ENGINEERING RESEARCH INSTITUTE UNIVERSITY OF MICHIGAN ANN ARBOR STUDY, DEVELOPMENT, AND PRODUCTION OF FERROSPINELS APPLICABLE TO TUNING OF SEARCH RECEIVERS QUARTERLY PROGRESS REPORT NO. 4, TASK ORDER NO. EDG-6 Period Covering July 1, 1953 to September 30, 1953 Electronic Defense Group Department of Electrical Engineering By: D. M. Grimes B. Hershenov C. F. Jefferson Approved by: D. W. Martin H.,lch,, P. E. Nace Project Supervisor L. Thomassen Project 1970 CONTRACT NO. DA-36-039 sc-15358 SIGNAL CORPS, DEPARTMENT OF THE ARMY DEPARTMENT OF ARMY PROJECT NO. 3-99-04-042 SIGNAL CORPS PROJECT 29-194B-0 October, 1953

TABLE OF CONTENTS Page LIST OF ILLUSTRATIONS iii TASK ORDER iv ABSTRACT vi 1. PURPOSE 1 2. PUBLICATIONS AND REPORTS 1 3. FACTUAL DATA 2 3.1 Theoretical J-H Loop 2 3.2 Tuning Catastrophe 5 3.3 Transverse Permeability and Saturation Magnetization 8 3.4 Manufacture of the Ferrites 13 3.4.1 Equipment 13 3.4.2 Manufacture 14 3.4.3 Metallographic Polishing 17 3.5 Chemical Analysis 17 3.6 Low and Mid-Frequency Permeability Spectrum 18 3.6.1 Permeameter Measurements 18 3.6.2 Extension of Permeameter Range 20 3.7 VHF Permeability Spectrum 20 3.7.1 Analysis of data obtained 20 3.7.2 The Coaxial Line 21 3.7.3 Coaxial Inductor No. 2 26 3.7.4 The Z-0 Chart 27 3.8 Hall Effect 27 3.9 Magnetostriction 29 3.10 Specific Heat of the Ferrite Materials 29 4. CONCLUSIONS 30 5. PROGRAM FOR THE NEXT INTERNAL 30 REFERENCES 31 DISTRIBUTION LIST 32 ii

LIST OF ILLUSTRATIONS Page Fig. 1 The J-H Loop 3 Fig. 2 Tuning Curves for Different V-w Spectra 7 Fig. 3 Apparent Js vs Gap Width 11 Fig. 4 Apparent J vs Applied Transverse Field 11 Fig. 5 Remodeled Die 15 Figs 6 VHF Permeability Spectra 22 Fig. 7 Coaxial Line Assembly 23 Fig. 8 Coaxial Inductor Assembly No. 2 28 TABLES I Complex Permeability for Several Specimen 19 iii

TASK iRDER Title: STUDY, DEVELOPEDN, AIMfl PRODUCTION CW FERROSPINELS APPLICABLE TO TU ING OF SEARCH RECEIVERS Purpose of Task: To further the development of ferrospinels of different incremental permeabilities and low losses, with reference to specific applications of interest to the Signal Corps such as EF tuning units. Procedure: The approach to the general objective will include: a. The preparation, under controlled conditions, of specimens of different compositions; b. The measurement of parameters such as the incremental and initial permeabilities, the saturation inductance, the coercive force and the Q (figure of merit) at various frequencies; c. The interpretation of these magnetic parameters in terms of the composition, reaction temperature, pressure and other conditions in the preparation of the samples; d. The relationship of the solid state properties of the crystallite with the various measured magnetic parameters; e. Theoretical explanations, where possible, for the relationships found in d. above. Reports and Conferences: a. Quarterly Task Order Reports shall be submitted reporting technical detail and progress under this Task Order; b. Task Order Technical Reports of a final summary type are in general desirable and shall be prepared at the conclusion of investigations of each major phase. Such reports shall be prepared as iv

decided in conference between the Electronic Defense Group and the Contracting Officer's Technical Representative in the Counterneasures Branch, Evans Signal Laboratory. Personnel: Electronic Defense Group: Project Physicist: Mr. D. M. Grimes Countermeasures Branch, Evans Signal Laboratory: Project Engineer: Mr. Leon I. Mond Components and Materials Branch, Squier Signal Laboratory Project Scientist: Dr. E. Both Ccaments The classification of this Task Order as Unclassified shall not preclude the classification of individual reports according to the information they contain, as determined in conference with the Contracting Officer's Technical Representative. M. KEISER Chief, Countermeasures Branch Contracting Officer's Technical Representative v

