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CoreSelection forSaturating

Transformers

®Division of Spang & Company

A Division of Spang & Company

Core Selection forSaturatingTransformers

The advent of semiconductorsopened the door to a wide variety ofapplications using semi-conductorsand saturating transformers, such asdc to ac inverters and dc to dc con-verters. Presented is information onthe various saturable core materialsand how the various material char-acteristics relate to inverter size, ef-ficiency and cost.

The ideal core material wouldhave high flux density, low coerciveforce, high permeability when notsaturated and very low saturatedpermeability as shown in Figure 1.

Many available core materialshave one or more characteristics il-lustrated by the ideal B-H loop of Fig-ure 1. To approach ideal materialcharacteristics requires a core ge-ometry having a minimum air gap,such as strip wound toroids, ferritetoroids, ring laminations or DU lami-nations. Gapped structures, such asE-l laminations, ferrite pot cores andcut-cores, reduce the unsaturatedcore permeability, leading to in-creased core losses, and also in-crease the saturated permeability,leading to increased transistorswitching losses. Shown in Figure 2are the exciting current waveformsand B-H Loops of a MAGNESIL® tor-oid and of a comparable MAGNESILcut core used as a saturating invertertransformer.

Note that the toroid has lower ex-citing current and a shorter durationswitching spike. In spite of the highercore loss and switching loss of thegapped cores, they are often usedeffectively at lower frequencies topermit using low cost coil windingtechniques.

Figure 1

Figure 2Exciting Current Waveform and B-H Loop forToroid and Cut Core

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Figure 3 shows a typical B-H loopof Square Permalloy 80 materialand describes the various param-eters that are normally tested anddefined by the core manufacturers.The B M designation is the core satu-ration flux density; the higher theflux density, the smaller the size ofthe inverter transformer will be in aparticular design. BM is normallygiven in kilogauss and it is the dis-tance from the origin to saturationin one direction. Under normal op-eration, the total flux density swingwould be two times the BM. The BM

in kilogauss as shown in the dia-gram, however, is the number thatwould be used in Faraday’s law(V = 4BM NAF x 10-8) to determinehow many volts a given transformerwinding can support. The BM minusBR is the difference between themaximum flux density (BM) and theresidual flux density (BR). The lowerthis number, the lower the perme-ability in saturation and the lowerthe switching losses for a givencore material. H1/3 defines the widthof the B-H loop when resetting thecore 1/3 of the way from positivesaturation with a negative dc biasapplied to a core being excited witha half-wave ac signal. H1/3 relatesto the core loss; the smaller theH1/3 the lower the core loss. Thesetwo parameters are of most inter-est in designing inverter trans-formers.

Also shown in Figure 3 is a B-Hloop for the same material at 6,000hertz showing how the loop widthexpands and the core loss in-creases with increasing frequency.This increase in core loss dependson the strip thickness and the re-sistivity of the core material used.The higher the resistivity of the corematerial, the less core loss in-creases with increasing frequencyfor a given material thickness.

Figure 3

Hysteresis Loops for .002” Thick Permalloy 80

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Shown in Figure 4 are dc B-Hloops of all the commercially avail-able core materials which are suit-able for saturating type transform-ers. As can be seen, there is a widerange of magnetic characteristicsavailable to the saturating core de-signer. The problem is to pick theright material for the parameters re-quired in your inverter design.

As can be seen from these curves,Supermendur, the 50% iron – 50%cobalt material, has the highest fluxdensity of any of the materials andtherefore would give the smallestcore size, if size is the most impor-tant consideration in an inverter de-sign. Ferrite material, having thelowest flux density, gives the larg-est size transformer. AmorphousAlloy E has the lowest coerciveforce, therefore the lowest core lossof any other core materials avail-able. However, dc B-H loops don’tnecessarily give the true picture ofwhat happens to core loss at higherfrequencies. Table 1 lists these vari-ous materials by composition, tradenames and some of their more im-portant characteristics.

A core size should be selected sothat the wire size will completely fillthe window opening. If, at low fre-quencies, additional window area re-mains, increasing wire size to fill thewindow area will reduce copper lossand improve the efficiency of thetransformer. At high frequencies,cores with unused window area pro-duce excessive core losses due tothe unnecessary magnetic pathlength of the core. It is advisable inthis case to select a core with asmaller diameter, but with the samecross-sectional area, to insure thatthe windings will completely fill thecore window.

