ENGINEERING RESEARCH INSTITUTE UNIVERSITY OF MICHIGAN ANN ARBOR PERIYEABILITY MEASUREMENTS IN MAGNETIC FERRITES Technical Report No. 9 Electronic Defense Group Department of Electrical Engineering By: L. W. Orr Approved by: ~oW (L ch H. W. Welch,. Project M970 TASK ORDER NO. EDG-4 COTRACT NO. DA-36-039 sc-15358 SIGNAL CORPS, DEPARTMENT OF THE, ARMY DEPARTEV4T OF ARMY PROJECT NO. 3-99-04-042 SIGNAL CORPS PROJECT NO. 29-194B-O September, 1952

TABLE OF CONTENTS Page LIST OF ILLUSTRATIONS ABSTRACT iv ACKNOWLEDGIENT v 1. INTRODUCTION 1 2. GENERAL REIMARKS 3 3. MAGNETIC RADIUS AND APPLIED FIELD 4 4, KINDS OF PERMEABILITY 5 5. TEST CORES 8 6. B-H LOOPS 11 7.,/ -H PLOTS 15 8. MU SURFACE 22 9. APPLICATION OF MU SURFACES 23 9.1 Tuning Units 27 9.2 Modulator Units 28 9.3 Flip Flop Units 28 10. BUTTERFLY LOOPS 28 11. INITIAL PERMiEABILITY IEASUR1V2E 33 12. TEMPERATURE VARIATION OF Ar 36 13. TDIME VARIATION OF PRo 37 APPENDIX I 42 APPENDIX II 44 DISTRIBUTION LIST 47 ii

LIST OF ILLUSTRATIONS Fig. No. Title Page 1 Variation of 1Magnetic Radius R with Toroidal Radii r and R 6 2 Definitions of Magnetic Parameters 7 3 Diagram of Test Core Showing Windings and Thermocouple 9 4 Ferrite Test Cores and Housing 10 5 B-H Plotting Circuit 12 6 Symmetric B-H Loops for Ferramic H at Zero Bias Field 14 7 Minor B-H Loops for Ferramic H with Varying Bias Field 14 8 J4A vs Ho Positive Values Only 16 9 A -H Plotting Circuit 17 10 Waveforms in /E-H Circuit 18 11 u -H Oscillogram for Ferramic I 21 12 Mu Surface for Ferramic G 24 13 Mu Surface for Ferramic H 25 14 Mu Surface for Ferramic I 26 15 /,uA vs Ho Positive and Negative Values 30 16 Butterfly Loop Plotting Circuit 51 17 Butterfly Loop Oscillogram for Ferramic G 32 18 /1-H Oscillogram for Ferramic G 32 19 10o-Measuring Circuit 34 20 Transitron Oscillator Circuit 38 21 Frequency-Temperature Curves for Ferramic G at Various Bias Fields 39 22 Frequency-Time Curves for Various Materials 41 iii

ABSTRACT The introduction gives a brief note on the development of magnetic ferrites. Practical laboratory methods of measuring magnetic parameters are outlined with particular attention to various permeability measurements. Incremental permeability is presented as a three dimensional "mu surface," and applications of this are discussed. Sample results on several specimens are presented. The temperature variation of reversible permeability and the time decrease of permeability are given for several materials. ACKNOWLEDG1IIENT The author wishes to thank Mr. A. Van Bronkhorst for his assistance in proofreading and Mr. D. M. Grimes for preparing the mathematical development in Appendix II. iv

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN PERMEABILITY MEASUREP1NTS IN MAGNETIC FERRITES i. INTRODUCTION There has been a constant search over the last century for magnetic materials of high permeability. The demands of the communications field and others have intensified this search to the point of creating a science out of the art of metallurgy, with particular attention to magnetic alloys. The parallel studies of the solid state have indicated that quite interesting magnetic properties should be obtained if one could reduce both the crystal anisotropy constant, K, and the saturation magnetostriction coefficient Xs to zero. Noting this, various workers12l attempted to form high permeability trinary alloys by first making tri-axial plots of the cruves K = O and Xs = O as functions of the composition.3 In some trinaries these two curves intersected and an alloy of that composition invariably had an unusually large value of Lo. The chief difficulty with metallic alloys is their high electrical conductivity, which gives rise to excessive eddy-current loss at high frequencies A modern class of magnetic material of low conductivity is the ferromagnetic spinel, or ferrospinel structure, commonly termed'ferrite." Synthetic ferrites were first suggested for high frequency applications by Hilpert4 in 1909. But it 1Zaimovski, A.S., J. Phys (USSR), 4, p. 563, 1941 2Snoek, J.L., New Developments in Ferromagnetic Materials, Elsevier, New York, 1947 3See for instance, Bozorth, R.M., Ferromagnetism, p. 100, D. Van Nostrand, New York, 1951 4Hilpert, S.,"MIagnetic Properties of Ferrites," Bert Deut. Chem. Ges., 42, pp. 2248-61, 1909