ABSTRACT Theoretical work on an extension of the reversible magnetization to include the entire J-H loop is described. "Tuning Catastrophe" is described and predicted under certain conditions. Our technique for making ferrites is described, together with the results of permeability measurements on these cores at various frequencies. vi

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN STUDY, DEVELOPM1ENT, AND PRODUCTION OF FERROSPINELS APPLICABLE TO TUNING OF SEARCH R"ECEIVERS'QUARTERLY PROGRESS REPORT NO. 4, TASK ORDER NO. EDG-6 Period Covering July 1, 1953 to September 30, 1953 1. PURPOSE The purpose of this report is to summarize the progress made by Task Group 6 of the Electronic Defense Group from July 1, 1953 to September 30, 1953 on the Signal Corps Contract No. DA-36-039 sc-15358. The purpose of the task is to further the development of ferrospinels of different incremental permeabilities and low losses, with reference to specific applications of interest to the Signal Corps such as r-f tuning units. The proposed program of Task Group EDG-6 was outlined in previous progress reports. Only those items will now be reported which have been worked on during the period. 2. PUBLICATIONS AND REPORTS Mr. Paul Nace attended the National Electronics Conference in Chicago on September 28, 1953. No publications were issued during the quarter.

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN 3. FACTUAL DATA 3.1 Theoretical J-H Loop (D. M. Grimes) It has become necessary to alter the simple procedure of Sec. 4.1, QPR No. 3. Our object now is to attempt to first of all describe the J-H loop, and then to obtain an expression for it. Once this is gotten it is hoped that Xo will follow from it. To obtain the J-H loop we first note, as is very well known, that for low fields magnetization occurs through wall movement, at high fields through rotation of the direction of magnetization inside a domain away from the easy directions. On the basis of Brown's workl (Eq. 12 of II) one is lead to an expression of the form: J 1 Js 17 j- - ctnh X -; X = LoHJS (1) for the high field region. Lo is defined by X = 1/3 LoJs2. However Brown evaluates X at H = J = 0, and thus obtains X = Xo. It would seem that the X to be used here should be the X which represents the susceptibility due to rotational processes rather than X. However, Xrot and X o are usually of the same order so the difference probably would not show up experimentally. In the low field region the situation is complicated by "snagging" of the domain walls by internal potential energy minima. Without this snagging, the magnetization should be given byl: (Eq. 22 of II) - shown by the dashed curve of Fig. 1. 2

S 10LZ 80.J I. -99-V OL6-W J /a lb r Il I I~~~~ H I I FIG I THE J-H LOOP 3

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN d17 _Js 7s23 jFL tanh,ud (2) 313 X tJH L= 3 X 1 = HJS We now consider the question, what value of X should be substituted into the value for L here. When going from H = + to - o, the value of J is'- always greater than it would be were there no "snagging". When wall movements start the walls are restricted by snags from moving freely. Thus curve "a" is traced out. The dashed curve, for H > 0O is a monotonic increasing function of H with a monotonic decreasing derivative. From simple arguments one can show that the maximum slope of the dashed curve must be very nearly equal to the maximum slope of line "a". The maximum slope of the dashed curve occurs at J O0. Therefore in Eq. (2), LJUH 3v/I Xmax X7 = and L =. (2') -/3 where XmaX is the maximum slope of the J-H curve. These expressions, Eq. (1) and Eq. (2), were derived by Brown for the case made reversible by considering only minute changes in H. In effect we are now assuming they apply equally well to a system made reversible by hypothesizing the non-existence of snags. This, however changes the boundary conditions so that X,max appears in Eq. (2'). 4

