12.2 The ‘digital’ defects of the long-playing record
In the previous section we considered the signals used to communicate information. But what about the physical processes and sensors we use to create or collect information? In general we tend to assume that a measurement system operates in an analog manner. An input is sensed by some form of detector and produces a voltage or current whose magnitude varies in proportion with the stimulus. This voltage or current is then taken as an analog of the input we wish to measure.
Despite this assumption we can expect that any physical process must, at some level, be affected by the quantum mechanical behaviour of the real world. In order to see how this influences a real measurement we can consider the example of a Long Playing (LP) record. This sound recording system makes a useful contrast to the Compact Disc which we have already examined. It is also considered by some Hi-Fi audio enthusiasts opposed to digital audio as a paragon of ‘analog virtues’.
Information is stored on an LP in the form of a modulated spiral groove pressed into its surface. The measurement sensor consists of a stylus which is placed in the groove whilst the LP is rotated at a constant angular velocity. An output signal is produced which is proportional to the instantaneous radial velocity of the stylus The signal is recorded in the shape of the groove surfaces, or ‘walls’. The stylus is connected to some form of electrical generator (usually a coil in the vicinity of a magnet) which produces an output voltage proportional to the transverse velocity of the stylus. In general, sensors which convert one form of energy into another are called Transducers. In this case some of the rotational energy of the LP is converted into electronic energy. The combination of stylus and generator is usually referred to as a ‘cartridge’. (It can also be called a ‘pick-up’, but this term is confusing as it's sometimes used for the arm which supports the cartridge above the LP record.)
For the sake of simplicity we can assume that the LP is Monophonic and that the nominal centre line of an unmodulated groove would cause the stylus to move inwards at a constant rate, . We can represent the recorded signal as illustrated in figure 12.1 by an offset distance, , between the actual position of the stylus at time, t, and the position it would have if there were no modulation. The radial velocity of the stylus, , of the stylus at any instant will be
In practice the steady spiral velocity, , simply causes the pick-up arm to move slowly inwards so we can say that the output voltage generated by the stylus movements will be
where k is the appropriate conversion coefficient (the cartridge's Sensitivity or responsivity) of the cartridge. For a real LP system, k is typically in the range 0·1 — 1 mV/cm/s. Ideally, we would like to obtain an output signal, , which is a faithful reproduction of the required sound pressure variations. In any real system, however, some problems must be taken into account. For example, various processes will restrict the dynamic range of the system. Mechanical problems will place limits on the maximum possible size of the displacement, , and the maximum achievable acceleration, . The noise level will also prevent us from observing changes in displacement smaller than a given size.
The record industry adopted a standard level of 5 cm/s (peak velocity for a 1 kHz sinewave), as the nominal 0 dB Reference Level. A reasonably good cartridge would have been able to Track (maintain its stylus in the groove) modulation levels around 20 dB greater than this reference level. For a sinewave of frequency, f, amplitude, A, the offset displacement will have the form
hence the velocity will be
and the acceleration
A 1 kHz sine wave recorded at a +20 dB level will have a displacement of peak value, microns, and a peak acceleration, km/s/s. (i.e. a peak acceleration around 320 times bigger than that due to the Earth's gravity!)
No matter how well they have been made, every cartridge will ‘mistrack’ groove modulations above a given magnitude. This is usually because the accelerations and displacements become too large and the stylus either loses contact with the groove walls or gouges into them, damaging the record! In other cases the stylus may remain in contact, but the cartridge's electrical output saturates. Whatever the exact cause, above a given level the cartridge (sensor) output ceases to be a faithful representation of the groove modulation. These electro-mechanical problems will limit both the maximum signal level and the maximum rate of change of the signal level we can obtain using a given cartridge.
The smallest signal levels we can sense using the cartridge will be partly set by electronic noise produced in its generator resistance and in the amplifier used to boost its output. There is also a mechanical limit on the smallest signal level which will be clearly measurable.
