10 A JUNCTION TRANSISTOR T E T R O D E FOR H I G H F R E Q U E N C Y U S E , R. L . Wallace, Jr., L. G. Schimpf, E. Dickten. Proceedings, Institute of Radio Engineers, vol. 40, Nov. 1952, pp. 1395-1400. 11. D O U B L E B A S E E X P A N D S DIODE.APPLICATIONS, J. J . Suran. Electronics, New York, Ν. Y., vol. 28, Mar 1955, pp. 198-202.

Synopsis : A fairly simple theory is given and criteria have been established for analysis or design of magnetic circuits in which there are an unbalanced or d-c magnetization and a high alternating induction. High values of alternating induction and a nonlinear relation between induction Β and field strength Η are characteristics of magnetic circuits in power apparatus, in contrast to magnetic circuits in audio components. The relation be­tween induction and field strength during cyclic variation is given approximately by the d-c magnetization curve of the magnetic circuit. Maximum and mini­mum values of induction correspond to maximum and minimum values of field strength, but the average values of Β and Η are not simply related. The demagne­tizing effect of an alternating field super­imposed upon a direct field is the reduction of average induction after the application of the alternating field. This effect is due to the nonlinearity of the magnetization function. A simple circuit using the test sample and an auxiliary transformer has been devised for obtaining data on magnetic cores by direct measurement. Test results for representative cores have been organ­ized in a manner suitable for design use. Excitation volt-amperes, optimum per-cent gap, and core loss may be found as a function of a-c induction and unbalanced field strength. The data on magnetic materials are applicable to reactors and to transformers with unbalanced direct current such as units for supplying half-wave rectifiers. Analysis of the frequency com­ponents aids in understanding the operation

Paper 5 7 - 5 9 9 , recommended by the AIEE Basic Sciences Committee and approved by the AIEE Technical Operations Department for presentation at the AIEE Great Lakes District Meeting, Des Moines, Iowa, April 15-17, 1957. Manuscript submitted October 16, 1956; made available for printing March 20, 1957. H. L. G A R B A R I N O is with the Armour Research Foundation, Illinois Institute of Technology, Chicago, 111. This paper is based upon part of an investigation conducted for the Signal Corps Engineering Laboratories and Wright Air Development Center. The support of these organizations and the as­sistance of their technical staff members are gratefully acknowledged. This material is part of a thesis submitted to Illinois Institute of Tech­nology.

12. L O W - F R E Q U E N C Y C I R C U I T T H E O R Y OF T H E D O U B L E - B A S E D I O D E , J. J. Suran. Transactions, Professional Group on Electron Devices, Institute of Radio Engineers, vol. ED-2, no. 2, Apr. 1955. 13. D Y N A M I C S OF T R A N S I S T O R N E G A T I V E - R E ­SISTANCE CIRCUITS, B . G . Farley. Proceedings, Institute of Radio Engineers, vol. 40, Nov. 1952,

of half-wave supply circuit. Only the induced voltage of the primary winding and the average secondary current affect the magnetic circuit.

TH E P U R P O S E of this paper is to present criteria for the design of

magnetic circuits in which there are a combined d-c magnet izat ion and a high alternating induction. Electromagnetic devices in which there is an unbalanced magnetic force present difficulties as a result of the nonlinear relationship between induction or flux density and magnetic field s trength. This factor is of less importance when either the un­balanced magnetizat ion or the super­imposed al ternat ing induction is small, because existing design methods for such cases are reliable and widely used, principally in the design of inductance units and audiotransformers for elec­tronic circuits. In such cases inductance is almost independent of the magni tude of the al ternat ing induction. In power appara tus , however, al ternat ing induc­tion is always much larger, and the non­linear characteristics of the mater ial make it impractical to apply algebraic methods for obtaining relations among the magnetic quant i t ies . The quant i t ies are the instantaneous values of induction or flux density and the magnetizing force. Other impor tan t variables are the con­figuration of the magnet ic circuit, the type of joint used, and the grade and thickness of the material .

The superposition of d-c and alter­nating components of magnetizing force on magnetic mater ials gives character­istics which are quali tat ively similar in some respects to the case of an alter­nat ing magnetizat ion alone. In both instances the magnet ic quant i t ies m a y be related b y a hysteresis curve, which is usually given with induction or Β as

pp. 1 4 9 7 - 1 5 0 8 . (Additional references in this paper.) 14. N E G A T I V E I M P E D A N C E T E L E P H O N E R E ­P E A T E R S , J. L. Merrill, Jr., A. F. Rose, J. O. Smethurst. Bell System Technical Journal, vol. 33, Sept. 1954 , pp. 1 0 5 5 - 9 2 . (Additional refer­ences in this paper.)

ordinate and magnetizing force or Η as abscissa. Wi th an unbalanced magnetiza­tion, the curve is dissymmetrical. In addition, the average values of Β and Η are not simply related to each other by the d-c magnetizat ion characterist ic of the material , i n power appara tus , the hysteresis loop is relatively narrow, with or wi thout an unbalanced magnetiza­tion, so t h a t the relation between Β and Η is practically single-valued. There­fore the max imum and min imum values of induction and magnetizing force re­spectively are approximately related by the d-c magnetizat ion characterist ic.

The parameters which m u s t be deter­mined in the design of magnet ic circuits are : suitable material , value of flux density, proportions for the magnet ic circuits, and the nonmagnet ic gap in the core. I t is desirable t h a t the resulting device be as small as possible for the required power rat ing. This means t h a t operating densities—flux density in the core and current densities in the windings —should be made as high as design limitations will permit . Such l imitations m a y be core or winding losses, voltage regulation, efficiency of the unit , or permissible heating. T h e most universal l imitation in power and communicat ion equipment is permissible tempera ture rise. Regardless of other impor tan t specifications to be met, excessive tem­perature mus t be avoided. A char­acteristic of almost all power equipment is t h a t tempera ture rise increases as size decreases, for a given output . T o obtain max imum rat ing with least ma te ­rial; the designer should approach the permissible operat ing tempera tures of bo th core and winding. T h e quant i t ies which determine whether the magnet ic circuit has been properly designed are the core loss and the magnetizing reactive power required b y the core. Ei ther of these quanti t ies m a y limit flux density in the core. In physically small appara tus , the contr ibut ion of the magne­tizing power to the heat ing of the windings is usually the impor tan t design limitation, while in large equipment , core loss is usually the l imitation.

T h e analysis and da t a to follow are quant i ta t ively applicable to magnet ic cir­cuits in which there is an unbalanced

M a g n e t i c Circuits w i th D - C M a g n e t i z a t i o n

and H i g h A l t e r n a t i n g Induct ion

H . L. G A R B A R I N O ASSOCIATE MEMBER AIEE

3 3 8 Garbarino—Circuits with D-C Magnetization and High A-C Induction J U L Y 1 9 5 7

magnetization and a sinusoidal variation in induction or flux density. This implies a sinusoidal power source and a negligible resistance in the winding which excites the magnetic core. Appli­cations are transformers and reactors which carry an unbalanced direct current . Such an unbalance m a y be a recognized feature of a design, such as in a t rans­former supplying a half-wave rectifier, or it may represent a malfunctioning of some associated equipment, such as the failure of one rectifier in a full-wave ou tpu t circuit.

A device very closely related to the given examples is the saturable reactor or magnetic amplifier. Qualitatively, performance characteristics are similar to the transformer or reactor with un­balanced magnetizing force. The basic difference is t ha t the saturable reactor is employed with relatively large impedance in series with the winding which pro­vides an alternating excitation to the magnetic core.

Background References

There have been many publications on unbalanced magnetization of magnet ic circuits, which generally fall into the following categories : basic characteristics of magnetic materials, methods of mag­netic measurement, design of transformers and reactors which carry unbalanced direct current, saturable reactor circuits or magnetic amplifiers, and analyses of nonlinear circuits. Two extensive bibli­ographies have been published by R e x 1

and by Miles , 2 bo th primarily intended to present a background on magnet ic amplifiers.

