On the S-curve of a Magnetic Recording Channel in the Presence of Partial Erasure and Transition Shift

As magnetic recording density grows, the nonlinear distortions, known as transition shift and partial erasure,arise and limit the performance of the detector. In designing a detector, a phase detector is required to estimate the timing error in a timing recovery loop; the Muller & Mueller's phase detector is often adopted for its simple realization. In this article, we focus on the characteristics of the corresponding S-curve of the Muller & Mueller's phase detector in the presence of the non-linearities. In the presence of the partial erasure effect, the derived timing function is a suitable timing function with a decreased slope at the origin and it is a linear combination of two odd functions. One of the two functions is identical to that of a magnetic recording channel in the absence of the nonlinear distortions, and the other is itself a suitable candidate for a timing function. The transition shift causes a non-uniform shift of the S-curve with a different timing error. Computer simulations are given to verify these results.