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN remained for Snoekl to apply the technique of K = 0, Xs = O to ferrites of various compositions, thereby obtaining new materials having high permeabilities together with the desired low conductivity. The saturation magnetization of magnetic ferrites (ca. 5000) is much less than that of iron, and they therefore find use at low inductions. The initial permeability is often 1000 or better, and values up to 4000 have been reported. Specific resistivity is generally in the range 104 to 109 ohm-cm, so that eddy-current losses are negligible even at high frequencies. The crystal structure of magnetic ferrites is described in the literature.2'3 In ferrite single crystals, and other grain oriented magnetic specimens the magnetic parameters vary widely with the direction of measurement.4 However, the ferrite specimens treated in this report are believed to be polycrystalline and of random orientation, so that their magnetic parameters are independent of the direction of measurement. In samples having internal strain where K and Xs are not zero, the magnetic parameters are again not exactly independent of the direction of measurement. The variation due to this cause in the specimens measured is not yet known. The initial permeability of a ferrite rises as the temperature is increased up to a point somewhat below the Curie temperature. Above this point the permeability falls off rather rapidly until the Curie temperature is reached. Since Curie temperature is a function of composition, it is possible to obtain 1Snoek, J.L., op. cit., p. 1 2Harvey, R.L., Hegyi, I.J. and Leverenz, H.W., "Ferromagnetic Spinels for Radio Frequencies," RCA Rev, XI, No. 3, pp. 321-362, Sept. 1950 3Bozorth, R.M., Ferromagnetism, p. 244, D. Van Nostrand, New York, 1951 4See for instance, Bozorth, R.M., Ferromagnetism, pp. 12, 44

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN materials with a variety of permeability temperature coefficients within a limited temperature range.l 2* GENERAL REMARKS The variety of methods -low used in various technical laboratories to measure magnetic parameters sometimes leads to confusion and misunderstanding. There is an obvious need for standardizing such methods. It is the hope of the Michigan Group that through this and future reports, a measure of understanding between various organizations can be reached regarding the magnetic rnarameters of significance, and the choice of techniques to measure them. It is hoped that this understanding will lead to the establishment of standard methods of measurement. The criterion of a good method is that it be simple, reasonably accurate and easily performed. The equipment involved should be capable of construction with readily available electronic components, and easily duplicated in other laboratories with modest facilities. The methods to be discussed were developed with this in mind. The determination of magnetization curves, hysteresis loops, and permeabilities depends upon (a) the application of known magnetic fields to the specimen, and (b) the determination of the resulting flux, usually by a sensing winding from which the flux density changes are calculated. The techniques for performing these measurements vary, depending upon the accuracy required and upon the shape of the specimen. For rod specimens, the most difficult quantity to determine is the field strength because the field See for instance, Harvey, R.L., Hegyi, I.J. and Leverenz, H.W., "Ferromagnetic Spinels for Radio Frequencies," RCARev, XI, No. 3, p. 359, Sept. 1950

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN created by a solenoid wound around the specimen is disturbed by the magnetic poles generated in it. The resulting "demagnetization factor" is a function both of the permeability and of the diameter - length ratio. Several schemes have been devised to overcome this difficulty by closing the magnetic circuit by means of a yoke. For ring specimens, the demagnetization factor is absent since no salient poles are generated in the specimen, and the applied magnetic field is easily determined. Various ferrites are available in both rod and ring forms as well as a variety of other shapes, however only ring samples were used in the work to be described. 3., MiGNETIC RADIUS AID APPLIED FIELD For a ring specimen wound with N turns of wire evenly disposed around the toroid, and carrying a current I amperes, the applied field H is given by the equation H = 4NI 4= NI _ NI oersteds (1) 10l 20tR 5R where R is the toroidal radius in cm, and ~ is the magnetic path length. If the inner and outer radii, r and R. of the specimen are different, a mean magnetic radius R must be found in terms of r and R so that the effective field H is given by H = NI/5R oersteds (2) As might be expected, the form of the expression for R depends upon the shape of the cross section. Expressions for rectangular and elliptical sectioned

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN toroids have been derived,l and are as follows: Rectangular cross section: R - r (3) logeR - loger Elliptical cross section: R I ( /a + Jr)2 (4) Plots of these functions are given in Fig. 1. The ratio R/r is plotted against R/r so that the curves may be applied universally. In a particular case, measurements of R and r are made, R found from the appropriate curve and the effective field obtained by applying Eq 2. 4. KINDS OF P.ERmSABILITY The normal permeability, AL, is generally considered to mean the ratio B/H in a magnetic specimen when it is in the "cylic magnetic state." The incremental permeability, AiL, refers to the permeability measured with superposed a-c and d-c fields, and indicates the ratio \B/Mi when a specimen is cycled around a minor hysteresis loop, such as that shown by path 12341 in Fig. 2. Here we have a d-c bias field HIo with a superposed a-c field of amplitude 1/2AH. The dashed curve represents the saturation B-H loop for the material. As aLi approaches zero, EL'A approaches a limiting value of tLr, the reversible Prmeability. When the material is demagnetized (B = 0), and no d-c bias is applied (Ho = 0), the reversible permeability,Lr becomes iLo' the initial permeability. The maximum permeability, ALm, is the largest possible value of uz when no bias field is applied (Ho = 0). In many ferrites materials ALL reaches the value ILm for AI - 4Hc. See Appendices I and II 5

