CHAPTER 4

Loudspeakers

The Moving-Coil Loudspeaker

Other Loudspeaker Types

Mounting and Loading Drive Units

‘Infinite baffle’ systems

Bass reflex systems

Coupled cavity systems

Horn loading

Complete Loudspeaker Systems

Two-way systems

Three-way systems

Active Loudspeakers

Subwoofers

Loudspeaker Performance

Impedance

Sensitivity

Sensitivity: practical design limitations

Distortion

Frequency response

Power handling

Directivity

‘Modulated Ultrasound’

Panel speaker dispersion

Setting Up Loudspeakers

Phase

Positioning

Thiele-Small Parameters and Enclosure Volume Calculations

Digital Signal Processing in Loudspeakers

 

A loudspeaker is a transducer which converts electrical energy into acoustical energy. A loudspeaker must therefore have a diaphragm of some sort which is capable of being energized in such a way that it vibrates to produce sound waves which are recognizably similar to the original sound from which the energizing signal was derived. To ask a vibrating plastic loudspeaker cone to reproduce the sound of, say, a violin is to ask a great deal, and it is easy to take for granted how successful the best examples have become. Continuing development and refinement of the loudspeaker has brought about a more or less steady improvement in its general performance, but it is a sobering thought that one very rarely mistakes a sound coming from a speaker for the real sound itself, and that one nevertheless has to use these relatively imperfect devices to assess the results of one’s work. Additionally, it is easy to hear significant differences between one model and another. Which is right? It is important not to tailor a sound to suit a particular favorite model. There are several principles by which loudspeakers can function, and the commonly employed ones will be briefly discussed.

A word or two must be said about the loudspeaker enclosure. The box can have as big an influence on the final sound of a speaker system as can the drivers themselves. At first sight surprising, this fact can be more readily appreciated when one remembers that a speaker cone radiates virtually the same amount of sound into the cabinet as out into the room. The same amount of acoustical energy that is radiated is therefore also being concentrated in the cabinet, and the sound escaping through the walls and also back out through the speaker cone has a considerable influence upon the final sound of the system.

THE MOVING-COIL LOUDSPEAKER

The moving-coil principle is by far the most widely used, as it can be implemented in very cheap transistor radio speakers, PA (public address) systems, and also top-quality studio monitors, plus all performance levels and applications in between. Figure 4.1 illustrates a cutaway view of a typical moving-coil loudspeaker. Such a device is also known as a drive unit or driver, as it is the component of a complete speaker system which actually produces the sound or ‘drives’ the air. Basically, the speaker consists of a powerful permanent magnet which has an annular gap to accommodate a coil of wire wound around a cylindrical former. This former is attached to the cone or diaphragm which is held in its rest position by a suspension system which usually consists of a compliant, corrugated, doped (impregnated) cloth material and a compliant surround around the edge of the cone which can be made of a type of rubber, doped fabric, or it can even be an extension of the cone itself, suitably treated to allow the required amount of movement of the cone.

The chassis usually consists either of pressed steel or a casting, the latter being particularly desirable where large heavy magnets are employed, since the very small clearance between the coil and the magnet gap demands a rigid structure to maintain the alignment, and a pressed steel chassis can sometimes be distorted if the loudspeaker is subject to rough handling as is inevitably the case with portable PA systems and the like. (A properly designed pressed steel chassis should not be overlooked though.) The cone itself can in principle be made of almost any material, common choices being paper pulp (as used in many PA speaker cones for its light weight, giving good efficiency), plastics of various types (as used in many hi-fi speaker cones due to the greater consistency achievable than with paper pulp, and the potentially lower coloration of the sound, usually at the expense of increased weight and therefore lower efficiency which is not crucially important in a domestic loudspeaker), and sometimes metal foil.

The principle of operation is based on the principle of electromagnetic transducers described in Fact File 3.1, and is the exact reverse of the process involved in the moving-coil microphone (see Fact File 3.2). The cone vibration sets up sound waves in the air which are an acoustic analog of the electrical input signal. Thus in principle the moving-coil speaker is a very crude and simple device, but the results obtained today are incomparably superior to the original 1920s Kellog and Rice design. It is, however, a great tribute to those pioneers that the principle of operation of what is still today’s most widely used type of speaker is still theirs.

OTHER LOUDSPEAKER TYPES

The electrostatic loudspeaker first became commercially viable in the 1950s, and is described in Fact File 4.1. The electrostatic principle is far less commonly employed than is the moving coil, since it is difficult and expensive to manufacture and will not produce the sound levels available from moving-coil speakers. The sound quality of the best examples, such as the Quad ESL 63 pictured in Figure 4.2, is, however, rarely equaled by other types of speakers.

Another technique in producing a panel-type speaker membrane has been to employ a light film on which is attached a series of conductive strips which serve as the equivalent of the coil of a moving-coil cone speaker. The panel is housed within a system of strong permanent magnets, and the drive signal is applied to the conductive strips. Gaps in the magnets allow the sound to radiate. Such systems tend to be large and expensive like the electrostatic models, but again very high-quality results are possible. In order to get adequate bass response and output level from such panel speakers the diaphragm needs to be of considerable area.