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN We note the "snagging" will in effect change the value of H in the argument of Eq. (2). The value of the displacement, i.e. if one assumes = -yi(H-Ho), the value of Ho, will depend upon the volume of material through which a wall would have passed but is restrained from doing so by the internal snags. This can be represented by a distribution function representing the number of "potential" holes with a depth within a given region. The results of this model are currently being considered in some detail. 3.2 Tuning Catastrophe (D. M. Grimes; P. E. Nace) Several mechanisms affect the frequency dependence of the permeability of ferrite material. These arise from the effective mass of the domain wall, from precession of the direction of orientation of the domains and from dimensional resonances. These result in a given ~ - o curve for a given specimen with a given geometry. When one designs a tuning unit it is necessary to consider the above relationship between L and X in addition to the change in permeability of the material as a result of a change in its internal magnetization. It is intuitively obvious that, if i decreases with o, when J is increased in the core of a tuning unit causing V to decrease and thus o to increase, the frequency change is augmented by the original L-o relation. The result is a larger frequency range for the unit. We will now consider this quantitatively. 5

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN Consider Ct as a function of 4 and c. 4 can represent either magnetic biasing field or the internal magnetization. Thus: ~= ( 4(, ~) d = ild4( d +) + doc (1) It should be emphasized that Eq. (1) is a property of the particular ferrite core. If the permeability is measured by means of a parallel resonant circuit we have an additional relationship X —_ 1 Define (2) 50so 02 This givos: This gives: db = - 2d dw (3) Equations (2) and (3) are properties of the circuit into which the core is placed. Upon substituting (3) into (1), we obtain dlin 1 (lnp/ adln )J dlni (4) 6ln~9 1n

~291DOLZ HI8 Zt-99-V OL6-VN I C FIG 2 TUNING CURVES FOR DIFFERENT /o-@ SPECTRA

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN Note that if 1 ( lfpn) < -1, the slope of the ca- curve becomes infinite. A family of curves (-+ ) is plotted in Fig. 2 for different L-w spectra. Curve "b" in the shaded area represents a decreasing frequency for a decreasing magnetization. It can have no physical significance. If the oscillations are not large enough for the oscillations on line "a" to alter line "c" both frequencies may be present at the same time. In this case the frequency which suffers the largest loss, usually the higher frequency, will soon be damped out. Thus the path to be expected is that shown by the arrows. This effect could lead to holes in the frequency spectrum the receiver is being swept over. We will call the above discontinuity the tuning catastrophe. There is nothing in the above equations to limit them to ferrites. They would be equally applicable to ferromagnetic material. Also t could be replaced by ~ and the equations would be valid for the ferroelectrics. 3.3 Transverse Permeability and Saturation Magnetization (D' W. Martin; D. M. Grimes) A considerable difficulty encountered in magnetic measurements is the "demagnetizing field" induced in a specimen by free poles appearing at its surface when it is magnetized. This field is roughly proportional to the magnetization, where the _.... 8

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN proportionality constant N is dependent upon the shape of the specimen. N can range from zero, for special geometries, up to the value 4r for the limiting case of an infinitely short cylinder magnetized along its axis. In this instance, the demagnetizing field entirely cancels any applied field within the cylinder, and there can be no magnetization at all. Transversally, a toroidal core is essentially a disk, or very short cylinder. It is estimated that its "demagnetizing factor" N_ is about 0.8, although it is not precisely known, and 41 is really not even a constant. To see how this will effect measurements, let the true field H be given by: H = Ho - NJ where Ho is the applied field, and J the magnetization. Then 4rJ = (B - H) (B TH0)/ (l ) so the true J would be 5 times as great as the apparent magnetization, Ja = (B - Ho)/4rT for N = 0.8 Even more drastic is the 4w effect on the applied field necessary for a given degree of magnetization. For: Ho = H + NJ -1+ i (p - 1)] H

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN If L is large and N is not almost zero, Ho N = LH (2) 4w which may be larger than H by whole orders of magnitude. If the pole faces of the external magnet make perfect magnetic contact with the specimen surface, and the yoke provides a zero-reluctance path outside the sample for the flux, then ideally the effective demagnetizing factor will be reduced to zero. The new magnet mentioned in QPR No. 3, and now in service, was designed for this purpose. It has accurately parallel plane pole faces, of diameter over 40% greater than the core diameter, and the gap is continuously variable from zero to about 1 cm. To check its effectiveness, an old core has been fitted with a groove to hold the leads from the inside girdle winding, so that the latter do not project above the surface. Thus measurements could be made with both pole faces in firm contact with the core surfaces. The apparent Js of the core was then measured by the method of QPR No. 3, Sec. 4.2 with this geometry, as well as with several different gaps between core and pole face. In fig. 3, the apparent Js (in arbitrary units) is plotted against the height of this gap. It is seen that the curve rises sharply near the nominal zero, so that true Js (for perfect contact) is rather indeterminate. Further steps such as careful polishing of core surfaces, or filling the space between surfaces with a ferromagnetic dust, must be attempted in order to pin down a reproducible zero gap. 10

