix
Date: 1 1 JAN 2001

1 hereby declare that the thesis is based on my original work except for
quotations and citations which have been duly acknowledged. I also declare
that it has not been previously or concurrently submitted for any other degree
at UPM or other institutions.
x
LUCT
Date: :2.3 - J' - ;WOO

TABLE OF CONTENTS
Page
DEDICATIONS ... ... ... ..... , ... ...... '" ., . ... .......... '" ... ... ... .... 11
ABSTRACT ..... , ... ... ... ... . , ...... , ...... ... ....... '" ., ...... , '" ... .... 111
ABSTRAK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
ACKNOWLEDGEMENTS ... . .... . ... .................. . . .. . ..... . . . ... VB
APPROVAL SHEETS ... ... ... . . .... ... ... ... ...... ... .. . ............ . .... V1l1
DECLARATION FORM ... ......... ........... . .... ... ... .. . ...... .. , ... x
LIST OF TABLES ... ....... ... ... ... ... ... ....... ... ... ... ... ... ... ... .... XIV
LIST OF FIGURES .... ... ........ ... .................. ......... ... ...... ... x"V
LIST OF PLATES ..... .... ........... ... . ..... ...... . ..... ... ...... .. , .. XVll
LIST OF SYMBOLS & ABBREVIATIONS ....... ... ...... .......... XVlll
CHAPTER
I INTRODUCTION
Ferrites ., ............. ......... ....................... .... ,. 1
Nickel Zinc Ferrite ... ... .. , ............ . , . ..... , ... ... .. 2
Some Magnetic Parameters ............................. 2
Mutilayer Inductor ............... ......... ......... ....... 4
Objectives .. . .. . ... .... , ...... , '" ...... ... ........ , ... ... ... 5
n LITERATURE REVIEW
Intr� .............. ... ....... .. ...... ...... ...... .... 7
"Some Aspects on Ni-Zn Ferrites ..... ... ................. 7
Trend in Modem Technology .... , ... ... ... ... ... ... ... ... 9
Multilayer Components ........ ............... ... ......... 10
Configurations and Parameters ... ... ... . ,. ... ... ... ... .... 12
ill SOME BASIC THEORY
Electromagnetic ..... ...... ...... .. , ......... ... . , .... .. , 15
Definition for B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . ... 15
Magnetic Field Due to Current .. . . .. ... ..... . .. , ... . .. .. . 16
Current-flow Direction of the Magnetic Field... ... ... .... 17
Inductance ... ... ... ...... ...... ... .... ,. ... ... ... ... ... ..... 19
Power/Energy Relationships for Inductors... . . . ... ... 23
Magnetic Flux Density Tn A Multilayer Inductor .... 24
Crystal Structure ofNi-Zn Ferrites ... ...... ...... ........ 26
Ionic Charge Balance and Crystal Structure ...... '" .... 27
Site Preferences of the Ions .. . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . 28
Xl

Interactions Between Magnetic Moments On the
Site I..attice .................. ......... ... .................. ... 29
The Magnetic Properties ofFerrites . . .. . . . .. . . . . .. . . . . .. . 31
Intrinsic Properties ... . ....... . . . . '" ...... '" . .. .. 31
Extrinsic Properties ....... .. ... ... . .. ... ... ... . . . 34
Effect of Grain Size and Porosity on Permeability .... . 39
Tape Casting . . . . . . . . . . . . . . . . . .. . . . .. . . .. . . . . . . . . ... . .. . . . . .. 41
Tape Casting Process ........................ ......... ..... 42
Skin Depth ... . .... . ...... . ..... . .. ... .. . ......... .. . . .... .... , 45
IV SOME BASIC CONSIDERATION ON MULTILAYER
V METHODOLOGY
Introduction ............... ... ...... . ..... .................. 46
Deflocculant . . . . . . . . , ... ... ...... ...... ... ... ......... ... .. , 47
Sur factant ..... , ... ... ... . .. ... ... ... ... ... ... .. . .. . ... ... .. . 47
Binder ..... ....... ......... ......... ...... ...... .......... .... 49
Pla sticize r... ... ...... ... ...... ...... ...... ......... ... ... ..... 50
Lubricant .. . . . ... . . . , ... ... ... .. . ... ... . .. ... ... ... ... ... ... . 51
VISCOSIty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Num ber of Layer s ..... , ..... , '" ... .... , ..... , .... '" ... . 53
Wet Laye r Thickne ss ...... ..... , ......... ...... . " ... ..... 54
Control of Cast Defects ... . .... . . . ..... . . . .. . ..... ... .. , ... 54
Introduction .. .... . .. ..... .. . . . . , .... , . ... '" ... ... ... ... .. 56
Experiments ......... ........................... ......... .. 59
Two Stage-milling .................. .. , ..... , ... 60
Weighing . . . . .. . .. . .. . . ,. ... ... ... ... ... ... ....... 60
Mixing . . . . .. . . . . . . . . . . . . . . . . . . . .. . . ... . ... . . . . ,. ... 61 .
Pre-smtenng . .... . ...... '" ... ... ... ... ... ... ... ... 62
Add ition of ZnO , Bi 62
Crushing and Sieving . . .. . . . . . . . . . . . . ... . ..... . . . 63
Forming ..... . . .. . ..... . .. . .. ...................... 64
Sinte ring ........ . ... ... ... .............. , ... ... ... 66
VI RESULTS AND DISCUSSION
Introduction ' " ... ........ ... ... ... .. . ... ... ... ...... ... .... 68
Experimental Set-up .. . ... ...... ... ....... ,. ... ... ... .. . . 68
Rheology of Slurry . . . . . . . . . . . . . .. . .. . . .... . . . . . , '" .. . ...
Electrical Analysis of Inductance and Loss Factor
69
l/Q . . . . . , '" .. , ... ... .... ,. '" .,. ... ... ... ... ... .... ..... 70
Microstructure Analysis . ... . . .. . .. . . . . . . . . .. . ..... . ... . . . 80
Xli
xii