 

The ribbon loudspeaker principle has sometimes been employed in high-frequency applications (‘tweeters’) and has recently also been employed in large full-range models. Figure 4.3 illustrates the principle. A light corrugated aluminum ribbon, clamped at each end, is placed between two magnetic poles, one north, one south. The input signal is applied, via a step-down transformer, to each end of the ribbon. The alternating nature of the signal causes an alternating magnetic field around the ribbon, which behaves like a single turn of a coil in a moving-coil speaker. The magnets each side thus cause the ribbon to vibrate, producing sound waves. The impedance of the ribbon is often extremely low, and an amplifier cannot drive it directly. A transformer is therefore used which steps up the impedance of the ribbon. The ribbon itself produces a very low acoustic output and often has a horn in front of it to improve its acoustical matching with the air, giving a higher output for a given electrical input. Some ribbons are, however, very long-half a meter or more-and drive the air directly.

A recent panel type of speaker is the so-called ‘distributed mode loudspeaker’ (DML), developed by the NXT company following the UK’s Defence Evaluation and Research Agency’s discovery that certain lightweight composite panels used in military aircraft could act as efficient sound radiators (Figure 4.4). Its operating principle is the antithesis of conventional wisdom: whereas it is normal practice to strive for ‘pistonic’ motion of a cone driver or panel, the complete area of the radiating surface moving backwards and forwards as a whole with progressively smaller areas of the surface moving as frequency increases, the DML panel is deliberately made very flexible so that a multiplicity of bending modes or resonances, equally distributed in frequency, are set up across its surface.This creates a large number of small radiating areas which are virtually independent of each other, giving an uncorrelated set of signals but summing to give a resultant output. The panel is driven not across its whole area but usually at a strategically placed point by a moving-coil transducer. Because of the essentially random-phase nature of the radiating areas, the panel is claimed not to suffer from the higher-frequency beaming effects of conventional panels, and also there is not the global 180° out-of-phase radiation from the rear.

Further research into DML materials has brought the promise of integrated audio-visual panels, a single screen radiating both sound and vision simultaneously.

There are a few other types of speaker in use, but these are sufficiently uncommon for descriptions not to be merited in this brief outline of basic principles.

MOUNTING AND LOADING DRIVE UNITS

‘Infinite baffle’ systems

The moving-coil speaker radiates sound equally in front of and to the rear of the diaphragm or cone. As the cone moves forward it produces a compression of the air in front of it but a rarefaction behind it, and vice versa. The acoustical waveforms are therefore 180° out of phase with each other and when they meet in the surrounding air they tend to cancel out, particularly at lower frequencies where diffraction around the cone occurs. A cabinet is therefore employed in which the drive unit sits, which has the job of preventing the sound radiated from the rear of the cone from reaching the open air. The simplest form of cabinet is the sealed box (commonly, but wrongly, known as the ‘infinite baffle’) which will usually have some sound-absorbing material inside it such as plastic foam or fiber wadding. A true ‘infinite baffle’ would be a very large flat piece of sheet material with a circular hole cut in the middle into which the drive unit would be mounted. Diffraction around the baffle would then only occur at frequencies below that where the wavelength approached the size of the baffle, and thus cancelation of the two mutually out-of-phase signals would not occur over most of the range, but for this to be effective at the lowest frequencies the baffle would have to measure at least 3 or 4 meters square. The only practical means of employing this type of loading is to mount the speaker in the dividing wall between two rooms, but this is rarely encountered for obvious reasons.

Bass reflex systems

Another form of loading is the bass reflex system, as shown in Figure 4.5. A tunnel, or port, is mounted in one of the walls of the cabinet, and the various parameters of cabinet internal volume, speaker cone weight, speaker cone suspension compliance, port dimensions, and thus mass of air inside the port are chosen so that at a specified low frequency the air inside the port will resonate, which reduces the movement of the speaker cone at that frequency. The port thus produces low-frequency output of its own, acting in combination with the driver. In this manner increased low-frequency output, increased efficiency, or a combination of the two can be achieved. However, it is worth remembering that at frequencies lower than the resonant frequency the driver is acoustically unloaded because the port now behaves simply as an open window. If extremely low frequencies from, say, mishandled microphones or record player arms reach the speaker they will cause considerable excursion of the speaker cone which can cause damage. The air inside a closed box system, however, provides a mechanical supporting ‘spring’ right down to the lowest frequencies.

A device known as an auxiliary bass radiator (ABR) is occasionally used as an alternative to a reflex port, and takes the form of a further bass unit without its own magnet and coil. It is thus undriven electrically. Its cone mass acts in the same manner as the air plug in a reflex port, but has the advantage that mid-range frequencies are not emitted, resulting in lower coloration.

A further form of bass loading is described in Fact File 4.2.

Coupled cavity systems

A form of bass loading that has found much favor in small domestic surround sound subwoofers is the coupled cavity, although the technique has been in use even in large sound reinforcement subwoofers for many years. The simplest arrangement of the loading is shown in Figure 4.6a. The drive unit looks into a second or ‘coupled’ enclosure which is fitted with a port. Whereas reflex ports are tuned to a specific low frequency, here the port is tuned to a frequency above the pass band of the system, e.g. above 120 Hz or so, and the port therefore radiates all sound below that. Above the tuned frequency, it exhibits a 12 dB/octave roll-off. However, secondary resonances in the system require that a low pass filter must still be employed. The increased loading on the driver-it now drives an air cavity coupled to the air plug in the port-produces greater efficiency. Figures 4.6b and 4.6c show other arrangements. In (b) two drivers look into a common central cavity. In (c), the two drivers are also reflex loaded.

