IEEE TRANSACTIONS ON COMPUTERS, VOL. C-18, NO. 10, OCTOBER 1969

ACKNOWLEDGMENT

The author wishes to thank D. B. Zeh and D. R.Lewallen of the National Cash Register Company fortheir valuable comments.

REFERENCES[1] Y. T. Yen, "Intermittent failure problems of four-phase MOS

circuits," IEEE J. Solid-State Circuits, vol. SC-4, pp. 107-110,June 1969.

[2] --, "A mathematical model characterizing four-phase MOScircuits for logic simulation," IEEE Trans. Computers, vol. C-17,pp. 822-826, September 1968.

[3] S. Seshu and D. N. Freeman, "The diagnosis of asynchronoussequential switching systems," IRE Trans. Electronic Computers,vol. EC-11, pp. 459-465, August 1962.

[4] S. Seshu, "On an improved diagnosis program," IEEE Trans.Electronic Computers (Short Notes), vol. EC-14, pp. 76-79,February 1965.

[5] E. G. Manning and H. Y. Chang, "A comparison of fault sim-ulation methods for digital systems," Digest 1st Ann. IEEEComputer Conf. September 6-8, 1967, pp. 10-13.

[6] E. R. Jones and C. H. Mays, "Automatic test generationmethods for large scale integrated logic," IEEE J. Solid-StateCircuits, vol. SC-2, pp. 221-226, December 1967.

[7] F. P. Preparata, G. Metze, and R. T. Chien, "On the connec-tion assignment problem of diagnosable systems," IEEE Trans.Electronic Computers, vol. EC-16, pp. 848-854, December 1967.

[8] L. Cohen, R. Rubinstein, and F. Wanlass, "MTOS Four PhaseClock Systems," Northeast Electronics Res. and Engrg. MeetingRec., vol. 9, pp. 170-171, November 1-3, 1967.

[9] J. L. Seely, "Advances in the state-of-the-art of MOS devicetechnology," Solid State Tech., pp. 59-62, March 1967.

[10] J. P. Roth, "Diagnosis of automata failures: A calculus and amethod," IBM J., pp. 278-291, July 1966.

Magnetic-Field Design Considerations for

a Plated-Wire MemoryHELMUT K. V. LOTSCH

Abstract-Permeable keepers are used in a plated-wire memoryto reduce the adjacent bit interference and the current requirement.Computations of a magnetic field have been performed to determinethe quantitative effect of the keeper size on the field enhancement inthe region where the information is to be stored and on the field re-duction outside this region. The field enhancement can be interpretedas the reduction in current for a given magnetic field, and the reduc-tion of the fringing field as the reduction in adjacent bit interference.The numerical results which represent valuable design considera-tions for a plated-wire memory are presented in graphical form.

Index Terms-Effect of keepers, magnetic-field computations,plated-wire memory, reduction of fringing field, reduction of inter-ference.

INTRODUCTION

HE PLATED-WIRE memory has recentlyshown great potential as a nondestructive, high-storage-density, random-access, high-speed, low-

power-consumption, low-weight memory. Its state ofthe art was reviewed by Fedde and Chong at the 1968INTERMAG Conference [1]. The basic principle of amemory element is schematically illustrated in Fig. 1 (a).A fine copper-beryllium wire, which is electroplatedwith a thin permalloy film [2 ], is perpendicularly placedbetween two straps carrying word current of oppositedirection. An anisotropy is established during the plat-ing so that the magnetization vector curls around thesupporting wire in the easy direction of magnetization

Manuscript received February 24, 1969.The author is with Autonetics, North American Rockwell Corpo-

ration, Anaheim, Calif. 92803.

