RESEA R CH DEI:.§.R T LIE.~NT
SOiJE FACTORS AFFECTING THE OVt:HALL FRE'Q1JgNCY ~.:QlthllA.C!f.HIST~Q
IN LA GHETIC .J1ECORDING
Report No. C.0'14 Serial No. 1950/5
, ./ '/.' '~ ..y~·l /""{",,"~" "'~-' . ----3e.Qort Written By.! (W. Proctor Wilson)
P .E. ,Axon
..
•
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P.BIVt~ TE & ..-QONFIDENI:li~~
Research Department Mar(Jh 7 1950.
Hr.3port No. C'.074 Serial No. 1950/5
Figs. Nos. C.074.1-7
SOiilE FA.CTORS AFFECTING THE OVERb.LL FR.E@~Cy CHhRZiERIST rc
11L. Htl.GNETIC, BECORi;-f~LQ-
SWlll1laa
A. l118thod is described of determining the recorded characteristic on a magnetic tape inde~endently of the char~cteiistic of the reproducing head. The relative selfdemagnetisation existing in various tapes is determined ,and it is shown thot the results can be used to specify the recording tape and reproducing head p~railleters in a magn~tic recording equipl1lent from which a given overall frequency , response is required. TUG predictions are shQwn to a groe well with practice and the .r8sults of .recording at slow tap8 speeds ~re described.
1 0 Introdu9:~ion
The overall ftequency response of a magnetic recording system is determined by two factors (1) the recording characteristic, (2) the reprodu9ing chQractori~tic.
, . 2 t The:; Rocord.ing Characteristic
The tecording ch8r~cteristic may be altered in shape by pre-Gqualisation but its fuild~'}mental characteristics are determined by two f2ctors, Ca) the recordin~process, this term being, considored to include the influence of the phy sical constant s of the hC/Qd (such as g.3p width and core m:ttorial) clnd the effoctiv8ness of tho HF bins nnd (b) salf-deD.lugnetisation in the; magnetic tapG~ the m:3gnitude of which depends on the wavelength of tho recorded signal and on the tape illoteriQl.
It can be nssumed~ to ;.1 first a)proximntion, that if
2.
the rebording huad is bi~sed correctly~ factor (c) is not n function of tap..::: speed and v/ill not contribute to the ch-::lllges in til8 overnll chDracteristic whon the tEliJe is run'Dt diff 8rcnt speeds, F? ct or (b)? hOil/ever? iw s n profound influence orrthe overall char~cteristic. Firstly, the more ,slowly the t'ipu is run~ the shorter is the wDvelength on' the tSlpe of a given signal and henco the more lllarkod will be the effocts of self-demagnetisation, Secondly~ the tape fl1nterinl greatly influences s(}lf-d'G{l~agnGtisation in that tnpes of high coerci vi ty are le ss sub'joct to self-do!TID gneti s~~ t ipn, an effect which would be (;xpectod, since the definition of the term c oerci vi ty implh.: s a mG3 sure of t'ho difficulty in demagnetising 8, El2lgnBt formed' of the Il1c:terin:I,'.,
3. ~ho Re.Q:!:.QQucing: Cllilrcwteristic'
Vilhen thG w2velangth of a r(:corded sign::'ll is largo compared with the gap width of the reproducing head the signal induced in the head, as the tape passes it~ is almost directly pro-portional to frequency. Hovvover? even at 30 inche s per second tnpe speud the; gap width bocomcs an npprcciable fraction of the recorded wnvclength within the ::.:udio frequency s cnle and the 6 db rise of reproduced level peroct3ve is then no longer obt8ined. ~ more preCise expression may be deduced from first principles, namely that
ERIvTS =Kl • P 08, ,2 sin (11' L) ( " ) • " 0 • 0 • " .' ~ ••• ' ••••• (1),
where Kl is constant, P is the ~Jeak flux Associated with the recorded frequency, 8 is the tape speed, A is the wavelength on the tape and I, the g8p length. P is proportional to tho intensity of XflJgnetis3tion on thE) tape and is considered constant for all fr",ouencies ':It const:lnt currant in the recording hQ:J.d. 1 l'his eX~H'essj.on, the dcri v:::tion of whiqh is given in ~p~endix 'al ~ shows that the rise of,6 db per octClve obtained at long w,,;velengths is'Llodifiod by [;\ sine 'terni, ·the magnitud8 of which depcmds upon the ratio of J.. to A. Wher(l. = A. then sin( n·l/A.) is zor 0 and ,the vol ta ge induced in the re producing head is zoro. When L = ).../2 thon sin( 1Tl,!A.) is ' unity and [] maxiLlWl1 voltage is induced in the reproducing hoad. k curve of this function for Cl 10-Qicron gap in the reproducing h0ad and tape speed of 30 'inches per second is shown in ' Figure 1.
