inverter transformer design and core selection

8/3/2019 Inverter Transformer Design and Core Selection

1/18

Division of Spang & Company

Inv ert erTransformer

Core Designand

MaterialSelect ion


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INTRODUCTION ................................................................................................................................... 2

TYPICAL OPERATION.......................................................................................................................... 2

MATERIAL CHARACTERISTICS ........................................................................................................ 2,3

CORE SATURATION DEFINITION........................................................................................................ 4THE TEST SETUP................................................................................................................................ 5

AIRGAP .............................................................................................................................................. 10

EFFECT OF GAPPING ........................................................................................................................10

CONCLUSIONS ................................................................ .................................................................. 16

TABLES

1. Magnetic Core Material Characteristics...........32. Materials and Constraints...............................6

3. Comparing Br/Bm on Uncut and Cut ..............14

4. Comparing H-Hp on Uncut and Cut ........... 14

FIGURES1. Typical Driven Transistor Inverter ................... 2

2. Ideal Square B-H Loop ................................... 2

3. The Typical dc B-H Loops of MagneticMaterials........................................................ 3

4. Defining the B-H Loops .................................. 4

5. Excitation Current ..........................................4

6. B-H Loops With dc Bias ................................. 5

6A. Typical Square Loop Material Withac Excitation ................................................... 5

7. Dynamic B-H Loop Test Fixture ......................5

8. Implementing dc Unbalance. ...........................6

9. Magnesil K B-H Loop ...................................... 7

10. Orthonol A B-H Loop ...................................... 7

11. 48 alloy H B-H Loop ....................................... 7

12. Sq. Permalloy D B-H Loop............................. 7

13. Supermalloy F B-H Loop................................ 8

14. Composite 52029-2K, A, H, D, F, B-H Loops.. 815. Magnesil K B-H Loop With and Without dc...... 8

16. Orthonol A B-H Loops With and Without dc..... 8

17. 48 Alloy H B-H Loop With and Without dc......9

18. Sq. Permalloy P B-H Loop With and Withoutdc ................................................................ 9

19. Supermalloy F B-H Loop With andWithoutdc .................................................... 9

20. Air Gap Increases the Effective Length of theMagnetic Path ............................................10

21. Implementing dc Unbalance........................ 10

22. Magnesil 52029-2K B-H Loop Uncutand Cut ...................................................... 11

23. Orthonol 52029-2A B-H Loop Uncut and Cut 12

24. 48 Alloy 52029-2H B-H Loop Uncut and Cut 12

25. Sq. Permalloy 52029-2D B-H Loop Uncut andCut..............................................................13

26. Supermalloy 52029-2F B-H Loop................. 13

27. DefiningH andHOp ................................ 14

28. Inverter Inrush Current Measurement ...........15

29. TR Supply Current Measurement .................15

30. Typical Inrush of an Uncut Core in a DrivenInverter:.......................................................15

31. Same as Figure 30 But the Core was Cut andOperating With a Maximum Flux Density Valueof B operate = Bmax imum Bres idual ..........15

32. Typical Inrush Current of an Uncut Core

Operating From an ac Source .....................1633. Same as Figure 32 But the Core was Cut and

Operating With a Maximum Flux Density Valueof Boperate = Bmax imum Bres idual ...........16

ACKNOWLEDGEMENT

This paper has been prepared by, and is used with the permission of

Colonel Wm. T. McLyman Spacecraft Power Section Jet Propulsion LaboratoryMember of the Technical Staff Guidance and Control Division


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PrefaceA program was conducted to

study magnetic materials for use inspacecraft transformers used instatic inverters, converters, andtransformer rectifier supplies. Notonly did this program investigatedifferent magnetic alloys best suitedfor high frequency and high effi-ciency applications but investigatedinherent characteristics of the mag-netic materials. One of the charac-teristics that is detrimental in

transformer design is the residualflux density which could be additiveon turn-on causing the transformerto saturate. Investigation of thisproblem led to the design of a trans-former with a very low residual flux.When the data of many trans-formers and in many configurationswere compiled the optimum trans-former was the transformer with thelowest residual flux that containeda small amount of air gap in themagnetic material.

This program also included aseries of tests on magnetic alloysand evaluation of spacecraft trans-former design.