Horn loading

Horn loading is a technique commonly employed in large PA loudspeaker systems, as described in Fact File 4.3. Here, a horn is placed in front of the speaker diaphragm. The so-called ‘long-throw’ horn tends to beam the sound over an included angle of perhaps 90° horizontally and 40° vertically. The acoustical energy is therefore concentrated principally in the forward direction, and this is one reason for the horn’s high efficiency. The sound is beamed forwards towards the rear of the hall with relatively little sound reaching the side walls. The ‘constant directivity’ horn aims to achieve a consistent spread of sound throughout the whole of its working frequency range, and this is usually achieved at the expense of an uneven frequency response. Special equalization is therefore often applied to compensate for this.

The long-throw horn does not do much for those members of an audience who are close to the stage between the speaker stacks, and an acoustic lens is often employed, which, as its name suggests, diffracts the sound, such that the higher frequencies are spread out over a wider angle to give good coverage at the front. Figure 4.7 shows a typical acoustic lens. It consists of a number of metal plates which are shaped and positioned with respect to each other in such a manner as to cause outward diffraction of the high frequencies. The downward slope of the plates is incidental to the design requirements and it is not incorporated to project the sound downwards. Because the available acoustic output is spread out over a wider area than is the case with the long-throw horn, the on-axis sensitivity tends to be lower.

The high efficiency of the horn has also been much exploited in those PA applications which do not require high sound quality, and their use for outdoor events such as fêtes, football matches and the like, as well as on railway station platforms, will have been noticed. Often, a contrivance known as a re-entrant horn is used, as shown in Figure 4.8. It can be seen that the horn has been effectively cut in half, and the half which carries the driver is turned around and placed inside the bell of the other. Quite a long horn is therefore accommodated in a compact structure, and this method of construction is particularly applicable to handheld loudhailers.

The high-frequency horn is driven not by a cone speaker but by a ‘compression driver’ which consists of a dome-shaped diaphragm usually with a diameter of 1 or 2 inches (2.5 or 5 cm). It resembles a hi-fi dome tweeter but with a flange or thread in front of the dome for fixing on to the horn. The compression driver can easily be damaged if it is driven by frequencies below the cut-off frequency of the horn it is looking into.

COMPLETE LOUDSPEAKER SYSTEMS

Two-way systems

It is a fact of life that no single drive unit can adequately reproduce the complete frequency spectrum from, say, 30 Hz to 20 kHz. Bass frequencies require large drivers with relatively high cone excursions so that adequate areas of air can be set in motion. Conversely, the same cone could not be expected to vibrate at 15kHz-15,000 times a second to reproduce very high frequencies. A double bass is much larger than a flute, and the strings of a piano which produce the low notes are much fatter and longer than those for the high notes.

The most widely used technique for reproducing virtually the whole frequency spectrum is the so-called two-way speaker system, which is employed at many quality levels from fairly cheap audio packages to very high-quality studio monitors. It consists of a bass/mid driver which handles frequencies up to around 3 kHz, and a high-frequency unit or ‘tweeter’ which reproduces frequencies from 3 kHz to 20 kHz or more. Figure 4.9 shows a cutaway view of a tweeter. Typically of around 1 inch (2.5cm) in diameter, the dome is attached to a coil in the same way that a cone is in a bass/mid driver. The dome can be made of various materials, ‘soft’ or ‘hard’, and metal domes are also frequently employed. A bass/mid driver cannot adequately reproduce high frequencies as has been said. Similarly, such a small dome tweeter would actually be damaged if bass frequencies were fed to it; thus a crossover network is required to feed each drive unit with frequencies in the correct range, as described in Fact File 4.4.

In a basic system the woofer would typically be of around 8 inches (20cm) in diameter for a medium-sized domestic speaker, mounted in a cabinet having several cubic feet internal volume. Tweeters are usually sealed at the rear, and therefore they are simply mounted in an appropriate hole cut in the front baffle of the enclosure. This type of speaker is commonly encountered at the cheaper end of the price range, but its simplicity makes it well worth study since it nevertheless incorporates the basic features of many much more costly designs. The latter differ in that they make use of more advanced and sophisticated drive units, higher-quality cabinet materials and constructional techniques, and a rather more sophisticated crossover which usually incorporates both inductors and capacitors in the treble and bass sections as well as resistors which together give much steeper filter slopes than our 6 dB/octave example. Also, the overall frequency response can be adjusted by the crossover to take account of, say, a woofer which gives more acoustic output in the mid-range than in the bass: some attenuation of the mid-range can give a flatter and better-balanced frequency response.

Three-way systems

Numerous three-way loudspeaker systems have also appeared where a separate mid-range driver is incorporated along with additional crossover components to restrict the frequencies feeding it to the mid-range, for example between 400 Hz and 4 kHz. It is an attractive technique due to the fact that the important mid frequencies where much of the detail of music and speech resides are reproduced by a dedicated driver designed specially for that job. But the increased cost and complexity does not always bring about a proportional advance in sound quality.

ACTIVE LOUDSPEAKERS

So far, only ‘passive’ loudspeakers have been discussed, so named because simple passive components-resistors, capacitors and inductors-are used to divide the frequency range between the various drivers. ‘Active’ loudspeakers are also encountered, in which the frequency range is divided by active electronic circuitry at line level, after which each frequency band is sent to a separate power amplifier and thence to the appropriate speaker drive unit. The expense and complexity of active systems has tended to restrict the active technique to high-powered professional PA applications where four-, five- and even six-way systems are employed, and to professional studio monitoring speakers, such as the Rogers LS5/8 system pictured in Figure 4.10. Active speakers are still comparatively rare in domestic audio.

