ARTICLE IN PRESS

te/jmmm

Journal of Magnetism and Magnetic Materials 297 (2006) 76–83

www.elsevier.com/loca

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High-performance zig-zag and meander inductors embeddin ferrite material

Goran Stojanovica,�, Mirjana Damnjanovica, Vladan Desnicaa, Ljiljana ZivaRamesh Raghavendrab, Pat Bellewb, Neil Mcloughlinb

aFaculty of Technical Sciences, Department of Electronics, University of Novi Sad, Trg Dositeja Obradovica 6, Novi Sad 2

Serbia and MontenegrobLittelfuse Ireland Limited, Ecco Road, Dundalk, Co. Louth, Ireland

Received 29 December 2004; received in revised form 11 February 2005

Available online 16 March 2005

bstract

dded in

cessing

surface-

and for

ductors

sing an

This paper describes the design, modeling, simulation and fabrication of zig-zag and meander inductors embe

low- or high-permeability soft ferrite material. These microinductors have been developed with ceramic copro

technology. We compare the electrical properties of zig-zag and meander inductors structures installed as

mount devices. The equivalent model of the new structures is presented, suitable for design, circuit simulations

prediction of the performance of proposed inductors. The relatively high impedance values allow these microin

to be used in high-frequency suppressors. The components were tested in the frequency range of 1MHz–3GHz u

Agilent 4287A RF LCR meter. The measurements confirm the validity of the analytical model.

r 2005 Elsevier B.V. All rights reserved.

PACS: 84.32.Hh

Keywords: Inductor; High frequency; Surface-mounted devices; Soft ferrite

. Introduction

gh-useat R

microwave frequencies. Their size, performancefor a

romag-iversalnalingcorpo-puters,

Miniature inductors embedded in a hilow-permeability soft ferrite material, findapplication in the suppression of EMI

le be-direct

304-8853/$ - see front matter r 2005 Elsevier B.V. All rig

oi:10.1016/j.jmmm.2005.02.058

�Corresponding author. Tel.: +381 21 459 449;

x: +381 21 475 0572.

E-mail addresses: sgoran@uns.ns.ac.yu (G. Stojanovic),

aghavendra@littlefuse.com (R. Raghavendra).

orfulF

and reliability make them very attractivewide range of applications, such as electnetic interference (EMI) suppression in unseries bus (USB), low-voltage differential sigand in other high-speed digital interfaces inrated in notebooks and personal comdigital cameras and scanners.

Planar magnetic components are suitabcause of their small size. This is a

hts reserved.

manifestation of the general principle that the sizequenopet amu

quenagnesed

urfasuchagneroledingefferipti

ctrobviodesieve

ts chereblishckshe laypesarermaon aile tlead

ss tired toquencyGHz).the fullminia-nd the

and labels of mechanical dimensions of the chiphanical0:075;Fig. 2ag andaterial.eramiclayer,lower

ctor toctor islayer isin thels haveaterial)whosefrom

el–zincuenciesequen-rial isy 1000These

n EMI

eanderquiva-of theepictedindinglementctance

ARTICLE IN PRESS

DL

E

G. Stojanovic et al. / Journal of Magnetism and Magnetic Materials 297 (2006) 76–83 77

of magnetic components is reduced as freincreases. Unfortunately, high-frequencytion gives rise to unwanted skin effecproximity effect losses. In recent yearsliterature [1–8] has studied the high-frecharacteristics of ferrite core and/or mcomponents such as ferrite inductors, bafinite element method or physical analysis.

Miniature inductors can be installed as smount devices (SMDs) [9]. Parasitic effectsstray capacitance, self-resonance and mlosses of ferrite, etc., play an importantthe design of such inductors. An understanthe high-frequency parasitic and packagingcan be gained from equivalent circuit descof the inductor.

