1150 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 



with magnetic structures such as are used in transformers and the Hke 

 that intimate mechanical contact between two parts of a magnetic circuit 

 does not imply intimate magnetic contact. In fact, even when great care is 

 taken in fitting such parts together, measurements invariably show an 

 effective air gap between them and the effective width of this gap usually 

 amounts to appreciably more than one mil. One reason for this is that the 

 permeability of soft materials such as are used in the cores of transformers 

 and reproducing heads is very sensitive to strain. Even the light cold work- 

 ing which a surface receives in being ground flat is sufficient to impair very 

 seriously the permeability of a thin surface layer. 



In view of this it is to be expected that the magnetic contact between 

 reproducing head and medium is less than perfect. If cold working during 

 the fabrication of the head or due to abrasion by the recording medium 

 should result in an effective air space between head and medium amounting 

 to as much as one mil, the effect on frequency response would be pro- 

 nounced indeed. At a recording speed of 7.5 in./sec. this amount of spacing 

 would cause a loss of 7.3 db at 1000 cps, 14.6 db at 2000 cps, 21.9 db at 

 3000 cps, 29.2 db at 4000 cps, etc. 



It seems certain that in a practical recording system some loss of this 

 sort must occur. The problem of determining the magnitude of the loss or 

 in other words the amount of the effective spacing in a practical case is, 

 however, a difficult one. So far, no direct experimental method for its deter- 

 mination has been found. 



Theoretical Calculations for an Idealized Case 



In the preceding section an experimentally determined spacing loss func- 

 tion has been discussed. It was shown that as the reproducing head is moved 

 away from the recording medium the reproduced signal level decreases. 

 This means that the magnetic flux through the head decreases. If the dis- 

 tribution of magnetization in the recording medium were known, it should 

 be possible to compute the flux through the head and thereby to derive 

 the spacing loss function on a theoretical basis. Unfortunately it seems 

 almost impossible to do this calculation in an exact way because very little 

 is known about the magnetization pattern in the medium and because the 

 geometry of the usual ring type head makes the boundary value problem 

 an exceedingly difficult one to solve. 



It is possible, however, to obtain a solution for an idealized case which 

 bears at least some resemblance to the practical situation and this solution 

 will be presented. The results must, of course, be viewed with due skepti- 

 cism until they can be proved experimentally or else recalculated on the 

 basis of better initial assumptions. It is hoped, however, that in some 



