246 IEEE TRANSACTIONS ON MAGNETICS, VOL. 44, NO. 2, FEBRUARY 2008
The Effect of DC Bias Conditions on Ferrite Core LossesC. A. Baguley1, B. Carsten2, and U. K. Madawala1
Department of Electrical and Computer Engineering, The University of Auckland, Auckland 1142, New ZealandPower Conversion Consulting & Research, Corvallis, OR 97330 USA
In switched-mode power supplies—the predominant type of power converter in contemporary electronic equipment—ferrite mag-netic components under dc bias conditions are typically large and have relatively high losses. The nature of these losses is not widelyunderstood, and research in this area has been hampered by the difficulty of obtaining accurate core loss measurements. This paperreviews previous studies on the nature of core losses under dc bias, and presents new results, measured by a technique that has notpreviously been utilized for the measurement of core losses under dc bias conditions. The results show that ferrite core losses increasesignificantly with an increasing dc bias, and highlight the need for further research over a wider range of conditions to fully characterizethe phenomenon.
Index Terms—Core losses, ferrite, switched-mode power supply.
I. INTRODUCTION
BECAUSE of their low cost, small size, and high efficiency,switched-mode power supplies (SMPS) are currently the
predominant form through which power conversion is imple-mented in electronic equipment. The extremely large quantitiesin which SMPS are produced have generated economic pres-sures to minimize the size of SMPS circuitry, and regulatorypressures to improve power supply efficiencies [1]–[5]. A crit-ical factor that affects both the size and efficiency of SMPS arethe core losses of its magnetic components which operate underdc bias conditions. To minimize magnetic component designtime, it is necessary to accurately predict these losses. How-ever, ferrite manufacturers typically do not publish informationon core losses under dc bias conditions, and therefore resort tocore loss measurement techniques.
A number of techniques exist by which core losses can bemeasured. These include: calorimetric techniques, field-basedtechniques which rely on the measurement of the Poyntingvector, and circuit-based techniques which rely on the accu-rate sensing of the winding electromotive force (EMF) andexcitation current waveforms, and the associated phase angle.However, all of these techniques are prone to measurementerrors which, for the field and circuit-based techniques inparticular, are difficult to minimize [6], [7]. The existence ofcore loss measurement errors is especially significant in thecase of low permeability ferrite cores for which losses are smallin relation to the excitation VA that is required. Therefore, itis necessary to closely monitor and account for any sources oferror in a measurement setup. As well as properly accountingfor measurement errors, it is also necessary for core lossmeasurements under dc bias conditions to be measured as afunction of the dc flux density, , for the measurements tobe of practical use to magnetic component designers. This isbecause is directly related to the energy handling capabilityof magnetic components under dc bias, and is therefore a keydesign parameter [8].
Digital Object Identifier 10.1109/TMAG.2007.911594
This paper explains why the measurement of core lossesunder dc bias conditions is difficult, and reviews variousmeasurement techniques that are available. Also reviewed arepreviously reported core loss measurements under dc biasconditions and issues that have not been addressed are raised,highlighting the need and importance for further research.Finally, new results are presented, using a technique that hasnot previously been used to measure core losses under dc biasconditions, which show that ferrite core losses for MMG typeF49 material increase significantly with an increasing dc bias.
II. AC CORE LOSS MEASUREMENT
Average core losses can be measured by exciting a winding onthe ferrite core under test (CUT) then finding the product of thewinding EMF and the excitation current, before integrating theresult over one cycle. This procedure however is prone to largecore loss measurement errors if the CUT is a low permeability,low loss type, and the phase shift between the winding EMFand excitation current waveforms is measured incorrectly. It hasbeen shown that the relationship between the core loss measure-ment error and the phase shift measurement error is given by [9]
(1)
where
percentage error in the measurement of core loss;
phase shift between the winding EMF and excitationcurrent waveforms (degrees);
error in the measurement of (degrees).