How the wc:welength A. on tl~2 tape e qu::::ls 'S/f wher:e f is the frequency of the r(;corded signal. Thc;ruforo the, slovrer ,the ,
, ,
•
•
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..., j.
sp(jed? the lovver the frequency cl t 'which L == A. When a re~roducing head with 1 ID-micron gap is used at Cl tape speGd of 30 1nc.hc S p,-r se; cond? Uld frequc::ncie s at which the fir st maXiEllliil 8nd fir st ElinillllEl occur (38.1 kc/ s ,3nd 76.2 kc/s res~ectively) arc fa~ outside the audio range. When hOw l2v,.:.:r c~ head vd th [: vdder gap (such El s 20-r111cron8). is used at speeds of 15 inc}H';s pi..;r second and 7.5 inches psr second then this interference phenoDcnon can oarkodly affect tile sh:lpe of thd re sponse curve pnrticular ly a t the higher frequoncJes, the rn3xirmm occurring at 9.5 kc/s and 4.75 kc/s respectively.
b. theOretical analysis of the J.ilagnitude of the effects of self-dmiJ.c;ghet1sation is difficult t:ven for a homogeneous magnet of siaple goohl0trical shape. The problem becooes even Dore difficult, and the validity of the analysis Gven
t o I • " to' .. f l~lOrc uncer 2:Hl? Wlwn tlK liwgne 1n CiueSG10n 1S ono 0 aany forucd in a powdered 80terial in a thin layer of great length such as a uagnctic recording tape. It is pOSSible, however? to l~181\.c ~jn ,:;;;lpiricnl c;stlmat'J of the offect by a El\3thod which has been dE3velcp<Jd .in the Research DC;jJnrt:Glento Paragraph 3 has doscribed how the reproducing head deter@ines to some extent the overall fr~quency response of the recording system. If the gap width of the reproducing head is made comparatively large it will be seen? from Equ2tion 1, thcit nn appreciClble m.lDbcr of the interference L18xin8 Gnd Llininl2. will occur in the reproduced lovel within thE.' range of the Qudio spectrlliJ. That is to say the condition
1 == n"-2
where n is an integer, will be fulfilled clany times. Now L1DxiiJB occur when
and Equ,~tion 1 shows that if P is l!lnintained constant over . the frequc;ncy rung.:' then the absolute repro.duced level of all the waxima should also be constant. However, the effect of d,'~magnetisation? and losses in the recording hi?ad, cause P to decrease with frequency. Consider then the overall frequency response obtsined when using a normal
4.