I.-. (C) 5000 r 0 at~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~t _ _ * ~~~~~~~~~~~~~~~~~~~~~~I (0 4000 +0 0 2 0 - i i -, 4 ~~~~~~/ ~ >-,, 3000 CL~~~~~~~~~~~~~~~~~~~~~~~~~I (010 _03(1+ 0 1.0 2.0 GAP (mm) FIG 3 1000 APPARENT Js VS MAGNET GAP 0~~~~~~~~~~~~~~~~ 0 1000 2000 3000 APPLIED FIELD Ho (OERSTED) FIG 4 B AND APPARENT J VS APPLIED FIELD

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN Although the windings are of No. 34 wire, the total area embraced by the B winding is several percent greater than the core area. Since the applied field is large, of the same order as B (eq. 2), the flux through this additional area constitutes an appreciable correction to B. Fig. 4 shows part of the B and{4rJa = (B - Ho)} vs. Ho curve of core GC-G5 for a geometry in which there are equal gaps on each side of the core, each of about 1/2 the sample thickness. Note that, with the above correction, the Ja curve levels off nicely beyond saturation. The saturation value of 1890 for 41Ja would be consistent with the parallel field value of 3400 if we take for the effective demagnetizing factor N.. 1890 _ A - 1 -- s — - 0.44 It should be emphasized that the abscissa of Fig. 4 is the applied field Ho. The true field H given by H Ho - NJ Ho B N 4r 4rr N is essentially unknown, since it is a small difference of two large terms. It is zero within experimental error up to the base of the curve, beyond which it increases rapidly up to about 1500 oersted. The apparent Js of this core has bqen found for several geometries, and each can be made to agree with the parallel data by a reasonable and consistent value of. One preliminary recheck 12

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN of the transverse incremental permeability has been done so far, by the method of QPR No. 2, using the new magnet. In this method, it is assumed that 4TJs is essentially equal to the measured B at which VA reaches its minimum, since H should be much smaller. In QPR No. 3 it is stated that this gives Js values some 50% larger than do the parallel measurements. The present readings give a value still somewhat large, but much less so. It would appear that the improved homogeneity of the field is probably responsible. So it appears at present that the difference in Js for the two directions is not real. Further study is in order to refine the methods and the corrections to settle the question fully. The present fluxmeter is found to be too sensitive. It must be shunted to stay on scale, and presents annoying drift problems. A less sensitive instrument has been ordered, which will help reduce experimental uncertainties. We believe that this and other refinements of technique will soon permit definite answers to some of the questions. Issuance of the Technical Report on the Theory of Reversible Susceptibility must await these developments. 3.4 Manufacture of the Ferrites ( C. F. Jefferson; L. Thomassen) 3.4.1 Equipment. The Harper Electric furnace, Model HL-6 arrived early in the quarter. The oven has a maximum temperature variation of 100 C at 12000 C when it is set on thermostatic control. The rate of heating and cooling is controlled by manually regulating a multiple tap transformer. The General Electric Reactrol system is being investigated as a means of automatically regulating the power input. 13

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN A 10 ton hydraulic laboratory press was obtained to use in pressing the cores. A heavier press is available for higher pressures. It was found that there was a considerable amount of magnetic material in the nickel oxide. A magnetic separator was constructed in the laboratory for removing it. The die used for pressing the cores has been modified to facilitate removal of the core from the die. Fig. 5 shows the die now in use. 3.4.2 Manufacture. The search for a better method of mixing the oxides is being continued. A high-speed mixer was tried, but since it was found that the mixer did not crush the lumps in the oxides the possibility of using an ultrasonic vibrator as a means of mixing the oxides is being investigated. Until a more satisfactory method is found the oxides will be mixed in the ball mill. Most of the cores made prior to this quarter were made without the use of a binder. This was done in order to reduce the number of variables in the preparation of the cores. Now that a greater number of cores are being made it has been found necessary to use a binder to lubricate the die and facilitate removal of the cores from the die. Several binders were tried, such as aerosol, carbowax and ammonium oleate. Ammonium oleate has proven to be the most satisfactory binder tried to date. This 14