The momentum towards high-density elecircuits continues unabated. The effects are oin very large scale integration (VLSI)component densities are being quadrupledthree years. Planar magnetic componenbecome an integral part of the process, wresistors and capacitors are already estacomponents. One of the major drawbaestablishing planar magnetic technology is tof accurate analytical models for different tthese structures. Experimental prototypespensive to fabricate and test. One would noexpect to complete a second cycle of fabricatitesting before a final design is achieved. Whprocedure may give better insight, it does notan established design methodology.

The purpose of this paper is to addresituation. In many applications, it is requdesign miniature inductors with resonant freextending into the RF regime (100MHz–1Thus, there is a pressing need to understandcircuit modeling and characterization of theture inductor, including the circuit parasitic amaterial effects mentioned above.

2. Inductor structures and description of calculation

ucturesip size,

W

Fig. 1. Label of mechanical dimensions of inductor SMD

packages.

techniques

The proposed zig-zag and meander strare realized as SMDs for the typical 0805 ch

cyra-ndchcyticon

ce-asticinofctson

nicusgn:ryanbyedinckofex-llyndhisto

his

are shown in Fig. 1 (for chip size 0805 mecdimensions are D ¼ 1:1mm; E ¼ 0:25mm�

L ¼ 2:01mm� 0:2; W ¼ 1:25mm� 0:20).shows the cross-section of fabricated zig-zmeander inductors embedded in ferrite mThe components were fabricated using the ccoprocessing technology. The conductiveplatinum, Pt ðr ¼ 10:6� 10�8 OmÞ with theelectric resistivity was chosen as the conduform inductors. The width of the condu150 mm and the thickness of the conductive10 mm. The microinductor is embeddedmiddle of a ferrite layer. The ferrite materiaremarks as LP (low-permeability ferrite m

and HP (high-permeability ferrite material),characteristics are available commerciallyNeosid [10], Hereaus, Ferro, etc. LP nickferrite has low loss factors at medium freqand high suppression impedance at high frcies (over 100MHz). HP ferrite matenickel–zinc ferrite, with initial permeabilit(while LP has initial permeability 220).ferrite materials find typical applications isuppression components.

In order to analyze zig-zag and minductors embedded in ferrite material, the elent circuit describing electrical propertiespresented structure is determined, and is din Fig. 3. Resistances Rw and Rf are the wand ferrite resistances, respectively. The eRDCT presents the total DC resistance. Indu

L is the frequency dependent inductance of tcitanurn-eratiited

The permeability of the ferrite material is am0r and

(1)

ortionponentperme-seen inl m0rðf Þfitting

, whichl coresnot beshape

eanderwere

PISTM

basedin this

(induc-zig-zagrefore,small,

correctnce M

to begmentsce L is

(2)

crosslowing

ð3Þ

ductorf) is atation

aments

ARTICLE IN PRESS

Fig. 2. (a) Zig-zag inductor and (b) meander induc

embedded in ferrite material.

RDCT RW Rf L

Cp

Fig. 3. The lumped parameter equivalent circuit of an induc

embedded in ferrite.

G. Stojanovic et al. / Journal of Magnetism and Magnetic Materials 297 (2006) 76–8378

inductor and Cp is the overall parasitic capaincluding the distributed turn-to-turn and tferrite stray capacitance. The useful opfrequency range of the inductor is thus limits self-resonant frequency.

heceto-ngby

complex parameter consisting of a realimaginary part m00r ;

mrðf Þ ¼ m0rðf Þ � jm00r ðf Þ.

The real component represents the reactive pof impedance, and the imaginary comrepresents the losses. Both parts of theability are frequency dependent, as can beRef. [10]. The analytical expressions for reaand imaginary part m00r ðf Þ are obtained usingtechniques according to measurement (dataare derived from measurements on toroidaand the values obtained in Ref. [10], candirectly transferred to products of anotherand size). Simulations of zig-zag and minductors embedded in ferrite materialsperformed using our software tool—S(Simulator for Planar Inductive Structures)on the calculation method described brieflysubsection.