From (1), it is apparent that the closer the angle is to 90then the greater is for a given value of . To illustrate theimpact of phase shift measurement errors, an example is givenbased on the equivalent circuit of the CUT shown in Fig. 1, andthe results given in Table I.
Based on the manufacturer specified properties given inAppendix A, Table I lists the calculated core loss resistances,
, and calculated magnetizing reactance, , at 100 C, of
BAGULEY et al.: THE EFFECT OF DC BIAS CONDITIONS ON FERRITE CORE LOSSES 247
Fig. 1. Equivalent circuit of the CUT.
TABLE IPROPERTIES AND CALCULATED PARAMETERS OF E20/10/5, 3C90, AND 3F3
UNGAPPED CORES
E20/10/5 cores in Ferroxcube 3C90, and 3F3 materials [10],which are wound with 10 turns and excited sinusoidally. Alsolisted in Table I is the power factor, pf, which is derived fromFig. 1 and calculated using (2). For the derivation of theseresults the calculated winding resistance, , is 0.0189(using 180 0.05 mm Pack Feindrahte litz wire [11]), and theleakage reactance, , is assumed to be 1% of
(2)
It is apparent from Table I that the calculated power factor isvery low, and therefore that is close to 90 . Based on thesecalculations, the error in the measurement of , which results ina 5% error in the measurement of core loss can be determinedfrom (1). For 3C90 material this error is 0.21 at 25 kHz, and0.24 at 100 kHz, and for 3F3 material it is 0.36 at 400 kHz.These errors correspond to time delays of 23.4 ns at 25 kHz,6.59 ns at 100 kHz, and 2.53 ns at 400 kHz. It is apparent thatthese very small time delays require the voltage and currentsensing channels to be phase/time matched extremely preciselyin order to obtain accurate core loss measurements.
From (1), it is intuitively obvious that the sensitivity ofto can be reduced by decreasing . This can be achieved byminimizing gaps within the magnetic path of the CUT, as thisdecreases the excitation VA required to generate a given level ofcore loss [9]. However, the reductions in that can be achievedin this way are limited and, significantly, the method also doesnot allow for the core losses of gapped cores to be measured. Toillustrate the impact of core gaps on core loss measurement er-rors, an example is given based on the results shown in Table II.Table II shows the calculated , and power factor of thesame core types as used in Table I, with the exception that thecores are gapped so that the Al value is reduced to 100 nH. Withthe presence of a core gap, the leakage reactance is assumed tobe 2% of .
It is apparent that the power factor is dramatically reducedby the introduction of a core gap. Consequently, the error in
TABLE IIPROPERTIES AND CALCULATED PARAMETERS OF E20/10/5, 3C90,
AND 3F3 GAPPED CORES
the phase shift/time delay measurement which results in a 5%error in the core loss measurement for 3C90 material is only0.0476 /5.3 ns at 25 kHz, and 0.0241 /669ps at 100 kHz, and for3F3 material is 0.0278 /193 ps at 400 kHz. In practical terms,the phase shift/time delay matching of the voltage and currentsensing channels to a degree equal to or better than that givenby the above figures is not a tractable engineering task.
Core losses can also be measured through the determinationof the B/H loop of the CUT [6], or through the use of a networkanalyzer [9]. However, because both these techniques rely onthe accurate sensing of the winding EMF, the excitation current,and the phase shift associated with these waveforms, they sufferthe same disadvantage as the preceding technique.
A technique that has been proposed to decrease the sensitivityof to requires the placement of capacitors across the excita-tion winding of the CUT in order to reduce the value of [12].In this case, however, the magnitude of the potential error iscontrolled rather than eliminated. A similar technique involvessizing a capacitor to resonate with the excited winding [6]. Inthis case the inductance of the core is tuned out by the capac-itor, leaving an equivalent loss resistance. Power loss can then bemeasured as the product of the input current and voltage appliedto the resonant circuit. In addition to reducing and thereforesensitivity of to , this also has the advantage of lowering theVA required to excite the CUT. However, this technique resultsin distorted measurements at high levels of excitation for whichthe CUT traverses a nonlinear region of the B/H loop. Other dis-advantages include: the requirement for a large number of lowloss capacitors in order to test over a wide frequency range, theneed for large capacitors for tests at low frequencies, and the in-clusion of winding and capacitor losses in the total loss figurethat is measured. Furthermore, the technique is laborious as itrequires the resonating capacitor to be changed for every newtest frequency and, to a lesser extent, excitation level as the av-erage permeability changes.