1.9 1.8 O 0` 1.7 1.6 1 2 V'.5 I r 1.4 1.2 1.1 i N 0 R 1.0R 1.0 1.5 2.0 2.5 FIG. I VARIATION OF MAGNETIC RADIUS R WITH TOROIDAL RADII r AND R

SI313WV8Vd 3113N9~1Y SO SNOI.LINI-3a z91HV =V7 a- log ('H + EH)Z/I OH ~ H 0/ /0'H-2H = HV I / H+ ~H H V/ >tld/ - m -w- 8+ M-970 A-S4-10 RKL 4-7

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN Both t/ and /.r are dependent on the value of Ho and on the previous magnetic history of the specimen. /a is also dependent on the size of AH as will be shown later. In most ferrites, when operated well below the Curie temperature, the temperature coefficient of /lr is positive for low values of Ho and negative for high values of Ho. There is a value of Ho called the crossover field for which dpzr/dT = 0 over a wide temperature range. The crossover field for Ferramic G is ca. 4.5 Oe. from 25~C to 750C. 5. TEST CORES For testing magnetic properties, ferrite toroid cores are furnished with H and B windings, and occasionally with a thermocouple,l as illustrated in Fis. 3. The H winding is evenly spaced and extends the full 360 degrees around the toroid producing a uniform field, and minimum leakage flux. The B winding, or sensing winding, need not be evenly distributed, but may be lumped in one part of the toroid, because the total flux through any cross section is substantially the same at any instant. However, for the sake of symmetry, the B winding is also a 360 degree distributed winding. Figure I shows typical toroid cores in various stages of assembly. The cores at the top of the picture are shown as furnished from the suppliers. At the lower left is shown a core after applying a 200-turn B winding. At the lower right is shown a core in its housing. 1When measuring magnetic parameters in an oven, the voltage at the thermocouple tcrmiinals indicates the difference between core temperature and oven temperature. A copper-constantan thermocouple gives 40 millivolts per ~C difference in temperature. Since the thermal inertia of the thermocouple is small, it permits readings to be taken before the core comes to thermal equilibrium.

J JUNCTION AT OVEN TEMP. JI JUNCTION AT CORE TEMP. T TERMINALS T, HZ2B I T TERMINALS. WINDING Nm TURNS DIAGRAM OF TEST CORE SHOWING WINDINGS AND THERMOCOUPLE

t ~ ~ l ~~~~~~~~~j ra.i i.. iij /? -~~~~~~,: i a FIG. 4 FERRITE TEST CORES AND HOUSING 10

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN 6. B-H LOOPS Since ferrites are noted for their rather high resistivity, eddy current losses at audio frequencies are negligible. Hence, the B-H loop of a ferrite taken at 1000 cycles will be almost identical with the d-c B-H loop. (As the B-H loop of a material is traced arbitrarily slowly, it approaches a limiting position known as the static B-H loop or d-c B-H loop.) Oscillograms of 1000 cycle B-H loops may be obtained from test cores using the circuit shown in Fig. 5. In this circuit, an audio oscillator feeds a power amplifier which furnishes the 1000 cycle magnetic field to the core through the H winding. If desired, a d-c bias field may be applied by closing switch S1 and adjusting the d-c bias control. The bias in oersteds may be found by reading the current I indicated on the meter, and applying Eq 2. Both a-c and d-c components of current flowing in the H winding also flow in the resistor RH, forming a voltage drop proportional to the applied field. This voltage is applied to the X input of a d-c coupled oscilloscope, such as a Dumont Mod. 3041-H, so that horizontal displacement of the beam is always proportional to the applied field. The X axis of oscillograms may be calibrated in oersteds using the bias circuit described above and Eq 2. The capacitor CH is so chosen that its capacitive reactance at oscillator frequency is low compared with other impedances in the H circuit. Thus different values of d-c bias may be applied without affecting the amplitude of the applied a-c field. Components RB and CB form an integrating network which connects the B winding with the Y input of the oscilloscope. The time constant RBCB of this network must be several orders of magnitude larger than the period (I/f) of the| 11 -

N - 81- 1 7)1i E - t's -, OL6 - Y ~CONT~COROLRE Si " 45V H, B R AUDIO POWER-H PLOTTING CIRCUIT C CILLATOR 1 IAMPLIFIER RH 2 H Bl BIAS CO.NTROL S2!2

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN oscillator, in order to obtain a faithful B-H display. % must also be chosen several orders of magnitude larger than the inductive reactance of the B winding, so that errors due to loading of the B winding will be negligible. The instantaneous voltage el at terminals B1, B2 is given by el = NBA dt x 10-8 volts (5) where NB is the number of turns of wire on the B windings, A is the core cross section area in cm2, and B is the mean flux density in gauss through the area A. If RBCB >> l/f, the voltage e2 across CB is given by Np II eJAB -8 "e2 ~ _1__ el dt = x 10 volts (6) RBCB RBCB and hence B' RBCB x o10 e2 gauss (7):NBA Equation 7 is used in calibrating the B axis of the oscillogram, after a voltage calibration is made. Figure 6 is an oscillogram showing a series of symmetric B-H loops obtained with the B-H circuit of Fig. 5, and a test core of Ferramic H. The largest loop has a tip induction of 2.76 kga. at a tip field of 1.8 oe. The meas ured parameters from the oscillogram are as follows: Br = 1.76 kga. f"max 3500 Bm = 2.76 kla. Lo' 830 (estimated) Hc = 0.25 oe. These values approximate the data furnished by the supplier.