The materials evaluated were:

TRADE NAME MAGNETIC ALLOYS

Orthonol 50% nickel 50% iron

Sq. Permalloy 79% nickel 17% iron 4% moly

48 Alloy 40% nickel 52% iron

Supermalloy 78% nickel 17% iron 5% moly

Magnesil 3% silicon 97% iron

Tests were performed to deter-

mine the dc and ac magneticproperties at 2400 Hz using square-wave excitation. These tests wereperformed on uncut cores whichwere then cut for comparison of thegapped and ungapped magneticproperties. The data obtained fromthese tests are described, and thepotential uses for the materials arediscussed.

Static inverters, converters andT-R supplies intended for spacecraft

Introduction

power use are usually of squareloop toroidal design. The design ofreliable, efficent and lightweightdevices of this class for such usehas been seriously hampered by thelack of engineering data describingthe behavior of both the commonlyused and the more exotic corematerials with higher frequencysquare wave excitation.

A program has been carried outat JPL to supply this lack. An inves-tigation has been made to ascertainthe dynamic B-H loop characteris-tics of different core materialspresently available from variousindustry sources. Cores were pro-cured in both toroidal and Cforms and were tested in bothungapped (uncut) and gapped (cut)conf igurat ions. The fol lowingdescribes the resul ts of thisinvestigation.

Typical OperationTransformers used for inverters,

converters and T-R supplies oper-ate from the spacecraft power buswhich could be dc or ac. In somepower applications, a commonlyused circuit is a driven transistorswitch arrangement such as thatshown in Figure 1.

Figure 1

Typical Driven TransistorInverter

One important considerationaffecting the design of suitabletransformers is that care must betaken to ensure that operationinvolves balanced drive to the trans-former primary. In the absence ofbalanced drive, a net dc current willflow in the transformer primary,which causes the core to saturateeasily during alternate half-cycles.A saturated core cannot support theapplied voltage, and because oflowered transformer impedance thecurrent flowing in a switching tran-

sistor is limited only by its beta.Transformer leakage inductanceresults in a high voltage spike dur-ing the switching sequence whichcould be destructive to the transis-tors. In order to provide balanceddrive, it is necessary to exactlymatch the transistors for VCE(SAT)and beta and this is not always suffi-ciently effective. Also exact match-ing of the transistors is a majorproblem in the practical sense.

MaterialCharacteristics

Many available core materialsapproximate the ideal square-loopcharacteristic illustrated by the B-Hcurve shown in Figure 2.

Figure 2

Ideal Square B-H Loop

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A Division of Spang & Company


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Table 1 Magnetic Core Material CharacteristicsLOSS

FACTORW/LB

AT 3 KHz

5 KG

TRADE NAMESSPECIFICGRAVITY

Magnesil 3% Si 15-18 4 - .6 0.85 - 1.0 .276 15.0 7.64Silectron 97% IronMicrosilSupersil

Deltamax 50% Ni 14 - 16 .1 - .2 0.94 - 1.0 .298 8.00 8.25

Orthonol 50% Iron49 Square Mu

Allegheny 4750 48% Ni 11.5 - 14 .05 - .15 0.80 - 0.92 .296 5.00 8.2048 Alloy 52% IronCarpenter 49

4-79 Permalloy 79% Ni 6.6 - 8.2 .02 - .04 0.80 - .90 .3156 2.50 8.74Sq. Permalloy 17% Iron80 Sq. MU 79 4% Moly

Supermalloy 78% N 6.5 - 8.2 .003 - .008 0.40 - 0.70 .3166 1.70 8.7717% Iron5% Moly

COMPOSITION

SATURATEDFLUX

DENSITY

(KG)

DC

COERCIVEFORCE

(Oe)

SQUARENESSRATIO

Figure 3

Representative dc B-H loops forcommonly available core materialsare shown in Figure 3. Othercharacteristics are tabulated inTable 1.

MATERIALDENSITY

Ib/in

The Typical dc B-H Loops of Magnetic Materials

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Many articles have been writtenabout inverter and converter trans-former design. Usually, the authorsrecommendation represents a com-promise between material charac-teristics such as those tabulated inTable 1 and the B-H characteristicsdisplayed in Figure 2. These dataare typical of commercially availa-ble core materials which are suita-ble for the particular application.

As can be seen, the materialwhich provides the highest flux den-sity (silicon) would result in smallest

component size, and this wouldinfluence the choice if size is themost important consideration. Thetype 78 material (see the 78% curvein Figure 3) has the lowest flux den-sity. This results in the largest sizetransformer, but on the other hand,this material has the lowest coerciveforce and the lowest core loss of anyother core material available.

