6M 4089_Geometry_of_Magnetic_Memory_Elements_Jan56 4089 Geometry Of Magnetic Memory Elements Jan56
6M-4089_Geometry_of_Magnetic_Memory_Elements_Jan56 6M-4089_Geometry_of_Magnetic_Memory_Elements_Jan56
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Memorandum 6M=4089 Page 1 of 7 Division 6 - Lincoln Laboratory Massachusetts Institute of Technology Lexington 73, Massachusetts 'SUBJECT: GEOMETRY OF MAGNETIC MEMORY ELEMENTS To: Group 63 ~ Staff From: James Do Childress Abstractg Two possible memory element geometries == the thin film and the toroid == are considered o The calculations show that under certain conditions the thin film geometry may be preferable for use in a very high=speed memoryo "" JDC/md Distributiong The following ~ to receive ~ complete memorandum~ Best, Ro, B=131J) Papian',9 WoNo Bradspiesj) So Gurley.9 Bo Brown, Do Ro Childress~ JoDo Davidson.9 Go Ellis, Do Ho Freeman.5l J o Re Goodenough9 'J o Be GuditZ9 EoAo Mitchell.9 J o Lo Menyuk.9 No Olsen, KoHo Pacl, RoAo Sarles, F Wo Smiths Do O~ ZopattiJ;l Ho Other staff in Group 63 are to receive abstracts onlyo 0 This document is issued for internal distribution and use only by and for Lincoln Laboratory personnel. It should not be given or shown to any other individuals or groups without express authorization. It may not be reproduced in whole or in part without permissioD in writing from Lincoln Laboratory. The research reported in this document was supported jointly by the Department of the Army, the Department of the Navy, and the Department of the Air Force under Air Force Contract No. AF 19(122)-458. Memorandum 6M-4089 Introduction: The peak current and Page 2 of 1 average power which the memor,r-plane drivers must deliver can be reduced by decreasing the dimensions of the magnetic memory elements o The following analysis indicates the limits of size reduction and the results which such reductions may yield 0 I. Theoretical Ruminations Ao Possible Geometries The two geometries to be considered and their dimensions are shown in Fig. lA - Thin Film and Fig. IB - Toroid. Fig. 1A - Thin Film Fig. IB - Toroid Memorandum 6M-4089 Page 3 of 7 B Primary Limits on Geometry The primary limits on geometry are (1) the peak voltage signal V must be great enough to be sensed reliably and (2) the p . switch time ~ must be suitable to the desired memor,y cycle time s (certainly less than half the cycle time). The instantaneous output voltage for a one turn sense winding is -8 dB v( t) = 10 A Cit • 0 Therefore where V is in volts,~ in seconds, A in square centimeters, and B p s m (the maximum induction in the square hysteresis loop) in gauss. We can express the requirement on A in terms of the material parameter B m and the memor,y limits Vp and ~ s as (I) c. Cross-Sectional Areas Thin Film Let w = C t, where Cl is a constant determined by the 1 magnitude of the demagnetizing field tolerable for a square loop; C is in the order of 103 0 The cross-sectional area is thus l 1. 2 A 2. =..!. C l (2) Toroid Because about four mutually perpendicular wires of a~sumed diameter d must pass through the toroidal memory element, the w inner diameter d. has a lower limit, d.> 2d ; also geometry dictates that 1 I W Memorandum 6M-4089 Page 4 of 7 the following assumptions be made: (a) do = C2 d i ; C2> 1 (b) h = C d ; C /1 3 i 3 The area is given as k=C 41 Do C -1 3 2 Ld 2 i (3) H-I Relationships: Thin Film In the calculation of the field between two sheets of current, the following approximations are made: 10 (a) (b) The field inside a rectangular coil of length w centimeters and of N turns is the same as for a similar solenoid. The current sheets above and below the thin film can be created by overlapping the rectangular coil as shown in Fig. 20 Figo 2 - Approximation of Current Sheets Memorandum 6M-4089 Page 5 of 7 From this crude analysis we get H~ 4nN. ---2:. law 4I (4) n = lOw where I is the total current in amperes flowing in both sheets (split equally between the two) and H is in oersteds. 2. Toroid The field in a toroid is H ~ 8I (5) ~ --IO---l(-d-+~d-..... ) o E. ~ Geometry Factor We define a geometry factor F as g H F g = -I (6) • SUbstituting the cross-sectional area limit of Eq. (1) into Eqs. (2) and (3) and these into Eqs. (4) and (5), respectively, gives F (thin film) g ~ 1 8n x 10-5 'fCi vBm \ p't s and (8) F (toroid) g F. Order-of - Magnitude Calculations For purposes of comparison, the geometry factor of the F397 toroid (d.= 54 mills, d0 = 80 mills, h = 22 mills) is 2.4. ~ We make the following general assumptions for both geometries: (1) V ~ 10-2 volt (in present memory V ~ 10-1 volt) p (2) 't s ~ p 10-7 second (present 't s is 10-6 second). Page 6 of Memorandum 6M-4089 7 With these assumptions, we get for thin films F (thin film) ~ 16 oersted g ampere where 01= 2 x 103 ; Bm= 8 x 103 gauss, typical for square loop metalso For a toroid where 02= 1; 03= 2; Bm= 1~5 x.l0 3 gauss, typical for ferrites, . F (toroid) ~ 50 oersted g ampere The next section indicates the relative difficulty of obtaining the above geometry factors o IIo Discussions and Conclusions: The ease of fabrication is one factor governing the practica:Lity of a given memory-element geometry. In the Fg .factors '. . -2,:1.; above, the thin film would have the dimensions w = 7x lO'em by t = 305 x 10 ....5 cm; the toroid, d. :;::: 3 x 10';"3 em, d = 6 x lO-3 cm, h =3xlO-3cm o . ~ 0 The thin film could be made by evaporation techniques with relative ease; but the ultra-small toroid would .be almost·~ impossi'ble to make. A toroid a scale magnitude larger would be possible; this. gives Fg -:=.50 Also it must be remembered that a miniDllm of' three conductors each capable of carrying milliampere currents must pass through the toroid 0 Thus fabrication difficulties seem to make the thin film geometry more feasible o other geometries may offer mo~e ~han.the thin film so that a further study of geometry is worthwhile. Changing geometry alone is not the answer to the very-fastmemory. problem. In the preceding calculations it has been assumed that magnetic materials and memory scheme exist such that a memory cycle time 2 of about 2 x 10 -7 second is possible and the V ~ 10- volts can be p sensed reliably. In conclusion, a memory element can be reduoedin size (1) yielding an improvement in the peak current-average power requirement of the memory (2) at the expense of the peak signal voltage i f and only if Memorandum 6M=4089 (3) a material and memory scheme exist such that possible e JDC/md Page 't' s 7 of ~ 10-7 second is 7
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