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Physica B 405 (2010) 1018–1021

Contents lists available at ScienceDirect

Physica B

0921-45

doi:10.1

� Corr

E-m

(Z. Lan)

journal homepage: www.elsevier.com/locate/physb

Temperature dependence of core losses at high frequency for MnZn ferrites

Ke Sun �, Zhongwen Lan �, Zhong Yu, Lezhong Li, Xiaona Jiang, Haining Ji

State Key Laboratory of Electronic Thin Films and Integrated Devices, University of Electronic Science and Technology of China, Chengdu 610054, PR China

a r t i c l e i n f o

Article history:

Received 25 June 2009

Received in revised form

25 October 2009

Accepted 27 October 2009

Keywords:

MnZn ferrite

Core losses

High frequency

Temperature dependence

Imaginary permeability

Residual loss

26/$ - see front matter & 2009 Elsevier B.V. A

016/j.physb.2009.10.047

esponding authors. Tel./fax: +86 28 8320167

ail addresses: sunkoa811028@yahoo.com.cn (

.

a b s t r a c t

The core losses (PL) of MnZn ferrites prepared by a solid-state reaction method were investigated as a

function of magnetic induction and frequency (PL ¼ kBxmf y). The exponent (x) of magnetic induction was

2.58 at 1000 kHz and 2.01 at 3000 kHz, and the exponent (y) of frequency was 2.22 at 30 mT and 2.73 at

10 mT. The core losses (PL) were divided into hysteresis loss (Ph), eddy current loss (Pe) and residual loss

(Pr). Each loss contribution was discussed to be dependent on temperature. Ph decreased monotonically

with increasing temperature. Pe firstly decreased with increasing temperature, minimized at 100 1C, and

then increased. As the temperature increased, the imaginary permeability at MHz was significantly

enhanced and the resonance frequency (fr) decreased. The increase in Pr with increasing temperature

should be attributed to the decreasing fr which is due to the resonance in the domain wall caused by

high speed rotation of spin inside the domain.

& 2009 Elsevier B.V. All rights reserved.

1. Introduction

As the electronic systems require a more integrated and lighterswitching mode power supply (SMPS) AC–DC and DC–DCconverter, the research on the low-loss ferrite at high frequencyover a wide temperature range is highly demanded.

MnZn power ferrite mainly acts as transformer core operated inthe state of high power, which must be with high saturationinduction (Bs), high permeability (mi) and low core losses (PL). It iswell-acknowledged that the core losses of MnZn ferrite aredetermined by its compositions, the kinds and weights of additivessuch as CaO, SiO2, TiO2, SnO2, Ta2O5 [1–6], the characteristics ofpowder and sintering conditions [7–9]. Fujita and Gotoh [10]detailedly investigated the temperature dependence of core lossesin Co-substituted MnZn ferrites, while the frequency was 100 kHz,staying at low or intermediate frequency range. However, thetemperature characteristic of core losses at high frequency (MHz)is of great importance for the stable operation of downsizingelectronic devices. This paper addresses the temperature depen-dence of core losses at high frequency for low-loss MnZn ferrite. Itwill demonstrate that the core losses (PL) are divided intohysteresis loss (Ph), eddy current loss (Pe) and residual loss (Pr).Each loss contribution is discussed to be dependent on tempera-ture. Especially, the increase in residual loss (Pr) with increasing

ll rights reserved.

3.

K. Sun), zwlan@uestc.edu.cn

temperature is attributed to the decreasing resonance frequencywhich is due to the resonance in the domain wall caused by highspeed rotation of spin inside the domain.

2. Experimental procedures

2.1. Sample preparation

MnZn ferrite, as a nominal composition of Mn0.78Zn0.13Fe2.09O4.00,was prepared by a solid-state reaction method [11]. The analyticalgrade raw materials of Fe2O3, MnCO3 and ZnO powders wereweighed in stoichiometric proportion and mixed in planetary millfor 4 h. The ball-milling media were steel balls with super-hardnessand the rotation velocity was 196 rpm. The slurries, after dried, werehomogenized and calcined at 950 1C in air for 1.5 h. Then, theresulting powders, added with 0.30 wt% of CaO, 0.20 wt% of TiO2,0.10 wt% of SnO2 and 0.05 wt% of Nb2O5, were milled in deionizedwater for 10 h. The ball-milling media were zirconia balls withsuper-hardness and the rotation velocity was 196 rpm. After furtherdried, the powder was granulated with 8% poly-vinyl alcohol (PVA).Then it was pressed into toroidal shapes with the dimensions ofouter diameter in 16 mm, inner diameter in 10 mm and height in7 mm. Finally, the samples were sintered in a computer-controlledfurnace at 1250 1C for 4 h and cooled at equilibrium conditions in aN2/O2 atmosphere driven by Morineau and Paulus [12] equation forequilibrium oxygen partial pressure.

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Table 1Electromagnetic properties and average grain size (D) of MnZn ferrite.