Figure 4B-H Loops of Saturable Materials

B (Kilogauss)

H (Oersteds)

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Table 1 — Saturable Core Material Characteristics

METALOR

ALLOY

COMMONTRADENAMES

COMPOSITION FLUX DC

IN % DENSITY COERCIVERESISTIVITY CURIE Available Thickness

I N TEMP. and Recommended

(Balance Iron) (Kilogauss) FORCE MICRO-OHMS(oersteds) CENTIMETERS

Upper Frequency for°C Saturating Transformer

Silicon-Iron Hypersil 3.5% Si 18 .4-.6 50 750 .012"-.025" 100 HzMagnesil (Grain Oriented) .006"-.012" 250 HzSelectron .004" 1000 HzOrthosil .002" 2000 HzMicrosil .001" 5000 HzSupersilSquare Mu-3

Cobalt-Iron Supermendur 49% Co 22 .15-.35 25 940 .004" 800 Hz2% V .002" 1500 Hz(Magnetic Anneal) .001" 3000 Hz

Nickel-Iron Orthonol 45-50% Ni 15 .1 45 500 .014" 100 HzDeltamax (Grain Oriented) .004" 1500 HzOrthonik .002" 4000 HzHypernik-V .001" 8000 HzHCR .0005" 20,000 Hz49 Square Mu .00025" 35,000 Hz

.000125" 50,000 Hz

Nickel-Iron Hy Ra 80 79% Ni 7 .02 57 460 .014" 400 Hz4-79 Permalloy 4% Mo .004" 4000 HzSquare Permalloy 80 .002" 10,000 HzSquare Mu-79 .001" 20,000 Hz

.0005" 40,000 Hz

.00025" 70,000 Hz

.000125" 150,000 Hz

Amorphous METGLAS 3.5% Si 16 .03-.08 135 370 .001" 25,000 Hz(iron-base) Alloy 2605SC 13.5% B

2% C

Amorphous METGLAS 66% Co 5 .008-.02 140 205 .001" 500,000 Hz(cobalt-base) Alloy 2714A 15% Si

14% B

Ferrites J MnZn 4 .1 10x106 170 35,000 Hz3E2A Permeability0-6 equals 5000H5B2T-3524H

Ferrites G MnZn 4 .2 40x106 170 50,000 Hz3B7 PermeabilityN-29 equals 2300

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Another important considerationis that each half of the primary of asaturating type transformer usingthe center-tapped configuration tocontrol two transistors, carries cur-rent during only one-half of thecycle. Since the winding “sees” onlya 50% duty cycle, the selection ofthe primary wire size is influencedby this factor. For example, if a 12watt inverter is designed to workfrom a 12 volt power source, and aprimary wire size is chosen to carry1 ampere continuously, the trans-former primary is really capable ofsupplying 24 watts. Core loss willbe comparable to that found in a24 watt transformer even thoughthe rated output power is only 12watts because of the increasedcore diameter required to accom-modate the unnecessarily largerwire size used. Therefore the trans-former efficiency is reduced.

Another important factor in theoperation of a saturating type in-verter transformer is the couplingbetween the primary winding, thefeedback winding, and the core.This is best accomplished by wind-ing the center-tapped primary bifi-lar (2 windings in parallel) com-pletely around the core and thenplacing the feedback windings,again bifilar wound, directly, uni-formly around, and over the pri-mary. Generally it is best to tapeover these windings and then ap-ply the secondary winding last. Thistechnique is especially important forgood starting when working into acapactive load, which appears likea partial short circuit when attempt-ing to turn the inverter “on”.

In the center-tap primary saturat-ing transformer type inverter, thetransistors will see twice the batteryvoltage across the collector-emitterjunction and should be rated towithstand at least two times thebattery voltage.

To minimize switching losses, thecut-off frequency of the transistorsshould be at least ten times the

desired operating frequency of theinverter.

Normally, inverter transformersare designed for smallest size,highest efficiency, lowest cost, andwidest environmental conditions.Unfortunately, the material produc-ing the smallest size may have thepoorest efficiency and highest cost.Materials giving the highest effi-ciency may have high cost andlarge size. Therefore all designs willtend to be a compromise on mate-rial selection to achieve the bestcharacteristic on the most importantparameter with some compromiseon other parameters.