P.-Z t-d-V - W FIG. 6 SYMMETRIC B - H LOOPS FOR FERRAMIC H AT ZERO BIAS FIELD FIG. 7 MINOR B-H LOOPS FOR FERRAMIC H WITH VARYING BIAS FIELD

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN It is possible to display minor hysteresis loops at various values of d-c bias field, Ho. Oscillograms of such loops are shown in Fig. 7. From left to right the loops are for Ho = 0, 0.25, 0.50, 0.75, 1.00 and 1.25 oe. The specimen is a core of Ferramic H. If the tips of a minor hysteresis loop are joined by a straight line, its slope is the incremental permeability, /AL. If such lines are drawn on the loops of Fig. 7 their slopes, being measures of Ah, indicate the variation with Ho. From this figure, six points could be plotted on a /iA - Ho curve. 7. - H PLOTS A plot of incremental permeability /Lz as a function of uni-directional bias field Ho is shown in Fig. 8. The plot shows that /a is double valued, being generally larger for an increasing bias field than for a decreasing one. In addition, the value of /z is also a function of AB, the magnitude of the AC field. Continuous plots of this type may be obtained from oscillograms made with the circuit shown in Fig. 9. A free-running, symmetric multivibrator, VT1, having a period of approximately one second, drives the relay open and closed. Capacitor C4 is thus alternately charged and discharged, generating a sawtooth voltage which varies betwreen ca. -50 volts and -5 volts (Fig.lOA) when resistors R15 and R16 are suitably adjusted. This sawtooth voltage, applied to the control grid of VT2, produces a d-c plate current variation (Fig. 10B) from substantially zero (cut-off), to a maximum of ca. 150 milliamperes, furnishing a slowly varying bias field, Ho. It is noted that this current variation is quite non-unifom, but tehis is no disadvantage, and there are two distinct advantages: 15

O 1.0 2.0 OERSTEDS FIG. 8 ~a VS. Ho POSITIVE VALUES ONLY N~~~~~~~1

INTEGRATOR r~CR0 IAUK AUDIO E SS 10 VTVM OSC I CORE 7R5 } R7 RELAY 470 lOOK 51K 2W VT2 _ PK.5 Ft-H PLOTTING CIRCUIT I VTI H2 Rg 6J6 5 =R5 Re 470 47 1OOK,' R15 CV.5M 1.0 FIG. 9~~ c~-!LTIG ICI ~._'.~4M!",'

RELAY RELAY RELAY RELAY CLOSES OPENS CLOSES OPENS I I I I II I PI 0 0 5 1.0 SECONDS 1.5 A GRID VOLTAGE OF VT 2 B PLATE CURRENT OF VT 2 FIG. 10 WAVEFORMS IN,.-H CIRCUIT

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN a. It produces a fairly uniform rate of change of magnetic flux which is sufficiently slow at all points so that the resulting emf induced in the B winding is negligibly small. b. It produces a horizontal oscilloscope sweep which is slow near zero current and rapid near the extreme. This is very helpful in photographing the oscillogram, for the a-c envelope has a large vertical dimension near Ho = 0 requiring a longer exposure for proper density on the film. The plate current of VT2 is passed in series through the H winding, the milliameter MA and resistor R4. The horizontal displacement of the beam is proportional to the voltage across R4 and hence to the bias field Ho. An oscilloscope with d-c coupled amplifiers (such as the Dumont 3041-H) is used to avoid low frequency phase shift. To furnish the aL-measuring signal, a sine-wave audio oscillator is connected to the B winding in series with resistors R2 and R3. It is found convenient to work the oscillator at a frequency between 1 kc and 10 kc. The actual frequency is not important, since it does not enter the calculations. LAH may be varied by adjusting either the oscillator gain or R2, It is desirable to have R2 large compared to the maximum impedance of the B winding so that the a-c current in this winding is sinusoidal and of constant amplitude despite winding impedance variations. It is also desired to keep the a-c impedance of the Ho circuit large to prevent excessive loading of the H winding. This is accomplished by the large plate resistance of VT2 (ca. 40,000 ohms) in series with the H winding. The value of All is found by reading the r.m.s. voltage drop e) across the standard 10 ohnm resistor R3 with a vacuum tube voltmeter (such as the Hewlett-Packard lod. 400 C). The quantity B is found by means of the integrating circuit R1C1 connected across the B winding. The vertical dimension of the 19

