PCIM MARCH 2000 � 11

FFiinniittee EElleemmeenntt AAnnaallyyssiissSSooffttwwaarree DDeetteerrmmiinneessMMaaggnneettiiccss PPrrooppeerrttiieessAdrian Perregaux, Ansoft, Pittsburgh, Pennsylvania

Electrical response of amagnetic component canbe dramatically impactedby its physical construc-

tion. Many configuration possibili-ties exist, such as the type of core,whether the core has a gap, type ofwire, wire size, winding strategy,configuration of turns, and amountof insulation needed. Finite Ele-ment Analysis (FEA) softwareallows the designer to easily explorethe impact of all of these considerations, and provides elec-trical response data so that quantifiable performance canbe evaluated.

Although particular effects are very well known by mostdesigners, quantifying them is difficult without building aphysical component. This is especially true when combin-ing more than one conceptual idea in the same configura-tion. For example, it is well known that the leakage induc-tance increases when the separation between primary andsecondary windings increases, and also that interleavingreduces the leakage inductance and the ac resistance.

The designer must have a timely and cost effective wayin which to quantify a component�s electrical response. Insome instances a build and test methodology is sufficientfor this issue. In many other instances, component com-

plexity, component response, ortime constraints may require analternate methodology. FEA soft-ware is an alternative methodologyfor the designer. One type of FEAsoftware is PEmag that builds a vir-tual picture of the component andthen supplies the appropriate elec-trical response quantification need-ed. This software allows designersto put their knowledge of physicalcomponent layout to practical use.

It also allows designers to weigh the impact of each con-sideration involved in the creation of the component sothat the appropriate electrical response is achieved.

Gap ConsiderationsPEmag was used to evaluate the impact of different

core gaps for a specific transformer configuration: 0.28 mm,0.7 mm, 1.4 mm, and 2.4 mm. The fringing flux due to thecore gap will impact the winding�s ac resistance, but towhat extent? Figure 1 is a transformer cross section and ref-erences two simple observations for the dc effects pertain-ing to the winding. These two effects are, namely, that thedc quantities for resistance and inductance are simple to

Finite Element Analysissoftware can generate

frequency, geometric andmaterial property

dependent models for awide range of magnetic

components.

Figure 1. Physical layout differences, dc parasitics computation. Figure 2. Resistance vs. gap size.

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of understanding the full nature of thefactors involved with manufacturingmagnetic components. Quantitativeunderstanding about how these con-figuration alternatives impact thebehavior of the magnetic componentcan be achieved through simulation.Characterizing the component allowsthe use of this information to pick theoptimum magnetic configuration.

Sensitivity AnalysisOnce the optimum component

configuration has been determined, itis important that it can be manufac-tured with a high degree of confi-dence in its performance. Thisrequires a second evaluation phase forthe design, that is a �sensitivity analy-

sis.� This must encompass the devia-tions in behavior due to manufactur-ing tolerances in general, but specifi-cally as it pertains to physicaltolerances and material properties.Physical tolerances that impact per-formance are typically the core fea-tures, core gap size, bobbin features,bobbin placement, and winding place-ments. The difference in the averageoperating permeability of the core willoften dramatically impact the mag-netic component performance as well.The goal of the sensitivity analysis isto provide a clearly defined band ofbehavior for which the device can beexpected to perform.

PEmag addresses the sensitivityanalysis issues surrounding the design.

Magnetics FEA

Figure 3. Physical layout differences.

Figure 4. Short circuit inductance vs. frequency.

Figure 5. Comparison of short circuit inductance vs. frequency with measurements and PEmag.

compute from known relationships,length of the conductor, cross sectionof the conductor, and the number ofturns. The relationships for ac quanti-ties are not simple especially in thepresence of a gap in the core, andoften they cannot be simply comput-ed. FEA allows the designer to accu-rately compute these quantities. Theresults of the FEA simulations areshown in Figure 2.