Usually, inverter transformerdesign is aimed at the smallest size,with the highest efficiency, and ade-quate performance under the widest

range of environmental conditions.Unfortunately, the core materialwhich can produce the smallestsize, has the lowest efficiency. Thehighest efficiency materials result inthe largest size. Thus the trans-former designer therefore mustmake tradeoffs between allowabletransformer size and the minimumefficiency which can be tolerated.The choice of core material will thenbe based upon achieving the bestcharacteristic on the most critical or

important design parameter, andacceptable compromises on theother parameters.

Based upon analysis of pastdesign performance, most engi-neers select size over efficiency asthe most important criteria andselect an intermediate core materialfor their designs. Consequentlysquare-loop 50-50 nickel iron hasbecome the most popular material.

Core Saturat ionDefinitionTo standardize the definition of

saturation, we first define severalunique points on the B-H loop asshown in Figure 4.

The straight line through (H 0 ,O)and H s , Bs) may be written as:

dBB = ( (H - H 0) (1)dH )

The line through (0, B s) and (Hs,Bs ) has essentially zero slope and

may be written as:B = B 2 Bs (2)

Figure 4

Defining the B-H Loop

|DC (B s B1 )0 N , amperes (9)

Expressions (1) and (2) togetherdefine saturation conditions asfollows:

dBBs = ( )dH

(H s - H0) (3)

Solving (3) for H s we obtain:B

Hs = Hs

0 + (4)0

wheredB

0 = by definition

dHSaturation occurs when the peak

exciting current is twice the averageexciting current, as shown in Figure5. Analytically this means that:

Hpk = 2Hs (5)

Solving (1) for H1 , we obtain:B

H1 = H 0 +1

(6)0

To obtain the pre-saturation dcmargin (), we subtract (4) from(3) and obtain:.

B = H s - H 1 =

s B1 (7)0

The actual unbalanced dc currentmust be limited to:

N = TURNS

l= mean magnetic lengthH l

|DC N, amperes

Figure 5

Excitation Current

Combining (7) and (8) gives:

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As mentioned earlier, in an effort

to prevent core saturation, theswitching transistors are matchedfor beta and Vtics. The effect of core saturation

CE (SAT) characteris-

using an uncut or ungapped core isshown in Figure 6 which illustratesthe effect on the B-H loop whentraversed with a dc bias. Figure 6Ais a typical B-H loop of 50-50 nickeliron excited from an ac sourcewhere the vertical scale is 4 KG/cm.

It can be noted that the minorloop remains at one extreme posi-tion within the B-H major loop afterremoval of dc offset. The unfor-tunate effect of this random minorloop positioning is that when con-duction again begins in the trans-former winding, flux swing couldbegin from the extreme, and notfrom the normal zero axis. Theeffect of this is to drive the core intosaturation with the production ofs p i k e s w h i c h c a n d e s t r o ytransistors.

The Te st Set-Up

N =4.0 Bm F Ac

A test fixture, schematically indi-cated in Figure 7, was built to effectcomparison of dynamic B-H loopcharacteristics of various corematerials.

Cores were fabricated from vari-ous core materials in the basic coreconfiguration designated No. 52029for toroidal cores manufactured byMagnetics. The materials used werethose most likely to be of interest todesigners of inverter or convertertransformers. Test conditions arelisted in Table 2 (page 6).

Winding data was derived fromthe following:

V 1 0 8T

where

N T = Number of turns

B m = Flux density gausses

F = Frequency Hertz

A c = Core area cm 2

V = Voltage

Figure 6

B-H Loop With dc Bias

Figure 6A

Typical Square Loop Material With ac Excitation

Figure 7

Dynamic B-H Loop Test Fixture

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Table 2 Materials and ConstraintsCORE TYPE

52029-2A

52029-2D

52029-2F

52029-2H

52029-2K

MATERIAL

Orthonol (A)

Sq. Permalloy (D)

Supermalloy (F)

48-Alloy (H)

Magnesil (K)

B m NT FREQ ml

14.5 KG

7.5 KG

7.5 KG

11.5 KG

16.0 KG

54 2.4 KHz 9.47 cm

54 2.4 KHz 9.47 cm

54 2.4 KHz 9.47 cm

54 2.4 KHz 9.47 cm

54 2.4 KHz 9.47 cm

The test transformer representedin Figure 8 consists of a 54 turn pri-mary and secondary winding, withsquare wave excitation on the pri-mary. Normally switch S1 is open.With switch S1 closed, the secon-dary current is rectified by the diodeto produce a dc bias in the secon-dary winding.