1. Minimum Size and WeightSupermendur, the oriented 50%

iron – 50% cobalt material, with its22 kilogauss flux density, gives thesmallest size and weight, particu-larly at lower frequencies. Under1000 hertz, Supermendur will givea real size and weight reduction,with MAGNESIL® being the secondbest choice. At frequencies above2500 hertz, the ORTHONOL® ma-terial becomes a good choice. Thismaterial has much lower core lossthan Supermendur or MAGNESILmaterials and generally a thickergauge material can be used athigher frequencies. At 3000 hertzfor example, 2 mil thick ORTH-ONOL material would have lowercore loss than wou ld 1 m i lSupermendur material or 1 milMAGNESIL material. The differ-ence in stacking factor essentiallyoffsets the higher flux density ofMAGNESIL and Supermendur.

The stacking factor for a stripwound core is the ratio of the effec-tive core cross sectional area to thegross cross section of magneticcore material. The standard stack-ing factor for the various materialthickness is as follows:

IEEE STANDARD FACTORSMATERIAL THICKNESS STACKING FACTOR

.010” - .014” .95

.004” - .009” .90.002” .85.001” .75.0005” .50.00025”

.375

.000125” .25

2. Maximum EfficiencyAt frequencies below 1000 hertz the

M A G N E S I L m a t e r i a l , o r t h eORTHONOL material, is the bestchoice for a high efficiency trans-former. Even though these materialshave higher core loss than squarePermalloy 80, their much higher fluxdensity allows a significant reductionin copper loss. At low frequencies, thecopper loss is the predominant lossfactor in the transformer. This reduc-tion in copper loss more than offsetsthe increased core loss using thesecore materials. Above five kilohertz,where core loss is the predominanttransformer loss, Square Permalloy80 is the best choice. Above 25 kHz,Amorphous Alloy E is best.

3. Minimum CostFor low frequency applications un-

der 100 hertz, MAGNESIL is by farthe least expensive core material. If“X” represents the $ cost per poundof 12 mil thick Silicon - Iron, the rela-tive costs per pound of the other ma-terials would be about 2x for ferrite,11 x for ORTHONOL and AmorphousAlloy B, 10.5x for Square Permalloy,25x for Supermender, and 60x forAmorphous Alloy E.

As operating frequency is in-creased, thinner gauge materialsmust be used; at thinner gauges, theMAGNESIL material loses much of itscost advantage. For example, a 2,000hertz transformer using MAGNESILshould use 1 mil thick material. How-ever, 2 mil thick ORTHONOL wouldhave essentially the same core lossas 1 mil MAGNESIL. The cost of 2 mil

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O R T H O N O L v e r s u s 1 m i lMAGNESIL could be less.

When designing above 2,000-3,000 hertz, ORTHONOL becomesthe most economical material. Fer-rite material, although inexpensive,does not save money at low fre-quencies as the savings in corecosts are more than offset by theadditional copper and the largercore size required to compensatefor the ferrite’s low flux density(4,000-5,000 gauss). Above tenkilohertz, the ferrite material maybecome more attractive from a coststandpoint.

4. Minimizing Audible NoiseAudible noise can be reduced by

designing the inverter for operationabove ten kilohertz, where audiblenoise is not a problem. If the oper-ating frequency must be in the 60hertz to 10 kilohertz region, whereaudible noise is a problem, SquarePermalloy 80 or cobalt - basedAmorphous Alloy E tend to give thelowest audible noise in a saturat-ing transformer because of lowmagnetostriction and low saturationflux density.

5. Operation Over Extreme

Temperature RangesFor operation over an extreme

temperature range of -65 degreesC to +200 degrees C, any of themetal strip wound cores in an alu-minum core box with silicone damp-ening compounds are quite suit-able. These magnetic materialshave relatively high Curie tempera-tures, and their flux density changewith temperature is such that from-65 degrees C to +200 degrees Cthere would be less than a 30%change in operating frequency. Thecore loss in these materials variesin such a way that transformer effi-ciency will tend to be self-compen-sating over the temperature range.

Although core loss increases atlower temperatures, the frequencywill decrease because of increas-ing flux density, thus reducing theamount of core loss increase.

