468 IEEE TRANSACTIONS ON ELECTRONIC COMPUTERS, VOL. EC-15, NO. 4, AUGUST, 1966

Propagation of Sense Signals in Large-ScaleMagnetic Thin Film Memories

FRANK C. YAO, MEMBER, IEEE

Abstract-A dynamic analysis has been made of the behavior of PREAMPVsense signals in large-scale magnetic thin film memories. The timed 7 REF. COEF.effects of attenuation, distortion, cross coupling and interconnection -are superimposed on the transmitted waveforms. The computed sig-nals can be used as a design guide to determine the length of sense -lines, the number of intersecting word lines, the sense amplifier re- ciquirements, etc. The key limiting factors are the resistance of lines D

and the capacitance at the line intersections. Design criteria are Fig. 1. An ideal sense line.discussed.

I. INTRODUCTION

rT HE SENSE signal of magnetic thin film memory film site. Ignoring the reflections higher than the secondsustains various losses in the course of travel order, we express in the Laplace transform (for the sakeaIong the sense lines. These losses are: attenua- of convenience) the waveform of sense signal seen by

tion of magnitude, distortion in phase, reflections the preamplifier as follows [1]caused by interconnection of sense lines; and deteriora- V-(P)tion of waveform due to the cross coupling of word V(P) = (1 + ri)[e - rie-r(2D-d)] (1)lines. By studying the propagation function of thesense lines, the attenuation and distortion can be calcu- where r1 and r2 are the reflection coefficients at the twolated within the operating ranges of memory. The mul- ends, -y is the propagation function, and V8 is the out-tiple reflections and deterioration can be expressed as a put signal of magnetic film.temporal sequence of traveling waves. Adding all the The conventional design matches the line at the sens-above effects together we may, as a guide to design, ing end and shorts it to the ground at the other end.predict the waveform of sense signals at any point The above equation can be simplified asalong the line. Vs(P)By using traveling waves, the analysis yields a gen- V(P) = VP -yd[ + e-y2(D-d)] (2)

eral solution suitable for both low and high speed appli- 2cations. A straight strip-line in TEM mode is adopted The time separation of the two components within thefor illustrative purposes, and the sense signal under brackets means the flattening of the composite wave-consideration is measured from the sense wire to the form. The separation is maximum for the signal com-ground plane. ing from the site nearest to the preamplifier, and mini-

II. STATEMENT OF THE PROBLEM mum for the one from the farthermost site.During the,"Read"time, the magnetizatin of t

For simplicity, the output of the magnetic film willDuring the "Read" time, the magnetization t be approximated by a triangular wave as shown in Fig.

filmsit isswiche bythefiel ofthedriingcurent2. It iS repDresented byz the followingy source functionand an output signal is induced on the sense line. Thepotential of this signal is in series with the line. It FI /1 e-Ptl e-Ptl eP(t1+t2)\]

V, (P) = V,,- ± (3)propagates in both directions. One may postulate that V8 -= P2VtL t- t2 t2/1its positive half travels in one direction and the nega-tive half goes in another, as shoxvn in Fig. 1. For an ideal line, the propagation funcuton is

Let us start with an ideal case in which the line has PVLC which means a time delay. By substituting (3)no discontinuities and no crossing of other lines. The for V17(P) in (2), we then have the whole picture of atwo halves of the sense signal arrive at the preamplifier sense signal seen by the preamplifier, as shown in Fig.with a time separation depending on the location of the 3. However, the sense signal under study is in the sub-

millivolts range. We have to take into consideration all

Manuscript received February 4, 1966; revised March 18, 1966.deratosfthsinlueodvainsrmteTh uhr is wit th Copue Dearmet Geea Elcti ideal line characteristics, and we shall do so in the suc-

Company, Phoenix, Ariz. ceeding sections.

YAO: PROPAGATION OF SENSE SIGNALS 469

SIMULATING TRIANGULAR R R/ CWAVE FORM Iy = x/(R + PL)PC LPv\LC +±YV -i (5)

ACTUAL WAVE FORM The loading effect of the magnetic film is nil, because

VS the sense signal does not perform any switching. The

I g \ calculation of parameters L and C has been reportedti 123+ extensively in literature [3]-[5]. R will be discussed in

VS(t)=Vs [t(+ A-)t(t-4+ -(-.tIl Section IlI-A.A. Resistance at High Frequency

Fig. 2. Triangular wave representation of output signal.Due to the skin effect, resistance increases as the

operating frequency goes up. For a conductor with a

To =TIME FOR TRIP ON THE LINEthickness much greater than the depth of penetration,