VII CONCLlJSION AND SUGGESTIONS
Conclusions
Suggestions
BffiLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . ... .. . . . .. . . . . . . . . . . .. . . . . . .. . . . . . . . ... . 90
APPENDIX A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
APPENDIX B . . .. . .. ........ ... . . . .... ..... . . . . . .. . . ... .. . . . .. .. . . . ... . . . . . . . 97
APPENDIX C '" .. , ......... ... ............... '" ...... ......... '" ... ... ... . 98
VITA '" ... '" ........ , ... '" ........... ...................... ......... '" '" .... 99
xiii
87
88

Table
LIST OF TABLES
Page
2. 1 Some dimentions of multilayer induct ors manufactured
by AEM ,Tn c. ...... ... ... ... ... ... ... ... ... ... ...... ...... ... ... ...... 12
2.2 Some Feat ures of Multilayer In duct ors Man ufact ured
by AEM,ln c. ... ... . . . ... ............... ...... ... ... ......... ... ...... 13
2.3 Some Diment ions of Multilay er Inductors Manufact ured
by TO KO . . 13
2.4 Some Features of Mut itay er In duct ors Manufact ured
by TO KO .. 13
2.5 Som e Dim entions of Multilay er Inducto rs Manu factu red
by TRIGONCO MPO NEN 14
2.6 Some Feat ures of Multilay er In ducto rs Ma nu factu red
by TRIGON CO MPON ENTS... ... ... .............. . ...... ...... 14
3.1 Site Pr eferenc e and Ma gnetic Moment for Som e Metal Ion s.. . 29
4.1 Some Comm on Plas ticiz er ..... . ..... . ... . . . '" .. , ... ...... ... ..... , 51
4.2 Comm on Lu bricants . . . .. , .............. ...... ......... ... ... ... ... .. 53
S. l Stag e I of the Two Stag e-miling ... .
...... . _ _ . .... _ _ . . . . . . _ _ . ..... 60
5.2 Sta ge IT of the Two Sta ge-millin g ........... , ............ ...... . ,. 60
XlV