without an axial component. The element is bistable inthat the sense of rotation of the magnetization may beeither clockwise or counterclockwise. An interaction ofthe magnetic fields due to simultaneously flowing bitand word currents is utilized to restore or to change thesense of rotation of the magnetization. In this way, onecan either write information into or read stored infor-mation out of the plated wire. Additional backgroundmaterials may be found in [3], or the interested readercan trace his search to the original literature throughChang's bibliography [4].A storage element is determined by the crossing of

current straps and a plated wire in the memory matrix.The density of such elements is limited by the fact thatthe pulsing of the word current to read or to write onebit of information may influence bits stored in adjacentmemory elements. Magnetic keepers backing up thecurrent straps are used to reduce the adjacent bit inter-ference. In addition, these keepers provide an enhance-ment of the magnetic field between the current straps,thus permitting reduction of the word current for agiven magnetic field. The conflicting needs of shorterbit length and reduced adjacent bit interference de-mand an examination of the quantitative effect oflimited keepers on the magnetic field, assuming arealistic configuration. Magnetic field calculations havebeen carried out on the basis of idealized models. Raviand Koerber [5] and Feltl and Harloff [6] ignored thepresence of the thin information-storing film and calcu-lated the magnetic field between two current strapsbacked up by semi-infinite keepers. This kind of in-

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LOTSCH: MAGNETIC-FIELD DESIGN FOR PLATED-WIRE MEMORY

SENSE

(a)/ PERMEABLE KEEPER (40

mjj 73 Bx

(9 OR Q9 \ (., t) Si,ABS:IMUL)ATINGrHIN CURRFNT SHFET b) PlATED WIRE(y)

(it0 O

(b)Fig. 1. (a) Schematical representation of plated-wire memory. (b)

A view of the cross section of a memory element is shown to il-lustrate and to define the configuration under investigation.Because of the symmetries, the calculation can be restricted tothe first quadrant showing the greater detail.

vestigation was recently extended to the case of keeperswith limited size [7]. Dove and Long [8] consideredthe demagnetizing field in the plated wire due to spati-ally periodic applied fields. A first attempt to accountfor the presence of both the plated wire and keepers(but of semi-infinite extent) was recently reported byDove [8b] and, in particular, by Mo and Rabinovici[9].For a high-density, low-power consumption, and

light-weight memory, there is an important tradeoffbetween the width and the thickness of the keepers andthe bit spacing on the plated wire. A study of thistradeoff is possible only by calculating the magneticfields when keepers of varying width and thickness con-sisting of different permeable materials are present. Anintegral/matrix equation technique was developedfor the calculation of a magnetic field produced by sta-tionary current in the presence of permeable material[10]. This technique is applied to a model for theplated-wire memory element,' consisting of two planeand parallel current straps which are backed up bypermeable keepers of limited cross section. The plated

This model was suggested by Professor A. V. Pohm of IowaState University, Ames, Iowa.

wire is simulated by an infinite slab of permeable ma-terial in order to make the problem two-dimensional.The relative permeability of the slab is determined bythe condition that the reluctance of the model is equalto that of the actual device.The magnetic field inside the simulated wire has been

computed numerically for different configurations ofthe plated wire. The graphical results exhibit the influ-ence of the keeper thickness and width on the magneticfield inside the simulated wire, assuming two differentwidths of the current straps. The field enhancementsdue to the presence of the keepers are indicated in eachgraph. An enhancement can be interpreted as the re-duction of current for a given magnetic field.

DEFINITION OF THE PROBLEMAND ITS SOLUTION

The problem under investigation is illustrated inFig. 1(b), showing the view upon the cross section of amemory element. Two "infinitely" thin straps of 2a-unit width are located at + b units from the x axis whereunit is a short hand for any unit of length. These strapswhich carry current of opposite direction are backed upby permeable keepers with the relative permeability .k.Each keeper is 2w units wide and placed c units awayfrom the x axis, assuming a keeper thickness of either 1or 3 units. The plated wire is simulated by a 4-unit thickslab in order to obtain a two-dimensional problem.This slab is assumed to be 100 units wide for computa-tional reasons. Assuming that unit stands for 10-3 inch,our model represents a realistic configuration for aplated-wire memory element.