T the skin-effect resistance, is [6]

2TT04 per square 8=,4 )(a) SIGNAL FROM SENSING END aw cT/

v where u, of course, is the conductivity. For magneticthin film memory applications, the line is extremely

T thin. Usually, the thickness of the conductor is com-#Q d!^1 parable to, or less than the penetration depth. There-

(b)SIGNAL FROM CENTER OF LINE fore the above formula should be modified [6], [13].v - 2b 2b

2 COMIPONENTS COINCIDE WITH Sinh + Sin-,^ \ EACH OTHER 8 8

t '\ ~~t 22bper square.(Cosh --Cos-

(c) SIGNAL FROM REMOTE END _ 7 1 s

Fig. 3. Composite sense signals on an ideal liniewith exaggerated time separations. We have, then, the resistance term for a line W units

wide and b units thick:

III. PROPAGATION FUNCTION = Rd[t +±7]/unit length (see Appendix I). (6)

The quality of a transmission line depends entirely The q is plotted in terms of b/I in Fig. 4.on the propagation function y which is defined as fol- Next, we come to an actual system, such as onelows: shown in Fig. 5. The conductors in the middle layer are

Vy(R + PL)(G + PC), (4) the sense lines. The current goes down the center con-ductor, and on the return trip it divides equally between

R, L, G, C being, respectively, the resistance, induc- two ground planes. With small off-center conductor dis-tance, leakage, and capacitance per unit length of the placements, the electric field pattern is confined as

line. The leakage G represents the conductance of di- shown with dotted lines. For the case 2W> h, the effec-electric loss in the memory array. It can be expressed tive width W1 is reported by McQuillan [7] as

as follows [2], [6] 1

G = wC X Power Factor. WI = W + 2h loge2.7r

It is very small and can be ignored. The condition 2W>h is easily met in magnetic filmFor magnetic film memories, the resistance of lines memories. In fact, it is mandatory in order to make a

should be small to keep the attenuation of signals low. lThe sense signal has a short rise time which corresponds We extract one nt ofthe

to hig freqency omponets. W can ssumeredraw it in Fig. 6. Based on the discussion in the pre-

R < PL. ceding paragraph, we should treat this segment as aunion of two lines in parallel, each carrying one-half of

So it is permissible to expand (4) in the following the current. The total high-frequency resistance of thefashion sense line can be arrived at in the following way

470 IEEE TRANSACTIONS ON ELECTRONIC COMPUTERS AUGUST

R?(FOR FI)ORs ZI)____ ____ '2 ~~~~~~~~INLOG.SCALE

0 V

1 I~~~~~~~~~~~~15

1 2 3 4 5 6 7 8 9 10 0 .4 .6 .8 1.0

0 .2~~~~~~~~~~~~~~~

b b

(a) (b)

Fig. 4. X vs. b/5.

.W

,tINE /7// ,\/7// / ////, I IT LINEf 1' -E--FIELD

LINEb/7/ ~ /

SI ;F~~~~~~~~~~~~~~~~~~~~~~~ILN

Fig. 5. A typical memory line matrix. - W

Fig. 6. Equivalent transmission lines for a sense line.+ f(Resistanlce of conductor of 2 thickness

2i+ Resistance of one ground plane of Wi width} u is the speed of travel, so the first term on the rightside of the equation represents the delay or phase shift.

1 -m+Rd[1± [e(6]The second term is commonly known as the attenua-= -2 {Rde1[1 + t7]+RC2l+X2]} [e(6]tion function and the last one is the distortion [8].

The distortion function is complex and frequency-= Rdel + Rdo2 ± 1 Ren + RdC2n2] dependent. The whole expression is

2 2C

=Rd7+ H. (7) 4/13 = IL[RdCl ±+RdC2n. (9)

B. Attenuation and Distortion It is difficult to achieve an analytic solution. How-

With all the parameters known, let us go back to ever, with a graph shown in Fig. 4, one can evaluate itstudy the propagation function, which can now be ex- at a known frequency, and treat it as a constant at thatpressed as frequency. Therefore, we can rewrite (2) as follows

=PVLC +-1Rde/I -

= V8(P) e(PdIu)eded

=~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -jyHP+ k+IS 8

v/ +1za -F- (8) By substitu6ting ()a for Vs(P)isi iCsreadlysoslvable.