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN oscillogram is a measure of AB, and thus proportional to tAd for a fixed AH. The values of R1 and C1 are chosen to minimize the loading on the B winding, and to have a time constant R1 C1 such that i <<R1Cl<<T T1 where f is the oscillator frequency, and T is the period of the multivibrator VT1. An electrostatic shield surrounds the integrator circuit preventing the pickup of stray fields. A typical oscillogram, Fig. 11, indicates for Ferramic I the variation of zA over a range O0tHo t1.4 oe. The horizontal calibration is 0.05 oe. per small square. The value of AH is 0.74 oe. (peak to peak). The two horizontal streaks have a vertical separation of t~A = 1200. Oscillograms are easily made with the Land Polaroid Camera, and an exposure of several seconds at F:5.6 or F:8. They are reduced to plots such as Fig. 8 by voltage calibrating the horizontal and vertical axes, and employing the following calibration equations. Horizontal Io = HH oersteds (8) 5R R4 Vertical = 108 RCleV gauss (9) ANB lI = 2..lBe3 oersteds (10) 5R R3,u/'1 AB (11) 20

-6 c - d - vt OL6 - V FIG. II,- H OSCILLOGRAM FOR FERRAMIC I 21

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN where A = core cross section area (cm2) AB = range of flux-density change (gauss) produced by AR e3 = indicated r.m.s. voltage across R3 (volts) eH = horizontal dimension on oscillogram (volts) eV = vertical dimension on oscillogram (volts) Ho = d-c bias field (oersteds) LAI = range of a-c field (oersteds) TTB = number of turns on B winding II = number of turns on H winding R = *mean magnetic radius (cm) R 1C = time constant of integrator (sec) R3 = 1H - measuring resistor (ohms) R4 = Ho - measuring resistor (ohms) 8. ME) SURFACES It is of particular interest in many applications to present the incremental permeability ALa as a function of the two variables Ho and H. This can conveniently be done by a three-dimensional solid, the curved surface of which represents the function tzLA. It is convenient to present this solid in isometric projection, in which the axes of bLa' Ho and AH intersect at 120~. The mu surface is described by drawing the projected curves of intersection when it is sliced by two perpendicular sets of vertical planes which are parallel to the planes H = 0 and AZI = 0 respectively. See Eqs 3 and 4, p. 5 22

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN Since each slice for a plane of constant AH will have the doublevalued form of Fig. 8, the surface also will be double-valued except at Ho = O and Ho = Hax. To avoid confusion, only the upper branch of the mu surface will be presented here (i.e., the surface for Ho increasing). Figures 12, 13 and 14 show the upper mu surfaces obtained for Ferramics G, H and I. Each projection was plotted from a set of properly calibrated oscillograms made with the Land Polaroid Camera and the circuit in Fig. 9. Since no oscillogram is possible when Al = 0, the curve in the AlH = O plane is obtained by extrapolation, and is shown as a dashed curve in the figures. A study of mu surfaces gives a new insight into the magnetic properties of these materials and their specific applications. It is seen that the permeability changes rapidly with Al for small values of Ho but only slowly for large values of Ho. To understand this effect, it is helpful to refer to Fig. 2. Here the dashed curve shows the saturation B-H loop and represents the outer limits of the magnetic condition of the core. When Ho is large, the minor hysteresis loop is drastically confined by the branches of the dashed curve, and therefore its slope ( En) cannot change much with a variation in the size of AH. The intercept of the mu surface at the origin is denoted by ~Zo' the reversible permeability at Ho = O0 B = Br. This is not to be confused with the initial permeability 1o, which in ferrites is larger than io&'. A method of measuring oL is described in Section 11. 9. APPLICATION OF iMU SURFACES MIany magnetic applications are greatly facilitated by the use of mu surfaces, and three examlples are given as illustrations. 23

9 OIWV't3. 80.IO 3OlV.JnS n"Y 1'91-I M-0C1

/i - 420 zoo0o s00 loo *eo FIG. I3 MU SURFACE FOR FERRAMIC H 25~~~~

I)INb ~~ IZ -VO-0 OL6-WY / mox 2900 f~,' = 750 00-~~~~~~~~~~~~~~~~~~~- 16~~~~~~~~~~~~~~~~~~~~~~~~\ \~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~00~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~0 -%% f" ~~000' 00 0- > 11000 0lM S F F I 26~~~~~~~~~~~~~~~C ~~~~~~~~~~~~PO ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~.~.>.~!'',.~~~~~~ ~~~~~~~~~~~~~~~~~\I ~8 FIG. 14 MU SURFACE FOR FERRAMIC I 26

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN 9.1 Tuning Units Magnetic tuning units are of particular interest in radio receivers where electronic tuning is desired. Such units are ideally constructed of ferrite materials because of the low losses at high frequencies and the remarkable ability to change the incremental permeability, and hence the inductance of the unit, by applying a current to the control winding which produces a varying bias field. It is of primary interest to know the range of permeability for a particular material under various ranges of bias field. It is desirable, for instance, that the control field requirements be small for a given change of permeability. Such information is adequately given by a curve such as Fig. 8 drawn for a quite small r-f field, as would normally exist in the r-f stages of a receiver. In a superheterodyne circuit it is necessary to vary the local oscillator unit so that it tracks with the r-f unit. For most oscillators of variable frequency in which the frequency variation is obtained by changing the inductive element, the circulating current in the tank, and hence the value of AH in the core of the inductor, will vary with frequency. A permeability curve of constant AH, such as Fig. 8, is no longer useful for engineering design purposes, since one must examine the manner in which the permeability changes when both H and AH vary as dictated by the circuit The mu surface for a particular material permits this type of analysis to be made without constructing a test unit. A laborious trial and error solution is thus avoided. One can see the variations of incremental permeability of a proposed tuning unit by tracing the curve of H vs All over the mu surface. An estimate of the tracking error may be made by such an analysis and certain materials may be discarded at once as unfavorable by inspection. 27