Core losses can also be measured using calorimetric tech-niques [13]–[15]. For techniques of this type the CUT is placedin a well-insulated measurement chamber, usually containinga dielectric fluid which is stirred to enhance thermal unifor-mity. Magnetic losses are then determined by exciting the core,then measuring the temperature rise of the thermal mass withinthe chamber. This technique, which does not require the dif-ficult measurement of , is suitable for the determination ofcore losses with any shape of excitation waveform, and doesnot require the use of instrumentation that has high accuracyat high frequencies. However, a significant disadvantage is thelong duration of time that is required to allow the CUT to reacha steady-state operating temperature. Other disadvantages are:
248 IEEE TRANSACTIONS ON MAGNETICS, VOL. 44, NO. 2, FEBRUARY 2008
the inclusion of winding losses in the measurement, the needto limit the temperature rise in order to avoid changes in tem-perature causing changes in core losses, and the high degree ofexperimental virtuosity that is required.
A core loss measurement technique which overcomes manyof the disadvantages given above is reported in [6]. In thisapproach, the switches of an extremely efficient zero-voltageswitching (ZVS) half-bridge are used to circulate excitationenergy through the CUT. A simplified schematic of the circuitis shown in Fig. 2. The dc input power to the circuit is measuredto directly determine the core loss, thereby eliminating thedependency of core loss measurement errors on the accuratedetermination of the phase shift between an ac voltage andcurrent. The dc input power very closely approximates the corelosses of the circuit because circuit losses are minimized. Coremagnetization energy is used to commutate current from thefield-effect transistor (FET) just turning off to the FET to beturned on, charging junction and parasitic capacitances nondis-sipatively and eliminating switching loss. FETs are turned offhard and fast enough to hold all gate voltages below the con-duction threshold, diverting all drain current into junction andparasitic capacitances, and thus avoiding turn-off loss. Turn-onlosses are eliminated by turning the next FET on 10–20 ns aftera monitor has detected that its drain voltage, , has fallenbelow 1 V. Oversized FETs are used to minimize conductionlosses, and the FET drive and the control power are suppliedfrom a separate source and do not affect the loss measurement.Furthermore, the technique allows core loss measurement datato be quickly and easily obtained. The disadvantages of thetechnique due to practical switching considerations includeupper limits on the input voltage, current, and the switchingfrequency of the test circuit to 90 V, 8 A, and 2 MHz, respec-tively. Practical considerations also require the inductance ofthe CUT to be within maximum and minimum values accordingto the input voltage and frequency. The minimum inductance isdetermined by the peak current ratings of the FETs, while themaximum is limited by the zero voltage switching requirementsof the circuit. Additional disadvantages include the fact thatonly square wave voltage waveforms can be used to excite theCUT, and the need to separate the residual circuit losses fromthe core losses. The residual circuit losses are due primarily toFET conduction losses, and secondarily to the CUT windingresistance, and capacitor ESR. These losses are calculatedthrough the sensing of the excitation current in the circuit, andsubtracted from the measured dc power to determine the coreloss.
The flux density of the CUT could be simply calculated usingthe dc input voltage, excitation frequency, excitation windingturns, and core area. However, at high frequencies both leadinductance, and increasingly finite voltage rise and fall timesbegin to result in significant calculation errors. To overcome thisissue the excitation voltage is sensed directly through a separate“excitation sense” winding on the CUT, and the average voltageis also used to maintain the correct flux density. An appropri-ately terminated 50 coax cable is used to couple the excitationsense signal to the control circuitry to prevent unwanted trans-mission line reflections.