1966 YAO: PROPAGATION OF SENSE SIGNALS 471

IV. CROSS-COUPLING EFFECTS Z 1 I I

When a sense line crosses over a word line, there is c Tcapacitance created at the intersection. This capacitoris basically a drain for the energy contained in the sense nsignal. It deteriorates the waveform while delaying thepulse at the same time. In a large scale memory, the SCHEMATICsense line crosses numerous word lines. The capacitivecouplings will be proved to have a very damaging effect a, hon the signal.The capacitors are shown shunting the sense line

schematically in Fig. 7. The shunting branch has an T3impedance of (l/PC)+(Z,/2). The impedance of theword line Z,, is quite low (generally <25 ohms). Onthe other hand, the 1/PC term is in the order of 10-100kilohms. (Assume a 20 nanoseconds rise time for thesignal.) It is, therefore, allowable to drop the secondterm in this case.The number of the capacitor branches runs into LATTICE DARAM

thousands in a large matrix. Usually, they are approxi- Fig. 7. Equivalent representation of capacitivemated as evenly distributed capacitance. This metocouplings shunting a sense line.

is adequate for low speed applications. However, athigh speed, the spacing between two capacitive branches V / a ,VI t Tn-I

- ( I~- e (t- r 'is long electrically in respect to the rise time of the sig- a-r - _=) drnals, even though it is short physically. A more accurate ti p2\P + a ti Jo(n-1)!way should be used to describe the reflections. There- V/ 1\ (n, at)fore, it is proposed that the capacitors actually be _ lt--) (12)treated as recurrent impedance discontinuities to the t\ a/ ir(n, oo)line. We can then accurately calculate the distortion (See Appendix II)and delay time as well. Observe the reflection latticediagram at the bottom half of Fig. 7. The transmitted where J'(n, at) is the incomplete Gamma function. Thewave after one discontinuity is result indicates that the original ramp function has to

be degraded by the ratio of the incomplete Gamma2 2 function and the factorial function. For large "n," we

PCc + 1/Zo zoc6 a can apply the Stirling's formula, and it can be shownT = - - that this ratio means a time delay of n/a and a slope of

1 2 P + a Vi/27rna [9], [10]. The net results are the flattening ofPC, + 1/Zo ZOc the signal and, therefore, the reduction of the signal-to-

noise ratio.and the voltage at Point b due to discontinuities only is The composite sense signal should be rewritten by

including the effects of cross couplings in the following./a \3 Let

Vb(P) = Va(P)T3 = Va(P) (p + Let e7ade fdF1 = P(n, oo)

The reflections of the second order and above are neg-ligible. If there are n crossings of word lines, we have e-a (2D-d) e-A (2D-d)then the transmission coefficient F(2N - n, oo)

n ~~~~~~d2D-dTn + ) (11) ta = t tb = t

This factor should be included in (10) to find the dc 2D--l d=t -a

waveform. Its effect can be demonstrated by translat- u uing into the time domain the product of (11) and the d2first component of the source function (3). We then te= t--- - 12 2DI-d t -1have u X

472 IEEE TRANSACTIONS ON ELECTRONIC COMPUTERS AUGUST

U(ta) -a step function starting at la, etc., EXAGGERATED GAP

then, GRUND

V(t) = 2a1FLYLEaC2 Fl (n, ala) C//-e~~~~~~~~~~I

(1

- \(,ae U(te)] Fig. 8. Interconnecting two sense lines.

+(1 te- (n ,at,,e)I2 a ti

r I I

L(\tb-t ) +F( T - n,at,) U(tb) GR LOU\ a ti 12 SCHLANEI

+ (.f - )_ (2-n, aif)-UQ)} ' (13) a,

N = total number of word lines. F Inte ct t ses lines.

For large scale memories, we should reduce the cross- LATTICE FORMcoupling capacitance between the sense and the wordlines. To reduce the capacitance, it is preferable to in- Fig. 9. An1 equivalent circuit of interconnected lines.crease the separation. At the same time, both the senseand the word lines should be close to the magnetic ele-ments to provide adequate coupling. ZO to ZA be T1 = 2Z

zo+ zV. INTERCONNECTIONS

If the conductor iS deposited on the substrate by a adfrasotitroncigscinfovacuum process, it has more uniform characteristics 4Z0(Z02 ± Z2)than those overlaid on the substrate. For a large-scale Z1 to Z Zbe T2 - +A)memory which consists of an assembly of substrates,we therefore have to interconnect the deposited linesIntrconecio crae dicniute.nteln m Disregarding the second-order reflections on the main