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN 9.2 Modulator Units For a magnetic modulatorI of maximum sensitivity, the maximum value of d,>L/dHo is desired. This will produce the largest unbalance signal for a given change in control field Ho. The mu surfaces not only indicate the best materials for this criterion, but give the optimum values of Ho and Al for a particular materials. An examination of the three surfaces presented in Figs. 12, 13 and 14 shows that Ferranmic I is the best of the three for this, even though its maximum permeability (2,900) is less than that of Ferramic H (3,700). By interpolateion from Fig. 14 one obtains for Ferramic I dHo/] = 12,700 per oersted, dH0o max at Ho =.05 oe. and AlI =.37 oe. 9.3 Flip Flop Units For a dynamic magnetic flip flop,2 one criterion is that a large total change of'a be produced by varying bA. An associated criterion is that d,4 Jd(AH) be a maximum for most rapid transition from low current to high current conditions. These criteria are easily checked for various materials from their mu surfaces. An examination of Figs. 12, 13 and 14 shows that Ferramic H is the preferred material of the three, and should be operated at zero bias (Ho = O) in this application. 10. BUTTERFLY LOOPS If incremental permeability is plotted against bias field Ho as the latter is cycled alternately through positive and negative values, one obtains 1See for instance, Wennerberg, "A Simple Magnetic Modulator for Conversion of Millivolt D-C Signals," AIEE Conference, Pasadena, California, June, 1951 2See for instance, Isborn, Carl, "The Ferro-Resonant Flip Flop," IRE Convention, New York, March, 1952 28

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN the familiar butterfly loopI as illustrated in Fig. 15. The circuit of Fig. 9 may be modified to display such loops by installing a reversing relay in the Ho circuit. This relay must operate so that the Ho circuit is reversed each time the current in VT2 reaches its minimum value (substantially zero). The modified circuit for performing this operation is shown in Fig. 16. Here relay 2 is the reversing relay, and is actuated by a flip-flop tube VT3 having two stable states. Since the relay must reverse at the time of minimum current in VT2, or when the voltage on capacitor C4 is most negative, it must operate at the time relay 1 closes. At this time, the left-hand plate of VT1 goes into conduction, and its voltage drops suddenly. When this plate-voltage drop is differentiated by the network C620, a negative pulse is formed which is applied to the grids of VT3 through diode Dl and capacitors C9 and Cl0. The negative pulse upsets VT3 and relay 2 reverses. Diode Dl prevents positive pulses from being applied to the grids of VT3i, so that the flip-flop VT3 is upset only at the proper times. When relay 2 closes, a small switching transient sometimes produces a random pulse in the B winding, smearing the oscillogram slightly at Ho = O. This difficulty can be overcome by arc-suppressing capacitors across the contacts of relay 2, but these produce capacitive loading of the H winding which is reflected by transformer action into the IL-measuring circuit, causing somewhat erroneous results. A typical butterfly loop obtained with this circuit for Ferramic G is shown in Fig. 17. Figure 18 shows the corresponding uni-directional Ho oscillogram for the same core and conditions as in Fig. 17. (The circuit is easily restored to its original uni-directional operation either by opening the cathode ITote: A similar loop for 45 Permalloy appears in Bozorth, R.M., Ferromagnetism, p. 542, but the direction of the arrows on the solid curve is incorrect. 29

S3n1'VA 3A11V93N aNV 3A^11SOd ~H'SA V7f gl'91 J SOa3J.S30 0'1 __O O~H'O0- 0.1970 4 RKL 2152

6 I)IN V- S - V OJ-6 - INY f- -- -- - - - - - ~- - - - - - - - - - r- ~~~~~~CRO I IR,~~~~~~~~~R L-J 25 lOW R5I AUDIO8TEST R? 0SC 3OE ai VTVM H, HH lOOK RELA C5 RELAY _ _ _ __5lyK.001 2 ~~~~~~~R R'12 R 14 R17 (3K) 1 470 39K 447M 2 2W C2 ++~~~~~~~. C2C VT2 VTI.56L6:: -00V -- ~.. __00VR i6J6 Re lOOK 4 Rs 4t RK Rg R 47 R13 1K IM. IM Rl' I___ R1 IM 47 R5.5M C4 IW I.0 Ce'001 IOK RE2 R21 S 36K R~~~~~~l d, ~~~~~~~~~~~36K 39K C8 R24 R' C7 TOkuLfp IM IM 50/.l./.Lf J6 +_ =150V DI IN34 R,,27,.Ru 270 R2e.82M 1W 2M C9c; ~~~' CIO282M Ioo/.L,/.Lf FIG. 16 BUTTERFLY LOOP PLOTTING CIRCUIT