~S91OLZ U- 91-9S-V OL6-W 3"OD I" ID 9" ID 16 A A LONG PLUNGER SLUG DIE BODY FERRITE SHORT PLUNGER SECTION AA FIG 5 FERRITE DIE 15

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN binder works remarkably well under high pressing pressure. Pressing pressures as high as 40 tons/ sq. inch have been used on specimens 2.2 mm thick without laminations. No higher pressures have been tried. No attempt has been made to evaluate the effect of the various binders on the fired core. All binders were evaluated only insofar as they effected the pressing operation. Cores have been made using pressing pressures of from 2 to 40 tons/ sq. inch. The density of the cores were calculated from the volume and weight of the cores. There does not appear to be any increase in density as the pressure is increased. There is, however, a considerable change in the percentage of linear shrinkage as the pressure changes: PRESSURE % LINEAR SHRINKAGE DENSITY (tons/sq. inch) 2 20.5 4.75 16 13.4 4.75 20 12.2 4.80 30 11.2 4.75 40 10.5 4.80 Micrographs of cores pressed at 2, 10 and 20 tons/ sq. inch were made. No distinction could be made between the cores as far as the voids were concerned. The oven is so arranged that the cores can be fired in an atmosphere of oxygen. The oxygen flow is regulated with a gas flow meter. The oxygen is introduced into the oven through a vycor tube placed in the chamber. 16

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN 3.4.3 Metalogra phc Polishing. The ferrite material is difficult to etch. It has been found that the grain boundries can be brought out, however, by etching for 1 minute in a boiling solution of.05 N SnC12 in concentrated hydrochloric acid. 3.5 Chemical Analysis (C. F. Jefferson) An analysis of a ferrite material for nickel and iron was obtained from the National Spectrographic Laboratories. From the values obtained, the per cent of 02 was determined by difference. This calculation indicated that the material was deficient in oxygen. This would indicate that some of the cations were present in a reduced state. For this reason it was desired to determine the amount of ferrous iron present in the material directly. The most direct method would be to dissolve the ferrite in HC1 under a C02 atmosphere and titrate the ferrous iron with potassium dichromate. It was found, however that none of the common solvents would dissolve the ferrite. The ferrite was even insoluble in HF. The only convenient method found to dissolve the material was to use SnC12 in HC1. For this reason the following method was used: The material was dissolved in a standardized solution of SnC12 in HC1 under a C02 atmosphere. After the material was dissolved; the amount of ferric iron was determined by titration with the same standard solution of SnC12. The total iron was then determined in the same sample using the potassium dichromate method. The amount of ferrous iron was then calculated as the difference _ ___ ~17..

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN between the total iron and the ferric iron. An analysis of ferrous iron by the above procedure on the same sample submitted to the National Spectrographic Co. showed no ferrous iron present. In order to check the above procedure, a laboratory now running routine ferrous analysis has agreed to make a determination on several samples for us. 3.6 Low and Mid-Frequency Permeability Spectrum (B. Hershenov) 3.6.1 Permeameter Measurements. The primary core for the 4-9 mc/s range in the r.f. permeameter arrived this quarter. The core shipped previously was returned because the capacitance in the primary windings was too large. At 7 mc/s with this core, the permeameter yielded capacitive readings with the secondary opened. The cores that have been manufactured here have all been measured in the frequency range spanned by the permeameter cores. Table I indicates the results of four of the recent cores all manufactured under different conditions, as compared with the results of specimen A-5-2 reported in the last progress report and two cores, 305 and 306, General Ceramics G bodies furnished by the Mr. G. Dewitz of the C.G.S. Laboratories. 305 was listed as satisfactory and 306 as having a low Q. Within any one group of cores, such as A-16, all the cores yielded about the same values for,1 and 2.l The notable exceptions to this were the specimens in groups A-21 and A-22. At the lower frequencies i1 varied as much as 200, while l _ _ _ _ _ _ _ _ _ _ _ _ __ ~18