Fig. 2. Simplified schematic of the ZVS half bridge circuit.
III. CORE LOSS MEASUREMENT UNDER DC BIAS CONDITIONS
The core loss measurement techniques described in Section IIcan be adapted to measure ac core losses in the presence of a dcbias through the placement of a dc current carrying winding onthe CUT. This allows core losses as a function of the dc mag-netic field, , to be easily determined. However, as noted inSection I, core loss measurements should be made as a functionof . Unfortunately, the determination of is not a trivialmatter if the CUT is ungapped. This is because depends notonly on , but also core permeability, , and remanent fluxdensity, , which can both vary considerably between cores ofthe same geometry and material, as well as with temperature.These variations are significantly reduced by the placement ofan air gap in the flux path of the core, so allowing to bemore accurately calculated. However, as shown in Section II,core gaps significantly affect the accuracy of those measurementtechniques which multiply voltage and current waveforms thatare displaced by close to 90 . The presence of a core gap is alsodisadvantageous to techniques requiring the subtraction of testcircuit losses from the total measured losses to determine thecore loss. This is because core gaps introduce additional lossesinto the test circuit which, in some cases, are difficult to calcu-late, such as the higher dc and ac winding eddy-current lossesdue to the air gap fringing field. Other difficulties introducedby a core gap include: the existence of a fringing field aroundthe gap which causes the actual to be greater than that cal-culated by theory, and the nonuniform distribution of flux in thecore. The latter effect influences the measurement of core lossesin two ways. First, it influences where on the core an ac sensewinding can be placed if a core losses are measured by sensingthe winding EMF; ideally such a winding should be placed ona portion of the core that is distant from the core gap(s) to accu-rately sense the flux in the core. Second, the nonuniform distri-bution of flux means that those parts of the core in which flux hasa greater concentration will experience higher, localized corelosses, therefore distorting the total core loss measurement. Tokeep the distribution of flux in the core as uniform as possible,it is therefore preferable to implement the total core gap usinga number of smaller gaps to minimize fringing effects. By theplacement of ac excitation, and dc bias windings over the coregaps, the fringing field can be minimized further.
Various authors have addressed the issue of core loss mea-surement under dc bias conditions. In [16], ferrite core losses
BAGULEY et al.: THE EFFECT OF DC BIAS CONDITIONS ON FERRITE CORE LOSSES 249
under dc bias conditions are determined using a B/H loop mea-surement technique. The core loss measurements are related to
and , and are used to show that core losses can be mini-mized at a particular value of . However, it is not statedwhether the test cores are gapped nor how is determined,and for the tests under dc bias conditions, no account is given ofthe temperature of the CUT. This is necessary due to the strongdependency of core losses on core temperature.
In [17], the core losses of a ferrite toroid under dc bias condi-tions are measured at 100 C. The core loss measurements arerelated to and , and show that core losses do not de-pend on at low biasing levels, but increase significantly athigh levels for a given level of ac excitation. However, thevalue of that is related to the core losses is calculated usingan equation in which a dependence on temperature does not ap-pear. This is of importance to the accurate determination ofdue to the variation in permeability that occurs with tempera-ture for ferrite cores. In [18], the investigation presented in [17]is extended to determine the core losses under dc bias conditionsat various frequencies. It is stated that the values of used inthe results are calculated through the knowledge of and themeasured magnetization curve. In [19], it is shown that ferro-magnetic (laminated CK27 material) core losses increase with
in a similar way to that of ferrites. However, it is not statedhow is determined, and the dependence of and corelosses on temperature is not addressed. In [17]–[19], a test setupdescribed in the European CECC 25 300 and CECC 25 000 stan-dards is used, which consists of measuring the B/H loop of theCUT by monitoring the winding EMF, and excitation currentsupplied to the core.
