REPRODUCTION OF MAGNETICALLY RECORDED SIGNALS 1151 



measure they may serve as a guide to a better understanding of the mag- 

 netic reproducing process. 



The Idealized Recording Medium 



The problem will be reduced to two dimensions by assuming an infinitely 

 wide and infinitely long tape of finite thickness d. A rectangular coordinate 

 system will be chosen in such a way that the central plane midway between 

 the upper and lower surfaces of the recording medium lies in the x-y plane. 

 It will be assumed that the medium is sinusoidally magnetized in such a 

 way that in the medium the intensity of magnetization is given by 



Ix = Im sin {lirx/X) 



Iv = h = 0. (2) 



Equations (2) say that the recording is purely longitudinal. In a prac- 

 tical case, of course, the recorded signal is neither purely longitudinal nor 

 purely perpendicular but rather contains components of both sorts. In 

 Appendix I it is shown that the frequency response does not depend on the 

 relative amounts of these two components and hence that the computed 

 results are equally valid whether the recorded signal is purely longitudinal, 

 purely perpendicular, or a mixture of the two. 



Appendix II contains calculations for the case of a round wire sinusoi- 

 dally magnetized along its axis, and for a plated wire. These results, though 

 much different in mathematical form, are shown to be very similar to the 

 results for a flat medium. 



The Idealized Reproducing Head 



Figure 4 shows a semi-practical version of the sort of idealized repro- 

 ducing head which will be treated. 



It consists of a bar of core material with a single turn of exceedingly fine 

 wire around it. This head is imagined to be spaced d inches above the sur- 

 face of the recording medium. If the dimensions of the bar are made large 

 enough, the amount of flux through it will obviously be as great as could 

 be made to pass through any sort of head which makes contact with only 

 one side of the tape and so the open circuit reproduced voltage per turn 

 is as high as can be obtained with any practical head. 



Suppose a very narrow gap is introduced in this head where the single 

 turn coil was and that the magnetic circuit is completed by a ring of core 

 material as shown in Fig. 5. 



If the permeability of the head is very high and the gap very small then 

 the flux which passed through the single turn coil of Fig. 4 will now pass 