M a n y investigators have found t h a t losses in magnetic cores are increased b y an unbalanced magnetization, among them Vallauri , 3 Rosenbaum, 4 Holm, 5

C h u b b and Spooner, 6 and Ball. 7 Schunck 8

studies the effect of an unbalance on wave shapes of flux, current, and voltage, and the reduction in inductance caused by the unbalance. He also showed t h a t average induction and average magne­tizing force are not simply related by the magnetization curve, a fact which is still not always appreciated. Impor t an t contributions were made by Niwa and others , 9 - 1 0 who found t h a t for a certain d-c magnetization the superposition of an alternating field m a y either raise or lower the average value of induction. At low field strengths, an al ternat ing flux increases apparent permeability, while a t high field strengths, an alter­nat ing flux reduces apparent permeability. Another s tudy of the effects of a super­

posed al ternat ing field on permeabili ty and losses is t h a t of Spooner . 1 1 Tests on silicon steels have been made by Sims and C l a y 1 2 and results are given for incremental permeabili ty, current wave shapes, and losses a t relatively high values of a l ternat ing induction and d-c magnetizat ion. More recent tests have been m a d e b y Nolen and Nies ten , 1 3

Baner jee , 1 4 Battel le Memoria l In s t i t u t e , 1 5

and Armour Research Founda t ion . 1 6

Circuits for obtaining losses and effective inductance are in two general classes: null-balance or a-c bridge types, and direct measurement types. In the bridge circuits, a coil on the magnet ic sample const i tutes one a rm of the bridge. T h e d-c magnetizing force can be supplied through the same winding or by a second winding on the sample. Lan d o n 1 7 has used the H a y bridge, which is characterized by a series capaci­tance and resistance in the a rm opposite from the inductance, and resistances in the other two arms. This method is compared with the Maxwell and Anderson bridges. Harr is and Wil l iams 1 8 discuss an improved Maxwell bridge. Sa lmon 1 9

analyzes the Owen and Anderson bridges. Wilhelm 2 0 has used a Maxwell bridge with an a-c and d-c supply impressed across the bridge. Other references on bridges are Rehfisch and Bissmire, 2 1

Welsby , 2 2 H a r r i s , 2 3 Dieterly and W a r d , 2 4

and R y d e r . 2 5 Charl ton and Jackson 2 6

have presented a circuit for direct measurement , using two similar cores with two windings on each. Teuche r t 2 7

used a comparat ive method, whereby a resistance s tandard is varied to draw the same current as t h a t drawn by the inductance to be measured. S ims 2 8

proposed the use of one core with two windings, each excited with bo th alter­nat ing and direct current . A circuit given by Nowotny and Sôcht ing 2 9 con­sists of one core and two windings, one with a-c and one with d-c excitation, a method which requires a high impedance in the d-c circuit. Danie ls 3 0 describes a method for obtaining a high impedance with an electronic circuit.

M a n y references deal with the char­acteristics and the design of transformers and chokes where one winding carries direct current . In 1909, Coales 3 1 devised a circuit to provide an inductive load for testing a l ternators . Two windings of two cores were connected in parallel for use as the load and two additional windings were connected in series to a d-c control source in such a way t h a t the induced a-c potentials cancel. This circuit appears to be the first application of a d-c controlled inductance used as a

load element. Coales found tha t in­ductance decreases and loss increases with the magni tude of the direct current. In 1927, H a n n a 3 2 published a widely used article on design of reactances and transformers, which relates inductance, direct current, magnet ic field, core geometry, and air gap in the core. Curves presented by H a n n a make it possible to select an opt imum air gap. Most of the da t a and design methods published subsequently are applicable only to much smaller a-c densities than would be used in power appara tus . Magnet ic and mater ia l da t a and analyses have also been given by H o w e , 3 3 Minton and Maloff, 3 4 Turne r , 3 5 - 3 6 Gur t le r , 3 7 - 3 8

Lanches ter , 3 9 Bea t t y , 4 0 Cosens , 4 1 Bag-gally,42^ Pa r t r idge , 4 3 Glazier , 4 4 and Lee . 4 5 - 4 6

Legg 4 7 has extended the method of H a n n a by devising an orderly design method for transformers and reactors carrying unbalanced direct current . Fur­ther analysis of this problem is given by Carter and Richards , 4 8 who also show t h a t average induction and average magnet ic field s t rength are not simply related unless a-c induction of density is small. Inductance design charts which account for winding resistances and turns are given by Crowhurs t . 4 9 An impor tan t factor in the design of t rans­formers supplying a half-wave rectifier is the type of ou tpu t filter circuit. Schade 5 0

has given widely used curves which relate transformer secondary and load quanti t ies according to frequency, load resistance, filter capacitance, and cir­cuit resistance. Seely 5 1 has studied the interesting half-wave rectifier ou tpu t circuit consisting of an inductance and resistance in series.

M a n y of the reference works on saturable reactors of magnet ic ampli­fiers provide qual i ta t ive information applicable to magnet ic circuits having an unbalanced magnetizat ion and an alter­nat ing induction. One of the early applications for saturable reactors was for the measurement of direct currents, making use of the change in a-c impedance of a winding when another winding on the core is carrying direct current. Circuits are described by R y a n , 5 2

Besag, 5 3 K r a m e r , 5 4 and Specht and Wagner . 5 5 T h e theory and use of d-c controlled reactors for various applica­tions is described by Boyajian. 5 6 Johnson and Merre l l 5 7 show how induction and magnet ic field s t rength are related for a sinusoidally varying induction, and give design data . They also point out t h a t a superimposed al ternating induction tends to demagnetize the core, in t h a t the average induction is thereby reduced.

J U L Y 1 9 5 7 Garbarino—Circuits with D-C Magnetization and High A-C Induction 3 3 9

Smith 5 8 compares many basic magnetic amplifier circuits and gives algebraic relations among al ternating induction, average induction, and average field strength.

General Relations

The nonlinear characteristics of fer­romagnetic materials cause considerable complication in an analysis of magnetic circuits wi th unbalanced magnetization. The problem consists essentially of relating induction or flux density Β and magnetic field s t rength H. A typical d-c magnetizat ion curve is given in Fig. 1. When the material is subjected to alternating values of Β and Η about some average values, the normal curve describes the approximate performance. Qualitatively, there are two ra ther dif­ferent conditions: comparatively small variations and comparatively large vari­ations. References which give extensive algebraic relations among the circuit quanti t ies cover the first case for small variations in Β and H.

In the second case, where the variation in induction Β is large, the d-c curve describes fairly well the relation between Β and H, a fact which is used for the following quali tat ive analysis. During operation under unbalanced conditions, the exact function consists of a displaced (nonsymmetrical) hysteresis loop, en­closing an area proportional to losses per cycle, as for magnetic materials operated without an unbalance. With a large variation in B, the quant i ty correspond­ing to incremental permeability is some average slope of the d-c characteristic, and this magni tude is greatly affected by the magni tude of the variation in density B. This dependence makes the second case more complicated than the first, inasmuch as incremental permeability is no longer approximately constant, as for low values or alternating density. Therefore the term incremental per­meability has little significance for the second case. I t is found tha t the most useful means for understanding the problem are: a graphical analysis of the magnetic quanti t ies and a s tudy of frequency components of the electrical quanti t ies.

The impor tan t variables which deter­mine the characteristics of a magnetic circuit are the average and variable components of induction Β and magnetic field s trength H, the geometry and material of the magnetic circuit, and the frequency of variation. Average flux density is defined as B 0 , and the average field strength is defined as HDC. A

Fig . 1 . Re la t ions b e t w e e n induct ion a n d field strength

sinusoidal component of flux density is assumed wi th the max imum value B. This is one half of the max imum varia­tion about the average Bo. I m p o r t a n t geometric parameters of the magnet ic circuit are the dimensions and the type of joint used. I t is assumed t h a t the flux density is uniform in the core a t every ins tant of t ime. In general, the presence of a joint in the magnet ic circuit makes the field s t rength nonuniform around the magnet ic circuit. Therefore the given average field H^c is an average around the core circuit as well as being an average in t ime. This quan t i t y can be related directly to the direct currents in the windings surrounding the core. If there is a direct cur ren t IDC in one winding of Ν tu rns then the average field s t rength may be defined as

Ηζχ7 = oersteds ( 1 )

where m is the mean length of magnet ic circuit in centimeters.

Average flux density is no t a simple function of the average field s t rength HjDc. T h e relation between these quan­tities is given by Fig. 1. If an average value of flux density Bo is assumed, with a superimposed variation B, then the resulting function of field s t rength H is uniquely determined by the d-c magnetizat ion curve, in so far as the hysteresis effect can be neglected. T h e average of the H function mus t be HDC. This establishes a relation between Bo and HDC. Average flux density cannot

be readily determined from the magnet ic characterist ic by graphical means, since repeated trials would be required, as­suming each t ime a certain value of average density. In a closed magnetic circuit i t is also difficult to determine average density by experimental methods. T h e only possible way is to t race the magnet ic history of an initially demagne­tized specimen.