A 0 dB 1 kHz sinewave corresponds to a peak offset, , of just 8 microns. An LP record is made from a solid assembly of real atoms and molecules. In practice, LPs are made of an amorphous polymer, PolyVinyl Chloride (PVC), to which various other materials have been added. The precise properties of this material are quite complex and were the subject of quite a lot of research and development by the music industry (tobacco-ash, insects, etc, have also been found in LP material!). To avoid the complexity of the details of PVC's properties we can imagine an LP made of crystalline carbon (diamond!). It must be admitted that manufacturing such an LP would be rather difficult!
The walls of the groove of such an LP would be made from layers of carbon atoms. Each carbon atom has an effective diameter of around half a nanometre so the thickness of each layer will be approximately 0·5 nm. The position of the stylus is determined by resting on top of the uppermost layers of atoms. Hence we can see that the stylus position will be roughly quantised by the finite thickness of the atomic layers. When playing a sinewave whose peak size is 8 microns the movement of the stylus would take place in 1 nm steps. Instead of smoothly varying, the stylus offset would therefore always adopt one of the set of available levels,, where m is an integer and is the thickness of the atomic layers. The effect is to divide the microns swing of a 0 dB 1 kHz sinewave into 32,000 steps — just as if the signal had passed through an ADC!
If we assume that the largest possible recorded signal level is +20 dB (i.e. microns) and accept that the signal is quantised in 0·5 nm steps then the diamond LP has a dynamic range, D, of
This compares very well with the Compact Disc system which employs 16-bit digital samples and hence has a dynamic range of about 96 dB. Alas, the performance of a real LP and stylus may be very different from the imaginary example made from diamond! The actual dynamic range of a real vinyl LP is normally much less than 100 dB!
PVC is a Polymer. This means its molecules have been grown by joining together lots of smaller molecules. The results of this polymerization process will depend upon the details of the process. The average molecular weights of the polymer chains which are formed can range from a few tens of hydrogen atom masses to hundreds of thousands. As a result, the PVC molecules are much larger than carbon atoms. This has the effect of producing a material which is ‘lumpy’ with a typical quantisation size far bigger than a carbon atom. As a result, the value for we should have used for the above expressions is hundreds of times larger than 0.5 nm, producing a much smaller dynamic range. As an example, if we assume the molecules in LP Vinyl are 100 times larger than a carbon atom, then resulting dynamic range might be expected to fall by 40dB to around 70dB.
The purpose of the above example was to help us recognise that, since LPs are made from a collection of real molecules, the signals they hold must be quantised. Fortunately for the LP this usually isn't obvious. The underlying signal quantisation is usually masked by various effects.
Although the PVC molecules are much larger than carbon atoms they aren't arranged into a regular crystalline pattern. PVC is usually formed as a sort of Glass. Molecules nearby one another tend to be approximately aligned, but the alignments tend to alter slowly and randomly from one place to another in the solid. The material is a bit like a frozen liquid, or a liquid with a very high viscosity. The result is as if we had started to built a crystal, but kept changing our mind about where to put the layers of molecules. In any small region the groove wall may be quantised, but the details of the quantisation vary from place to place along the groove. For a recorded signal this produces an effect similar to dithering a signal before digital sampling. The randomised quantisation becomes indistinguishable from random noise. This dithering effect is enhanced by random thermal movements of the molecules. When playing an LP the effects of this molecular quantisation therefore appear as noise, not obvious quan-tisation distortions.
Another factor working in the LP's favour is that the stylus does not just touch the groove wall at a single point. Instead it presses against a finite Contact Area. This means that the force which positions the stylus is produced by a number of atoms in the groove surface. The contact area of a good stylus is typically the order of 10 microns square. Hence the stylus rests upon hundreds or thousands of PVC molecules at any time. The pressure of the stylus will tend to squeeze the groove surface. This makes it deform elastically until the total force exerted by all the displaced molecules is enough to support the stylus. Adding or removing a few PVC molecules in the contact area would shift the stylus by an amount which is much less than the size of a single molecule. The finite contact area of the stylus means that it essentially making a measurement which is averaged over many molecules. A larger contact area would permit the stylus to resolve smaller changes in the groove wall by averaging over more atoms. This averaging process, along with the physical dithering mentioned earlier, can let the stylus recover signal levels equivalent to changes in the groove wall which are smaller than an individual molecule.