T (1C) mi PL (kW/m3) r (Om) Bs (mT) D (mm)

f=1000 kHz f=3000 kHz

Bm=30 mT Bm=10 mT

25 917 143 226 10.0 428 3.8

60 1106 130 234 7.0 396

80 1164 123 245 4.4 384

100 1184 130 256 3.1 362

120 1213 175 300 1.8 345

Fig. 1. Core losses for various frequencies as a function of magnetic induction.

K. Sun et al. / Physica B 405 (2010) 1018–1021 1019

2.2. Properties measurements

The initial permeability (mi) was measured by a LCR meter(TH2828) at 10 kHz and 10 mV. Core losses (PL) and saturationinduction (Bs) of the sintered samples were measured by anIwatsu BH Analyzer (SY-8232). After samples were coated withindium–gallium electrodes on both surfaces, the resistivity ofsamples were measured from 25 to 120 1C by using the LCR meter(YY-2812). From enlarged SEM micrographs of the samples,average grain sizes (D) of 5 micrographs for each sample wereestimated by the intercept method. All the results listed in Table 1are average values carried out from ten independent samples.

Fig. 2. Core losses for various magnetic inductions as a function of frequency. The

inset shows the local enhancement of the same data at 30 mT.

3. Results and discussion

3.1. Electromagnetic properties

Electromagnetic properties of MnZn ferrite measured atdifferent temperatures are listed in Table 1. It demonstrates thatMnZn ferrite prepared by the above experimental proceduresexhibits high permeability (mi), high saturation induction (Bs) andlow core losses (PL) at high frequencies over a wide temperaturerange from 25 to 120 1C. The average grain size (D) of the sampleis 3.8mm, which, according to Zaag’s report [13], is at thetransition from single to multiple domain behavior.

3.2. Temperature dependence of core losses

The core losses (PL) can be expressed as a function of magneticinduction (Bm) and frequency (f) [14,15]:

PL ¼ kBxmf y ð1Þ

Where x is the Steinmetz exponent between 2 and 3, y thefrequency exponent and k a constant. Theoretically, PL iscomposed of hysteresis loss (Ph), eddy current loss (Pe) andresidual loss (Pr) [16,17]. Thus, it can be further explained by thefollowing equation [17]:

PL ¼ PhþPeþPr ¼ KHB3mf þKEB2

mf 2=rþPr ð2Þ

Where KH and KE are constants, Bm the magnetic induction in mT, f

the frequency in kHz and r the electrical resistivity in Om.Fig. 1 illustrates the core losses (PL) of MnZn ferrite as a

function of magnetic induction (Bm) at two frequencies of 1000and 3000 kHz at 100 1C. The PL increases with rising Bm, asdescribed in Eq. (1). The Steinmetz exponent (x) is related to themeasuring frequency. It is 2.58 at 1000 kHz, approaching toJeong’s report (x=2.48) [15]; but 2.01 at 3000 kHz, approximate to2, the exponent of magnetic induction (Bm) in the second term ofEq. (2). Thus, Ph can be ignored at 3000 kHz. The followingdiscussion will prove it.

Fig. 2 shows the core losses (PL) plotted as a function offrequency at two magnetic inductions of 10 and 30 mT at 100 1C.

The inset shows the local enhancement of the same data at 30 mT.The PL increases linearly with a lower slope in low-frequencyrange and then deviates from the linearity above 500 kHz at30 mT. Thus, PL is proportional to the frequency, indicating the Ph

is the primary contributor to the PL. The deviation from thelinearity indicates that the contribution of Pe and Pr becomesdominant when the frequency is higher than 500 kHz according toEq. (2). The exponent of frequency (y) is about 2.22 at 30 mT,which is different from Jeong’s report (y=1.18, at Bm=25 mT) [15].Furthermore, y increases with decreasing induction and is 2.73 at10 mT, indicating that Pe and Pr predominate. In order to assessthis postulation, the division of PL into Ph, Pe and Pr is undertakenon the low-loss MnZn ferrite.

Fig. 3 demonstrates a method to separate each losscontribution, where PL/f of MnZn ferrite at 30 mT at 100 1C isplotted as a function of frequency. PL/f, deduced from the Eq. (2),can be written as the following equation [17]:

PL=f ¼ Ph=f þPe=f þPr=f ¼ KHB3mþKEB2

mf=rþPr=f ð3Þ

According to Eqs. (2) and (3), Ph and Pe are given by the zerofrequency intercept and the linear part, respectively. Thedeviation from linearity is due to residual loss. As shown in Fig.3, below 400 kHz, the losses are mainly composed of Ph and Pe.While beyond 400 kHz, Pr appears.

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Fig. 3. Separation of PL into Ph, Pe, and Pr of MnZn ferrite.

Fig. 4. Ph, Pe and Pr as a function of temperature.

K. Sun et al. / Physica B 405 (2010) 1018–10211020

Fig. 4 shows the temperature dependence of the core losses(PL) and each loss contribution. It is observed from Fig. 4(a) that Ph

decreases with increasing temperature, while Pr changescontrarily. Pe firstly decreases with increasing temperature,minimizes at 100 1C, and then increases.