In the actual memory element, the plated wire con-sists of a copper-beryllium core with about 125-,u diame-ter, electroplated with a 1-,.t thick permalloy film. Thehysteresis loop of this uniaxial anisotropic film is cus-tomarily described by the Stoner and Wohlfarth model[11]. Accordingly, if the applied magnetic induction re-mains below the saturation level Bs, the relative per-meability of the anisotropic film (in the hard direction)is given by the slope of the linearized hysteresis loop,i.e.,

BsAf iim =-

HK(la)

where HK denotes the anisotropy field. In the problemdefined above, the plated wire is simulated by a 4-unitthick slab of permeable material. In order to obtain aphysically realistic model, the condition is adopted thatthe magnetic flux through the slab should be approxi-mately equal to that through the wire plating at thex =0 plane. Unfolding the wire plating makes a con-

tinuous sheet 125wr , in length. This length correspondsroughly to the distance between the axes of adjacentplated wires. Accordingly, we have for the equivalentrelative permeability ,ui of the slab simulating theplated wire

895

YI

% N 1-- , I

IEEE TRANSACTIONS ON COMPUTERS, OCTOBER 1969

ap=ating BS

s lab HK

where 6plating; 1-U is the thickness of the wire platingand 6slab 100jIO is the thickness of the slab.The two-dimensional magnetic field which is pro-

duced by a steady word current can be described by aninhomogeneous Fredholm vector integral/matrix equa-tion [10]. This equation has been solved by iterationusing an IBM system 360. The numerical results arepresented and discussed in the following section.To simplify computation, we took advantage of the

symmetries of the configuration with respect to the xand y axes (see Fig. 1 (b)). Thus, the calculation wasrestricted to the first quadrant, as indicated by thegreater detail in Fig. l(b). For ease of reference, weshall henceforth talk of one keeper and one strap. Theirhalf-dimensions are given by the respective quantitiesa, b, c, and w, which specify the coordinates in the firstquadrant. The cross sections of the permeable mediawere approximated by square meshes for computationalreasons, and the magnetic field was determined at thecenter of each square [12].

MAGNETIC FIELD INSIDE SIMULATED PLATED WIRE

The magnetic-field distributions are given by thesolution of the aforementioned integral/matrix equa-tion. Only the distribution inside the slab simulatingthe plated wire is explicitly shown and discussed indetail; distributions of magnetic field inside a keeperwere presented in [7b ]. The slab extends into thefirst quadrant by 2 units (see Fig. 1(b)) and is, there-fore, approximated by two strings of squares withAx-=y = 1 unit. The field was always computed at thecenter of each square, i.e., for y=0.5 and 1.5, but nu-merical results are presented only for y = 0.5. This planeis indicated by the dash-dot line in Fig. 1(b). The par-ticular configurations for which the results are presentedare determined by a =10 or 16 units both with b= 5units, and c and w were chosen as stated. The keeper isassumed to be either 1 or 3 units thick.The effective permeability of the keeper material

usually encountered in practice is in the order of mag-nitude of 10. Therefore, the computations to be pre-sented were performed with /Uk = 10 as a typical value forthe relative permeability. The saturation induction BSof the permalloy wire-plating is usually 8 to 12000 Gand the anisotropy field HK is, say, about 5 to 10 Oe.2Using (lb), we calculate the typical values of 10 and 25for the effective permeability of the simulated wire.Hence, in order to study the effect of the relative per-meabilities on the magnetic field, we present the nu-

2 rhe ranges for these values have been chosen somewhat largerthan customarily specified in practice.

merical results for both btv = 10 and 25, assuming gk = 10.The dependence of the magnetic field on the choice ofboth gk and z,,,, has been investigated in [10].The x-component of the magnetic B or H field is the

quantity of prime interest. The B.-component is plottedversus x for x up to 45 units in Figs. 2 through 6. Theheavy solid curve is the reference curve exhibiting themagnetic field in the absence of the keeper. When thekeeper is introduced, the magnetic field between thecurrent strap increases. The relative field enhancementis always indicated in the lower left corner of thosefigures. This field enhancement can be interpreted asthe reduction in current for a given field at the centerdue to the use of keepers. The main portion of eachfigure is devoted to show the effect of the keeper on thefringing field beyond the current straps for a givenmagnetic field at the center.

