LP Distortion Mechanisms
Distortion mechanisms in reproduction from gramophone (phonograph) records
If we leave aside the linearity of the electromechanical transducers of the cutter head when recording and the cartridge, when playing the record - which may in any case be reduced to low levels - the majority of the distortion generated in reproduction from records is due to the differences in the various geometries of the recording and reproduction processes.
When a record is recorded, a flat chisel, driven by a moving-coil mechanism rather like a loudspeaker, is drawn in a radial line across the soft, acetate disc. When being played back, a conical (or elliptical) stylus supported on a cantilever rides in an arc across a plastic disc at the end of a pivoted tone arm. This leads to, at least four distortion mechanisms which are described below.
Tracking distortion (lateral)By far the most discussed of the distortion mechanisms is lateral tracking distortion. This arises due to differences in the path of the recording cutter head, which is driven in a straight-line across the radius of the disc by a worm gear arrangement, and the cartridge which moves in an arc at the end of freely pivoted tone arm. A simple, straight tone arm carries with it the very considerable compromise that the stylus is only on a tangential line to the groove at one point on the record.
The effect of reading the disc in a direction other than which it was recorded is complex, as the drawing (right) illustrates1. Essentially, the sine wave, shown in the upper diagram and recorded tangentially to the disc, is read along axis A. This has the effect of elongating the positive modulation and shrinking the negative: a frequency modulation effect which causes a very serious type of distortion capable of producing a very complex and dissonant distortion.
So far, so serious. However, the mathematics of the geometry of the tone arm path (and the distortion mechanisms) have been well understood since the days of the early, pre-electric gramophone. All modern tone arms are arranged to overhang the centre of the record, and have a "crank" so that the cartridge sits at an angle relative to the tone arm. By these two simple geometrical means, the tracking error (the angle of the cartridge relative to the tangent of the groove) is reduced to a few degrees at any point on the record. When the error angle is this small, the frequency modulation effects are reduced so that the resulting sidebands are equivalent to second harmonic distortion.
Note that, whilst tracking distortion may be reduced to low levels by correctly setting the overhang and crank angle of the cartridge, the distortion due to this cause may become very great indeed if these are incorrectly set - especially towards the centre of the record. In fact tracking distortion ∝ (tracking angle error/ groove radius); an often overlooked fact. It means that distortion is 3 times higher on an inner revolution of the groove than it is on the outer edge of the record for the same angle of tracking error.
Tracing distortions are quite separate from tracking distortions. The origin of all tracing distortion is that a groove cut by a flat-faced chisel is being read by a rounded (conical or elliptical) stylus. Tracing distortion is responsible for the majority of distortion (and not just harmonic distortion) when reproducing gramophone records. There are three components to tracing distortions: pinch-effect; vertical tracing distortion; and tracing-loss.
Constrained as it is to follow a path along the disc radius, the cutter chisel cuts a groove which is only the width of the cutter at the peaks of the wave and which shrinks to a minimum as the wave passes through the zero position. This has the effect of squeezing the stylus up and down in the groove even when the modulation is entirely lateral. This phenomenon is termed, appropriately enough, pinch effect.
This effect of pinching the stylus in the narrowing groove may be seen to be at a frequency double that of the lateral modulation; because the stylus rises and falls twice over in one cycle of the modulation wave (see the illustration left).
The pinch-effect upon the stylus is greater as the wavelength of the modulation falls. Besides being frequency dependent, wavelength is also a function of the angular velocity of the recording chisel in the groove. In a conventional gramophone record, this velocity falls as the cutter (or stylus) moves towards the centre of the record because the record turns at a constant number of revolutions per minute, but the radius of the groove falls throughout the playing of one side of the disc.
Additionally, the degree of the pinch-effect depends upon the radius of the stylus. Special stylus shapes have been developed to reduce the pinch-effect. Elliptical styli are shaped so that the major axis of the ellipse has the dimensions of a conical stylus and is perpendicular to the groove. This ensures the stylus rides in the groove at the same level as a conical stylus and doesn't wallow about in the bottom of the groove where no information resides. However, the minor axis of the ellipse is arranged to be considerably smaller than the major axis and this is parallel with the groove. By these means, the stylus is less squeezed as the groove narrows in the direction of the stylus travel.
Vertical tracing distortion
The figure above shows the cross section of a vertically modulated groove (the grey is the disc in cross-section). Whilst the recording is made with a sharp edged chisel, playback is accomplished by means of the spherically rounded cone of the playback stylus. The figure clearly illustrates that the motion of the playback stylus fails to follow the groove's shape. The problem being that the point of contact between the spherical playback stylus and the groove wall wanders as it traces the groove, causing the stylus to trace a path indicated by the dashed line.
Once again, an elliptical stylus helps here as the point of contact wanders less far from the base of the stylus if the stylus is smaller in the direction of groove travel.
Distortion due to vertical tracking angle (VTA)
In the analysis of vertical tracing distortion above is was assumed that playback is accomplished at right angles to the disc surface and, ideally, it would be! However, this is usually not possible due to the mechanical design of the cartridge in which the stylus is carried on the end of a cantilever set at an angle to the disc's surface. This angle is known as the vertical tracking angle (VTA).
The geometry of this distortion is the same as that illustrated for lateral tracking distortion and the same, complex harmonic distortion results from an incorrect "angle of read". In an effort to remove the vertical tracking angle error problem at its source, disc recording standards worldwide specify that recordings be made with a particular value of vertical tracking angle; which is accomplished in the recording by tilting the cutter head in the direction of groove travel. Playback cartridge manufacturers are similarly urged by these standards to adopt the equivalent angle for the rake of the cantilever.
The success of this compensation-at-source technique is somewhat limited by various factors: a lack of international standardisation as to correct angle of tilt (values range from 15 to 25 degrees); so called lacquer spring back effects which result from the acetate disc deforming under the strain of cutting and then springing back after the cutter has passed; and the choice of a rather low standard value of VTA. A angle of 15 degrees requires the cartridge to ride so close to the disc surface that it can fail to clear moderate warps in the disc. Most cartridge manufacturers adopt a higher angle of rake: from about 22 degrees amongst the best to 30 degrees and over for the worst. This severe degree of vertical tracking error can create easily audible harmonic distortion of several percent (being essentially an FM effect upon the vertical component).
Tracing loss is another distortion due to the physical fact that a sharp chisel is used in recording and a rounded stylus is used in reproduction. The sharp chisel is capable of cutting "sharper corners" than the stylus can read and this results in high-frequency loss at small recorded wavelengths. Once again, wavelength on a record is a function of groove radius, and tracing loss is only a problem towards the centre of the record. Here too, the elliptical stylus helps because its smaller radius is the one involved with reading the groove information. But most cartridges, even those with elliptical styli, manifest a falling frequency response as the groove appraoches the centre.
1Kinematically, the effect constitutes an alternating advance and delay on the reproduced signal or a frequency modulation effect on the signal by itself. Historically, it may be of some interest to know that the solution for the prediction of tracking distortion on a sinusoidal signal proves to be the same mathematical proposition as the classical two-body (or Kepler) problem in classical mechanics which involves the the description of the elliptical motion of a planet about the sun. The full analytical solution to this was not derived until 1824 by Bessel
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