The next thing to examine is theinsulation spacing between primaryand secondary windings for the sametransformer core with the no gap con-figuration. The impact of 125 µm, and375 µm spacing will be examined.The general transformer configura-tions are shown in Figure 3. The solu-tion results are shown in Figures 4- 7.Note that there is a dramatic changein open circuit characteristics pro-duced by the change in insulationthickness (effective spacing).

It is interesting to evaluate thechanges in characteristics as a func-tion of frequency. The results pre-sented in Figures 5 and 7 indicate thatthe FEA software accurately predictsthe characteristics of the prescribedtransformers; not only at a particularfrequency, but throughout a fairlywide range of frequencies. The simu-lations also represent the importance

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The software enables designers tocreate geometry and material propertydefinitions that depict the nature ofthe manufacturing tolerance devia-tions that they wish to explore.

One sensitivity example examinesthe impact that may occur if the lastturns of the primary winding in atransformer (for example the last 6 of150 turns) end up in either of two dif-ferent locations in the bobbin. Thefirst location explored is with theseend turns located in the upper part ofthe bobbin, and the second locationexplored is with these end turns beingin the lower part of the bobbin. Figure8 shows the difference in the minorphysical layout.

Figure 9 shows the wide range ofvalues that can result from the loca-tion of the end turns. This indicatesthat the designer must evaluate per-turbations within the extremes of pos-sible tolerances expected. Measure-ments taken for this transformer fallwithin the computed band of behaviorfor the winding positioning.

A second sensitivity analysis exam-ple evaluates the impact that a changein permeability can have on the com-ponent performance. The magneticresponse of a core is generally nonlin-ear. Most core manufacturers providea single permeability for the core.This assumes a specific excitation onthe core, and a constant responsethroughout the volume. This singlevalue for response is an approxima-tion, and there is a degree of uncer-tainty associated with it.

Figure 6. Open circuit inductance vs. frequency using PEmag.

Figure 7. Comparison of open circuit inductance vs. frequency with measurement and PEmag.

Figure 8. Physical layout differences.Figure 9. Short circuit inductance vs. frequency for the two different end turn locations usingPEmag.

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For example, changing the perme-ability from 4,000 to 1,500 can affectthe overall component performance. Alook at how the permeability caninfluence the behavior of a whole cir-cuit for this typical example can beseen with the waveforms in Figure 11,which shows how the drain-to-sourcevoltage (VDS) in a forward with a reso-nant reset converter is affected fortwo different core materials. It can beseen that the voltage spike due to the

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Magnetics FEAFinite Element Analysis

Mathematical relationships forelectromagnetic behavior have beenknown for over 100 years, and theyare best described by Maxwell�sEquations, developed by JamesClerk Maxwell. Unfortunately, theserelationships are very complex andmost often do not lend themselvesto simple computational methods.Many physicists and mathematicianshave worked their entire lifetimes incomputing a single physics result.

Methods for handling these rela-tionships have evolved over the past30 years to make the process of solv-ing electromagnetic physics reason-able and easily available to the engi-neer. Finite Element Analysis (FEA)is one of these methods.

FEA is a multi-step process.These steps are sequential, as fol-lows:� Maxwell�s Equations are trans-

formed from integral to differen-tial form

� The total physical volume of aphysics problem is broken upinto smaller, well defined pieces.These smaller pieces are oftentriangles in 2D, and tetrahedralin 3D.

� The physics is computed locallyin each piece

� The physics is computed global-ly for the total volume by com-bining the contributions of eachpiece

� Physical relationships can beobserved from the physics result

FEA has evolved over the pastfive years into a cost effective, time-ly method for solving electromagnet-ic behavior. FEA will revolutionizethe development of componentsexhibiting or dependent upon elec-tromagnetic behavior. Prototypingcan now be done �virtually� and notphysically.

Figure 10. Comparison of short circuit inductance vs. frequency using measurements and usingPEmag.

leakage inductance is almost the samein both cases, but the frequency of theresonance produced in the waveformsis drastically different because of thevariation in magnetizing inductanceproduced within the transformer. Theresultant waveform is dramatically dif-ferent, and unacceptable under thelower permeability.

Figure 11. Drain-to-Source voltage in a forward converter with high and low values of perme-ability.