Fig. 2 illustrates the effect on the magnetic field of thekeeper thickness and width, assuming a= 10 units,b=c=-5 units, and gk=,UW= 10. When a 1-unit thickkeeper which precisely backs up the current strap isintroduced, the field at the center increases by about 24percent and the fringing field reduces, as shown by thebroken curves. An increase of the keeper thickness to 3units leads to a 39 percent field enhancement at thecenter and a somewhat larger reduction of the fringingfield (dash-dot curves). The numerical results for a 3-unit thick keeper exceeding the current strap by 10units on each side (a = 10 units and w =20 units) aredisplayed by the thin solid curves. The magnetic fieldunder the current strap spreads out, yielding a fieldenhancement at the center of about 45 percent. Thisoverhanging keeper has a noticeable effect on the fring-ing field beyond its extent, i.e., for x>20. Right underit, the field is somewhat enhanced and more uniform.Fig. 3 illustrates the same cases as Fig. 2 except that Itwis increased from 10 to 25. The field enhancements atthe center are now approximately 27, 46, and 55 percent,respectively.

Fig. 4 exhibits the effect on the magnetic field of anair gap between the current strap and keeper, assuminga 3-unit thick keeper with ,uk =g,UW = 10, which preciselybacks up the current strap (a =w = 10 units, b = 5 units).The curves illustrating the case of no gap, i.e., c=5units, are repeated from Fig. 2 for ease of reference(thin solid curves). When current strap and keeper areseparated by one unit (c=6 units), the field enhance-ment at the center is substantially reduced to about 31percent, and the fringing field increases noticeably(dash-dot curves). A further increase of the separationto 4 units leads to a field enhancement at the center ofonly 14 percent and a substantial increase of the fringingfield. This result is not unexpected since the shieldingeffect of the limited keeper reduces rapidly as the keeperis removed more and more from the current strap. Fig. 5exhibits the same cases as Fig. 4, except that uk is in-

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LOTSCH: MAGNETIC-FIELD DESIGN FOR PLATED-WIRE MEMORY

1.0 \ a = 10 UNITS

b = 5 UNITS~09 " = 5 UNITS.

N~~~~~~~~~~~~k= 10

f 0.9 [ , | _ _ NO KEEPER0.* \\\ -----1-UNIT THICK KEEPER WITH w = 10 UNITS

O \\ \ -~- 3-UNIT THICK KEEPER WITH w = 10 UNITS0.7 \- -3-UNIT THICK KEEPER WITH w = 20 UNITS

07

0.5

0.4

0.3

0.2 \

0.1

0 5 10 15 20 25 30 35 40 45x IN UNITS

0

0z2

xI

Fig. 2. B,-component of magnetic induction is plotted versus x aty=0.5 for different thicknesses and widths of the keeper with1.1k= 10, assuming a = 10 units and A,, = 10. The curves in the lowerleft corner exhibit the relative field enhancement due to the useof keepers.

Fig. 4. Br-component of magnetic induction is plotted versus x aty = 0.5 for different separations between current strap and keeperwith 4k= 10, assuming a= 10 units and 1uw= 10. The 3-unit thickkeeper just backs up the current strap. The curves in the lowerleft corner exhibit the relative field enhancement due to the uiseof keepers.

x IN UNITS

Fig. 5. Same results as shown in Fig. 4 except that IA.is increased from 10 to 25.

1.0

a = 10 UNITSb = 5 UNITS

0.9 w = 10 UNITS

l'k = 10\\\\\ F~~~~~~W= 10

_ NO KEEPER0.0 \\ '\ ~ ~~~~3-UNIT THICK KEEPER AT c = 10 UNITS3-UNIT THICK KEEPER AT c = 6 UNITS

___3-UNIT THICK KEEPER AT c = 5 UNITS

0.7

I ~ ~ I

0.6

I~ ~ ~ ~~

0.5

0.4

0.3

0.2

0.1

897

5 10 15 20 25x IN UNITS

x IN UNITS

Fig. 3. Same results as shown in Fig. 2 except that jx.is increased from 10 to 25.