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN TABLE I f=1.2x106cps f=4x106 f=7xlO6cps SPECIMEN 1 V2 P1. 2 v1 12 A-5-2 334 66 324 250 262 227 A-16-1 184 12 212 50 201 81 A-17-4 400 36 475 238 367 237 A-21-1 681 98 774 638 637 718 A-22-2 680 74 763 540 633 525 305 345 9 430 129 428 272 306 357 30 431 141 380 208 COMPLEX PERMEABILITY FOR SEVERAL SPECIMENS.... 19

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN at the higher frequency ~2 varied by as much as 200. The specimens in this group were pressed at a load of one ton (approximately 2 tons/in2) as opposed to the other cores which were pressed at loads ranging from 8 to 20 tons. At the lower frequencies 1l is relatively high and remains high at the upper frequencies, but 12 increases rapidly with frequency. 3.6.2 Extension of Permeameter Range. A recent communication from P.H.Haas of Magnetic Measurements and Standards Section, National Bureau of Standards, indicates that coils are now available for the r.f. permeameter which will extend its upper limit to 20 mc/s. These coils can be used without correction for capacitance in the primary windings. The National Electronics Labs. has informed us that cores will soon be available which will extend the lower limit of the permeameter to 100 kc. Orders have been placed for both type cores with delivery in about six weeks. 3.7 VHF Permeability Spectrum (P. E. Nace) 3.7.1 Analysis of data obtained. Measurements of the permeability and Q in the frequency range from 30 to 500 mc/sec. have been made in the past quarter on a selected number of our ferrite cores. These cores exhibited almost identical vhf permeability curves although they were subjected to different manufacturing processes. All the cores were 20-30 nickel-Zino cores with some containing 0.75 mole per cent V205. Of all the manufacturing parameters involved only one had an appreciable effect on the vhf permeability. Those cores which were prefired had lower 20

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN permeability, lower losses, but higher Q. These prefired cores are quantitatively and qualitatively in agreement with Fig. 5 of QPR No. 3. Those cores which were not prefired showed higher permeability and losses, but lower Q. Fig. 6 shows the range of pl and ~2 observed for eleven of our cores. These cores were subJected to different manufacturing processes, but none were prefired; all were 20-30 Ni-Zn cores, and all contained either zero or 0.75 mole per cent of V205. Also falling in this range were two types of General Ceramic G-body cores obtained from Mr. G. Dewitz of the C.G.S. Laboratories. One of the two was deemed satisfactory; the other was considered by Mr. Dewitz to have too low a Q at i mc/s to be satisfactory. Fig. 6 indicates that the manufacturing parameters other than prefiring have little effect on the vhf permeability. All these data were obtained with the coaxial inductor described in QPR No. 3. 3.7.2 The Coaxial Line. A coaxial line for measuring permeability, magnetic losses, dielectric constant, and conductivity of toroidal specimens has been constructed. Fig. 7 is an assembly drawing of the coaxial line. Flexible inner and outer conductors will allow a small range of toroidal core sizes to be measured. The inner conductor is compressed by the core. The outer conductor is compressed by a hose clamp. Thereby a given core is mounted with the inner and outer conductors fitting tightly on the inner and outer radii of the core. The characteristic impedance of the line is not altered if the ratio of the 21

150 0 ~c' Range in IL, and,L2 encountered in eleven 20-30 Ni-Zn cores in which only the manufacturing process was varied. Some of the cores contain 0.75 mole per cent of V-05 These cores were not prefired. And two General Ceramic G-body cores 100~also fall within the range shown. a. 50 50 n3~ - 30 100 200 300 400 FREQUENCY (MC) FIG 6 VHF PERMEABILITY SPECTRUM

POLYSTYRENE SPACER 24 AXIAL SAWOUTS IN OUTER CONDUCTOR MINIATURE GROUNDING FINGERS ALONG 2 ~~~~~~~~~~~INNER AND OUTER RADII. Q 12 AXIAL SAWCUTS IN' CENTER CONDUCTOR N~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~NR IF~~~~~~\ ERRITE TORROIDAL SAMPLE POSITIONING 1.0.=0.992" RODS O. D. =0.582" 20 3' 52" FIG. 7 COAXIAL LINE ASSEMBLY.