In [20], very extensive tests over a large number of frequen-cies are undertaken on toroidal cores placed within a tempera-ture chamber using an impedance analyzer. It is shown that fora given level of , core losses increase with increasing levelsof dc bias. Although core losses are graphed as a function of
and frequency, relationships between and core lossesare not reported. In [20] it is also shown that, at particular ex-citation frequencies, core losses increase dramatically. This isattributed to the phenomenon of domain wall resonance.
In [12], results based on the measurement of winding EMFand excitation current waveforms are presented showing thatcore losses increase with increasing levels of for a givenpeak flux density. Although an error analysis of the measure-ment setup is also undertaken, the relationship between andcore loss is not addressed. Furthermore, although it is stated thatthe core loss tests are done at room temperature, no account ismade for the self heating of the CUT in the core loss results.
In [21], the core losses under dc bias of an inductor, imple-mented using an EFD20 3F3 core with a total air gap of 0.1 mm,are measured with the inductor operating in a buck-boost con-verter circuit. The core losses are determined using a B/H loopmeasurement technique, and are given as a function of the peakoperating flux density of the inductor. It is reported that thephase shift error between the voltage and current sensing chan-nels is less than 5 ns, and therefore that phase shift/time delayerrors may be ignored. Detail on the placement of the ac sense
winding is not given in [21], and therefore the issue of the ac-curate sensing of core flux is not addressed.
In order to obtain core loss results that are representative ofa particular ferrite material, it is desirable for the CUT to havea uniform cross-sectional area so that a constant flux density ismaintained throughout the core. Therefore, although the resultsobtained in [21] characterize the particular losses of an EFD203F3 type of core, they cannot be generalized to characterizethose of 3F3 ferrite material because of the nonuniform crosssection of the EFD20 core. This issue is also of note in [22].
In [22], an ungapped ETD44 core is tested at various dc biaslevels, and at ac excitation frequencies of 20, 100, and 500 kHz.Experimental results are presented showing that core losses in-crease dramatically with increasing dc bias levels at an ac excita-tion frequency of 20 kHz, but that as the excitation frequency isincreased, dc bias conditions impact less significantly on losses.The core loss measurements, made by sensing and multiplyingthe winding EMF and the excitation current together, are not re-lated to . Furthermore, the temperature at which the tests areundertaken is not specified. However, it is noted that some errormay exist in the core loss measurements made at 500 kHz dueto self heating of the CUT.
Each of the techniques reported in [12], [16]–[22] suffer tosome extent from the difficult issue of precisely time/phasematching the voltage and current sensing channels as noted inSection I. A core loss measurement technique which overcomesthis issue is given in Section IV.
IV. RESULTS OF CORE LOSS MEASUREMENT UNDER DC BIAS
Thecore lossmeasurement techniqueusedin thispaperutilizesa “hyper efficient” ZVS half bridge, as described in Section II,and described in detail in [6], to drive the CUT such that thecore losses can be measured from the dc input power to the halfbridge. This technique overcomes many of the significant diffi-culties associated with other core loss measurement techniques,is low in cost, and enables measurements to be quickly and easilyundertaken. Because switching losses in this application are of anorder of magnitude lower than the core losses, then correctionsfor switching losses can be made with ease.
The core type tested is a ferrite toroid in MMG F49 mate-rial [23], with: 3.067 cm (OD), 1.843 cm (ID), 0.623 cm (H),0.381 cm , 2.94 cm , and 7.71 cm . F49 is a corematerial with a high saturation flux density, making it particu-larly suitable for the design of dc biased magnetic componentsand therefore relevant for core loss testing under dc bias condi-tions. A toroidal core is specifically used because of the relativeuniformity of the flux path which lessens the influence of the coregeometry on core losses. This is discussed further in Section V.
One method by which a dc bias can be placed upon a core isthrough the supply of current from a dc current source to a des-ignated bias winding. A dc choke is commonly placed in the dcbias circuit in order to minimize induced ac voltages in the biaswinding. However, as reported in [24], the dc choke impedancereflects into the other windings on the CUT, and generates anerror in the measured core loss. This error can be reduced by:increasing the value of the dc choke inductance relative to that
250 IEEE TRANSACTIONS ON MAGNETICS, VOL. 44, NO. 2, FEBRUARY 2008
Fig. 3. Winding connection diagram of the core loss test circuit.