I

U..v5 30 35 40} 45

IEEE TRANSACTIONS ON COMPUTERS, OCTOBER 1969

a

<o

zw

o e

MX

x IN UNITS

Fig. 6. Br-component of magnetic induction is plotted versus x aty=0.5 for different thicknesses and widths of the keeper withk= 10, assuming a =16 units and j,', = 10. The curves in the

lower left corner exhibit the relative field enhancement due tothe use of keepers.

creased from 10 to 25. The corresponding field enhance-ments at the center are now approximately 37 and 17percent, respectively.

Fig. 6 illustrates the effect on the magnetic field of thekeeper thickness and width for a different width of thecurrent strap, namely a = 16 units, assuming b = c =5units and 1k =iw = 10. When a 1-unit thick keeper whichprecisely backs up the current strap (a =w = 16 units) isintroduced, the field at the center increases by about 18percent, and the fringing field reduces, as shown by thebroken curves. An increase of the keeper thickness to 3units leads to a 34-percent field enhancement at thecenter and a somewhat larger reduction of the fringingfield (dash-dot curves). The numerical results for a 3-unit thick keeper exceeding the current strap by 14units on each side (a = 16 units and w =30 units) aredisplayed by the thin solid curves. The field enhance-ment at the center is about 37 percent. Comparing theseresults with those illustrated in Fig. 2 reveals the effectthat the width of the current strap has upon the mag-netic field.The numerical results presented in the lower left

corners of Figs. 2 through 6 may be interpreted as rela-tive values of the magnetic field due to the choice of thecurrent I. To obtain absolute values, we inultiply thenumerical results (1 + field enhanicenment) by B,, wherefor a = 10 units, B,,/I is either 2.3 if ,u/,, = 10 or 4.1 if ,Aw

= 25, and for a = 16 units, B,,/I is 1.9. Then, if the cur-rent I is measured in amperes, the absolute value of themagnetic induction is obtained in gaussX (meter/unit).The dimensionless ratio (meter/unit) takes care of theparticular unit (of length) which, as stated above, canbe chosen at convenience.

CONCLUSIONPermeable keepers are used in a plated-wire memory

to reduce the adjacent bit interference and the currentrequirement, but they add somewhat to the weight. Atradeoff to optimize the design necessitates the knowl-edge of the magnetic field produced by the keeperedcurrent straps inside the plated wire as a function of thedesign parameters. The numerical results presentedabove are rather valuable in this respect since theyshow quantitatively the effect on the magnetic field ofthe keeper thickness, width, and location for two per-meabilities of the wire plating, assuming two differentwidths of the current straps. They exhibit the enhance-ment of the magnetic field in the region where the infor-mation is to be stored and the reduction of the fringingfield outside this region. The field enhancemnenit can beinterpreted as the reduction in current, and the reduc-tion of the fringing field can be interpreted as the reduc-tion in adjacent bit interference, both due to the use ofpermeable keepers.

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IEEE TRANSACTIONS ON COMPUTERS, VOL. C-18, NO. 10, OCTOBER 1969

REFERENCES[1] G. A. Fedde and C. F. Chong, "Plated wire memory-present

and future," IEEE Trans. Magnetics, vol. MAG-4, pp. 313-318,September 1968.

[21 T. R. Long, "Electrodeposited memory elements for a non-destructive memory," J. Appl. Phys., vol. 31, pp. 123S-124S,May 1960.

[3] A. V. Pohm, "Magnetic film memories," Amplifier and MemoryDevices, New York: McGraw-Hill, 1965, pp. 245-293.

[41 H. Chang, "Bibliography of thin magnetic films," IEEE Trans.Magnetics, vol. MAG-3, pp. 653-700, December 1967.

[5] C. G. Ravi and G. G. Koerber, "Effects of a keeper on thin filmmagnetic bits," IBM J. Res. and Dev., vol. 10, pp. 130-134,March 1966.

[61 H. Feltl and H. J. Harloff, "Flux keepers in magnetic thin-filmmemories," IEEE Trans. Magnetics, vol. MAG-2, pp. 516-520,September 1966.

