REPRODUCTION OF MAGNETICALLY RECORDED SIGNALS 1153 



V is the velocity in cm./sec. with which the recording medium 

 passes the reproducing head. 

 Im is the peak value of the sinusoidal intensity of magnetization 

 in the recording medium measured in gauss, 

 8 is the thickness of the recording medium measured in the same 



units as X, 

 X is the recorded wavelength measured in any convenient units, 

 d is the eflfective spacing between the reproducing head and the 

 surface of the recording medium measured in the same units 

 as X, and 

 CO is 27r times the reproduced frequency in cycles per sec. 

 Note that equation (3) applies to a ring type head with no back gap. 

 If the head has a back gap then not all the available flux will thread through 

 the ring. Some of it will return to the medium through the scanning gap 

 and hence will not contribute to the reproduced voltage. This does not 

 aflfect the shape of the frequency response curve but does contribute a 

 constant multiplying factor (less than unity) to the right hand side of 

 equation (3). The value of this factor depends on the reluctances of the gaps 

 and of the magnetic parts of the reproducing head. If the reluctance of 

 the magnetic parts is negligible and the reluctance of the back gap is equal 

 to the reluctance of the front gap then the available flux will divide equally 

 in the two gaps and the factor will be one-half. This factor will not be con- 

 sidered further in this paper because it does not contribute to the shape 

 of the response curve but only to the absolute magnitude of the repro- 

 duced voltage. It could be interpreted as reducing the effective number of 

 turns on the reproducing head to a value somewhat lower than the actual 

 number of turns. 



Spacing Loss 



The term e~^''^'^ tells how the reproduced voltage depends on spacing. 

 In order to compare this computed effect with the experimentally observed 

 one it is necessary to put it in decibel form by computing twenty times the 

 logio of e-2'^'^/\ This gives 



Spacing Loss = 54.6 {d/\) decibels . 



This agrees very well indeed with the experimentally determined equation 

 (1) in which the constant is 55 instead of the computed 54.6. The com- 

 puted spacing loss function is plotted in Fig. 6. 