pedance and causes reflections to the pulses transmitted. line, we have the ratio of two voltages in the lattice dia-For the sense signal, reflections will cut down the gram to be

peak and impair the waveform generally. To evaluate T1T2.the effect, we shall look at the two sense lines of twosubstrates joined together by another short piece, as If there are m interconnecting joints, then the totalshown typically in Fig. 8. Let the impedance of sense transmission isline be ZO and that of the joint, Z1'. The resistance of (TT)mthe solder joint r8 is in the order of micro-ohms. We can ( )T.lump rgwith the impedance Z' of the short joining Thisproductof T1and T2 reduces the sense signal andpiece, and the corrected value Z1 is [g] should be kept close to unity. A graph has been prepared

lines. Tordctecpciac,itirfin Fig. 10 with the value of T1T2 plotted against the/RI+--- + jwoLi ratio of impedance-mismatching (|Z1-Z0 /Z0). It is

t11 apparent that the degradation of the signal intensifiesV Gd + jteCo as the number of interconnections goes up.

The transmission coefficients are linear. They can beFor all practical purposes, we can assume that the inserted into (13), and we obtain the final expression

lines are connected together as shown in Fig. 9. Let the for the sense signal waveform complete with all the de-transmission coefficient from grading effects discussed above.

1966 YAO: PROPAGATION OF SENSE SIGNALS 473

M RVI. CONCLUDING DISCUSSIONFor a good signal-to-noise ratio, the sense amplifier

1.o 1-S = 1 input should maintain a sufficient amplitude with an

adequate time duration. To achieve this, we must re-

duce the degrading effects.The attenuation term EXP(-Rd/2Zo) strongly in-

fluences the allowable length of the line. To extend theline without unduly attenuating the signal, we shouldkeep the ratio of R to VL/C small. It is not advisableto raise the impedance ZO because there would be ex-

10_ _ __ _ __ _ A < \ > cessive noise due to the proximity of other lines. Theonly recourse is the reduction of R.

.5 >9 >\A conductor deposited by vacuum processes is quite

\4 \ thin, and therefore has relatively high resistance. Acopper laminate provides thicker conductors and lower

.3___

l__ resistance than the deposited lines do, but the overall

impedance varies due to manufacturing and assembling

__ ltolerances. The lack of uniformity affects the couplingsof both driving and sensing fields. A compromise may

l - __A- l__ j_ll4 be reached if deposited lines are reinforced by electro-plating to the desired thickness.

l ___ l___ l___ l___ l___ ____ ____ - ____ j When compared with other losses, the effect of dis-o .2 .4 .6 .8 I.o 1.2 1.4 1.6 1.8 2.0 tortion is small, because the conductor is not thick in

JZ~ZI relation to the depth of penetration.The capacitive couplings of word lines are very dis-

Fig. 10. Transmission vs. impedance-matching. turbing. As indicated in Section IV, the wavefront isdegraded by a factor proportional to C, X \/n. To ac-commodate a large number of word lines, one has to

1 U(/ ) minimize the capacitance at line intersections. The ca-VV(t) Fl(TlT2)Ft(- (n,a1 pacitance is equal to dielectric constantXarea/separa-

2 a ti tion. Not much can be done in reducing the area be-cause it is dictated by the requirements for the line

-IC-- (-+--) I(n, at,)U(t,) parameters. A thick insulating layer between the worda ti t2 and sense line is thus preferred.

In view of the reflections, one should avoid the inter-+/(e 1)( U(te) 1 connecting of lines. However, if the circumstances de-

+ tet- r(n, at,) Ia 12 j mand such interconnection, extreme care is to be exer-

cised to keep the discontinuities as small as possible.Ft 1 \ U(tb) Next, we shall consider the time separation between

+ F2(TlT2)2M1 tb --) b(2N -n, a/i) the two components of the sense signal as shown in(13) or (14). The composite amplitude diminishes as

/ 1 \ /1 1\ the time separation increases, as shown in Fig. 3, drawn-ttd _ _) t +-) Y(2)V -n, atd) U(td) for an ideal line. The worst-case time separation is the-a /t\i t2 , time for one round trip on the line. Therefore, for long

/ 1 \ U(tf) ] lines, high magnetic film output signals are needed.+ (i - -) F(27 - n, atf) , (14) The only advantage of signal attenuation is that it helps\ a / t2 to make the signals less irregular in magnitude at the

where sensing terminal.A computer program was used to evaluate (14). The

m=number of joints within the distance d ratio of incomplete Gamma function to factorial func-M=total number of joints on one sense line tion is replaced by [11]F's and t's are the same as defined in (13). n-i (at)n _