F rom the foregoing discussion it is found t h a t the magnet ic variables of a given magnet ic circuit are uniquely determined b y the average and varying components of flux density. Since both of these together determine the un­balanced magnetizat ion HDC, it can be reasoned t h a t the performance could also be described b y the values of Β and HDC, which are readily determined.

S tudy of Fig. 1 shows t h a t the actual value of B 0 is smaller than i t would be if Β were zero. This is an il lustration of the demagnetizing effect which has been noted by several investigators. Smi th 5 8

shows this algebraically, and it can readily be confirmed from Fig. 1, t h a t for a constant value of HDC, B 0 decreases when Β is increased, and conversely. Also, if B 0 were held constant , then HDC increases when Β is increased. A demagnetizing effect is obtained only when the slope of the d-c curve decreases for an increasing H , or when the second derivative of the B-H function is negative. If the slope were increasing instead, the presence of an al ternat ing induction component Β would increase the value of B 0 . However,

3 4 0 Garbarino—Circuits with D-C Magnetization and High A-C Induction J U L Y 1 9 5 7

I N D U C T A N C E F i s . 2 ( l e f t ) . Cir ­cui t for magnet ic tests requ i r ing a large inductance

there is no advantage in finding the magnitude B 0 , since i t is only indirectly related to the more readily measurable quanti t ies. Similarly there is no need to find the values of the maximum and minimum induction.

Effect of a Nonmagnetic Gap

In addition to the other physical properties of a closed magnetic circuit, core geometry and material , an impor tan t variable is the nonmagnetic gap which may be introduced in some cases to obtain improved characteristics. A core joint of any type has an effect on the core properties which is similar to t h a t of the nonmagnetic gap. In most applica­tions of magnetic cores to power appara­tus it is desired t h a t the self-inductance of a given winding on the core have the highest possible value. When there is no unbalanced magnetization present, the highest self-inductance is obtained when a core joint of minimum reluctance is used. If the d-c magnetization curve of Fig. 1 is considered to be a plot of flux density or induction Β against average magnetic field s t rength Η around the entire magnetic pa th then the introduc­tion of a nonmagnetic gap increases the value of Η for each value of B, or bends the curve to the right.

A gap m a y yield an increase in self-inductance when a core has an unbalanced magnetizing current in one winding, which can be demonstrated qualitatively. The change in the magnetization char­acteristic of the core then tends to reduce the average flux density Bo of the core. The quanti t ies Β and H^e are considered constant and independent. The maximum flux density (B+Bo) is decreased and so is the maximum field strength corresponding to (B+Bo) . The cost of obtaining this advantage is a decrease of slope of the B-H curve in the regions of low H. In another sense, instantaneous permeability (actually a variable during a cycle) is increased a t high values of Η and decreased a t low values of H. Since i t is apparent t ha t a sufficiently large gap would decrease self inductance in any case, there m a y be some optimum value of nonmagnetic gap, which depends on B, HDC, core material and geometry. In a t rans-

F i g . 3 ( r ight ) . Circui t for m a g . net ic tests using an aux i l i a ry

transformer

former with unbalanced magnetization, the requirement of max imum self-in­ductance is equivalent to a requirement for min imum magnetizing current in the winding which provides a-c excitation to the core.

T h e quanti t ies Β and HDC are used to predict magnet ic characteristics of var­ious cores of various shapes and sizes. Similarly, i t is desirable to express non­magnet ic gap in a manner such t h a t the results for one size and shape can be used for others. I t can be readily shown t h a t per-cent nonmagnet ic gap should be used, or the rat io of air-gap length t o magnetic-circuit length. Although the rat io of gap-length to magnetic-circuit length is most impor tant , another con­sideration is the min imum effective gap length obtainable in par t icular cores. This effective gap length is present because of the necessity for joints, and depends very little on the size of the core. Typical effective gap lengths for various joints range from 0.0005 to 0.003 inch.

Because of difficulties associated with bridge circuits, a method of direct meas­urement is preferred for obtaining basic da ta on magnet ic cores and materials , even though i t m a y not yield the sensi­t ivi ty obtainable from a null-balance circuit. A suitable degree of accuracy in measurements on magnet ic materials is achieved when the measurement error is a small fraction of the variabili ty of the mater ial among identical samples. F rom this s tandpoint a direct method should give reasonable absolute and relative accuracies for typical da ta . A direct measurement can be made on a sample which has either one or two windings. When one winding is used, a-c and d-c excitation sources are interconnected. Adjus tment of the input and maintenance of a sinusoidal a-c wave shape can be obtained only with testing appara tus of unusual versati l i ty. Therefore a sample with two windings should be considered. T h e simplest example of a circuit wi th two windings is shown in Fig. 2. Ideally, the inductance in the d-c circuit should

A U X I L I A R Y T R A N S F O R M E R

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be infinite, such t h a t no al ternat ing current flows in the d-c winding. When this si tuation is obtained, the to ta l core excitation a t any t ime is the sum of the ins tantaneous pr imary current and the d-c secondary current . T h e power measured b y the wa t tme te r is composed of the pr imary winding losses and the core losses, while the ba t t e ry in the secondary circuit supplies the resistive losses of the secondary winding, the choke, and the control resistance. P rac ­tically, i t is desirable to use sufficient impedance such t h a t power transferred from the a-c winding is negligible. This could be accomplished wi th a choke m a n y t imes the size of the sample under test, and suitable for carrying the direct current . An al ternat ive is to measure t h e a-c real and reactive power components in the d-c circuit.

A solution to the problems presented by the circuit of Fig. 2 is provided by the circuit shown in Fig. 3. An alter­nat ing voltage can be introduced in the d-c circuit in such a manner as to oppose the voltage induced in the d-c winding around the test sample. This is ac­complished with an auxiliary transformer which need have only the same turns rat io as t h a t of the sample, and be capable of carrying the direct current . Wi th this circuit there will still be a relatively small net a l ternat ing voltage in the d-c circuit which is due to dis­tortion of the induced voltages from a sinusoidal wave shape. This in tu rn is caused b y resistances in the pr imary circuits of bo th test sample and auxiliary transformer. The net induced voltage will be of harmonic frequencies. How­ever, since the ne t voltage is of relatively low magni tude and of higher frequencies, a small inductance in the d-c circuit is adequate to make the a-c secondary current negligible.

T h e circuit of Fig. 3 is actually the same as t h a t described b y Coales , 3 1

which was used as an inductive load for al ternator tests. I t has apparent ly not been used to obtain da t a on magnet ic materials . The circuit is also the same

J U L Y 1 9 5 7 Garbarino—Circuits with D-C Magnetization and High A-C Induction

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F ig . 5 . C o r e loss of w o u n d core at 8 0 k i lo l ines per square inch ( 6 0 cps)

as t h a t of a simple, parallel-connected amplifier in which load resistance is very small and control circuit impedance is high. T h e major difference between the magnetic amplifier and the test circuit is t ha t the flux density variation in the magnetic amplifier is not sinus­oidal. Also, the maximum current cor­responding to maximum Η in the mag­netic amplifier is determined approx­imately by instantaneous applied voltage and load resistance, ra ther than by maximum B, as in the test circuit of Fig. 3 .

Test Results and Design Curves

The variables which have been studied experimentally to compile da ta for design use are a-c or incremental flux density B, average magnetic field strength HDC, length of nonmagnetic gap, grade of core material and thickness, core geometry, and frequency of the power supply, representative of parameters used in small electronic power t rans­formers. In using the circuit of Fig. 3, it would be desirable to measure core loss directly with the wat tmeter . How­ever, the window areas of typical small cores are not sufficiently large to accom­modate the wire sizes of the a-c winding tha t would make winding losses negli­gible. This is a disadvantage which could be overcome by using a much smaller ratio of core cross section to window

area. I t is less likely t h a t this difficulty would be encountered on much larger cores, because flux density is then limited by core loss ra ther t h a n b y exciting current . Wi th the typical small cores selected, i t is easy to measure winding resistance and to calculate winding loss. This is subt rac ted from to ta l input losses to obta in core loss. I t is desirable to use a low-power-factor-type wat t ­meter for magnet ic measurements .

Descriptions of two of the cores tested and graphical results are given in the Appendix. These da t a are con­sidered to be typical, b u t since only one sample of each was tested, the varia­tions which would exist among cores of the same type and construction are not known. Figs. 4 and 5 give excitation (volt-amperes per pound) and core loss (watts per pound) for the one core a t a typical a-c flux density. T h e abscissa HDC is defined by equat ion 1. T h e parameter is t he effective per-cent non­magnet ic gap, or rat io of effective gap to length of the magnet ic circuit.