Each driver has its own power amplifier, which of course immediately increases the cost and complexity of the speaker system, but the advantages include: lower distortion (due to the fact that the signal is now being split at line level, where only a volt or so at negligible current is involved, as compared with the tens of volts and several amps that passive crossovers have to deal with); greater system-design flexibility due to the fact that almost any combination of speaker components can be used because their differing sensitivities, impedances and power requirements can be compensated for by adjusting the gains of the separate power amplifiers or electronic crossover outputs; better control of final frequency response, since it is far easier to incorporate precise compensating circuitry into an electronic crossover design than is the case with a passive crossover; better clarity of sound and firmer bass simply due to the lack of passive components between power amplifiers and drivers; and an improvement in power amplifier performance due to the fact that each amplifier now handles a relatively restricted band of frequencies.

In active systems amplifiers can be better matched to loudspeakers, and the system can be designed as a whole, without the problems which arise when an unpredictable load is attached to a power amplifier. In passive systems, the designer has little or no control over which type of loudspeaker is connected to which type of amplifier, and thus the design of each is usually a compromise between adaptability and performance. Some active speakers have the electronics built into the speaker cabinet which simplifies installation.

Electronic equalization has also been used to extract a level of bass performance from relatively small-sized enclosures which would not normally be expected to extend to very low frequencies. For example, looking at Figure 4.16a, the response of this speaker can be seen to be about 6dB down at 55 Hz compared with the mid frequencies, with a roll-off of about 12dB per octave. Applying 6dB of boost at 55 Hz with an appropriate filter shape would extend the bass response of the speaker markedly. However, a 6dB increase corresponds to a four times increase in input power at low frequencies, causing a large increase in speaker cone excursion. For these reasons, such a technique can only be implemented if special high-powered long-throw bass drivers are employed, designed specifically for this kind of application.

SUBWOOFERS

Good bass response from a loudspeaker requires a large internal cabinet volume so that the resonant frequency of the system can be correspondingly low, the response of a given speaker normally falling away below this resonant point. This implies the use of two large enclosures which are likely to be visually obtrusive in a living room, for instance. A way around this problem is to incorporate a so-called ‘subwoofer’ system. A separate speaker cabinet is employed which handles only the deep bass frequencies, and it is usually driven by its own power amplifier. The signal to drive the power amp comes from an electronic crossover which subtracts the low bass frequencies from the feed to the main stereo amplifier and speakers, and sends the mono sum of the deep bass to the subwoofer system.

Freed from the need to reproduce deep bass, the main stereo speakers can now be small high-quality systems; the subwoofer can be positioned anywhere in the room according to the manufacturers of such systems since it only radiates frequencies below around 100 Hz or so, where sources tend to radiate only omnidirectionally anyway. Degradation of the stereo image has sometimes been noted when the subwoofer is a long way from the stereo pair, and a position close to one of these is probably a good idea.

Subwoofers are also employed in concert and theater sound systems. It is difficult to achieve both high efficiency and a good bass response at the same time from a speaker intended for public address use, and quite large and loud examples often have little output below 70 Hz or so. Subwoofer systems, if properly integrated into the system as a whole, can make a large difference to the weight and scale of live sound.

LOUDSPEAKER PERFORMANCE

Impedance

The great majority of loudspeaker drive units and systems are labeled ‘Impedance = 8 ohms’. This is, however, a nominal figure, the impedance in practice varying widely with frequency (see ‘Sound in electrical form’, Chapter 1). A speaker system may indeed have an 8 ohm impedance at, say, 150 Hz, but at 50 Hz it may well be 30 ohms, and at 10 kHz it could be 4 ohms. Figure 4.11 shows the impedance plot of a typical two-way, sealed box, domestic hi-fi speaker.

The steep rise in impedance at a certain low frequency is indicative of the low-frequency resonance of the system. Other undulations are indicative of the reactive nature of the speaker due to capacitive and inductive elements in the crossover components and the drive units themselves. Also, the driver/box interface has an effect, the most obvious place being at the already-mentioned LF resonant frequency.

Figure 4.12 shows an impedance plot of a bass reflex design. Here we see the characteristic ‘double hump’ at the bass end. The high peak at about 70 Hz is the bass driver/cabinet resonance point. The trough at about 40 Hz is the resonant frequency of the bass reflex port where maximum LF sound energy is radiated from the port itself and minimum energy is radiated from the bass driver. The low peak at about 20 Hz is virtually equal to the free-air resonance of the bass driver itself because at very low frequencies the driver is acoustically unloaded by the cabinet due to the presence of the port opening. A transmission-line design exhibits a similar impedance characteristic.

The DC resistance of an 8 ohm driver or speaker system tends to lie around 7 ohms, and this simple measurement is a good guide if the impedance of an unlabeled speaker is to be estimated. Other impedances encountered include 15 ohm and 4 ohm models. The 4 ohm speakers are harder to drive because for a given amplifier output voltage they draw twice as much current. The 15 ohm speaker is an easy load, but its higher impedance means that less current is drawn from the amplifier and so the power (volts x amps) driving the speaker will be correspondingly less. So a power amplifier may not be able to deliver its full rated power into this higher impedance. Thus 8 ohms has become virtually standard, and competently designed amplifiers can normally be expected to drive competently designed speakers. Higher-powered professional power amplifiers can also be expected to drive two 8 ohm speakers in parallel, giving a resultant nominal impedance of 4 ohms.