2.1. Inductance calculation

The calculation of electrical parameterstance, resistance, impedance, Q-factor) ofor meander inductors is very complex. Thethe inductor is divided into segments havingrectangular cross sections. To obtain thetotal inductance L, the mutual inductabetween all segments of the inductor hascalculated and added to the sum of all seself- inductance LS [11]. The total inductan

L ¼X

LS �X

jM�j þX

Mþ.

For a straight conductor of rectangularsection, self-inductance is given by the folformula:

LSðf Þ ¼m0l

2p

� �m0rðf Þ ln

2l

w þ t

� ���

þ0:25049þðw þ tÞ

3l

�þ

Tðf Þ

4

�,

where w is conductor width, t is conthickness, l is conductor length and T(frequency-dependent factor. The compuconcept considers segments as simple fil

tor

tor

for the calculation of mutual inductance. Depend-ent

curreM�

s. Tated

gmetang

D2Þ�

D=lÞ

nts ae pa. U

ovidarioGMicknay

d mU

GM

t cand t

gmesecoctan

between the two conductors with lengths l and m is

(7)

gmentswhenlatter

s m anden thec). Theby [12]

mÞ arth

ð8Þ

R21,

(9)

��l,�

m,

ð10Þ

R3 ¼

ffiffiffiffiffiffiffiffiffiffifficos �.

ð11Þ

ARTICLE IN PRESS

l

m

d

δ

l

m

d qpR1

R2

R3R4

l

m

µ

νε

(a) (b) (c)

Fig. 4. The possible mutual position segments of zig-zag and meander inductors.

G. Stojanovic et al. / Journal of Magnetism and Magnetic Materials 297 (2006) 76–83 79

ing on the current vectors in segments (filamthe mutual inductance is positive M+ if thevectors are in the same direction or negativethe current vectors are in opposite directionpossible configurations in space are illustrFig. 4.

The mutual inductance of two parallel seof equal length l, forming an orthogonal recis given by

Ml ¼ 2lU ¼ 2l lnfðl=GMDÞ þ ½1þ ðl2=GM

� ½1þ ðGMD2=l2Þ�1=2 þ ðGM

All other configurations of parallel segmebased on this equation. Attention should bto the U factor in the equation abovecalculated using closed-form expressions prin the open literature, and concerns the vcases of the geometric mean distance (between two conductors of width w and tht, separated by d. The concept of GMD mused for parallel segments, which are couplestrongly. Mutual inductance parametercalculated from the equation above, whereis given:

lnGMD ¼ ln d � 112ðd=wÞ2

� �þ 1

60ðd=wÞ4

� ��þ 1

168ðd=wÞ6

� �þ 1

360ðd=wÞ8

� �þ 1

660ðd=wÞ10� �

þ � � ��.

When the segments are parallel, two distincmay appear. The first is shown in Fig. 4(a) amutual inductance is calculated by

2M ¼ ðMlþm�d þ MdÞ � ðMl�d þ Mm�dÞ,

where d is positive for non-overlapping seand negative for overlapping ones. In thecase as shown in Fig. 4(b), the mutual indu

s),ntifhein

ntsle,

1=2g

.

ð4Þ

reidisedusD)essbeostisD

ð5Þ

seshe

(6)

ntsndce

calculated by

2M ¼ ðMmþp þ MmþqÞ � ðMp þ MqÞ.

The mutual inductance of two straight se(filaments) have lengths l and m andproduced to their point of intersection theis distant from their nearer ends by distancen; respectively. The four distances betweends of the filaments are as shown in Fig. 4(formula for the mutual inductance is given

M ¼m0mr

4pcos � ðmþ lÞ arth

m

R1 þ R2þ ðnþ

�

�l

R1 þ R4� m arth

m

R3 þ R4

�n arthl

R2 þ R3

.