Results of the tests have been studied to find if the gap which gives min imum excitation also yields min imum core loss. If the values of nonmagnet ic gap for min imum core loss and min imum excitation are appreciably different, then both should be considered in selecting the nonmagnet ic gap. In general, there is a fair correlation of conditions for min imum core loss and min imum ex­

citation current. T h a t is, min imum core loss and excitation, a t the various values of density Β and magnetizat ion HDC, are usually obtained with the same, or almost the same effective gap. There is bet ter correlation between the conditions for minimum total loss and minimum excitation current . To ta l input loss in these tests is the sum of core loss and pr imary winding loss. Since core pro­portions and winding sizes in the ex­perimental transformers are typical of those t h a t might be used in production units, it is indicated t h a t designing for minimum excitation will tend to yield min imum tota l losses, even though core losses are not quite a t the min imum in all cases.

In accordance with the foregoing discussion, i t is desirable to select a non­magnet ic gap which yields minimum excitation. Therefore the design con­ditions are determined b y the envelopes of the curves for excitation a t each flux density. F rom the da t a for a large range of flux densities, design curves have been derived, Figs. 6-9. Each design curve for excitation permits the deter­mination of excitation (the ordinate) and nonmagnet ic gap from two independent quanti t ies, flux density Β (the abscissa) and magnet ic field s t rength H^c (the parameter ) . T h e appropr ia te values of effective gap are marked off on the curves. T h e design curves for finding core loss also yield this quan t i t y as a function of density and magnet ic field s t rength. T h e core loss values given are those for

342 Garbarino—Circuits with D-C Magnetization and High A-C Induction J U L Y 1957

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ç» 8 0

6 0 8 0 A - C FLUX D E N S I T Y

IOO 120 I 4 0 - K I L O L I N E S PER SQ. I N .

C c

O R E : >TEEL

E I L : NON

A M I N/ - O R I E

V T I 0 N . I N T E D , A I S i - M - i s , κ m i l ;

= 16

_i 12

AVER O E R S

AGE TEDS

= 16

_i 12

AVER O E R S

AGE TEDS

< Ci

> \ ° / / /

' / / a

O

/ 9 y )

/ V

/ . 1 7 %

- A 1 ^ H oc = 0

i A - C F L U X DENSITY - K I L O L I N E S P E R SQ. I N .

F i g . 6 . Exci tat ion a n d gap for w o u n d c o r e — d e s i g n curves ( 6 0 cps) F ig . 8 . Exc i ta t ion a n d gap for stacked c o r e — d e s i g n curves ( 6 0 cps)

( J :ORE: î T E E L

W0U1* : G R /

JD, T UN - 0

i 1

WO Bl RlENTi

i T T JC Ξ Ό SIL

) INTS . ICON 12 M I L S

H 0 c = 18, A \ 0

ΠR A G ERSTE

E DS —

15

18, A \ 0

ΠR A G ERSTE

E DS —

f Hoc = 0

4 0 6 0 8 0 1 0 0 120 140

A - C FLUX D E N S I T Y - K I L O L I N E S PER SQ. I N .

Fig . 7 . C o r e loss of w o u n d c o r e — d e s i g n curves ( 6 0 cps)

2 . 4

2 2

2 . 0

1.4

1.2

( : 0 R E : STEEL

E I L : NON

, Α Μ Ι Ν - O R N

Α Τ Ι Ο Ν ENTEC

S , A I S I - M - 15, 14 M I L î

= 16

/ := 6

I / H 0 c = <

Y / f

Λ O 4 0 6 0 8 0 1 0 0 120

Λ - C F L U X D E N S I T Y - K I L O L I N E S P E R SQ. I N .

Fig . 9 . C o r e loss of stacked c o r e — d e s i g n curves ( 6 0 cps)

the per-cent gap which yields minimum excitation. Qualitatively, i t can be seen from the design curves t h a t a non­magnetic gap is likely to be indicated when flux density is intermediate or low, and field strength is high.

Half-Wave Rectifier Supply Transformer

T h e half-wave rectifier circuit, shown in Fig. 10, has been widely used, b u t has received little analysis. I t is often

used in certain impor tan t applications, such as bias power supplies, ba t te ry-charging circuits, and high-potential sources. T h e design or evaluation of transformers for half-wave rectifiers is similar to balanced types in t h a t size

J U L Y 1957 Garbarino—Circuits with D-C Magnetization and High A-C Induction 343

depends upon rating, density in the core, and current densities in the windings. I n order to obtain the smallest size, i t is necessary to use the highest flux and current densities t h a t heating or other limitations will permit . Secondary rms current is a function of the secondary voltage, transformer impedances, and the ou tpu t circuit. Pr imary rms current is a function of the secondary load, excitation current, and losses. With un­balanced magnetization, the excitation current is not the same as no-load current, as i t is, approximately, in balanced transformers. The problem in core design is to select the highest flux density in order to approach one of the two possible limits, either core loss or ex­citation volt-amperes. Both of these quanti t ies are functions of load current, flux density, and geometry.

Two typical load circuits have been shown in Fig. 10, the resistance load, and a resistance load with capacitance filter. The lat ter is also equivalent to the battery-charging circuit. An inductance-input filter is not shown. Although this filter is used in other types of rectifiers to obtain an almost constant rectifier cur ren t , th i s effect cannot be obtained with the half-wave circuit. With a sinusoidal voltage input to the primary, the secondary current for the resistance load will be half-wave pulses of undirec-tional current, as shown in Fig. 10(A). With the capacitance-input filter, the current consists of sharply peaked pulses every cycle, as in Fig. 10(B), which flows when the ou tpu t voltage exceeds the voltage of the capacitance. With an inductance-input filter, Seely 5 1 shows t h a t the peak magni tude of current is reduced over tha t of the resistance load, and t h a t t ime of conductance becomes greater t han 1/2 cycle. T h e average ou tpu t current is reduced, depending on the size of the inductance, and an infinite inductance would give zero ou tpu t cur­rent .

T h e two ou tpu t circuits of Fig. 10 are equivalent to the more complex filter circuits, in so far as the transformer is affected. With the capacitance-input circuit, the peak of the current occurs in t ime slightly before the peak of the voltage because the difference between secondary and condenser voltages is greater when secondary voltage is in­creased toward, ra ther t han decreasing from the peak value. The ratio of secondary rms current to load direct current may be best found from curves given by Schade 5 0 as a function of circuit resistance, load resistance, and filter reactance.

Fig . 1 0 . Basic ha l f -wave rec t i ­fier circuits

+ - o o -

Transformer-Circuit Frequency Components

Consideration of the different frequency components of currents and voltages leads to a relatively simple me thod for finding the pr imary current and the magnetic characteristics of the t rans­former wi th unbalanced magnetizat ion. Although there is a d-c component in the secondary caused b y the rectifier, there can be no s teady-state , direct voltage in the primary, because the supply is assumed to be sinusoidal, and an induced direct voltage would require t h a t the core flux increase continuously in one direction. Since there will be some resistance in the pr imary winding and the connected supply, any unidirectional t ransient current will decay to zero.

In the circuit consisting of a t rans­former supplying a half-wave rectifier, there are in general two nonlinear elements, t he rectifier in t he secondary circuit and the impedance corresponding to exciting reactance. An ideal rectifier m a y be considered as a voltage source instead of an impedance. As such, the rectifier has zero impedance during forward conduction, and is equivalent to a voltage equal and opposite to the impressed voltage during nonconduction. T h u s when considered as a voltage source, the rectifier supplies a half-sine wave with magni tude corresponding to the secondary voltage during the non­conducting half-cycles. This voltage function consists of an average of d-c component, and fundamental-frequency component which is approximately half of the secondary voltage, and of even-harmonic voltages. If, then, the mag­netizing impedance of the transformer were linear, the equivalent circuit of the transformer consists of linear impedance and two voltage sources, the voltage applied to the pr imary and the rectifier voltage. T h e solution for currents and voltages can then be obtained from the individual equivalent circuits shown in Fig. 11. Fig. 11(A) is a circuit for funda­mental-frequency currents ; Fig. 11(B) is a circuit for harmonic frequencies; and Fig. 11(C) is a circuit for the d-c component .