A time-varying output signal is obtained by drawing the stylus along the groove. Hence the frequency of a recorded signal variation is inversely proportional to its length along the groove. Since the stylus cannot be expected to respond to surface details which are much smaller than the width of its contact area, it follows that any improvement in resolution obtained by increasing the contact area may be purchased at the cost of a reduction in the available signal bandwidth. Alternately, we could choose a smaller stylus and sacrifice resolution for a wider bandwidth. The recorded signal is essentially both quantised and sampled by the atomic structure of the LP material, although in a way which varies from place to place on the disc.
High performance LP systems usually employ an Elliptical stylus (or some other near-equivalent). These styli are manufactured to have a specially shaped contact area which is shortened along the direction of travel and elongated perpendicular to it. The modified shape helps the stylus trace out higher frequencies (shorter groove wavelengths) without reducing the contact area. This improves the noise/bandwidth/distortion performance, but it can't entirely overcome the problems mentioned above. The stylus must have a non-zero contact area, hence the physical problems we've considered always apply.
It would be possible to go on considering various other factors which alter the detailed performance of Long Playing records. For example, any serious comparison of ‘LP versus CD’ would have to take into account the relatively high levels of signal distortion which commercial cartridges produce when recovering signals louder than the 0 dB level. Typically, signals of +10 dB or above are accompanied by harmonic distortion levels of 10% or more — not a very high fidelity performance! Even at the 0 dB level, many cartridges produce around 1% (or more!) harmonic distortion. The frequency response of signals recorded on LP are also modified — the high frequency level boosted and the low frequency level reduced — to obtain better S/N and distortion performance. This means that an LP replay system must include a De-Emphasis network to Correct the recovered signal’s frequency response. Here, however, we are only interested in considering those physical factors which make the LP less than an ideally ‘analog’ way to communicate information. These extra factors affect the performance of an LP but they don't change the basic nature of the system.
The above analysis is a simplified one. It leaves out many features of a practical LP system. Despite that, it does serve to show that even a system which appears essentially ‘analog’ will still have underlying properties similar to a digital information processing system. In fact a similar situation arises with all analog signals in the real world since every physical process will be found to behave in a quantised manner when examined in sufficient detail. Despite this we do not usually observe any structured quantisation or sampling effects because they tend to be masked by a relatively high level of thermal noise and the averaging or smoothing effects of processes like the stylus's finite contact area. In effect, the real world beat us to the idea of using noise dithering to make quantisation effects invisible.
An argument similar to the one used to analyse the LP can be applied to sound waves themselves. The air consists of an enormous number of molecules whose sizes/shapes/energies/etc are quantised. The physical interactions between these molecules — i.e. they way in which they exchange energy and momentum with one another — follow the rules of quantum mechanics. Hence if we analyse sound waves in enough detail we should discover quantised behaviour once again. Just as with the LP groove, however, these effects are on such a small scale that we don't normally notice them. Usually we can describe sound in terms of the averaged statistical properties (pressures, mean velocities and displacements) of relatively large numbers of molecules without noticing this fact. This allows us to use the classical physics which describes sound in terms of continuous algebraic functions which satisfy a set of wave equations. Despite this, the individual molecules know nothing about our equations. The overall ‘analog-like’ properties of soundwaves arise because of the dithering/averaging effects of the countless individual quantised molecule—molecule interactions.
You should now understand that the terms ‘analog’ and ‘digital’ are based on idealisations. Real systems and signals will show a mixture of analog (smooth continuous) and digital (quantised) properties. Although it's often convenient to assume a signal/system is one thing or the other, this mixed behaviour is an unavoidable consequence of the way the world works.
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