LIST OF FIGlJRES
Figure Page
3.1 Magnetic Field Pattern of a Single and Long-straight Wire... . .. . 16
3.2 Magnetic Field Pattern of a Current Flowing Through a
Planal Round-turn . .. . . , '" ... '" ......... .. , '" .. , ............ .. , ... ... . 17
3.3 Magnetic Field Pattern of a Long-solenoidal Wire... ... ... ... ... .. 18
3.4 The Magnetic Field, B, set up by a Current i in a solenoid ... '" .... 20
3.5 Circuit Symbol For An Inductor, Along With Associated
Reference Direction For Current and Voltage .... , ............ , ... ... 22
3.6 Construction of A Multilayer Inductor... ... ... ... .................. 25
3.7 Current Flow Along AB Direction in Fig 3.6... ... ... ... ... ... ..... 25
3.8 Magnetic-flux Density Configuration of A Multilayer Inductor
Cross-sectional Area ......... . , ...................... .. , ... " . . .. ... ... 26
3.9 Crystal Lattice of Spinel Structure ..... , .............. , ... ... ... ... ... 28
3.10 Ferrimagnetism; (a) antiparallel alignment of moments of two
sublattices, (b) the net magnetic moment of the lattice. .. . . . . . . ... . . . 30
3.11 Magnetization Curve of a Material with Magnetic Anisotropy.... 32
3.12 . Schematic of Continuous Tape Casting Apparatus ............ '" '" 44
4.1 Structure of a surfactant molecule and its oriented
adsorption at water-oil and water-air interface .... .. ......... ... '" .. , 49
4.2 Molecular Structures of Hydrocarbon Chain and
Fully Hydrolyzed Polyvinyl Alcohol ... ... ..... , '" ... ... ... ... ... ... 50
5.1 HP16334A test Fixture ...... ...... ...... ... '" ... ... ... ... ... ... ... .... 58
5.2 Experimental Flow Chart......... ............... ............... ........ 59
6.1 Schematic of Tape Casting Apparatus... ... ... ... ... ... ... ... ... ... ... 69
6.2 Graph Inductance, Lp, Versus Frequency of Sample
102,202,302 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . '" '" ... ... 71
xv

6.3 Graph Lp Versus Co-firing Temperatures of Sample 102,202,
and 302 at Frequencies 10kHz, 50kHz, and 100kHz ........... , '" 71
6.4 Graph Lp Versus Particle Size of Sample 102,202, and
302 at Frequencies 10kHz, 50kHz, and 100kHz ... ...... . .. ... . ' . .. 72
6.5 Graph lIQ Versus Frequency of Sample 102 ... . ,. '" .. , '" ......... 73
6.6 Graph 1/Q Versus Frequency of Sample 202 ........... , . , . ' " .. , ... 74
6.7 Graph lIQ Versus Frequency of Sample 302...... ...... ... ... ...... 74
6.8 Graph lIQ Versus Frequency of Sample 102,202, and 302... ... . 75
6.9 Graph lIQ Versus Co-firing Temperatures of Sample 102,202,
and 302 at Frequencies 10kHz, 50kHz, and 100kHz ........ , .,. .... 76
6.10 Graph l/Q Versus Particle Size of Sample 102, 202, and
302 at Frequencies 10kHz, 50kHz, and 100kHz ... ......... '" ... . 76
6.11 Graph Inductance, Lp Versus Frequency of Sample T002... ... . 78
6.12 Graph l/Q Versus Frequency of Sample T002... ... ......... ....... 78
6.13 SEM Photo Shows the Microstructure of Top Ferrite Layer Before
Final Co-firing ... ... ... ...... ... ... '" ...... '" ... ... ... ... ... ... ... ... ... . 80
6.14 (a), (b) and (c) Shows the SEM Microstructure of Ferrite Layer
Co-fired at 620°C/8h ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... 80
6.15 SEM Photo Shows the Microstructure of Ferrite Layer Co-fired
at 600°C/8h ... '" ............... '" ... ...... ...... ...... '" ...... '" ... ..... 83
6.16 (a), (b) SEM Photo Shows the Microstructure of Ferrite
Layer Co-fired at 55 0°C/8h ............... ... '" ... ... ... ... ... ... ... ..... 83
6.17 SEM Photo Shows the Imperfections Between Silver and
Ferrite Layer. ........ ......... ......... ..... , ... ... ... .................. '" 85
6.18 SEM Photo Shows the Silver End-termination of the Multilayer
Inductor. .. ... . . . ... ... ... ... .. . ... ... ... ... ... .. . ... ... .. . ... ... ... ... ... . 85
XVI

LIST OF PLATES
�� h�
5. 1 Electronic Analytical Balance . .. .. . .... .. .... , ............. '" ... ... .... 61
5.2 Siever and Crusher. . . . . . . . . '" '" ..... , ... '" .. , ... '" '" ..... , ... '" ... .. 64
5.3 Mould . . . . . . . . , . . . . . . . . . . . . ' " ' " . . . . . , . . , . . . . . . . . . . . . . . . . . . . . . . . . . . , .. , ..... 65
5.4 Pressing Machine ... '" ... .. , .. , .. , ., ................ '" '" .... ,. '" ... ... 65
5.5 Electric Furnace .. . . . , .. , '" .. , ... '" '" ............ '" ... ... ... ... ... ... ... 67
xvii