Cores were fabricated from eachof the materials by winding ribbonof the same thickness on a mandrelof a given diameter. Ribbon termi-nation was effected by welding inthe conventional manner.

The photographs designated 9,10, 11,12 and 13 show the dynamicB-H loops obtained for the differentcore materials designated therein.Figure 14 shows a composite of allthe B-H loops. In each of these,switch S1 was in the open positionso that there was no dc bias appliedto the core and windings.

The photographs designatedFigures 15, 16, 17, 18 and 19 showthe dynamic B-H loop patternsobtained for the designated corematerials when the test conditionsincluded a sequence in whichswitch S1 was closed and thenopened. It is apparent from theseviews that with a small amount of dcbias, the minor dynamic B-H loopcan traverse the major B-H loopfrom saturation to saturation. InFigures 15 to 17, it will be noted that

after the dc bias had been removed,the minor B-H loops remainedshifted to one side or the other.Because of ac coupling of the cur-rent to the oscilloscope, the photo-graphs do not present a completepicture of what really happens dur-ing the flux swing.

Figure 8

Implementing dc Unbalance

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Figure 9 Figure 10

Magnesil K B-H Loop Orthonol A B-H Loop

Vert = 5 KG/cm

Horiz = 100 ma/cm

Vert = 5 KG/cm

Horiz = 50 ma/cm

Figure 11 Figure 12

48 Alloy H B-H Loop Sq. Permalloy D B-H Loop

Vert = 5 KG/cm

Horiz = 50 ma/cm

Vert = 2 KG/cm

Horiz = 10 ma/cm

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Figure 13

Supermalloy F B-H Loop

Figure 14

Composite 52029-2K, A, H, D, F, B-H Loops

Vert = 2 KG/cm

Horiz = 10 ma/cm

Vert = 5 KG/cm

Horiz = 50 ma/cm

Figure 15 Figure 16

Magnesil K B-H Loop With and Without dc Orthonol A B-H Loop With and Without dc

Vert = 3 KG/cm Vert = 2 KG/cm

Horiz = 200 ma/cm Horiz = 100 ma/cm

8


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Figure 17

48 Alloy H B-H Loop With and Without dc

Figure 18

Sq. Permalloy P B-H Loop With and

Without dc

Vert = 2 KG/cm

Horiz = 50 ma/cm

Figure 19

Supermalloy F B-H Loop With and Without dc

Vert = 1 KG/cm

Horiz = 20 ma/cm

Vert = 1 KG/cm

Horiz = 20 ma/cm

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Air GapAn air gap introduced into the

core has a powerful demagnetizingeffect resulting in shearing over ofthe hysteresis loop and a consider-able decrease in permeability ofhigh-permeability materials. The dcexcitation follows the same pattern.However, the core bias is consider-ably less affected by the introduc-tion of a small air gap than themagnetization characteristics. Themagnitude of the air gap effect also

depends on the length of the meanmagnetic path and on the charac-teristics of the uncut core. For thesame air gap, the decrease inpermeability will be less with agreater magnetic flux path but morepronounced in a low coercive force,high permeability core.

8

BE 10

ac = K F Ac N(gauss)

Effect of GappingFigure 20 shows a comparison of

a typical toroid core B-H loop with-out and with a gap.

The gap increases the effectivelength of the magnetic path. Whenvoltage E is impressed across pri-mary winding N1 of a transformer,the resulting current im will be smallbecause of the highly inductive cir-cuit shown in Figure 21.

For a particular size core, maxi-mum inductance occurs when theair gap is minimum.

When S1 is closed, an unbal-anced dc current flows in the N2turns, the core is subjected to a dc

magnetizing force resulting in a fluxdensity which may be expressed as:

where

m = Mean length (cm)

g = Gap (cm)

Bdc = dc flux density (gauss)

|dc = Unbalanced direct current(amperes)

dc

= dc permeability

N = Number of turns

In converter and inverter design,this is augmented by the ac fluxswing which is:

where

Bac = ac flux density (gauss)

E = ac voltage

F = Frequency (Hz)Ac = Area of core (cm)

K = 4.0 for a square wave

K = 4.4 for a sine wave

N = Number of turns

If the sum of B d c and Ba c shiftsoperation above the maximum oper-ating flux density of the core mate-rial, the incremental permeability(ac) is reduced. This lowers