The equation is lengthy but it accurately describes n=O nthe main body of the signal. The high-order reflections Only terms up to Kth are included wherewould reach the preamplifier at later instants in theform of noise. This is not desirable. A close matching of E(a/)K±l1Zi and ZO will alleviate the problem. l(K + 1) !l

474 IEEE TRANSACTIONS ON ELECTRONIC COMPUTERS

7nV 11.0 = X K

BROKEN LINE, Wo-3CALCULATED WAVE FORM

.5 /-SOLID LINE. = Rdc Rd [1 +ACTUAL WAVE FORM

____ ____ ____ = Rdi[1 + 71] per unit length.o 20 40 60 "s

(a) SIGNAL FROM NEAR END APPENDIX II

SENSE SIGNALS OF A 512-WORD MEMORY anSENSE LINE LENGTH 40 INCHES ____

P2(P + a)n7 r t TFn-1

1.5 =an e-aT(r r) dr

BROKEN LINE, J o (n-i)!1.0 / ~~~~~~CALCULATED WAVE FORM an Cat a)- a (

/@01 < 1 SOLID LINE. (n-i)! J a e'

20°~ 60 t (n-i)! L[aFn(- 1, at) - +1 T(n, at)](b) SIGNAL FROM1 fAR END FORM

Fig. 11. Sense signals on an actual line. (n-1) F(n 1, at) - (-) F(n, at) I*

For large n,e is a prescribed error. The signals plotted with the datafrom the computations generally agree with the experi- -a r 1\ F(n, at)ments, as shown in Fig. ii. p2(p+ a)n k\ a] F(n, oc)Although the sense signal will merge with the cross-

talk, the feeding-through "Read" current and other REFERENCESnoise, noatempt has ben made to exmine any on [1] E. Weber, Linear Transient Analysis, vol. II. New York: Wiley,

of them. They merit treatises in their own right. 1950, p. 286, and p. 411.This paper has discussed the propagation of sense [2] F. E. Terman, Radio Engineers' Handbook. New York: McGraw-

signals as a design guide to the sense line. Being an Hill, 1943, p. 110.[IS. B. Cohn, "Characteristic impedance of shielded-strip trans-integral part of a memory stack, the sense line plays an mission line," IRE Trans. on Microwave Theory and Techniques,important role in the overall planning of a memory. A vol. MTT-2, pp. 52-57, July 1954.successful design of the memory, in turn, will require [4] W. H. Hayt, Jr, "Potential solution of a homogeneous strip-talk, the feeding-throuh"oline of finite width," IRE Trans. on Microwave Theory andcareful consideration of all aspects and reacn a balance Techniques, vol. MTT-3, pp. 16-18, July 1955.anlong them. [5] R. H. Bates, "The characteristic impedance of the shielded slab

line," IRE Trans. on Microwave Theory and Techniques, vol.APPENDIX I MTT-4, pp. 28-33, January 1956.

[6] E. Jordan, Electromagnetic Waves and Radiative System. Engle-The dc resistance of a conductor, W units wide and wood Cliffs, N. J.: Prentice-Hall, 1950, p. 129 and pp. 156-157.

b units thick, is [7] J. P. R. McQuillan, "The design problems of a Megabit storagematrix for use in a high-speed computer," IRE Trans. on Elec-

1 tronic Computers, vol. EC-li, pp. 390404, June 1962.Rdc = per unit length [8] M. J. DiToro, "Phase and amplitude distortion in linear net-WbI work," Proc. IRE, vol. 36, pp. 24-36, January 1948.

[9] L. V. Bewley, Traveling Waves on Transmission Systems. Newand the high-frequency resistance York: Wiley, 1951, p. 104.[10] E. T. Mhittaker, A Course of Modern Analysis. Cambridge,

2b 2b- England: Cambridge University Press, 1952, p. 251.Rdcnpe unit length [11] M. Abramowitz et al., Handbook of Mathematical Functions.1

in - aI-Si National Bureau of Standards, 1964, pp. 260-262.

W bo- 2 wiley," 1942,c. 228vo. 3,p.2-6 aur98

j= [12] M. F. Gardner et al., Transient in Linear System. New York:

Cosh -- Cos -[13] 5. Ramo and J. R. Whinnery, Fields and Waves in ModernL a a Radio. New York: Wiley, 1953, p. 251.