FIG. 17 BUTTERFLY LOOP OSCILLOGRAM FOR FERRAMIC G FIG. 18,.-H OSCILLOGRAM FOR FERRAMIC G 52

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN circuit of VT3 with switch S, or by removing tube VT3 from its socket.) Calibration of butterfly loop oscillograms is done by employing Eqs 8 to 11 (incl.) as before. The shape of the butterfly locp is again a function of AH. The limiting position of the loop as {I —0 is a plot of /Ir vs Ho. Some authors apply the term butterfly loop to this plot only. The maximum value of /r in such a loop is never greater than /Loj and is obtained at a bias field equal to the coercive force Hc.l 11. ITITIAL PERMEABILITY MEASURvENT A simple and accurate method of measuring the low frequency initial permeability,0 of homogeneous toroids of uniform cross section will nowr be described. The precision is limited only by the precision of a standard resistance box and the precision of maintaining a given audio frequency. (It is assumed lthat the core dimensions may be measured to any desired degree of precision.) The circuit employed is very simple, and is shonm in Fig. 19. An audio oscillator of sinusoidal waveform and knowm frequency Xo is used in conjunction with a high impedance R1 to furnish a sinusoidal current. This current is passed in series through the U-turn winding on the toroid to be measured and the standard resistance box R2. In position 1, the reversing switch S permits measurement of the voltage drop across the coil, while in position 2 it permits measurement of the voltage drop in`2. In either position, the vacuuw-tube voltmeter and oscillator remain grounded. R2 is adjusted so that the two readings on the meter are identical. 0~3..

Zg- Z-6 lNl 9E - *S- V OL6-1N' TEST CORE I N TURNS RI AUDIO I I I o VTVM OSC - FIG. 19 o' - MEASURING CIRCUIT 34e

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN When the reversing switch S is in position 1, the input capacitance of the meter is across the coil. It is important to know the resonant frequency -1/2 Wo = (LC) where L is the inductance of the coil, and C is the sum of the meter, coil and stray capacitances. If the oscillator frequency W<< Wo, errors due to resonant effects will be avoided. If the sinusoidal current is small, the flux density may be assumed to be sinusoidal and in phase with the current so that B =- B sin w t gauss. (12) The r.m.s. voltage generated across the N turn winding (indicated by meter in switch position 1) will be E1 = 2Nx 0B volts. (15) Thus AB= 2 El 108 gauss. (14) WALA The applied field caused by a peak current Imax has amplitude 1/2A1 so that 2N Im 2WN _- " AH 2 N __ 2 oersted. (15) 5R 5n -2 Where E2 is the r.m.s. voltage across R2 (indicated by meter in switch position 2). The incremental permeability is thus: _= El.R R2 108 -A El T2 ~108 (16)

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN When The two voltages are equalized - 5R R2 108 (17) As the signal level is reduced by reducing the oscillator gain, R2 will approach a limiting value of Ro. The initial permeability is then found from the equation -La = O2 108 (18) In applying the method, the following steps are taken. 1. DemagnetizeI the core. 2. Disconnect the demagnetizing circuit completely. 3. Apply a signal to the core as shown in the circuit. 4. Adjust R2 for E1 = E2. 5. Ilake successive reductions in signal amplitude and repeat 4. 6. Find Ro, the limiting value of R2, and apply Eq 18. The earth's magnetic field will affect the measurement of,Lo in certain materials depending upon their shape, size and magnetic properties. It may therefore be necessary to work the core within a magnetic shield to make an accurate measurement of bo. 12. TEPEIRATURE VARIATION OF L r The reversible permeability of most ferrites operated well below their Curie temperature has a positive temperature coefficient for low values of HO, ~he core may be demagne'tized by either a. applying a slowly decreasing 60 cycle field of initial value above saturation and final value zero; or b. raising the core above its Curie temperature, and cooling slowly to the desired temperature 36

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN and a negative coefficient for high values of H0. At some value of Ho called the crossover field, the temperature coefficient is approximately zero over a wide temperature range. Since the inductance L of the winding on a magnetic toroid varies directly as its permeability, the resonant frequency f = 1/2i /aT of an oscillator tank circuit containing the toroid will represent the permeability variations An increase in F produces a decrease in f. A transitron oscillator circuit for examining such frequency variations is shown in Fig. 20. A very small circulating current is used in the tank circuit so that the variation of P'r will be represented. Frequencies may be measured with a calibrated communications receiver of suitable frequency range. The resonant frequencyl at room temperature (253C) is denoted as fo and the ratio f/fo is plotted for various values of bias field Ho and for different temperatures. The results on Ferramic G are illustrated in Fig. 21. It is seen that the crossover field for Ferramic G is about 4.5 oe. from 253C to 80~C, and about 3.0 oe. from 75~C to 100~C. Thus the crossover field decreases as the temperature is increased. It is noted that the temperature coefficient of frequency is rather large and positive above 1000~C at Ho = 6 oe. This indicates that the value of dILr/dT is strongly negative under these conditions. 13. TfIIE VARIATION OF /lo Some types of ferrites after receiving a demagnetization treatment and then left alone at room temperature, suffer from a slow decrease in initial The frequencies employed ranged from 0.2 mc to 5 mec 37