In Eq. (8) cos �; m; and n are

cos � ¼a2

2lm; where a2 ¼ R2

4 � R23 þ R2

2 �

m ¼2m2 R2

2 � R23 � l2

�þ a2 R2

4 � R23 � m2

�4l2m2 � a4

n ¼2l2 R2

4 � R23 � m2

�þ a2 R2

2 � R23 � l2

��4l2m2 � a4

and R1 ¼ Rðm; l;m; nÞ; R2 ¼ Rð0; l; m; nÞ;Rð0; 0;m; nÞ; R4 ¼ Rðm; 0;m; nÞ; where

Rðx; y; m; nÞ

¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðmþ yÞ2 þ ðnþ xÞ2 � 2ðmþ yÞðnþ xÞ

q

2.2. Resistance calculation

tal Dferrig.

(1

er (dn t

(1

r lay

s weffeld. Tts isreacurreindigrea

ð1

indient tindinuctos A

en tr rigof wire

iven

(1

nceis t

2.3. Capacitance calculation

ent of

ffiffiffiffiÞÞ

ð16Þ

ments,dth of

and aperme-al partfor annd theula for

(17)

ctures,

(18)

tion ofmean-as well

3. Results and discussion

of thegilentup to

for zig-ferrite

ARTICLE IN PRESS

G. Stojanovic et al. / Journal of Magnetism and Magnetic Materials 297 (2006) 76–8380

The total resistance R is the sum of toresistance RDCT, winding resistance Rw andresistance Rf (all parameters are shown in FTherefore, R can be expressed as:

R ¼ RDCT þ Rw þ Rf .

The total DC resistance is several times largto the resistance of the contacts) tharesistance calculated by

RDC ¼ rl

wt,

where r is the resistivity of the Pt conductoof thickness t, width w and length l.

The resistance of an inductor increasefrequency because of skin and proximitydue to the time-varying electromagnetic fiefinal result of these two combined effecreduction in the effective cross-sectional athe conductive material available for theflow. Therefore, the AC resistance (or wresistance) at high frequencies becomesthan the DC resistance [1]:

Rw ¼ RDCAe2A � e�2A þ 2 sinð2AÞ

e2A þ e�2A � 2 cosð2AÞ

�

þ2N2

i � 1

3

eA � e�A � 2 sinðAÞ

eA þ e�A þ 2 cosðAÞ

,

where A is a factor which depends on wgeometry. The first and second terms represskin effect and proximity effect in the wrespectively. For a strip wire, having condwith dimensions w and t, A becomeðw=dÞ

ffiffiffiffiffiffiffit=p

p; where p is the distance betwe

centers of two adjacent conductors (p � t foconductor segment) and d is the skin depthexpressed as d ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffir=pm0mrwf

p:

The lumped parameter Rf from Fig. 3 is g

Rf ¼ 2pfL0m00r ,

where f is frequency, L0 is the inductainductor in vacuum environment and m00rimaginary part of complex permeability.

Cite3).

2)

uehe

3)

er

ithctsheaofntngter

4Þ

ngheg,rs¼

heht

Expression for parasitic capacitance (elemequivalent model in Fig. 3) is

Cp ¼ ltot �0�r2p

lnð1þ 2h=t þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2h=tð2h=t þ 2

p"

þ�0�rw � t=2

h

;

where ltot is the total length of conductor segt the thickness of conductor, w the wiconductor, h ¼ 0:5� (width of ferrite layer).

2.4. Impedance calculation

As impedance consists of a reactiveresistive part, in order to represent this,ability should have two parts, too. The recorresponds to the reactance, positiveinductance, negative for a capacitance, aimaginary part to the losses. Thus, the formimpedance can be given as

jZj ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR2 þ ð2pf m0L0Þ

2

q.

2.5. Quality factor calculation

For an equivalent circuit of proposed struas in Fig. 3, the quality factor is

Q ¼ImðZÞ

ReðZÞ¼

oL

Rð1� o2LCpÞ � oRCp.