A cross sectional area
B induction
Bs
Di
Do
f
h hour
LIST OF SYMBOLS AND ABBREVIATIONS
saturated induction
inner diameter
outer diameter
frequency
H applied field
He
HK
coercive force
saturated anisotropy field
K anisotropy energy
L inductance
L/J length
Ms
saturation magnetisation
N number of wire turns
PYA polyvinyl alcohol
Q quality factor
RLF relative loss factort
tan B loss tangent
T thickness
XVIII

W width
XRD X-Ray Diffraction
�
�B
J..1,)
J..l
J..li
magnetic moment
Bohr magneton
permeabil ity of free space
permeability
initial permeability
� ' real part of permeability
J..l"
p
y
imaginary part of permeability or magnetic loss
resistivity
Gyromagnetic ratio
ill angular velocity
a internal stress
A magnetostriction
XIX

CHAPTER I
INTRODUCTION
Ferrites
Ferrites are magnetic ceramic materials, containing mostly iron which is derived
from Fe 2+ O.Fe;+. 03 , and mix with other oxides and carbonates in powdered
form, arranged in such a manner to produce spontaneous magnetisation (Gerald,
1975� Standley, 1972� Crangle, 199 1). There are soft ferrites as wen as hard
ferrites. Soft ferrites become magnetised by relatively low-strength magnetic
field When the applied field is removed, they returned to a state of relatively low
residual magnetism, whereas hard ferrites need high magnetising field and high
remnant magnetism to become magnetised. Since the pioneering works of Snoek
(1936) and Takei (1939), a very large number of studies have been published by
other ferrite scientists, and have generated a wide range of technological
applications (Snelling). In recent years, the rapid developements in the electronic
and electric industries, have created even larger and dynamic changes on the
demands for the uses of ferrites.
Ferrites are ferrimagnetic materials which have domain structures and hysteresis
loops, similar to those of ferromagnetic materials. They have three distinct
crystal structures: the hexagonal magnetoplumbite, dodecahedral garnet and the
spinel structure (Crangle, 1991� Standley, 1972). Hexagonal magnetoplumbite is
a hard ferrite structure, dodecahedral garnet and the spinel are soft ferrite

structures. Soft ferrites are used for applications in which the material must be
easily magnetised and demagnetised such as cores for power transformers, small
electronic transfonners etc. On the other hand, hard magnetic materials are used
for applications requiring pennanent magnets which do not demagnetise easily
such as the pennanent magnets in loudspeakers, telephone receivers, and
automotive starting motors. Anyway, it is the soft ferrites that are of concern in
this research project.
Nickel Zinc Ferrite
The type of ferrite which is used in this research work is Nickel Zinc (NiZn)
ferrite. It was developed for a wide range of applications where high
penneability and low loss were the main requirements. NiZn ferrite is still one of
the most important ferrites for such applications and constitutes a substantial
portion of present day soft ferrite production. NiZn ferrites have been extensively
used as core materials for large number of devices and electrical components such
as inductors, transfonners, antenna rods etc.
Some Magnetic Parameters
One of the most important pammeters in magnetic materials evaluation is the
permeability. Permeability is an extrinsic property and can be defines as ratio of
induction, B to the magnetizing field H.
2

B
1-1=- H
Permeability can also be written in complex form, where the real part f.l' showed
the energy stored, expressing the component of B in phase with H and the
imaginary part ll" indicating the energy dissipated, expressing the component of
B out of phase with H.
The permeability concept can be extended to include the losses. For time
hannonic fields,
H = Hoexp(joot)
where 00 is the angular frequency and t is the time. The dissipation can be
described as the phase difference between H and B, o. In the complex notation,
the frequency dependency of permeability becomes
ll(W) = B exp j(id +0)
H exp(ja>t)
which would give us, again,
3

where J.1" can actually be obtained from the relation
ll" = �l' tan 0
Permeability can not only be influenced by the chemical composition and
crystal structure, but is also strongly dependent on microstructure, temperature,
stress and time after demagnetization.
Multilayer Inductors
"Multi _" comes from the word "multiple" which means having many parts or
elements, or a quantity which contains another quantity an exact number of times
as we use in mathematics.
Multilayer chip inductors were introduced in 1987 and soon became the inductive
components of choice for many design engineers. For example, Toko, a Japanese
company, introduced the first microminiature multilayer chip inductor LL2012 in
the year 1992. And soon it became the inductive components of choice for many
design engineers.
Multilayer technology offers three advantages:
I. Monolithic structure which is good for high reliability
2. Magnetic shielding which is excellent for very high density applications
3. Low mounting cost as multilayer (chip) inductors do not require winding
4