BALLAST RESISTOR + Io5V + 105 V 68K 37v i20K ||| | CIOMH RFC 17V 17K 6.8 K.01 B-0 2 v G. 2TANK CORE FIG. 20 TRANSITRON OSCILLATOR CIRCUIT 38

1.20 H= 6.0 OERSTED 1.100 TH: 4.5 OERSTED 1.00 Do f/f H 5F0 OERSTED 0.90 E __ __ 0.80. 0.70 0.60 10 20 30 40 50 60 70 80 90 100 110 120 TEMP OC FIG. 21 FREQUENCY-TEMPERATURE CURVES FOR FERRAMIC G AT VARIOUS BIAS FIELDS

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN permeability. The effect may be observed by noting the resonant frequency over a period of time using a test core in the oscillator circuit of Fig. 20. The oscillator is left on continuously, but the core is inserted only long enough to permit a reading to be taken. Approximately twice the per cent rise in the resonant frequency indicates the per cent decrease in HDo. This effect is mentioned by Snoelk2 and was found to appear only in certain materials. It was not observed in Ferramic B or Ferramic I. The frequency drift in several other materials is illustrated in Fig. 22. Ferramic G shows the largest effect, and appears to take longest (ca. 20 hours) to come to equilibrium. 1The actual relation between LA/pz o and Af/fo is given by the series = -2 2 fo For example, a 4c5 rise in frequency represents a 7.5% decrease in permeability.'Snoek, op. cit., p. 1...._~~~~~ 4~0.... —~~II

N 0 x FERRAMIC G o FERRAMIC H o FERRAMIC J + FERRAMIC C w 0 / LL 0.01 0.1 I 0 100 TIME IN HOURS FIG. 22 FREQUENCY-TIME CURVES FOR VARIOUS MATERIALS

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN APPENDX I Mean Magnetic Radius of Toroid of Uniform Rectangular Cross Section It is desired to find R for the toroid such that the average field H= * f| dA (l9) A is given by H= 5R oersteds. (20) For a rectangular cross section, R dA = tdx ri t A=t dx xt(R - r)dx = t(R - r) The field in the element dA of radius X is given by = 5(21) Hence the average field from Eq 19 is R H =' t(R-r) dx loge R - loge r (22) =5 R-r..,.~~~~~~~~~~~1

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN And the value of R to be used in Eq 20 is therefore R log= R - r (.235) log R - looge r for a rc_?angular cross section. _~~~~~~~~~~~~c

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN APPENDIX II Mean MIagnetic Radius of Toroid of Uniform Elliptical Cross Section! R or The toroid has inner and outer i_ P a| q Iradii r and R, and thickness t. Let p -= (R + r) f and q = (R - r) The ordinate y will be given for an elliptic section by the equation y = [q2 (x p)2] 2 (23) where t k = 2q' The element of area dA = 2y dx 2k [q2 _d(xp)2] 2 dx (24) and the section area R P+q A fdA 2k j [2- (x p)] 2 dx (25) r p-q t44

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN This integral is equal to q A = 2k J (q2x2) 2 dx -q 1. ~-q~q = k [(q2 x2) 2 + q2 sin (x)] -q k q2it. (26) It is desired to find R such that the average field H= A Jf9dA (19) is given by H = 5R (20) Substituting Eqs 21, 24 and 26 in Eq 19 and simplifying, we obtain p+q H =2N 42 _ (xdx (27) 5q Jr x p-q To solve this integral, we shall let x - p = q cos G dx = - q sin e de and [q2(xp)2] 2 = q sin.

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN Substituting these in Eq 27, we obtain o H 2NI q2sin2 9 d.q H 5q J q cos e + p to H- q cos (p2de + q of cos9 1 2 q cos e + p 5q It q cos 9 + p This may be integrated by Pierce's Tables No. 300 giving 2IH = p9 - p2 q tP tan p2_ 2 tan 2111 - 2 (P_ 2_ q2 ) (28) Eliminating H from Eqs 20 and 28, and substituting for p and q, we have 2 2 (p-) (R- r)2 4 (R + r - 2 /Jr): ( JR ti+ fJ)2 (29) the mean magnetic radius for a toroid of unifozr.l elliptical cross section...,.46

DISTRIBUTION LIST 1 copy M. Keiser Chief, Countermeasures Branch Evans Signal Laboratory Belmar, New Jersey 75 copies Transportation Officer, SCEIL Evans Signal Laboratory Building No. 42 BeLnar, New Jersey FOR - Signal Property Officer Inspect at Destination File No. 25052-PH-51-91( 1443) 1 copy W. G. Dow Prof., Dept. of Electrical Engineering University of Michigan Ann Arbor, Michigan 1 copy 11. W. Welch, Jr. Engineering Research Institute University of Michigan Ann Arbor, Michigan 1 copy Docu-nent Room Willow Run Research Center University of Mlichigan Arm Arbor, Michigan 10 copies Electronic Defense Group Project File University of Michigan Ann Arbor, 1Michigan 1 copy Engineering Research Institute Project File University of Michigan Ann Arbor, Michigan 47

UNIVERSITY OF MICHIGAN IIU I I