rGcording head end o. wide ,gEt) rcproducing hc,Cid. Cl(n~('ly a nU.Ll-ber of mnxi~a will be obtsinud and the decr0ss~ of level of SUCCI?; 5 si ve m3xLl]'.J lilUS t b(:) dUG solely to sc; If-c1eE,-:i [;11(:;: ti S8. ti on and to losses in the recording h88.d since, at thcSJ points, the interf0rence effect in the reproducing head is eli~incted, sin (7f1/A.) ,being unity at ench point. Thus tLi"; ch:~.L'2ct<3ristic rec orded on the te:PL: can be Qete:l'.;iincd at a nUlilber of f~8quencies, without it being necossary to know the eff~ctive magnetic gap of the r(,;prodnciqg h8L"ld. By any, cthar iilethod it is iillpossiblG to sort out prwcisely the relative contributions of the r0cording 8nd re~roducins heads since only an cstill,l2lte can be uade of tkE effectiv~ gclp of u narrow· gap reproducing head, the effective gap beinz 81wnys larger than the physical gap. In addition reproducing head impedance, which· varies with frecudlcy, will h,~v8 SOlllO effoct on the reproduced lev~l but iu the cas~ of 2 wide gap rbproduciug head this VSI' i8 ti on is very L .. uch 18 ss tlwu in c: nOY'ual g::tp head ::::nd is not iLl..)ortc.:nt over the fr~~cluency rDUe}J conshtered. Fie;ure 2 shows [in 8xperL12litcl CUl'V8 obtDilkd uE.;ing ::: nOI'rJ.al recording heDel (40-,'1:Lcrons gap) E:nd ~~ raproducillt; :ncnd witl:l ;:1
gt.p width of 427-Elicrons. The c:.bsolut,:; lovl'ls of the Ll2xin3 are seen to fall ~WQy steadily with incr83se of fr~quency. Plottin;; the rel::::. ti vo lev01 s of the Sd "Jaxir.~,~ at \1[;\1' ious t2tpe speeds gives tIlT series of curves shown :Ln Figure 3.
The eff8cts of losses in thG h,",ads which [1Y'", a function of frequencY7 will add to the effect of de~3gnctisation in th~ t;;,i,Je w'~~lich is ::l function of vn:.velGngth. If the latter is predOLinJnt it would ba exp~ctod that a given.decrease in level b,c.;;lo1N the tUl.:l corrcs)onded at O!c;CI1 tcps Spt.:H,:;d to the S:::;c;l',~ w::velungtii. <.tl inspection of thG curves of Figuro 3 will show that thi,s ts in fact t::18 c::::se. For e:za;jpl8 it is found that in each curve the point lying 3 db below the level :::~t 281'0 freC:UdlcyWilere no c.lc.".c:gi"h.:ti,sDtion (;)xists,' uccurs [i't 8
frequency corres)onding to a wavelEngtn of 1.43 x 10-2 contidi:;tres. Clec:rly ti,dl tilt;: 8ffect of dCL.~cgnGtis::tion is predoLlin.':lnt over los:::;es in tile }lGc.1l1s at tlll;se frdJ,uenci"es and in any on(: tDpe (in "chis c~sc Ili3gn .... tclphori C.17) is J function of w::)velengtll oJ:11y.
This iilGthoJ ,.my bo used to C0111pare: tnc "Jagllitude of dCl]::;;Gnetis~Jtion existi.ng in w}i'ious cOi.l.uercial tz::pes, Clnd Figure 4 shows the results 3t 30 inches par second on four C()':11:1 c rC1' ''''1 t', .. ,c·os ;'1'" """lv "~C('tcl1 B' ., ;,.:]1' (' Tol c'rl'(', ;:nr'l F ll;: I ... " .. v __ ..... j:J ~ J, " • .1.*.;,,-,. tf? ....,...J 1. 9 4t.~ vJ .... 'lo U, \.A Cl. ..... ' .... l.. :.t.:.1.. •
t,~ pu s. Suppose? for CX;}~,lple? a recording is dude on Scotch B tape cmd T,.:lcna tepe under the S;:',\",18 conJitions such as ustng in 08Ch CDse th • ..:- bias rGquired for ElexiLlur:l 1 kc/s SCXLsitivity.