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN inner and outer radii is maintained. This ratio is essentially constant for our cores, and the line was designed with the same ratio for the inner and outer conductor radii. Z 60 = 6 In r = 60 n =32 ohms ri 58 For an ideal coaxial line the procedure of measurement would be as follows: (1) Position the shorting plunger adjacent to the ferrite ring and measure the impedance and phase angle by means of the HewlettPackard vhf bridge. (2) Correct the observed reading by means of the Z-0 chart because of a short length (about 8 cm) of 50 ohm coax joining the coaxial line to the bridge. This gives the impedance at the input end of the coaxial line. (3) Use the Z-0 chart to transfer the latter impedance into the impedance in the coaxial line at the bridge face of the ferrite toroid. This impedance2 ZfleJifl = Zof tanh Yftf where Zof (1) is the characteristic impedance of a coaxial line with a ferrite dielectric and yf is the propagation constant in the ferrite. tf is the thickness of the ferrite sample. (4) Reposition the shorting plunger 1/4 wavelength from the ferrite sample. Measure the impedance and repeat steps 2 and 3, thereby2 determining Zf2eiJf2 Zf2eJO2 = Zof coth Yftf (2)........... 24

ENGINEERING RESEARCH INSTITUTE i: UNIVERSITY OF MICHIGAN (5) From equations (1) and (2), Zof and Yf can be determined: Zof (Zf, Zf2)i e(+f + Of2)/2 ) I_ tanh' (Zf.)_ eP2fl c f2) (4) Yf=tf - Zf (6) For a coaxial line3: - jW / fEf (5) Zo~f f - r 2r e7r r (6) Here kf and ef are the complex permeability and dielectric constant in mks units. X is the frequency in radians/sec. (7) Finally OLf and Ef are determined from equations (5) and (6): 2I -7rP f (.-j) /=o (#j/t) (7) ji 36An10' ~1l 12' E1, and 62 are the constants relative to free space. The coaxial line we have is unfortunately not an ideal line. It suffers in the following respects: (1) The shorting plunger cannot be positioned adjacent to the ferrit sample because the grounding fingers protrude beyond the leading...~ ~ 25

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN face of the plunger. It is hoped this can be corrected without resorting to the necessary corrections in the formulas above. (2) There is a 1/2 inch taper in the inner and outer conductors that may introduce error. However, since 1/2 inch is so short compared to a wave length, the effect of the taper should be negligible. (3) The axial slots necessary to make the walls of the line flexible have a small but negligible effect on the characteristic impedance of the line. To date the line has not been placed in service. Some difficulties have been encountered and are in the process of solution. It should be pointed out that this method is long and involved. However, it is justified for the reasons enumerated in QPR No. 3. 3.7.3 Coaxial Inductor No. 2. A second coaxial inductor similar to that described in QPR No. 3 has been designed. The length of 50 ohm line Joining the bridge's impedance-measuring elements and the inductor No. 1 cavity had necessitated a transmission line correction by means of the Z-0 chart. Since this is a time consuming operation, the length of line was reduced in the new design from 8 to 3.5 cm. One can correct for such a short line without resort to the Z-0 chart except at the high end of the frequency band. Unfortunately this inductor is not satisfactory. It behaves as if it were approaching a resonance. The apparent inductance of the empty inductor increased with frequency.

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN This behavior is similar to that of a tank circuit at frequencies below resonance. Fig. 8 is a drawing of the second coaxial inductor. The capacitances which may be responsible for the increase in apparent inductance are shown. Coaxial Inductor No. 1 showed no such effect, since a taper section was used, minimizing the effect of shunting capacitances. 3.7.4 The z,9 Chart. The Z-0 chart, 24 inches in diameter, has been in use throughout the quarter. The formula used in calculating the chart was:4 ZeJYS 1 + x +) Z o' —'-' (9) where y and x are the ordinate and abscissa measured from the center of the chart. Zo is the characteristic impedance (50 ohms). Contours of constant Z and of constant 0 were plotted. 3.8 Hall Effect (B. Hershenov) A specimen has been placed in the magnet for measurement of the Hall emf. A determination has not been made as there were a few troubles located in the equipment. The majority of these failures have been located and remedied. One major difficulty remains and is located in the bucking section of QPR No. 1, P 36-37. The 60 cps pickup in the Hall circuit is balanced out without any difficulty. The 60 cps. pickup in the driver output is negligible so that the pickup loop made from one of the leads connecting the power amplifier to the primary electrodes is not necessary. This was not true for an n-type germanium specimen which was first inserted for a test run. However, the leads from 27