The proposed model allows accurate predicall the parameters affecting the zig-zag andder inductors embedded in ferrite materials,as their control during the design process.

by

5)

ofhe

The measurement and characterizationcomponents have been performed using an A4287A RF LCR meter for frequencies3GHz.

Electrical characterization data obtainedzag and meander inductors embedded in LP

material are shown in Figs. 5 and 6. For LP ferritefor a

g andmateri-, basedrevious

ed forin HPd 8.in thiss exist-due toThere-ed in

irtuallyents in

ARTICLE IN PRESS

1000000 1E7 1E8 1E9

10

100

LP meander

zig-zag

calculated measured

Impe

danc

e [O

hms]

Frequency [Hz]

1.0

1.5

2.0

2.5

meander

zig-zag

LP calculated measured

Q-f

acto

r

(a)

G. Stojanovic et al. / Journal of Magnetism and Magnetic Materials 297 (2006) 76–83 81

material, we are given measured data onlyzig-zag inductor. Simulation of the zig-zameander inductor embedded in soft ferriteal was done using our software tool SPISTM

on the calculation method described in a psection.

The measured and calculated data obtainzig-zag and meander inductors embeddedsoft ferrite material are shown in Figs. 7 an

The planar microinductors employedpaper generate well-localized magnetic fielding only in the vicinity of the inductor planesome kind of periodicity in the inductor.fore, the electromagnetic field is confinsandwich structure, hence resulting in vno EMI to other low-energy level componthe electronic systems.

The knowledge about the current distribution inl casesnce ofis thatre theyx. Toagneticfluenceductor

inantlyity. Atindingmetersially atferrite

eandershows

1000000 1E7 1E8 1E9

10

100

meander

zig-zag

LP calculated measured

Res

ista

nce

[Ohm

]

Frequency [Hz]

1000000 1E7 1E8 1E9

0

50

100

150

200

250 meander

zig-zag

LP calculated measured

Indu

ctan

ce [n

H]

Frequency [Hz]

(a)

(b)

Fig. 5. For LP ferrite material (a) measured and calcula

total resistance, (b) measured and calculated total inductan

1000000 1E7 1E8 1E90.0

0.5

Frequency [Hz](b)

Fig. 6. For LP ferrite material (a) measured and calculated

impedance, (b) measured and calculated quality factor.

a single rectangular conductor in elementaforms a base for understanding AC resistathe conductor. The nature of the currentsthey flow to the part of the conductor whesee less impedance or inter-linkage fluimmerse the conductor deep into the mmaterial is a good method to reduce the inof the frequency magnetic field on the conlosses.

Magnetic losses in the ferrite are predomdue to an imaginary part of the permeabilRF, these ferrite losses dominate the wlosses. It is emphasized that all circuit paraare in general frequency-dependent, especRF, because the constitutive parameters ofmaterial are frequency-dependent.

At RF frequencies, the zig-zag and minductor embedded in the ferrite materials

ted

ce.

high impedance, which suppresses unwanted inter-of tes thturencea coashanictanif

ts abori

a fcanhasm

. If te turondu

tors is equal to the conductor’s width w), this willd im-

raughtontam-

withPt intof bothductorble touccess-easure-es canthoughbeddedculatedts. Thek veryor foraterial.

ARTICLE IN PRESS

1000000 1E7 1E8 1E9

10

100

meander zig-zag

HP calculated measured measured

Res

ista

nce

[Ohm

s]

Frequency [Hz]

1000000 1E7 1E8 1E9

0

200

400

600

800

1000

zig-zag

meander

HP calculated measured measured

Indu

ctan

ce [n

H]

Frequency [Hz]

(a)

(b)

Fig. 7. For HP ferrite material (a) measured and calculated

total resistance, (b) measured and calculated total inductance.