T h e component circuits in Fig. 11(C) would be applicable in case the magnet ic

core material were operated in regions of induction Β and magnetizing force Η where the relation between these two is practically linear for an air-cored transformer. P r imary and secondary resistances are assumed to be relatively small, so t h a t the harmonic voltage in Fig. 11(B) will be impressed a lmost entirely across the load resistance RL. Similarly, the direct voltage in Fig. 11(C) will almost all appear across the load resistance. However, the direct cur ren t which flows in this circuit provides an unbalanced magnetizing force on the core which is no t represented by a voltage drop in the circuit.

Next, the effect of a nonlinear magne­tizing impedance can be considered. T h e principle of superposition prohibi ts sep­aration of current and voltage frequency components associated with a nonlinear impedance. However, currents and volt­ages of harmonic frequencies across t h e magnetizing impedance Xm are very small, as can be deduced from Fig. 11(B). Therefore it is possible, when winding resistances are relatively small, to analyze the circuit as in Fig. 12. Here the fundamental frequency and d-c com­ponents are together in one circuit. T h e equivalent rectifier voltage in Fig. 12(A) consists of fundamental-frequency and d-c components only.

These equivalent circuits are an aid in showing how the electrical quant i t ies affect the operation of the core. If the applied voltage is nearly sinusoidal then the core flux will also be nearly sinus­oidal. The other effect upon the core is t ha t of the d-c component in the secondary which is determined by the magni tude of the d-c component and the secondary circuit resistance. T h e mag­ni tude of the d-c magnetizing force resulting from this current depends upon the number of secondary tu rns and upon the core geometry, according to equat ion 1 .

Primary Current

The significance of the equivalent-circuit analysis is t h a t the al ternat ing components of secondary ampere- turns are equal to the load component of pr imary ampere- turns . T h e sum of this load component and the excitation

344 Garbarino—Circuits with D-C Magnetization and High A-C Induction J U L Y 1957

( A )

Ρ - A M r - W N r - Vf

FUNDAMENTAL-FREQUENCY CIRCUIT

F ig . 1 1 ( l e f t ) . Equ iva len t c i r ­cuits of c o m p o ­nent vol tages wi th l inear i m p e d ­

ances

( A )

- W S r - - Λ Λ Λ Γ -f DC

FUNDAMENTAL- FREQUENCY AND DC COMPONENTS CIRCUIT

" P - W v - -wv-

I

F i g . 1 2 ( r igh t ) . Equ iva len t cir-cuits of c o m p o ­nent vo l tages w i th non l inear magne t i z ing i n ­

duc tance

( g ) HARMONIC-FREQUENCIES CIRCUIT

V D C

(0 D-C COMPONENT CIRCUIT

component is the pr imary current . T h e a-c excitat ion-current function of t ime plus t he secondary d-c component deter­mines the to ta l magnetomotive force which is related to the core flux function by the magnetizat ion curve of the material . T h e pr imary component of load current for a half-wave rectifier with a resistance load is shown in Fig. 13(C) as a half sine-wave function with­out an average component . I t is next necessary to establish the excitation component in terms of phase and quali­ta t ive form. Since the peak values of the flux function lag the peaks of the applied voltage by 1/4 cycle by definition, the peaks of the excitation component must also lag the voltage peaks by 1/4 cycle or 90 electrical degrees.

I t mus t be found which peak of the excitation current is sharper because of the sa turat ion effect. To do this, the primary load component of Fig. 13(C) can be considered for the moment as two currents, one exactly like the secondary current, including d-c component, p lus a constant negative pa r t equal to the average of the other. If this second negative pa r t were absent, then average core flux would be zero, because the sum of the first pa r t and secondary current would provide no unbalanced magneto­motive force. T h e fact t h a t the hypo­thetical second par t is negative indicates

Fig . 1 3 . W a v e shapes in ha l f -wave rectif ier s u p p l y trans­

former

-ΛΛΛ/— - w v -

I (β) HARMONIC-FREQUENCIES CIRCUIT

SEC. C U R R E N T

A V E R A G E C U R R E N T - l n

( A ) S E C O N D A R Y C U R R E N T W I T H R E S I S T A N C E LOAD

A V E R A G E C U R R E N T 2 Ι β ε

(β) S E C O N D A R Y C U R R E N T W I T H C A P A C I T A N C E I N P U T LOAD

T O T A L P R I M A R Y C U R R E N T

A P P L I E D VOLTAGE

P R I M A R Y E X C I T I N G C U R R E N T

(Q)PHASE R E L A T I O N S OF C U R R E N T S , VOLTAGE A N D F L U X

t h a t sa tura t ion tends to occur during the negative half-cycles of t he flux and excitation current , as shown in Fig. 13(C). This reasoning establishes t he qual i ta t ive form of excitation cur ren t and the displacement of t he average flux as given in the figure. Next; t he sum of the load and excitation components gives the t ime function of to ta l pr imary current . For very small flux densities the pr imary current becomes very sim­ilar to the given load component .

An ideal core mater ia l hav ing infinite permeabil i ty cannot be assumed in an analysis such as this , because t he pres­ence of the unbalance in t h e secondary would yield an infinite flux. Therefore,

an excitation component cannot be eliminated in the consideration of an ideal material . However, excitation current could be made small compared to t he pr imary load component of current if t he a-c density were so small t h a t the cyclic variat ion in magnet ic field s t rength (and corresponding ampere-turns) were relatively small compared to load-cur­ren t ampere-turns. These conditions require a magnet ic mater ia l wi th less t h a n infinite permeabil i ty.

T h e qual i ta t ive shape of p r imary current has now been established, and next i t is possible to find methods for calculating t he rms magni tude which determines the size of wire needed for the

J U L Y 1 9 5 7 Garbarino—Circuits with D-C Magnetization and High A-C Induction 3 4 5

winding. One method for finding pri­mary current is by graphical addition of the components as in Fig. 13(C), followed by computat ion of the rms value from the resul tant t ime function, t h a t is, by squaring the function, taking the t ime average, and then the square root of the average. A bet ter method is based upon elementary a-c circuit algebra. In genera l both excitation and load com­ponents of primary current are non-sinusoidal. If the magni tude and phase of all frequency par ts of each component were known, then the value of primary current coidd be readily determined. The resultant of each frequency might be found by combining the parts of the same frequency as phasors. Finally, the total current would be determined by adding in quadra ture the contribu­tions at all different frequencies. These calculations could be made using and obtaining rms values of current.

The excitation and load components of pr imary current have fundamental-frequency components which are almost in quadrature , or 1/4 cycle out of phase. If, in addition, the two components were sinusoidal, or if only one were sinusoidal and the other nonsinusoidal, or if the two components contained different higher harmonics, or if the corresponding harmonics in the com­ponents were in time quadrature , then the rms values of the two components could be combined in quadra ture to obtain accurately the tota l rms pr imary current. Although none of these condi­tions is satisfied in general, the principles suggest combination of the two com­ponents in quadra ture for the purpose of obtaining an approximation of pr imary current, and in practice, this is a suitable procedure.

For a 2-winding transformer having a turns ratio of unity, the rms load com­ponent of pr imary current is defined as t he alternating par ts of the secondary current function, which is simply the secondary current with the d-c com­ponent removed. Since the rms value of secondary current is precisely the quadra ture sum of d-c and all a-c com­ponents, it follows t h a t

IPL = VIS2-IDC2 (2)

where

IpL = rms load component of primary current J s = r m s secondary current IDC = average secondary current

For the case of an unfiltered ou tpu t resistance (the first load circuit of Fig. 10), the secondary rms current is 1.57 IDC, and the pr imary component of

load current is 1.21 IDC. Therefore pr imary current m a y be less t h a n secondary current , b u t t he addit ion of excitation in practical designs will m a k e it greater.

To ta l p r imary inpu t can be calculated by summing in-phase and quadra tu re volt-ampere components . T h e inpu t component of o u t p u t vol t-amperes is secondary voltage t imes the load com­ponent of pr imary current .

WpL = VSIPL = VSVIS2-IDC2 ( 3 )

Other real power components are the winding losses Wc and core losses Wi. The magnetizing component of excitation power is — Wi2, where Wex is the excitation volt-amperes given b y the curves of the appendix. Leakage . re­actance is neglected here, so t h a t the difference between pr imary and second­ary terminal voltages (with un i ty tu rns ratio) is due to resistance drops in the windings. Approximate pr imary current is approximate i npu t volt-amperes divided b y pr imary voltage Vp.