~g-ZI-OI n3r 3 O-9-V Oz6- W,.IA. l~ \\\\ \\\\ SHUNTING CAPACItANCES.200 DI A. i-~~~~~~~ -~~~~~SLIP FIT TO BE' I r\ \\\I \SOLDERED FITS TYPE "N" I CONNECTOR FIG. 8 COAXIAL INDUCTOR 2 ASSEMBLY.: 28

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN the primary electrodes on the ferrite specimen are fixed to form a figure eight with the specimen body and this has eliminated any detectable 60 cps in the driver output. It has not been possible to balance out the 85 cps signal in the Hall circuit with the bucking section. The 85 cps signal of the bucking section is provided by a transformer in parallel with the output transformer. A measurement of this input indicates that it is about 10% of the primary voltage, as it should be. The amplifier adjustment is made with a 50n precision potentiometer with a minimum resistance increment of 5 x 10-5 times its total resistance. This resistor is reading properly. It will be necessary to check the sine-cosine resolver unit for the apparent lack of 85 cps for bucking. Once this has been remedied readings can be taken. 3.9 Magnetostriction (D. W. Martin) No work was done on magnetostriction during the quarter. Work was concentrated on Sec. 3.3. This program will be resumed when that of Sec. 3.3 is completed. 3.10 Specific Heat of the Ferrite Materials (D. M. Grimes) Since the measurement of the specific heat involves considerable effort, the measurement on one of our own samples has been suspended until the results of the analysis of Sec. 3.5 are known. Work is continuing on the manufacture of very pure Fe203. No further work on the specific heat in the region of sublattice alterations has been done. 29

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN 4. CONCLUSIONS The discrepancy between Js as measured around the toroid and across it has been partially accounted for. With the new magnet we are able to obtain quite accurate readings around the loop. From the differential equations of Sec. 3.2 we expect additional tuning range, which is intuitively obvious, and also a "tuning catastrophe". We have found that the closer temperature control afforded by our new oven, and a slow rate of heating through: (a) 1000 C (voltalize water) (b) 2700 C (voltalize binder) (c) 9500 C - 12000 C (core shrinkage) has allowed us to produce uniformally good physical properties. 5. PROGRAM FOR THiE NEXT INTERNAL All work reported on is to be continued. More time is to be devoted to the Hall Effect by Mr. Hershenov. Mr. Nace in addition to his high frequency measurements will test the equations of Section 3.2. Mr. Martin, now that the Js discrepancy is nearly understood, will turn over routine measurements to a technician and set up the magnetostriction measuring strain gauges. Mr. Jefferson will embark on a program of internal stress analysis. Low frequency dielectric constant measurement is being by passed temporarily. It is expected that the new specific heat measurement will be made shortly by Dr. Westrum. 30

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN REFERENC ES 1. Brown, William Fuller, Jr. Domain Theory of Ferromagnetics Under Stress I. Phys Rev 52, 325-334 (1937) II. Phys Rev 53, 482-491 (1938) III. Phys Rev 54, 279-287 (1938) Theory of eversible Magnetization in Ferromagnetics Phys Rev 55, 568-578 (1939) 2. Reference Data for Radio Engineering, Federal Telephone and Radio Corporation 949), American Book-Stratford Press. Pg. 313 3. Ramo and Thinnery, Fields and Waves in Modern Radio, Wiley and Sons, (1944), P 3323 4. Bronwell and Beam, Theory and Application of Microwaves, McGraw Hill, (1947) Pg. 167

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UNIVERSITY OF MICHIGAN III 9I0III 1l1115002111 1 i 891141 iL 3 9015 03026 8984