1000000 1E7 1E8 1E9

10

100

zig-zag

meanderHP calculated

measured measured

Impe

danc

e [O

hms]

Frequency [Hz]

1000000 1E7 1E8 1E90.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4HP meander calc.

meander meas. zig-zag calc. zig-zag meas.

Q-f

acto

r

Frequency [Hz]

(a)

(b)

Fig. 8. For HP ferrite material (a) measured and calculated

impedance, (b) measured and calculated quality factor.

G. Stojanovic et al. / Journal of Magnetism and Magnetic Materials 297 (2006) 76–8382

ference. For HP material, the maximalimpedance value is on some lower frequenciLP ferrite material, thus lending the strucusage in this frequency range. The inductathe meander inductor is greater becauseductor line for the zig-zag inductor hmaximal possible length (within the mecdimensions of an SMD chip), and the induof the zig-zag inductor can be increased,increase the length of conductor segmendecrease the angle between two neighconductors.

To achieve even higher inductance,changes of the meander inductor structuremade: the length of the conductor segmentbe maximal possible and/or the structurehave the maximal possible number of turnsmeander inductor is designed to have mor(if the distance between two neighboring c

heantoforn-nocalcewendng

ewbetousthensc-

result in the greater total inductance (anpedance, also) of novel structures.

Cofiring of ceramics is not easy and is fwith difficulty [13]. Material diffusion or cination is a key concern when dealingelectrical properties [14]. The diffusion offerrite materials can result in deterioration oferrite material characteristics and conmaterial characteristics. It is not possiinclude this phenomenon in the model sfully. Thus, the small deviation of the mment results compared to the calculated onbe a consequence of the above reasons. Althe analytical modeling of the inductors emin ferrite material is quite complex, our calresponses are very close to measured resulonly measured response that does not tracwell with calculated one is the Q-factinductors embedded in HP soft ferrite m

This slight discrepancy can be explained by meansqu

d thviatito tlexi

f a Han

Acknowledgement

Irelandld likeed forduring

References

ARTICLE IN PRESS

G. Stojanovic et al. / Journal of Magnetism and Magnetic Materials 297 (2006) 76–83 83

of formula (18). The quality factor iscomplex (it depends on R, L and Cp andepend on permeability). Thus, the small deof the measurement results comparedcalculated ones is a consequence of its compand this deviation is greater in the case oferrite because its permeability is higher thferrite.

4. Conclusion

abrir eferr

he chges.le tentslectnducstepof teandsimwsperftrolulateimpn alts oy goquen

U. Re-

9) 4185.

Trans.

U. Re-

4) 1839.

, D.C.C.

nference,

agn. 38

. Magn.

. Mater.

. Noyel,

) 121.

3 (2001)

om/pdfs/

. PHP-10

formulas

nc., 1946

. Ceram.

janovic,

lectron.

In this paper, the design, modeling and ftion of the zig-zag and meander inductobedded in the LP and HP nickel–zincmaterials have been discussed. The size of tconsidered structures is 0805 in SMD packacan be seen, the presented results enabapplication of the proposed new componEMI/EMC (electromagnetic interference/emagnetic compatibility) suppression of iand conductive EM noise in the secondaryEMI suppression. An accurate descriptionfrequency response of the zig-zag and minductor is achieved by means of aequivalent circuit model. The model alloparameters affecting the inductor electricalmance to be accurately predicted and conduring the design process. Theoretical (calcplots of inductors resistance, inductance,dance and quality factor have been drawcompared with measured data. The resutained by the proposed method are in veragreement with measured data over the frerange from 1MHz to 3GHz.

iteeyonhety,P

LP

This work was supported by LittelfuseLimited, Dundalk, Ireland. The authors wouto acknowledge Littelfuse Ireland Limitcontinuous support and understandingthe project.

ca-m-iteipAshein

ro-edofheerpleallor-ledd)e-ndb-odcy

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