Sensitivity

A loudspeaker’s sensitivity is a measure of how efficiently it converts electrical sound energy into acoustical sound energy. The principles are described in Fact File 4.5. Loudspeakers are very inefficient devices indeed. A typical high-quality domestic speaker system has an efficiency of less than 1%, and therefore if 20 watts is fed into it the resulting acoustic output will be less than 0.2 acoustical watts. Almost all of the rest of the power is dissipated as heat in the voice coils of the drivers. Horn-loaded systems can achieve a much better efficiency, figures of around 10% being typical. An efficiency figure is not in itself a very helpful thing to know, parameters such as sensitivity and power handling being much more useful. But it is as well to be aware that most of the power fed into a speaker has to be dissipated as heat, and prolonged high-level drive causes high voice-coil temperatures.

It has been suggested that sensitivity is not an indication of quality. In fact, it is often found that lower-sensitivity models tend to produce a better sound. This is because refinements in sound quality usually come at the expense of reduced acoustical output for a given input, and PA speaker designers generally have to sacrifice absolute sound quality in order to achieve the high sensitivity and sound output levels necessary for the intended purpose.

Sensitivity: practical design limitations

Designers have always had to work with the conflicting requirements of good sound quality and sensitivity. In the early twentieth century when valve (tube) amplifiers offered only a few watts of power, drivers had to be horn loaded to obtain adequate levels in sound reinforcement and cinema applications, and domestic speakers were often horn loaded too. The early drive units of the 1920s in fact incorporated electromagnets (‘energizing coils’) because the permanent magnets available at the time were of inadequate strength to give useful sensitivity. By the 1930s, permanent magnets had been developed with the necessary strength, and in particular an alloy of aluminum, cobalt, iron and nickel known as Alnico was offering high magnetic flux in a magnet structure that was quite compact. The addition of titanium and copper gave an alloy known as Ticonal which also gave high strength for a given weight and size.

The speaker cones of the time were invariably made of very thin, flimsy paper pulp, its light weight combined with the inherent stiffness of a conical form enabling high sensitivity to be achieved in conjunction with the new high powered permanent magnets and lightweight voice coils and formers. Such cones suffer from high coloration due to their lack of rigidity; the coil moving too and fro at the apex of the cone controlled its movement in the near vicinity, but further away severe ‘breakup modes’ appear due to cone flexure where areas of the surface vibrate at various different amplitudes, frequencies and phases causing frequency response irregularities and distortions of several types. Such lively cone behavior proved a good match for the electric guitar during its development in the 1930s and 1940s, and even in the twenty-first century one still finds thin, flimsy paper pulp cones in the best sounding guitar speakers. Alnico magnets shot up in price during the 1970s because of deteriorating political situations in the African countries from which cobalt was sourced, and many ‘vintage’ guitar speaker models are now fitted with the much cheaper, and much larger for a given magnetic strength, ceramic or ferrite magnets. The latter type of magnet has for many years been used widely in hi-fi and sound reinforcement drive units.

Later developments in magnetic materials have included samarium cobalt, and then an alloy of neodymium, iron and boron was found to give a magnetic strength of about a factor of ten greater than a ceramic magnet of comparable dimensions. Such magnets are notable for their physically small size, and they allow a very efficient magnetic circuit to be designed around the coil as a consequence. The material is however very expensive, and its principal advantage for sound reinforcement speakers apart from efficiency is its somewhat lighter weight for a given strength compared with other magnetic materials. It also comes into its own where high strength is needed in a very small device such as the in-ear headphone and similar applications.

During the course of the twentieth century when higher and higher powered amplifiers became the norm, it was possible to sacrifice sensitivity in the interests of improved sound quality and accuracy, and domestic hi-fi and studio monitor speakers began to be fitted with cones made of various plastic materials (e.g. Bextrene, Polypropylene and other co-polymers and materials, such as that shown in Figure 4.13) which, together with appropriately designed cone flare profiles, gave a much more predictable and consistent series of break-up modes, usually beginning at a somewhat higher frequency than was the case with paper pulp. Even metal has been used in some high quality examples, as shown in Figure 4.14. In partnership with advanced measuring techniques-anechoic chambers, high quality measuring microphones, spectrum and distortion analyzers, laser interferometry to give a visual picture of cone behavior and the like-considerable advances were made in the pursuit of accuracy; but usually at the expense of sensitivity.

In the 1980s the typical sensitivity of a good domestic hi-fi speaker was about 86dB/watt, this being perfectly adequate given that amplifiers of 30–100 watts and more were becoming commonplace and relatively cheap. The 1970s had seen an almost wholesale move from valves to transistors, except among guitarists and certain hi-fi enthusiasts. But since then there has been a trend towards improving domestic speaker sensitivity, and today the average is more like 89dB/watt. The extra 3dB is worthwhile for several reasons. It indicates developments in cone materials and profiles which can be lower in mass than older designs whilst improving on their performance. Other things being equal, a lighter cone will store less energy and give potentially lower coloration than its heavier counterpart, and improved voice coil, suspension and magnet designs have also made their contributions. One technique has been to increase the diameter of the voice coil considerably so that it now drives the cone a substantial way towards the centre of its area, which helps it to control cone behavior and break-up modes more effectively. Also, speaker distortion tends to be a function of power input rather than acoustical output, and less power needed for a given sound level brings the promise of a lower distortion design. A 3dB increase in sensitivity after all represents a halving of power needed for a given SPL.