The hysteresis loss (Ph) is inversely proportional to the cubic ofinitial permeability ðPhp1=m3

i Þ [18]. As shown in Table 1, mi

increases monotonously with rising temperature. Thus, thedecrease of Ph with increasing temperature at 1000 kHz and30 mT is attributed to increase in mi. It can be found from Fig. 4(b)that the temperature dependence of the core losses (PL) and eachloss contribution shows the similar regulation as demonstrated inFig. 4(a). At 3000 kHz and 10 mT, Pr absolutely predominates, andboth Ph and Pe are small enough to be ignored. This phenomenonmatches very well with the exponent (y=2.73) of frequencyshown in Fig. 2.

For Pe, the classical expression is that Pe,cl is inverselyproportional to electrical resistivity (r) and proportional to thesquare of average grain size(D2), Pe;clpD2=r [19]. As shown inTable 1, r decreases with increasing temperature [11]. But thevariation of Pe as a function of temperature is not consistent withthe classical expression ðPe;clpD2=rÞ. According to Fiorillo’s report[20], besides the classical expression, there is an excess lossðPe;excpbecPn

hf Þ which is proportional to Ph. Where bec is thedamping parameters. Thus, here Pe as a function of temperatureshould be the contribution of two parts, Pe,cl and Pe,exc.

Referring to Pr, it is important to know the rotation frequencyof the spin inside the domain due to the consideration of onedomain wall inside a crystal grain [13,21]. The motion velocity ofthe domain wall mainly depends on the driving frequency (f),magnetic induction (Bm) and saturation magnetic induction (Bs).As the domain-wall motion is assumed to be harmonized with thedriving frequency (f), rotation frequency of the spin inside thedomain wall (fs) is expressed in the following equation [21]:

fs ¼ LBmf=ðBs=dÞ ð4Þ

where Bs is the saturation magnetic induction, f the drivingfrequency, d the domain-wall thickness and L the domain size.The Pr can be known clearly followed Eq. (4). The parameters of L,d, Bm and f are constants in a certain condition (eg. f=1000 kHzand Bm=30 mT). But the Bs is a function of temperature as thefollowing equation [22]:

Bspð1� T=TcÞr

ð5Þ

where r is a constant ranging from 0.5 to 2.0, Tc the Curietemperature. The variation of Bs as a function of temperature isshown in Table 1, which indicates that Bs decreases withincreasing temperature. Thus, fs increases with rising tempera-ture. In order to assess this postulation in fs the imaginarypermeability as a function of temperature is undertaken on thelow-loss MnZn ferrite.

Fig. 5 shows the imaginary permeability of MnZn ferriteoperated at different temperatures. As the temperature increases,the imaginary permeability of MnZn ferrite at MHz is significantlyenhanced and the resonance frequency (fr) decreases. Thisphenomenon matches very well with the theoretical analysis infs. As the temperature increases, fs enhances, resulting in areduction of fr. It is well-acknowledged that the reduction of fr canproduce an increasing Pr. Therefore, the increase in Pr withincreasing temperature should be attributed to the decreasing fr.In other words, the raise should be due to the resonance in thedomain wall, which is caused by high speed rotation of spin insidethe domain.

Table 2 shows the ratio of each loss contribution (Ph, Pe and Pr)to the losses (PL) as a function of temperature. At 1000 kHz and30 mT, Ph/PL decreases with increasing temperature, while Pr/PL

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Fig. 5. Imaginary permeability of MnZn ferrite at different temperatures.

Table 2The ratio of each loss contribution to the core losses as a function of temperature.

T (1C) Ratio (%)

f=1000 kHz, Bm=30 mT f=3000 kHz, Bm=10 mT

Ph/PL Pe/PL Pr/PL Ph/PL Pe/PL Pr/PL

25 36 46 18 4 6 90

60 25 46 29 3 6 91

80 20 37 43 3 5 92

100 18 36 46 2 4 94

120 10 38 52 1 5 94

K. Sun et al. / Physica B 405 (2010) 1018–1021 1021

changes contrarily and Pe/PL shows a minimum (36%) at 100 1C.However, at 3000 kHz and 10 mT, Pr/PL is more than 90% over awide temperature range from 25 to 120 1C. Pr absolutelypredominates.

4. Conclusions

The core losses (PL) of a low-loss MnZn ferrite wereinvestigated in the frequency range from 1000 to 3000 kHz at

the temperature from 25 to 120 1C, and the following results havebeen obtained:

(1).

The exponent (x) of magnetic induction in equation, PL ¼ kBxmf y

is 2.58 at 1000 kHz and 2.01 at 3000 kHz, while the exponent(y) of frequency is 2.22 at 30 mT and 2.73 at 10 mT.

(2).

Hysteresis loss (Ph) decreases monotonically with risingtemperature. Eddy current loss (Pe) firstly decreases withincreasing temperature, minimizes at 100 1C, and thenincreases.

(3).

As the temperature increases, the imaginary permeability atMHz is significantly enhanced and the resonance frequency(fr) decreases. The increase in residual loss (Pr) withincreasing temperature should be attributed to the decreas-ing fr which is due to the resonance in the domain wallcaused by high speed rotation of spin inside the domain.

Acknowledgment

The authors are grateful for the financial support from thedepartment of defense of China (no. 41312040509).

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