•
Figure 4 shows that the 10 kc/s level in the case of Scotch B tape,,?~mpared to l'cs assoc1.ated 1 kc/s level, will be some 6 db nlgher than ttle 10 kc/s level on Tolana tape compared to its associated 1 kc/s level. It is thus possible to grade tapes according to the relative high frequency response which they may be expected to give.
5. The Overall Frequen£1... Cl:"c,ra.QterlstiQ
There are thus two factors involved (a) the sine function. whieh expresses the effect on frequency response of the reproducinG; head and (b) demagnetisation on the tape which is dependent upcn the [Jagnetjc illaterial and the thickne ss of the magnetic layer. Fi6v.re 1 shows the r€lati ve levels which would be reproduced at .30 inches per second by a reproducing head of ID-microns gap? if the peak flux p left recorded on the tape werc constant a tall fre':'1uencie s. FJ..;.;ure 4 shows how the remanent' flux departs from the ideal on various tapes recorded under the saIne conditions. Ti18 overall frequency character i stic for a 'ma gne tic recording sy stem may be predicted by the combination of a curve such as Fi""ure 1, depending on the h0ad gap employed, and' by a relevant curve of the type sli.own in Figure L~, depending on the tape employed. Suppose that a 10-·micron gap head is used with, say, Scotch B tape. Figure 1 shows tha t 3 S far as the head is concerned the 10 kc/s leVel vdll be 19.7 db ,')bove the I kc/s leveJ.. On the other h,).nd FL.LU·(; 4 shows that the effect of dem~gn~tisation is t~ drop the recorded level at 10 kc/s
~,some 16 db relative to the 1 1\:c/s level. T".G result of these .iwo factors. should than be that the 10 kc/s level in the overall characteristic lies some .3.7 db above the 1 kc/s level. A series of characteristics have boen predicted in this manner for the .foul' tape s s}lOwn 1n Fic.:u..:r:·e 4 and are shown GS solid line curves in Figure 5. S;;;p;erimposed on tAe solid line curves are points obtained experimentally with.a ID-micron gap head and the tape specified. T~e ngreeillent between the predicted and experimental results is seen to be close and it may thorefore be asswllod that the principal factors in the overall process are trlose which have bed.l cunsiderdd~na.mely~ the der;mgnetis.}tion effect and the rGproducin~ head characteristic. .
6. Design of R~cording EQuipment
A. combination of curves such as those of F'Lure 1 and Fit."ure 4 (;nable tIlt; gnp width .of the reproducing head to be specified? having Tsgard to the t~pes Dvailable for use, in
6.
order to obtain,a desired response. When a reproducing head has a wider gap it is, of course, more sensitive at lowert frequencies and in addition it is easier to manufocture. At slow speeds, however, too great a width PlaY entail an unacceptable amount of pre-equalisation with attendant distortion and noise.
7. -Results of....§.J.ow Ti:~iJe_Spegds Tests
The experimenta1 curves obtained with,the four tapes t,lsing a IO-micron gap h,ead) a~ speeds of 15 inches and 7.5 :1nches per second are s110wn :1n Figure 6{a), (b), (c) and (d). As would be e'xpected, in the light of the previous discussion, the frequency charDcteristics of Audio tape and Scotch 13 Plastic tape, both h:igh coercivity tapes, are much superior to those of Tolana and E .M. I. tape s. TJl\.:; conditions under which recor.ding has been carried out are, in each c~lse, to adjust, recording head blas to a vs.lue which giv~s El3.ximum sensitivity at I kcls recording tone.
8. Conclusions
By the use of a wide gap head it is po~sible to deter~ine the frequency ch~racteristic recorded on the tape independently of the reprbducing head characteristic. By, this wethod the magnit'lide of self-c1eLlo.gnetiso.tion in various COm.iilerc'ial tapes can be evaluated. This factor is of gre,3t importance in determining the relatiVe high frequency response which can be obtained fro1;1 the tap.es. Tii.e results obtained, used in conjunction with the calculated characteristic of the normal reproducing head, enable the overall ch3.ractcristic for 8 fit magnetlc recording equipment to be predicted. The results obt:; ined by this. method cue in good agreement with those obtained in practice.