The sensitivity trend for guitar and sound reinforcement drive units was rather different. In fact, little less than a sensitivity war was being waged between competing manufacturers during the course of the 1970s, and this had reached a plateau by 1980, arriving at values of about 102 dB/ watt for the most sensitive 12-inch models and in the region of 105dB for 15-inch drivers. That was about as far as the conventional cone speaker design could be taken, and this can be appreciated by considering the coil/ magnet gap relationship. Figure 4.1 shows how the coil sits in the magnet’s annular slot between its poles. When signal is applied, the coil moves to and fro to drive the cone. The most sensitive speakers employ a gap length which is equal to the coil length, so that the whole of the coil is immersed in the magnetic field, giving maximum efficiency for the system. Many guitar speakers are of this type (as are most high frequency drivers); voice coil and cone excursion for this application is minimal because the electric guitar frequency spectrum is weak in fundamentals, and the coil stays almost entirely within the magnetic field even for quite high power inputs. Increased input causes the ends of the coil to move to and fro beyond the magnet gap, introducing compression and distortion artefacts which have in fact played their part in electric guitar sound. Drive units intended for lower distortion sound reinforcement and hi-fi therefore employ a coil that is slightly longer than the magnet gap such that a small percentage of its length extends beyond the gap to both front and rear when no drive is being applied, as shown in Figure 4.15a. Such a design is slightly less sensitive because not all of the coil is immersed in the magnetic field, but the coil can now move a significant distance to and fro whilst keeping the same percentage of its length within the gap. Higher output for a given value of distortion is thereby achieved. The peak-to-peak linear excursion, equal to the total excess length of the coil compared to the magnet gap length, is the X_max value given in a drive unit’s specification.

It becomes clear then that a point will be reached where increasing coil length even further in pursuit of higher power handling and greater excursion brings with it reduced sensitivity, as a greater percentage of the coil now lies outside of the magnetic field. This portion of the coil still dissipates power, but it can contribute no driving force. Increases beyond a certain point therefore become self-defeating. The optimum was reached by about 1980, and drive unit sensitivities have not increased since then. Another, less-encountered alternative is to employ a short coil in a long magnet gap, considerable excursion being possible before the coil reaches either end of the gap, as shown in Figure 4.15b. The short, relatively low mass coil is capable of extending the frequency response well into the upper mid range as well as providing good bass extension by virtue of the long excursion. The X_max in such a design now specifies the total permitted travel of the coil whilst still remaining fully confined within that gap. The over-long coil is used successfully in high powered low frequency drivers where large linear excursions are required whilst retaining consistent immersion of the coil in the magnetic field. Somewhat reduced sensitivity has to be the trade-off, and the relatively large, high mass coil combined with a stiff straight-sided cone does not have an extended frequency response, this being a dedicated bass driver technique. Some domestic subwoofer drivers have X_max values as high as 25 mm, with corresponding sensitivities in the 80 dB/watt range, as shown in Figure 4.15c.

Since the 1980s, development of high temperature glues and coil formers such as polyimide (trade name Kapton) and efficient venting systems for them have allowed coil operating temperatures of up to 300°C or so to be withstood, considerably increasing power handling capacities and therefore output levels of drive units.

Distortion

Distortion in loudspeaker systems is generally an order of magnitude or more higher than in other audio equipment. Much of it tends to be second-harmonic distortion whereby the loudspeaker will add frequencies an octave above the legitimate input signal. This is especially manifest at low frequencies where speaker diaphragms have to move comparatively large distances to reproduce them. When output levels of greater than 90dB for domestic systems and 105dB or so for high-sensitivity systems are being produced, low-frequency distortion of around 10% is quite common, this consisting mainly of second-harmonic and partly of third-harmonic distortion.

At mid and high frequencies distortion is generally below 1%, this being confined to relatively narrow bands of frequencies which correspond to areas such as crossover frequencies or driver resonances. Fortunately, distortion of this magnitude in a speaker does not indicate impending damage, and it is just that these transducers are inherently non-linear to this extent. Much of the distortion is at low frequencies where the ear is comparatively insensitive to it, and also the predominantly second-harmonic character is subjectively innocuous to the ear. Distortion levels of 10–15% are fairly common in the throats of high-frequency horns.

Frequency response

The frequency response of a speaker also indicates how linear it is. Ideally, a speaker would respond equally well to all frequencies, producing a smooth ‘flat’ output response to an input signal sweeping from the lowest to the highest frequencies at a constant amplitude. In practice, only the largest speakers produce a significant output down to 20 Hz or so, but even the smallest speaker systems can respond to 20 kHz. The ‘flatness’ of the response, i.e. how evenly a speaker responds to all frequencies, is a rather different matter. High-quality systems achieve a response that is within 6dB of the 1 kHz level from 80 Hz to 20 kHz, and such a frequency response might look like Figure 4.16(a). Figure 4.16(b) is an example of a rather lower-quality speaker which has a considerably more ragged response and an earlier bass roll-off.

The frequency response can be measured using a variety of different methods, some manufacturers taking readings under the most favorable conditions to hide inadequacies. Others simply quote something like ‘± 3dB from 100 Hz to 15 kHz’. This does at least give a fairly good idea of the smoothness of the response. These specifications do not, however, tell you how a system will sound, and they must be used only as a guide. They tell nothing of coloration levels, or the ability to reproduce good stereo depth, or the smoothness of the treble, or the ‘tightness’ of the bass.

Power handling

Power handling is the number of watts a speaker can handle before unacceptable amounts of distortion ensue. It goes hand-in-hand with sensitivity in determining the maximum sound level a speaker can deliver. For example, a domestic speaker may be rated at 30 watts and have a sensitivity of 86dBW⁻¹. The decibel increase of 30 watts over 1 watt is given by:

Therefore, the maximum output level of this speaker is 86 + 15 = 101dB at 1 meter for 30 watts input. This is loud, and quite adequate for domestic use. Consider now a PA speaker with a quoted sensitivity of 99dBW⁻¹. 30 watts input now produces 99 + 15 = 114dB, some 13dB more than with the previous example for the same power input. To get 114dB out of the 86dBW⁻¹ speaker one would need to drive it with no less than 500 watts, which would of course be way beyond its capabilities. This dramatically demonstrates the need to be aware of the implications of sensitivity and power handling.