P~vP ~vP

x

V ( WpL + Wc + WtY + Wex2- Wi2 ( 4 )

where

Wrp = approximate total primary volt amperes

VP= primary voltage

A more refined method than equat ion 4 is no t justifiable in view of the variable na tu re of excitation among similar cores. However, the results obtained wi th the equat ion t end to be abou t 4 to 1 5 % too low for electronic power transformers. A reason for this is t h a t bo th WPL and Wex have higher harmonic components of the same frequency which are effectively added in quadra tu re regardless of actual phase. An inspection of Fig. 13(C) shows t h a t the second harmonics of the two components are actually in phase (of the phase + 7 2 cos 2ωή, so t h a t the approximate calculation might be ex­pected to give a low result.

Regulation and Turns Ratio

I n transformers carrying sinusoidal currents, corrections for voltage drops can be made using the rms current and resistance for each winding (and the leakage reactance, if appreciable). When secondary current or voltage wave shapes differ appreciably from sinusoidal forms, t he usual methods will yield voltage rat ios which are excessively in error. This problem has been m e t in tests on model transformers with un­

balanced direct current, which usually have complex current wave shapes.

To find a sufficiently accurate relation between pr imary and secondary volt­ages, an analysis has been made which is based upon an assumed sinusoidal applied pr imary voltage. If the secondary current is no t sinusoidal, secondary voltage mus t likewise be nonsinusoidal. Secondary rms voltage m a y be defined as an exact function of i ts several com­ponents.

Vs = VVsf2+Vsh

2+VsDc2 rms volts ( 5 )

where

F s / = rms fundamental volts F s ^ = rms harmonic frequency volts VSDC = voltage due to direct current

The te rm Vsh is composed of the second and higher harmonics, all of which add in quadra ture to yield Vsn>

Next, equat ions m a y be wri t ten for the secondary voltage components in te rms of the respective current components and impedances. These are obtained b y treat ing each of the three components of Vs independently.

VΡ Vs/±—-IsfR' ( 6 )

η

Vsh=ISHRF ( 7 )

VSDC=IDCRS ( 8 )

where

Vp = primary voltage η = turns ratio R ' = transformer equivalent series resistance

referred tô the secondary Rs = secondary resistance

To include the effects of leakage re­actance, to ta l impedance Z' could be subst i tuted in equat ions 6 and 7 for R'\ and i t would be necessary to consider the terms of the equat ions as phasors ra ther t han as magni tudes . T h e calculation of secondary rms load voltage Vs from equations 5 to 8 can be considered as successive operations on the no-load secondary voltage Vp/n. Firs t the term ISfR' is subtracted algebraically; then two other terms are added successively in quadra ture . However, in t rans­formers the voltage drop te rms are always small compared to Vp/n. Only the te rm subtracted directly in equat ion 6, makes an appreciable change in Vp/n ; t he addition of the quadra tu re terms can be neglected. I t follows t h a t Vs is closely equal to VSf, and t h a t the difference between Vp/n and Vs depends pri­marily upon the voltage drop of t he fundamental-frequency component of sec­ondary current through the transformer equivalen t resistance R'.

Garbarino—Circuits with D-C Magnetization and High A-C Induction J U L Y 1 9 5 7 3 4 6

S u m m a r y

Magnetic circuits with unbalanced magnetization, in many respects, per­form similarly to balanced circuits, b u t have additional characteristics which must be considered for accurate analysis or design. Special da t a on magnetic material properties are required to determine losses, excitation, and preferred gap of a core. To obtain these data, a convenient tes t circuit has been devised. Winding voltages and currents may be determined by the application of simple principles for nonsinusoidal quanti t ies.

A p p e n d i x . Test Data

Pertinent data on typical transformer cores tested are:

1. Wound-type core, windings on one leg Two butt joints Mean length of magnetic circuit: 7.22

inches Net cross-sectional area of core: 0.753

square inch Core weight: 1.5 pounds Steel: oriented silicon Thickness: 12 mils Test frequency: 60 cps (cycles per

second)

2. Shell-type core, EI laminations (scrap-less)

Leg width: 1 inch Mean length of magnetic circuit: 6

inches Core weight: 2.13 pounds Steel grade: audio-type equivalent to

AISI-M-15, nonoriented silicon Thickness: 14 mils Test frequency: 60 cps

The following equations give the ap­proximate per-cent gap which results in minimum excitation. In each of the cores it has been found tha t the per-cent gap is almost independent of flux density below some value of flux density.

1. Per-cent gap = 0.015 K D C - 0.003 B + 0.24

(Use Β = 90 if density is less than 90), where Hz>c = magnetic field strength in

oersteds, 0.495 times average ampere-turns per inch

Β = flux density in kilolines per square inch

2. Per-cent gap = 0.021 B.DC-0Me> B + 1.0 (Use Β = 70 if density is less than 70)

Application of these equations might yield a negative value for the per-cent gap. In this case the core joint with minimum effective gap should be used, a but t joint for cut, wound cores, and a lapped-butt joint for stacked cores.

References

1. BIBLIOGRAPHY ON T R A N S D U C E R S , M A G N E T I C AMPLIFIERS, Η. B. Rex. Instruments, vol. 2 1 , Apr. 1948, p. 3 3 2 .

2. BIBLIOGRAPHY OF M A G N E T I C AMPLIFIER D E ­

VICES A N D THE S A T U R A B L E R E A C T O R A R T , James G. Miles. AIEE Transactions, vol. 70 , pt. I I , 1 9 5 1 , pp. 2 1 0 4 - 2 3 .

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4. H Y S T E R E S I S L O S S I N I R O N T A K E N T H R O U G H TJNSYMMETRICAL C Y C L E S OF C O N S T A N T A M P L I ­T U D E , M. Rosenbaum. Journal, Institution of Electrical Engineers, vol. 4 8 , 1912 , pp. 5 3 4 - 4 5 . 5. E X P E R I M E N T S ON M A G N E T I C H Y S T E R E S I S , F. Holm. Elektrotechnische Zeitschrijt, vol. 3 3 , 1912 , pp. 9 2 8 - 2 9 .

6. E F F E C T OF D I S P L A C E D M A G N E T I C P U L S A T I O N S ON T H E H Y S T E R E S I S L O S S OF S H E E T S T E E L , L. W. Chubb, T. Spooner. AIEE Proceedings, vol. 3 4 , 1915 , pp. 2 3 2 1 - 4 2 .

7. T H E U N S Y M M E T R I C A L H Y S T E R E S I S LOOP, John D. Ball. AIEE Transactions, vol. 3 4 , pt. 11, 1915 , pp. 2 6 9 3 - 2 0 . 8. T H E A L T E R N A T I N G F L U X I N A N I R O N C O R E W I T H S U P E R P O S E D D I R E C T C U R R E N T M A G N E T I Z A ­TION, H. Schunck. Archiv fiir Elektrotechnik, vol. 12 , 1 9 2 3 , pp. 4 2 8 - 3 3 .

9 . M A G N E T I C P R O P E R T I E S O F S H E E T S T E E L U N D E R S U P E R P O S E D A L T E R N A T I N G F I E L D A N D UNSYMMETRICAL H Y S T E R E S I S L O S S E S , Y . Niwa, Y. Asami. Researches of the Electrotechnical Laboratory, No. 124 , June 1 9 2 3 . 10. F U R T H E R S T U D Y OF T H E M A G N E T I C P R O P E R T I E S OF ELECTRICAL S H E E T S T E E L U N D E R A S U P E R P O S E D A L T E R N A T I N G F I E L D A N D UNSYMMETRICAL H Y S ­T E R E S I S LOSSES, Y. Niwa, J. Sugiura, J. Matura. Ibid., No. 144 , May 1924 .

11 . E F F E C T OF A S U P E R P O S E D A L T E R N A T I N G F I E L D ON A P P A R E N T M A G N E T I C P E R M E A B I L I T Y A N D H Y S T E R E S I S LOSS, T. Spooner. Physical Review, vol. 2 5 , 1 9 2 5 , pp. 5 2 7 - 4 0 .

12 . I N C R E M E N T A L M A G N E T I Z A T I O N , L. G. A . Sims, D. L. Clay. Wireless Engineer, vol. 12, May 1935 , pp. 2 3 8 - 4 5 ; June, 1935 , pp. 3 1 2 - 2 0 .

13. SOME D A T A C O N C E R N I N G S U P E R P O S E D D . C . A N D A.C. M A G N E T I Z A T I O N OF M O D E R N T R A N S ­FORMER S H E E T S , H . G. Nolen, J. G. Niesten. Electrotechnik, vol. 2 4 , Apr. 1 1 , 1 9 4 6 , pp. 8 5 - 8 9 ; Apr. 2 5 , 1946 , pp. 1 0 3 - 0 6 ; May 9, 1 9 4 6 , pp. 1 1 4 - 1 5 .