Fig. 4. Core loss circuit test setup.
of the bias winding, and/or decreasing the turns ratio betweenthe bias winding and all other windings on the CUT. Becauseeach of the measurement circuits used in [16]–[19] utilize a biaswinding and a dc choke, they all suffer to some extent from theerror caused by the reflected dc choke impedance. For the mea-surement circuit used for this paper, this problem is overcome byusing the technique described in [24], which implements the dcbias in a way that decouples the bias winding from all the otherwindings on the CUT without the need for a dc choke. Using thistechnique two test cores are used, with ac excitation windingswound on each. The cores are stacked, with cooling space in be-tween, and the ac excitation windings on each are connected outof phase with each other, and driven by the ZVS half-bridge toprovide excitation. Sense windings, placed on each of the twocores, are also connected out of phase, and used to ensure thatthe correct ac flux density is maintained. The dc bias windingis then wound over both cores together, and the losses are mea-sured as the sum of the losses in the two cores. A diagram illus-trating the connection of the windings is given in Fig. 3.
Fig. 4 shows the experimental setup, including the oil bathtest chamber and ZVS half bridge inverter. The CUT, attachedto the top plug of the test chamber and the motorized paddleused to stir the test chamber oil, are shown in the inset.
The measured core losses shown in Fig. 5 give the variationof the core losses with (a) temperature and (b) frequency, inthe absence of a dc bias. From Fig. 5(a) it is apparent that coreloss varies dramatically with temperature in a nonlinear manner,
Fig. 5. Variation of core losses (without dc bias) with (a) temperature and(b) frequency.
which illustrates the importance of specifying the temperatureat which core loss tests are undertaken.
The measured core loss characteristics of a gapped MMG F49ferrite core under dc bias conditions with ac excitation are givenin Fig. 6 for two test frequencies. For the results shown in Fig. 6the test cores are gapped in order to reduce the tolerance of ,and the level of within the cores to allow to be accuratelydetermined. To this end, two small air gaps of 0.12 mm eachwere placed in each of the flux paths of the test cores. The useof two small gaps is preferable to using one large gap, becauselarger gaps: increase eddy-current losses in the ac windings dueto the fringing flux which must be subtracted from the total mea-sured loss to determine the core loss, result in a nonuniformdistribution of flux near the core gap, and increase the fringingfield around the gap which causes to be higher than thatcalculated by theory. To reduce the fringing field around thecore gaps, the ac excitation windings used to excite the CUTare wound within a short distance of the core gaps. To accu-rately sense the level of ac flux in the core, the ac excitationsense windings are wound on portions of the core that are dis-tant from the core air gaps.
It has been reported in [25] that the presence of a gap in aferrite core does not cause a significant increase in ferrite corelosses. Therefore, for the results presented in this paper, the
BAGULEY et al.: THE EFFECT OF DC BIAS CONDITIONS ON FERRITE CORE LOSSES 251
Fig. 6. Variation of core losses (with dc bias) at (a) 200 kHz and (b) 25 kHz.
presence of the core gap is not expected to have a significantinfluence.
The results in Fig. 6 clearly show that ac core losses are notaffected by the presence of a dc bias at low levels, but that be-yond a critical level the core losses in F49 ferrite material in-crease dramatically with an increasing . The significance ofthe increase in core losses is also apparent through the compar-ison of Fig. 6(a) and (b), with that of Fig. 5(b) which showsmeasured core losses in the absence of a dc bias. A direct com-parison between the results shown in Fig. 6, and those in [12],and [16]–[22] cannot be made. This is primarily because thepreviously reported core loss measurements were carried out oncore types different from that used for this paper. However, theresults can be compared in terms of the observed trends. Thetrends reported in this paper are in broad agreement with thoseobserved in [12], and [17]–[22], which show that ferrite corelosses increase significantly at high levels of dc bias. At lowlevels of , the trends observed in Fig. 6(b) agree with thosepresented in [16], in which it was reported that core losses reacha minimum at a certain ratio of .