A 30 watt speaker can, however, safely be driven even by a 500 watt amplifier providing that sensible precautions are taken with respect to how hard the amplifier is driven. Occasional peaks of more than 30 watts will be quite happily tolerated; it is sustained high-level drive which will damage a speaker. It is perfectly all right to drive a high-power speaker with a low-power amplifier, but care must be taken that the latter is not overdriven otherwise the harsh distortion products can easily damage high-frequency horns and tweeters even though the speaker system may have quoted power handling well in excess of the amplifier. The golden rule is to listen carefully. If the sound is clean and unstressed, all will be well.

Directivity

Directivity, or dispersion, describes the angle of coverage of a loudspeaker’s output. Very low frequencies radiated from a speaker are effectively omnidirectional, because the wavelength of the sound is large compared with the dimensions of the speaker and its enclosure, and efficient diffraction of sound around the latter is the result. As the frequency increases, wavelengths become comparable to the dimensions of the speaker’s front surface, diffraction is curtailed, and the speaker’s output is predominantly in the forwards direction. At still higher frequencies, an even narrower dispersion angle results as a further effect comes into play: off-axis phase can-celation. If one listens, say, 30° off-axis from the front of a speaker, a given upper frequency (with a short wavelength) arrives which has been radiated both from the closest side of the speaker cone to the listener and from the furthest side of the cone, and these two sound sources will not therefore be in phase with each other because of the different distances they are away from one another. Phase cancelation therefore occurs, perceived output level falls, and the effect becomes more severe as frequencies increase. The phenomenon is mitigated by designing for progressively smaller radiating areas of the speaker cone to be utilized as the frequency increases, finally crossing over to a tweeter of very small dimensions. By these means, fairly even dispersion of sound, at least in the mid and lower treble regions, can be maintained.

Various other methods have been used to control directivity (the acoustic lens has been covered) and one or two will be described. Low frequencies, which are normally omnidirectional, have been given a cardioid-like dispersion pattern by mounting large speaker drivers on essentially open baffles which by themselves give a figure-of-eight polar response, the output falling with falling frequency. To these was added a considerable amount of absorbent material to the rear, and together with appropriate bass boost to flatten the frequency response of the speakers, predominantly forward-radiation of low frequencies was achieved. A more elegant technique has been to mount essentially open-baffle speakers (the rear radiation therefore being 180° out of phase with the front producing a figure-of-eight polar pattern, and with bass boost applied to flatten the frequency response) adjacent to closed-box omnidirectional speakers. Their combined acoustical outputs thereby produce a cardioid dispersion pattern, useful for throwing low frequencies forwards into an auditorium rather than across a stage where low-frequency feedback with microphones can be a problem.

A more sophisticated technique has been to use a conventional forward-facing subwoofer, adding to it another which is behind, and facing rearward. Using DSP processing to give appropriate delay and phase change with frequency, the rear-facing driver’s output can be made to cancel the sound which reaches the rear of the enclosure from the front-facing driver. A very consistent cardioid response can thereby be achieved over the limited range of frequencies across which the subwoofer operates.

Another fascinating technique, introduced by Philips in 1983, is the Bessel Array. It was developed to counteract the beaming effects of multiple-speaker systems. Essentially it makes use of Bessel coefficients to specify phase relationships and output level requirements from each of a horizontal row of speakers necessary to obtain an overall dispersion pattern from the row which is the same as one speaker on its own. Normally, path-length differences between off-axis listeners and the various speaker drivers result in phase cancelations and consequent loss of level, particularly in the upper frequency range. For a horizontal five-speaker row, labeled A, B, C, D and E, the Bessel function gives:

In other words, speakers A and E are required to draw half the current of speakers B, C and D; and speaker D must be connected out of phase. A practical implementation would be to connect speakers A and E in series, with speakers B, C and D each connected straight across the system’s input terminals but with D wired out of phase. The speaker drivers are mounted side by side very close together to give good results across the frequency range.

For a seven-speaker row, the Bessel function gives:

Speaker D can therefore be omitted, but a space in the row must be left in its position so as to preserve the correct distance relationships between the others.

Both horizontal and vertical rows of speakers can be combined into a square arrangement so that an array of, for example, 25 speakers, together having potentially very high power handling and output level capability, can, however, give the same dispersion characteristics of one speaker on its own. The amplitude and phase relationships necessary in such an array are given by the numbers in the circles representing the speakers in Figure 4.17.

It is worth mentioning that the same technique can also be applied to microphones, offering potential for a high output, very low noise array whilst still maintaining a good polar response.

A highly directional speaker incorporating a parabolic reflector of about 1.3 meters in diameter has been developed by the Meyer loudspeaker company as their type SB-1. Designed to work between 500 Hz and 15 kHz, the system comprises an outrigger supporting a small horn and compression driver at the focus of the dish which fires into it, and a small hole at the dish’s center admits sound from a 12-inch cone driver. Claimed dispersion (−6dB points) is 10° vertical and 10° horizontal, and maximum peak output at 100 meters distance is 110 dB. The Watkins Electronic Music company (WEM) used this parabolic reflector technique at the Isle of Wight Music Festival in 1970.