Tests of over:Jll frequency characteristic' obtainable when the tapu is run at slow speeds show that if a rf:)c,sonable ahlount of equalisation is accepted it should be possible to obtain satisfactory frequency response on illtist ava,ilabl0 tapes at 15 inches per second. It is doubtful, howevur, whethor results nf any quality would be obtained at 7.5 inches per second using low coerqivity t3pes such as E.N.I. or Tolana tapes •. Hi.gher
coercivity tapes are required for this speed 3nd even with those tapes (o.g. Scotch B or Audio) the results at the higher end (9 - 14 kc/s) of the audio 1'3nge cannot be guaranteed as of very high quality.
MJB
I
'7 . ..
V&RIATION OF REPRODUCED FllEoUENg:y IN ...10NGITUDINf\.1
LEVEL WITH. REPRODUCI~~ ~EAD
, Figure 7 represents a reproducing gap ll3ngth " L" passing ,over a magnetised tape upon which an audio wavelength has been recprded •. If a point of. zero magnetic intensity on the tape is taken as reference, then at any moment the flux in the reprodu.cing gap is p ,
a + L
'Nher e p = I' p ~ sin _ L
2'
( 2x 7f ) • dx (A )
x is the distance of the small. ga'p element dx from the r'eference point. Evalua ting this integral, we have
p ~ p 0 ..L • ~ .. cos _.1f (2a -I, ) - cos_1L (2a + 1 )J ~ . A A
, -As the gap is moving over the tap~, it is the rate of change of flux with time which will determine the reproduced signal level. Now, the rate of change of flux with time is dp /dt and we may say'
Thus, ,-
£&. = Q£. • da dt, da· dt
dP = P. A. ! -21f. sin _1L.. (2a -.l.) + 2rr • dt ;"'Jrr i;;:- l ' A
L
= P r sin ,.1L (2a + 1 ) - s in..JL (2a - L A A.
--I sin..1L (2a + L ):
'\ I\. j
1 ) I. da
J dt'
= P. 2 cos ( IL • , ( A
sin ( ... .IL .• ( A. \
2 ~ da .;;J... •
2· dt
da dt
Now the spe:.::d S = f. A. , where f is frequency of the signal and A its wavelength on the tape. Clearly, S = da/dt so that instantaneous e.m.f. is given by
8.
,Einst = K. P .s. or the mean induced voltage
ER .M. S. _ = K l· P. S. 2 sin f 1'} j
• sin _pL.iJ ( A )
If we. consider speed constant, then E is 11 maximum when
1. = ~, ~A. -- etc·. 2 2
while E is zero when
1· = A , 2 A. , 3 A. 'etc.
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This drawII1glspeclf,cHion is the property of the British __ Broadcasting Corpor'Hlon and may not be reproduced _____________ , or disdosed to 1 th,,-d party in any lorm without thp wntten pernllHlon of the Corporation.
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FRE QUENCV IN kC/S.
FIG.6 (C)
BBC SOME FACTORS AFFECTING
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THE OVERALL FREQUENCY CHARACTERISTIC IN MAGNETIC RECORDING.
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RESEARI:.H DE PT REPORT
C.074. l' SHEETS N~ 9.
FIG. 6 (d.)
.-- - -----------, SOME FACTORS AFFECTING
THE OVERALL FREQUENCY CHARACTER IN MAGNETIC RECORDING.
RESEARCH DEPT
ISTIC OR'N. W.H"" REC5T CH'D, ff" c. 74. AP'D. ~ U SWEETS. H~ 10
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BBC SOME FACTORS AFFECTING THE OVERALL FREQUENCY CHARACTERISTIC
t--~-li IN MAG N E. TIC RECORDING.
REPORT.
C.074. 11 SH NO.H.