Figure 20

Air Gap Increases the Effective Length

of the Magnetic Path

Figure 21Implementing dc Unbalance

10

B1.25 N |dc

dc = (gauss)m

g + dc


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impedance and increases flow of

magnetizing current im.This can beremedied by introducing an air gapinto the core assembly which effectsa decrease in dc magnetization inthe core and increases ac magneti-zation current. However, theamount of air gap that can be incor-porated has a practical limitationsince the air gap lowers impedancewhich results in increased mag-netizing current (im). The magnetiz-ing current is inductive in nature.The resultant voltage spikesproduced by such currents apply agreat stress to the switching transis-tors, often causing failure. This canbe minimized by tight control of lap-ping and etching of the gap to keepthe gap to a minimum.

From Figure 20, it can be seenthat the B-H curves depict maxi-mum flux density Bm and residualflux Br for ungapped and gappedcores, and that the useful flux swingis designated B, which is thedifference between them. It will benoted in Figure 20A that the Br

approaches the Bm, but that in Fig-

ure 20B, there is a much greaterB between them. In either case,when excitation voltage is removedat the peak of the excursion of theB-H loop, flux falls to the Br point.It is apparent that introducing an airgap then reduces the Br to a lowerlevel, and increases the useful fluxdensity. Thus insertion of an air gapin the core eliminates, or reducesmarkedly, the voltage spikesproduced by the leakage induc-tance due to the transformersaturation.

Two types of core configurationswere investigated in the ungappedand gapped states, namely toroidalcores and rectangular C cores.Toroidal cores as conventionallyfabricated are virtually gapless. Toincrease the gap, the cores werephysically cut in half, the cut edgeslapped and acid etched to removecut debris, and banded to form thecores. A minimum air gap on theorder of less than 25 microns wasestablished.

Figure 22

Magnesil 52029-2K B-H Loop Uncut and Cut

As will be noted from Figures 22

to 26 which are photographs show-ing the results of testing, the uncutand cut cores designated therein,the results obtained indicated thatthe effect of gapping was the samefor both the C-cores and the toroi-dal cores subjected to testing.

It will be noted, however, thatgapping of the toroidal coresproduced a lowered squarenesscharacteristic for the B-H loop asshown in table 3 (page 14); this datawas tabulated from Figure 22 to 26.

Also, from Figures 22 through 26, H was extracted as shown in Fig-ure 27 and tabulated in Table 4

(page 14).A direct comparison of cut and

uncut cores was made electricallyby means of two different circuitconfigurations. The magnetic mate-rial used in this branch of the testwas Orthonol. The operating fre-quency was 2.4 KHz, and the fluxdensity was 6 kilogauss (KG).

Vert = 5 KG/cm

Horiz = 100 ma/cm

UNCUT

Vert = 5 KG/cm

Horiz = 500 ma/cm

CUT

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Figure 23

Orthonol 52029-2A B-H Loop Uncut and Cut

Vert = 5 KG/cm

Horiz = 50 m

UNCUT

Vert = 5 KG/cm

Horiz = 100 ma/cm

CUT

Figure 24

48 Alloy 52029-2H B-H Loop Uncut and Cut



UNCUT CUT

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Figure 25Sq. Permalloy 52029-2D B-H Loop Uncut and Cut

Vert = 2 KG/cm

Horiz = 20 ma/cm

UNCUT

Figure 26

Supermalloy 52029-2F B-H Loop

Vert = 2 KG/cm

Horiz = 100 ma/cm

CUT



UNCUT CUT

13

A Divisionof Spang & Company


15/18

Figure 28 shows a driven inverter

operating into a thirty watt load, withthe transistors operating into andout of saturation. Drive was appliedcontinuously. S1 controls the sup-ply voltage to Q1 and Q2.

With switch S1 closed, transistorQ1 was turned on and allowed tosaturate. This applied E-Vc (SAT)across the transformer winding.Switch S1 was then opened. Theflux in transformer T2 then droppedto the residual flux density Br.Switch S1 was closed again. Thiswas done several times in succes-sion in order to catch the flux addi-tive direction. It will be noted inFigure 30 that the uncut core satu-rated and that inrush current waslimited only by circuit resistance andtransistor beta. It will also be notedin Figure 31 that saturation did notoccur in the case of the cut core.

The second test circuit arrange-ment is shown in Figure 29. Thepurpose of this test was to excite atransformer, and to catch the inrushcurrent using a current probe. A

square wave power oscillator wasused to excite transformer T2.Switch S1 was opened and

closed intermittently several timesto catch the flux main additive direc-tion. The photographs designatedFigures 32 and 33 show inrush cur-rent for a cut and uncut corerespectively.