V. DISCUSSION
For the test results under dc bias conditions that are presentedin this paper, air gaps are placed in the magnetic paths of the test
cores. As noted in Section IV, this introduces potential sourcesof error into the core loss measurement circuit. An alternativeapproach is under consideration, which may avoid the need forcore air gaps and the attendant problems. The “initial magneti-zation curve” would first be measured under a range of temper-atures to accurately establish the relationship between and
. The level of required to obtain a specific wouldthen be applied to initially demagnetized cores along with thesuperimposed ac flux.
A toroidal core is used to gather the experimental resultspresented in this paper because of the uniformity of the reluc-tance of such cores along the mean magnetic path length relativeto other core shapes. This uniformity lessens the influence ofcore geometry on the measured core losses, and allows the corelosses to be more accurately characterized as a function of theferrite material. However, the loss measurements are not com-pletely independent of the core geometry because of the unequalreluctance of the core through its cross section. This affects thedistribution of flux, the actual flux density in the CUT, and sothe core losses. Ideally, a thin walled toroidal should be used,i.e., one for which the ratio of the outside diameter to the insidediameter is minimized. However, toroidals of this type are notcommonly manufactured, and are difficult to obtain. Therefore,when nonideal test cores are used in core loss tests under dc bias,it is necessary to verify that the correct value of flux density isused with the results that are presented. This can be achievedusing finite-element analysis and is under investigation.
The strong influence of dc bias conditions on core losses sug-gests it may be possible to optimize the shapes of cores to beoperated under dc bias conditions.
From the results presented in this paper it is obvious thatthe area of minor hysteresis loops must, for a given level ofac excitation, increase with dc bias. This is consistent with thewell-known fact that minor hysteresis loops of magnetic mate-rials are noncongruent [26], [27]. The reason minor hysteresisloop area, and therefore core losses, increase with dc bias is thatharder magnetization processes, i.e., increased local coercivefields for domain wall displacements, are found with increasingbias polarization values.
The core loss phenomenon under dc bias conditions couldbe simulated through the development of an accurate hysteresismodel, such as Preisach, integrated with a finite-element proce-dure, which would allow for coupled field-circuit simulations.It is noted in [28] that the inclusion of enhanced hysteresismodels into the finite-element procedure has become a majorresearch topic, and to the authors’ knowledge this has notbeen done under dc bias conditions. Therefore, it is underinvestigation.
VI. CONCLUSION
This paper has described various techniques that can be usedfor the measurement of ferrite core losses under both ac and dcconditions, and the difficulties associated with each technique.For core loss measurement techniques which rely upon the ac-curate sensing of the phase angle between voltage and current,an example has been given showing that very small errors in
252 IEEE TRANSACTIONS ON MAGNETICS, VOL. 44, NO. 2, FEBRUARY 2008
the measurement of the phase angle cause significant errors inthe core loss measurement. Previously reported core loss mea-surements under dc bias conditions have been reviewed and var-ious issues discussed. These include: the importance of relating
to core losses, how may be accurately determined, andthe importance of specifying the temperature at which core losstests are undertaken. Finally, tests results have been presented,based on a measurement technique that has not previously beenused for the measurement of core losses under dc bias condi-tions, which overcomes many of the problems associated withother techniques. These results show that core losses signifi-cantly increased under dc bias conditions.
APPENDIX
TABLE IIIFERROXCUBE E20/10/5 PARAMETERS AND SPECIFIED CORE LOSSES
ACKNOWLEDGMENT
This work was supported by The University of Auckland,New Zealand, under research Grant UARC:9273-3607841, andthe authors acknowledge the support of MMG (Ltd), U.K.
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Manuscript received May 31, 2007; revised October 28, 2007. Correspondingauthor: U. K. Madawala (e-mail: [email protected]).
