Analysis of Noise from Magnetic Storage Media

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Abstract
Noise arising from the transduction of a storage medium, such as a magnetic tape, is analyzed for the case where the storage elements (magnetic domains) are noninteracting and the magnetic tape, except where otherwise specified, is homogeneous. Since the fields arising from the tape are uniquely determined only if the boundary conditions (established by the presence of the reproduce head) are given, the broadband signal‐to‐noise ratio is a function not of the tape alone but of the tape‐head system. It is found that the signal‐to‐noise ratio is proportional to the square root of the ``effective'' number of particles detected by the head. Thus, the signal‐to‐noise ratio is proportional to the square root of a length of tape, which is a measure of the tape‐head resolution. The noise itself can be considered to arise from sources which add, in circuit terminology, serieswise across the width and along the length of the tape. The essential source of what we call the ``no‐signal'' tape noise is not in the surface roughness (assuming an otherwise homogeneous tape) or the physical distribution of the particles, but in the random orientation of the magnetic moments. Furthermore, a distribution in either the particle magnetization or the particle volume increases the noise. These conclusions are derived from purely statistical considerations. Although the basic concepts of tape‐head noise can be established without considering interaction of the tape particles, the formulas for dc and ac signal‐to‐noise and accurate quantitative results for the no‐signal noise can only be obtained if the effect of particle interaction is included in the analysis. An externally applied field divides the particles into two groups: ``unflipped'' particles, which strongly interact, and ``flipped'' particles, which weakly interact. Using this distinction, it is possible to derive the signal‐to‐noise ratio for dc‐ and ac‐magnetized tapes with no further reference to particle interaction. The formula for signal‐to‐dc noise is found; for small magnetizations it is seen that the noise voltage is proportional to the square root of the magnetization level. Alternating current noise is found to be purely a modulation of dc noise. Obtaining quantitative results, of course, involves interaction theory, a subject not treated here.

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