Analytic Treatment of Tracking Error and Notes on Optimal Pick-Up Design

A complete analysis is given of the non-linear distortions due to the tracking error of the pick-up mechanism in the reproduction of lateral-cut disk recordings. The separate treatment of tracking distortion is permissible as long as the overall distortion of the reproduction is tolerable, the system being “almost linear,” or the various distortion products superposable. — For the simplest case of a sinusoidal signal, it is possible to derive explicitly the whole Fourier spectrum of the reproduced signal, the mathematical proposition being the same as in the mechanical two-body problem. For general signals, an explicit operational expansion of the distorted signal is obtained. — As the kinematical effect of tracking error consists of an amplitude controlled advance and delay of the pick-up, the harmonic distortion may be characterized as made up of the side-bands of frequency modulation of the signal by itself. Compared with the ordinary type of non-linear distortion due to curved static characteristics, which may be correspondingly characterized as amplitude automodulation, the spectral character of tracking distortion stresses the higher frequency components. For second-order distortion which is prevalent, the emphasis is proportional to frequency. — The analysis shows, that both absolute and nuisance effects of tracking distortion are considerably greater than commonly assumed, published values usually being underestimates, due to omission of rigorous procedure. Tracking distortion is given approximately by the tracking error weighted with the inverse of the groove radius; the weighted error is referred to the mean groove radius of the record. The recording characteristic affects distortion products independently of their mechanisms. — Pick-up design as based on the analysis should reduce the weighted tracking error as much as possible. For optimal design, Tchebyshev approximation, commonly used in electric wave-filter design, is used. For straight arms, where only one design parameter, i. e., the underhang, is available, optimal approximation of zero distortion is of first order; for offset arms, where both offset angle and overhang are adjustable, it is of second order and thus much closer. The influence of deviations from optimal design due to errors of mounting is investigated as well as the combined effect of offset angle and stylus friction on the lifting force and its reduction by suitably modified design. The compromise design of multi-purpose arms is also treated. Simple design formulas are developed throughout, covering the various record sizes, speeds, and arm lengths. It is found that offset arms are much superior to straight arms. Tracking distortion can be reduced to negligible magnitude with properly designed offset arms even under adverse conditions, such as short arm length and appreciable mounting tolerance.

Print ISSN

0097-5834

Published

1941-12

Content type

Original Research

DOI

10.5594/J09947