14. O N T H E V A R I A T I O N S OF A.C. P E R M E A B I L I T Y OF T R A N S F O R M E R S H E E T S T E E L S W I T H D . C . M A G N E T I Z A T I O N , Β. M. Banerjee. Indian Journal of Physics, vol. 2 2 , 1948 , pp. 2 6 5 - 7 5 . 15. R E S E A R C H A N D D E V E L O P M E N T OF V A R I O U S C O N F I G U R A T I O N S OF C O R E M A T E R I A L S FOR OPTI­MUM T R A N S F O R M E R D E S I G N , F I N A L R E P O R T . Battelle Memorial Institute, Columbus, Ohio, Contract No. W 36-039-sc-38255, Department of the Army, Signal Corps Engineering Laboratories, 1952 .

16. R E S E A R C H A N D D E V E L O P M E N T OF N E W D E S I G N M E T H O D FOR P O W E R T R A N S F O R M E R S , F I N A L R E P O R T . Armour Research Foundation, Chicago, 111., Contract No. DA 36-039-sc-52656, Department of the Army, Signal Corps Engineer­ing Laboratories, 1955 . 17. B R I D G E C I R C U I T FOR M E A S U R E M E N T OF I N D U C T A N C E COILS W I T H A.C. S U P E R I M P O S E D ON D . C , V. D. Landon. Proceedings, Institute of Radio Engineers, vol. 16 , 1 9 2 8 , pp. 1 7 7 1 - 7 5 . 18. IMPROVED FORM OF M A X W E L L D . C . I N ­DUCTANCE B R I D G E , L. H. Harris, H. Williams. Post Office Electrical Engineers Journal, vol. 2 3 , 1930 , pp. 3 6 - 4 1 .

19. I N D U C T A N C E M E A S U R E M E N T S , R. D. Salmon. Electrician, vol. 113 , 1 9 3 4 , pp. 8 2 7 - 2 9 . 20 . M E A S U R I N G I N D U C T A N C E OF COILS W I T H S U P E R I M P O S E D D I R E C T C U R R E N T , Η. T. Wilhelm. Bell Laboratories Record, vol. 14 , 1935 , pp. 1 3 1 - 3 5 . 2 1 . A.C. I M P E D A N C E OF C H O K E S A N D T R A N S ­FORMERS, T. J. Rehfisch, Η. T. Bissmire. Wireless Engineer, vol. 18 , 1 9 4 1 , pp. 2 6 6 - 7 0 .

2 2 . T H E T H E O R Y A N D D E S I G N OF I N D U C T A N C E COILS (book), V. G. Welsby. MacDonald and Company, London, England, 1 9 5 0 . 2 3 . ELECTRICAL M E A S U R E M E N T S (book), F. K. Harris. John Wiley & Sons, Inc., New York, Ν. Y., 1 9 5 2 .

2 4 . A W I D E R A N G E A-C B R I D G E T E S T FOR M A G N E T I C M A T E R I A L S , D. C. Dieterly, C. E. Ward. Bulletin, American Society for Testing Materials, May 1952 , pp. 7 5 - 8 0 .

25. F E R R O I N D U C T A N C E AS A V A R I A B L E E L E C T R I C -CIRCUIT E L E M E N T , J. D. Ryder. AIEE Trans­actions, vol. 64 , Oct. 1945 , pp. 6 7 1 - 7 8 . 26 . L O S S E S I N I R O N U N D E R T H E ACTION OF S U P E R ­POSED A L T E R N A T I N G - A N D D I R E C T - C U R R E N T E X ­CITATIONS, Ο. E. Charlton, J. E. Jackson. Ibid., vol. 4 4 , 1925 , pp. 8 2 4 - 3 1 .

27 . E F F E C T I V E I N D U C T A N C E , H. Teuchert. Elek­trotechnische Zeitschrift, vol. 5 3 , 1932 , pp. 1 0 3 - 0 4 . 28 . I N C R E M E N T A L P E R M E A B I L I T Y A N D I N D U C T ­ANCE. L. G. A. Sims. Wireless Engineer, vol. 12, 1935 , pp. 8 - 1 6 , 6 5 - 6 9 .

29 . M E A S U R E M E N T OF I N D U C T A N C E OF D.C. LOADED T R A N S F O R M E R S , W. Nowotny, F. Sôchting. Elektrotechnik und Maschinenbau, vol. 54 , 1936 , pp. 4 7 3 - 7 4 .

30 . REACTOR M E A S U R E M E N T S , H. L. Daniels. Electronics, vol. 18, 1945 , pp. 1 4 6 - 4 8 . 3 1 . A M E T H O D OF U S I N G T R A N S F O R M E R S AS C H O K I N G C O I L S , J. D. Coales. Journal, Insti­tution of Electrical Engineers, vol. 4 2 , 1909 , pp. 4 1 2 - 5 4 .

3 2 . D E S I G N OF R E A C T A N C E S A N D T R A N S F O R M E R S W H I C H CARRY D I R E C T C U R R E N T , C. R. Hanna. AIEE Transactions, vol. 46 , 1927 , pp. 1 5 5 - 6 0 . 3 3 . D E S I G N OF C H O K E COILS A N D T R A N S F O R M E R S W H I C H C A R R Y A D I R E C T C U R R E N T , G. W. O . Howe. Wireless Engineer, vol. 5, 1928 , pp. 4 9 - 5 2 . 3 4 . D E S I G N M E T H O D S FOR SOFT M A G N E T I C M A T E R I A L S I N R A D I O , J. Minton, I. G. Maloff. Proceedings, Institute of Radio Engineers, vol. 17, 1929 , pp. 1 0 2 1 - 3 3 .

35 . C O N S T A N T I M P E D A N C E M E T H O D FOR M E A S U R ­ING I N D U C T A N C E OF C H O K E COLLS, F. M. Turner. Ibid., vol. 16, 1928 , pp. 1 5 5 9 - 7 0 . 36 . I N D U C T A N C E AS A F F E C T E D B Y THE I N I T I A L M A G N E T I C S T A T E , A I R - G A P A N D S U P E R I M P O S E D C U R R E N T S , F. M. Turner. Ibid., vol. 17, 1929 , pp. 1 8 2 2 - 3 3 .

37 . POLARIZED M A G N E T I C CIRCUITS, R. Gurtler. Hochfrequenztechnik und Elektroakustik, vol. 3 9 , Jan. 1 9 3 2 , pp. 2 - 7 ; Feb. 1 9 3 2 , pp. 4 8 - 5 9 .

38 . ECONOMY OF POLARIZED I N D U C T A N C E S , R. Gurtler. Ibid., vol. 3 9 , May 1 9 3 2 , pp. 1 7 1 - 7 3 . 39 . T H E AIR G A P T R A N S F O R M E R A N D C H O K E , F. W. Lanchester. Journal, Institution of Elec­trical Engineers, vol. 7 3 , 1 9 3 3 , pp. 4 1 3 - 1 8 . 4 0 . A L T E R N A T I N G - C U R R E N T I N D U C T A N C E OF A N . I R O N - C O R E D COIL C A R R Y I N G DC, R. T. Beatty. Wireless Engineer, vol. 11 , 1 9 3 4 , pp. 6 1 - 6 3 . 4 1 . S U P E R I M P O S E D DC A N D AC I N IRON-CORED-T R A N S F O R M E R S A N D C H O K E S , C. R. Cosensv Ibid., vol. 12 , 1935 , pp. 1 9 0 - 9 3 . 4 2 . I R O N C O R E D I N D U C T A N C E S , W. Baggallyv Ibid., vol. 13 , 1936 , pp. 7 - 9 . 4 3 . T H E I N D U C T A N C E OF I R O N - C O R E D COILS CARRYING D I R E C T C U R R E N T , G. F. Partridge. The Philosophical Magazine, vol. 2 3 , 1937 , pp. 9 9 - 1 0 6 .

4 4 . T H E INDUCTOR W I T H A I R - G A P P E D M A G N E T I C CIRCUIT, Ε. V. D. Glazier. Engineering, vol. 148 , 1939 , pp. 4 0 6 - 0 8 .

4 5 . REACTORS I N D.C. S E R V I C E , R. Lee. Elec­tronics, vol. 9 , 1 9 3 6 , pp. 1 8 - 2 0 , 7 6 . 4 6 . ELECTRONIC T R A N S F O R M E R S A N D C I R C U I T S (book), R. Lee. John Wiley & Sons, Inc., New York, Ν. Y., 1947 . 4 7 . OPTIMUM A I R G A P FOR V A R I O U S M A G N E T I C M A T E R I A L S I N C O R E S OF C O I L S S U B J E C T TO S U P E R ­P O S E D D I R E C T C U R R E N T , V. E. Legg. AIEE Transactions, vol. 64 , Oct. 1945 , pp. 7 0 9 - 1 2 .