[7] H. K. V. Lotsch and T. R. Waite, "Computation of magneticfield between keepered current straps used in plated wire mem-ories," IEEE Trans. Magnetics (Digests), vol. MAG-4, pp.

389-390, September 1968; and H. K. V. Lotsch, "Computationof magnetic field produced by two plane-parallel keepered cur-rent straps," IEEE Trans. Magnetics, vol. MAG-5, pp. 22-29,March 1969.

[8] D. B. Dove and T. R. Long, "Magnetization distribution inflat and cylindrical films subject to nonuniform hard directionfields," IEEE Trans. Magnetics, vol. MAG-2, pp. 194-197,September 1966; and D. B. Dove, "Demagnetizing fields in thinmagnetic films," Bell Sys. Tech. J., vol. 46, pp. 1527-1559,September 1967.

[9] R. S. Mo and B. M. Rabinovici, "Internal field distribution inkeepered and nonkeepered permalloy film memories," J. Appl.Phys., vol. 39, pp. 2704-2710, May 1968.

[10] H. K. V. Lotsch, "Magnetic-field computation for a plated-wirememory utilizing an integral/matrix-equation technique," J.Appl. Phys., vol. 40, pp. 2844-2851, June 1969.

[11] M. Prutton, Thin Ferromagnetic Films. Washington, D.C.:Butterworth, 1964.

[121 H. K. V. Lotsch and W. F. Hall, "A note concerning the integralequations for magnetostatic fields," Z. A ngew. Math. Phys., vol.20, no. 4, pp. 567-570, 1969.

Unified Interval Classification and Unified3-Classification for Associative Memories

ALBERT WOLINSKY

Abstract-Algorithms for a unified interval classification and aunified 3-classification for use in associative memories are pre-sented. The former, which is more generally known as between-limits classification, achieves the classification of the words of an as-sociative memory into those within and those without an intervalmarked by two given limits; the latter achieves the classification ofthe words into the three classes, between the given limits, above theupper limit, and below the lower limit. The term "unified," used forboth, denotes the contraction of the two limit classifications whichare required in the straightforward approach to either classificationinto one carried out simultaneously with respect to both given limits.Due to this unification, the presented algorithms are capable ofachieving considerable time savings in associative memories of a

frequent type. The designs of cryogenic associative memories of thistype, containing certain circuit requirements for the performance ofthe algorithms, are also presented.

Index Terms-Algorithm, associative memory, between-limitsclassification, classification into three classes, cryogenics, intervalclassification, microprogram, one-pass classification, parallel searchand processing memory, 3-classification, unified classification.

I. INTRODUCTION

T p HE CONVENTIONAL methods of determiningall words of a given set of words of an associativememory which lie in the interval specified by two

limits require the consecutive performance of two limitclassifications; the words found to lie both above the

Manuscript received October 31, 1967; revised May 15, 1969.This work was supported in part by the Information SystemsBranch, Office of Naval Research.

The author is with TRW Systems Group, Redondo Beach, Calif.90278.

lower limit and below the upper limit are the wordslying in the interval [1], [2]. Each of these classifica-tions requires one pass through the digits of the words;therefore, two passes are required for the completeinterval classification.

This paper describes a unified interval classificationwhich determines all words lying in the given intervalin a single pass through the digits of the words. Forassociative memories with bit-serial operation of theirdata sections and bit-parallel operation of their tagsections, this method is faster than the conventionalmethods.1 The paper then shows how a minor modifica-tion of the unified interval classification yields a unified3-classification. This method, too, is faster than thecorresponding conventional methods for associativememories of the type mentioned. In the subsequentdiscussion, the term "bit" is used to denote the storagefacility, and the term "digit" to denote the stored value.

A. Memory Requirements

The performance of the algorithms of this paperplaces the following requirements on the associativememory.

1) The memory must possess tagging capability ofits individual words; that is, each word register mustcontain, besides the data bits, a number of tag bits in

l For unified interval classifications using a different principle,see [31, [41. For interval classifications whose efficiencies lie betweenthose of the conventional and the unified methods, see [5], [6].

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