Maximum signal-to-noise ratio of a tape recorder

Using the Wiener autocorrelation theorem, the noise power spectrum of the pole strength in a thin lamina of an erased tape is shown to be approximately white. The noise power spectrum of the reproduce head voltage is calculated for a thick tape and compared with the signal power. The wide-band signal-to-noise ratio of a tape recorder equalized flat is deduced and expressed in very simple forms, which are inversely dependent upon the square of a bandwidth. Notably, in this special case the wide-band result is independent of reproduce head-to-tape spacing. Numerical examples demonstrate that this simple theory yields results in excellent agreement with practice.