Figure 27

Defining H and HOP

Table 3 Comparing Br/Bm on Uncut and Cut

MATERIAL UNCUT Br/Bm CUT Br/Bm

(A) Orthonol .96 .62

(D) Sq. Permalloy .86 .21(K) Magnesil .93 .22

(F) Supermalloy .81 .24

(H) 48 Alloy .83 .30

Table 4 Comparing H - H OP on Uncut and Cut

MATERIAL

UNCUT CUT

Orthanol

48 Alloy

Sq. Permalloy

Supermalloy

Magnesil

BMAX BOP BDC HOP H HOPKG KG KG 0e 0e Oe

14.4 11.5 2.88 0.01 0 0.716

11.2 8.9 2.24 0.02 0 1.28

7.3 5.8 1.46 0.008 0.004 0.787

6.8 5.4 1.36 0.014 0.004 0.393

15.4 12.3 3.1 0.06 0.02 5.72

H

0e

0.143

0.28

0.143

0.179

1.43

14


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Figure 28

Inverter Inrush Current Measurement

Figure 29

TR Supply Current Measurement

Figure 30

Typical Inrush of an Uncut Core

in a Driven Inverter

A small amount of air gap, lessthan 25 microns, has a powerfuldemagnetizing effect and this gaphas little effect on core loss. Thissmall amount of air gap decreasesthe residual magnetism by shearingover the hysteresis loop. Thiseliminates the ability of the core toremain saturated.

A typical example showing themerit of the cut-core was in thecheck out of a Mariner spacecraft.During the check out of a scienceprototype, a large (8A, 200s) turn-

on transient was observed. The nor-mal running current is .06 amps,and is fused with a parallel redun-dant 1/8 amp fuse. The MM71design philosophy requires the useof fuses in the power lines of allnon-mission-critical flight equip-ment. With this 8 amp, inrush cur-rent, the 1/8 amp fuses were easilyblown. This did not happen on everyturn-on, but only when the corewould latch up in the wrong direc-tion for turn-on. Upon inspection ofthe transformer it turned out to bea 50-50 Ni-Fe toroid. The designwas changed from a toroidal core toa cut-core with a 25 micron air gap.The new design was completelysuccessful in eliminating the 8-Aturn-on transient.

Figure 31

Same as Figure 30 But the Core was Cut and

Operating With a Maximum Flux Density Value

of Boperate = B maximum Bresidual

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Figure 32

Typical Inrush Current of an Uncut Core

Operating From an ac Source

Figure 33

Same as Figure 32 But the Core was Cut and

Operating With a Maximum Flux Density Value

of B operate = Bmaximum B residual

ConclusionsLow-loss tape wound toroidal

core materials which have a verysquare hysteresis characteristic(B-H loop), have been used exten-sively in the design of spacecrafttransformers. Due to the square-ness of the B-H loops of these

materials, transformers designedwith them tend to saturate quiteeasily. The result of this is that largevoltage and current spikes canoccur which cause undue stress onthe electronic circuitry. Saturationoccurs when there is any unbalancein the ac drive to the transformer, orwhen any dc excitation exists. Also,due to the square characteristic, ahigh residual flux state (Br) mayremain when excitation is removed.Reapplication of excitation in the

same direction may cause deepsaturation and an extremely largecurrent spike results, limited only bysource impedance and transformerwinding resistance. This can pro-duce catastrophic results.

By introducing a small (less than

25 microns) air gap into the core,the problems described above canbe avoided and at the same time,the low-loss properties of thematerials can be retained. The airgap has the effect of shearingover the B-H loop of the materialsuch that the residual flux state islow and the margin between oper-ating flux density and saturation fluxdensity is high. That is to say, theair gap has a powerful demagnetiz-ing upon the square loop materials.

Properly designed transformersusing cut toroid or C-coresquare loop materials will not satu-rate upon turn-on and can toleratea certain amount of unbalanceddrive or dc excitation.

It should be emphasized, how-

ever,that because of the nature ofthe material and the small size ofthe gap, extreme care and controlmust be taken in performing thegapping operation. Otherwise thedesired shearing effect will not beachieved and the low-loss proper-ties will be destroyed. The coresmust be very carefully cut, lappedand etched to provide smooth,residue-free surfaces. Reassemblymust be performed with equal care.

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