Copper loss decreases, tendingto offset the higher core loss. Withincreasing temperatures the coreloss decreases, while copper lossand frequency+ increase, tending togive a stable efficiency over a widetemperature range.

Ferrites are not generally suitableover wide temperature ranges dueto their very low Curie temperature.

Core SizeSelection

Upon selecting the transformercore material and material thick-ness, the next step is to select theproper size core for a transformerwith a given operating frequencyand output power. The power han-dling capability of a toroid core canbe determined by its WAAC productwhere WA is the available core win-dow area in circular mils and AC isthe core effective cross sectionalarea in cm². The curves in Table 2show the required core WAAC prod-uct for some of the common corematerials plotted against trans-former output power for a given fre-quency.

The WAAC relationships are ob-tained by solving Faraday’s Law inthe following manner:

FOR SATURATING TYPE TRANSFORMERS,Faraday’s Law = E= 4 B MAC N f x 10- 8

Solving for NA C =E

4 BMf x 1 0- 8

However,

the Window Utilization Factor K =NAW

WA

= .1, NAW = .1 W A

Multiply both sides by Ac and transpose:.1W AAC

NAC =AW

Combining and solving for WAAC :

. 1 WA AC = E WA AC = EA W

AW 4xBM x fx10 - 8 .4xBM x fx 10- 8

2.5xExA W

WA AC = BM xfx10 - 8Assume 85% efficiency

cir milsand 750 current capacity of wire.

amp

However, the primary winding has a 50% duty factor

giving a current capacity of 375cir mils

amp

Therefore the formula becomes:1 .1 Power Output

WA AC =BM xfx10 -11

Since the inverter is a saturating device,

BM = 21,000 (50% cobalt) BM = 14,500 (50% nickel& Amorphous Alloy B)

BM 17,000 (3% silicon) BM = 7,000 (80% nickel)

BM = 3,500 (Ferrites) BM = 4,500 (Amorphous Alloy E)

FORMULAS USED FOR INVERTER CURVES ARE:

WAAC =5.25 x Power Output x 106

50% cobalt)frequency

WA AC =6.5 x Power Output x 106

frequency(3% silicon)


frequency(50% nickel &Amorphous Alloy B)


frequency(80% nickel)

WA AC =24.4 x Power Output x 106 (Amorphous Alloy E)

frequency

WAAC =31.5 x Power Output x 106

(Ferrites)frequency

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Core LossCalculations

Shown in Table 3 are core losscurves for several materials andmaterial thicknesses. These curvesshow typical core loss in watts perpound versus operating flux densitylevels for various frequencies. To findthe weight of a given toroidal coresize, determine the core volume incubic inches from:Volume = .75(O.D. + I.D.)(O.D.-I.D.)(Ht)where the bare core inside diameter,outside diameter, and height are ininches.

Core weight in pounds = Volumex Stacking Factor x Density.

The densities of various core ma-terials are as follows:

MATERIALS DENSITY(LBS. / CU. IN.)

WA AC (x 10 6) (Cir. mils cm 2)

3% Silicon .2950% Ni & 50% Co .3180% Nickel .33Amorphous Alloy B .26Amorphous Alloy E .27Ferrites (MnZn) .19

Knowing the core weight, the ex-pected core loss can be found fromthese curves.

Core selection for inverter trans-formers often involves compromiseswhich affect inverter performance.Hopefully, by following the stepsoutlined, the designer will optimizethe final inverter performance.

Table 2Relationship of Core W AA C to Output Power Capability

PERMALLOY 80

ORTHONOL and Amorphous Alloy B

WA AC(x 10 6) (Cir. mils cm2)

For Amorphous Alloy E, multiply WAA Cdetermined from the formula by1.55 and use Permalloy curves above.

Note: To convert circular mils to cm²,multiply by 5.07 x 10- 6.

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Relationship of Core W AA C toOutput Power Capability (cont.)

)

WA A C (x 10 6) (Cir. mils cm 2)

WA A C ( x 1 0 6) (Cir. mils cm 2)

WA A C (x 106 ) (Cir. mils cm 2

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Table 3Core Loss Curves

FLUX DENSITY (GAUSS) FLUX DENSITY (GAUSS)


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10

Core Loss Curves



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FLUX DENSITY (GAUSS)FLUX DENSITY (GAUSS)


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