4 8 . I N C R E M E N T A L M A G N E T I C P R O P E R T I E S OF SILICON S T E E L , W I T H PARTICULAR R E F E R E N C E TO T H E D E S I G N OF A I R - G A P P E D SMOOTHING C H O K E S , R. O. Carter, D. L. Richards. Pro­ceedings, Institution of Electrical Engineers^ vol. 9 7 , 1950 , pp. 1 9 9 - 2 1 4 .

4 9 . D E S I G N OF I R O N - C O R E D I N D U C T A N C E S C A R R Y ­ING D . C , Ν. H. Crowhurst. Electronic Engi­neering, vol. 2 2 , 1950 , pp. 5 1 6 - 2 3 .

50 . A N A L Y S I S OF R E C T I F I E R O P E R A T I O N , O. H. Schade. Proceedings, Institute of Radio Engineers, vol. 3 1 , 1 9 4 3 , pp. 3 4 1 - 6 1 .

5 1 . E L E C T R O N - T U B E C I R C U I T S (book), Samuel Seely. McGraw-Hill Book Company, Inc., New York, Ν. Y., 1950 . 5 2 . T H E T R A N S F O R M E R FOR M E A S U R I N G L A R G E

J U L Y 1957 Garbarino—Circuits with D-C Magnetization and High A-C Induction 3 4 7

D I R E C T C U R R E N T S , Harris J. Ryan. AIEE Transactions, vol. 18, 1901, pp. 169-90. 53. M E A S U R E M E N T OF LARGE D I R E C T C U R R E N T S O V E R LONG D I S T A N C E S , E. Besag. Elektrotechnische Zeitschrift, vol. 40, 1919, pp. 436-37. 54. SIMPLE D.C. I N S T R U M E N T T R A N S F O R M E R S W I T H T R U E C U R R E N T T R A N S F O R M E R P R O P E R T I E S , W. Kramer. Ibid., vol. 58, 1937, pp. 1309-13. 55. T H E T H E O R Y OF T H E C U R R E N T TRANSDUCTOR A N D I T S APPLICATION I N T H E A L U M I N U M I N D U S T R Y , T. R. Specht, R. N. Wagner. AIEE Transactions, vol. 69, pt. I, 1950, pp. 441-52. 56. T H E O R Y OF D-C E X C I T E D IRON-CORE R E ­ACTORS A N D R E G U L A T O R S , A. Boyajian. Ibid., vol. 43, 1924, pp. 919-36. 57. U N I V E R S A L C U R V E S FOR D-C CONTROLLABLE REACTORS, Walter C. Johnson, B. C. Merrell, R. E. Alley, Jr. Ibid., vol. 68, pt. I, 1949, pp. 31-40.

58. T H E M A G N E T I C AMPLIFIER AS A N O N L I N E A R CIRCUIT E L E M E N T , E. J. Smith. Proceedings, Symposium on Nonlinear Circuit Analysis, Poly­technic Institute of Brooklyn, Apr. 23-24, 1953, pp. 274-319. 59. M A G N E T I C CIRCUITS WITH D-C M A G N E T I Z A -

EN G I N E E R S have searched for many years to find suitable yardsticks to

evaluate insulation. On a scientific plane, one of the earliest approaches was made by Lamme and Steinmetz in 1912. 1 Ulti­mately, their work resulted in the prepa­rat ion of A I E E Standard no. ί . 2 This S tandard outlines the principles underly­ing the accepted method of classifying electrical insulation material . As long as reliance was placed on the insulating materials t h a t existed in nature , it was reasonable to classify materials on the basis of their chemical composition. But , within the past few years, the chemi­cal industry has made great advances. Today, approximately 350 bonding and impregnating resins known by various t rade names are available. Wi th the coming of these chemical investigations

Paper 57-392, recommended by the AIEE Di­electrics Committee and approved by the AIEE Technical Operations Department for presenta­tion at the AIEE Southern District Meeting, Jackson, Miss., April 3-5, 1957. Manuscript sub­mitted January 7, 1957; made available for printing February 8, 1957.

M. L . M A N N I N G is with the McGraw-Edison Com­pany, Canonsburg, Pa.

TION A N D H I G H A L T E R N A T I N G I N D U C T I O N , H . L. Garbarino. Ph.D. Thesis, Illinois Institute of Technology, Chicago, 111., June 1955.

List of Periodicals AIEE Proceedings, New York, Ν. Y. AIEE Transactions, New York, Ν. Y. Archiv fur Elektrotechnik, Berlin-Charlottenburg,

Germany Atii Delia Associazione Elettrotecnica Italiana*

Milan, Italy Bell Laboratories Record, New York, N.Y. Bulletin, American Society for Testing Materials, Philadelphia, Pa. Electrician, London, England Electronic Engineering, London, England Electronics, New York, Ν. Y.

Elektrotechnik, Berlin, Germany

Elektrotechnik und Machinenbau, Vienna, Austria

Elektrotechnische Zeitschrift, Wuppertal-Elberfeld, Germany

and the creation of t ru ly synthet ic ma­terials, i t is no longer rat ional to fit existing insulations in to t he old chemical-composition classes.

Exper imental work b y users and manufacturers alike of electric equip­men t has disclosed t he need for an en­tirely new concept of insulation classifica­t ion and evaluat ion. I t was found t h a t insulations should be classified as systems as well as materials . T h e manner in which the materials are applied and processed is of equal importance wi th the basic materials used. T h e electrical in­dustry , working th rough t he A I E E , de­veloped the concept of functional evalua­tion of insulation systems. Th i s concept now appears in t h e revised A I E E Stand­ard no. 1 published in 1954. 3 Revisions are scheduled for publication about J u n e 1957.

W h a t does t h e philosophy mean to users of electric equipment?

1. I t recognizes the determination of insu­lation life by tests made in comparison with an existing insulation system in a motor or in a transformer.

2. I t necessitates the re-examination of

Engineering, London, England Hochfrequenztechnik und Elektroakustik, Leipzig,

Germany

Indian Journal of Physics, Calcutta, India Instruments, Pittsburgh, Pa.

Journal, Institution of Electrical Engineers, London, England

The Philosophical Magazine, London, England

Physical Review, New York, Ν. Y.

Post Office Electrical Engineers Journal, London, England

Proceedings, Institute of Radio Engineers, New York, Ν. Y.

Proceedings, Institution of Electrical Engineers, London, England

Proceedings, Symposium on Nonlinear Circuit Analysis, Polytechnic Institute of Brooklyn, Brooklyn, Ν. Y.

Researches of the Electrotechnical Laboratories, Tokyo, Japan

Wireless Engineer, London, England

all insulation systems used in electric machinery by the manufacturer.

3. I t provides assurance tha t the manu­facturer has taken care to provide in­sulation systems proved by prescribed test procedures.

4. I t gives more information concerning end of life of electric equipment using certain insulation systems.

Performance of insulating materials is of u tmost concern to anyone using or manufacturing electric equipment . Mos t troubles of electric devices can be t raced to l imitations of insulating ma­terials, to their inability to wi ths tand tempera ture , a tmospheric or environ­menta l conditions, voltage disturbances, short circuits and overloads. Conven­tional books on the subject fail to keep pace wi th t he swift progress of research, development, and applications. Courses of s tudy in technical schools have not recognized sufficiently t h e importance of the subject.

This paper will outline w h y there is a need for new concepts; a brief review of the kinds of mater ials generally used in electrical equipment in fluid, solid, and gaseous form; t he use of solid insulation in dry- type transformers and other equipment r a t ed 80 C (degrees centi­grade) and 150 C tempera ture rise b y re­sistance respectively; application of gases and bibliography of A I E E papers soon to be available; complexities found in the evaluation of insulation and un­answered questions to be faced t oday ; basic factors t o consider in determining the hot tes t -spot t empera tu re in windings of transformers in par t icular ; basic con­siderations t o be faced in t h e prepara t ion of S tandards for appraising or evaluat ing

N e w Concepts in Evaluat ing Electr ic

E q u i p m e n t Insulation S y s t e m s —

T h e Problems E n c o u n t e r e d

M . L . M A N N I N G F E L L O W AIEE

3 4 8 Manning—Evaluating Electric Equipment Insulation Systems J U L Y 1 9 5 7