‘Modulated Ultrasound’

The idea of directing sound via a tightly controlled beam in the manner of a spotlight was first investigated by both the USA and Soviet militaries in the 1960s in connection with sonar. Some decades later the idea was developed for propagating sound through the air, but considerable technical difficulties have meant that commercial designs have appeared only in recent years. These have included the Audio Spotlight (Holosonics), Hypersonic Sound and Sennheiser’s Audio Beam among others. The design concept is very simple. Both dispersion of sound from a conventional loudspeaker and reflections of sound from walls and other objects mean that sound can be heard throughout the listening space to a greater or lesser extent, and the prospect of directing a tight ultrasonic beam of sound, amplitude modulated by the audio signal, to deliver audio to a clearly defined location suggested itself as a viable technique analagous to the AM radio system. Those familiar with the principle of AM radio transmission will recall that a high frequency carrier wave is amplitude modulated by the audio signal, and at the receiving end the carrier wave is separated from the much lower audio frequencies, the latter comprising the program content. With a sound beam, no demodulation of the arriving sound is required because the ultrasonic carrier wave, typically about 50kHz in commercial systems, cannot be heard by human ears. Only the audio frequencies are perceived.

There were two principal problems to overcome. First, a speaker system had to be developed capable of directing a tight ultrasonic beam at a high sound pressure level to a destination some meters away. This was achieved using a large number of ultrasonic piezoelectric transducers-more than one hundred in practical examples-mounted on a surface of about 30 cm square, or alternatively on a disc of comparable area. The wavelength of sound at 50 kHz is just under a centimeter, and this ensures that any sound which is directed significantly off axis is subjected to efficient phase cancellations as the outputs from the variously spaced transducers will be substantially out of phase, their outputs only reinforcing each other in a tight forward beam. The many transducers provide the necessary high output, in the order of 130 dB, of the ultrasonic carrier wave. High output is necessary because the air absorbs high frequencies to a somewhat greater extent than the lower frequencies, and also because the level of the modulating audio frequencies is somewhat lower than that of the carrier wave. Health and safety issues have to be considered with such sound levels; for instance the USA’s Occupational Safety and Health Administration sets a top limit of 145dB for ultrasonic sound.

The second problem was that of distortion. A high level ultrasonic beam alters the speed of sound along its path and causes the air to behave non-linearly, and it also creates an environment of very short wave compressions and rarefactions of the air from which the contained audio frequencies have to emerge. The ensuing distortions are rather more complex than the familiar harmonic distortions of audio systems in general, and reciprocal distortion conditioning has had to be developed and added to the signal beforehand in order to bring distortion down to acceptable levels.

Applications have included trade fairs and theme parks where sound spillage can be a problem between events and exhibitions, the tightly controlled beam delivering sound only to the area where the listener is positioned. Museums and art galleries are other examples where their particular properties would be appropriate.

Panel speaker dispersion

The previous section describes how a tight beam of sound can be delivered to a specific location. Conventional panel speakers such as electrostatics have suffered in the past from inadequate dispersion of sound in the listening environment, particularly at the higher frequencies, for the same basic reason: that a relatively large vibrating diaphragm generates the sound from a large area rather than from a near-point source. Off-access phase cancellation is the result. The original Quad ESL63 electrostatic design and its successors such as the current model 2912 deal with the problem by the following means. Imagine the sound source coming not from the panel itself but from a virtual point source positioned about 30 cm behind the panel. The sound coming straight from the point source to the middle of the panel can be considered to continue through to the listener. But the sound travelling from the point source at an angle to a position elsewhere on the panel takes a little longer to reach it because the distance is now slightly greater. The sound coming from the panel, to recreate this mechanism, will need to be delayed incrementally as one moves towards its edges. The Quad designs achieve this in the horizontal plane by dividing the panel up into a series of concentric arcs of circles laterally, an array of inductors and capacitors providing the necessary incremental delays to feed the sections. By these means, the panel as a whole simulates a point source 30 cm behind it over the critical upper mid and high frequencies, somewhat improving lateral dispersion.

The DML panel loudspeakers do not however suffer from poor dispersion because the panel does not vibrate as a conventional single diaphragm would. Instead, a multitude of breakup modes exist across its surface which create a large number of small radiating areas, their outputs decorrelated with each other with respect to phase such that off-axis phase cancellations do not occur in a systematic and predictable way as is the case with conventional panels. In contrast with other loudspeaker types and electrostatic panels that do not have the Quad-style dispersion feature, the DML’s dispersion pattern does not therefore change significantly with panel size.

SETTING UP LOUDSPEAKERS

Phase

Phase is a very important consideration when wiring up speakers. A positive-going voltage will cause a speaker cone to move in a certain direction, which is usually forwards, although at least two American and two British manufacturers have unfortunately adopted the opposite convention. It is essential that both speakers of a stereo pair, or all of the speakers of a particular type in a complete sound rig, are ‘in phase’, that is, all the cones are moving in the same direction at any one time when an identical signal is applied. If two stereo speakers are wired up out of phase, this produces vague ‘swimming’ sound images in stereo, and cancelation of bass frequencies. This can easily be demonstrated by temporarily connecting one speaker in opposite phase and then listening to a mono signal source-speech from the radio is a good test. The voice will seem to come from nowhere in particular, and small movements of the head produce sudden large shifts in apparent sound source location. Now reconnect the speakers in phase and the voice will come from a definite position in between the speakers. It will also be quite stable when you move a few feet to the left or to the right.

Occasionally it is not possible to check the phase of an unknown speaker by listening. An alternative method is to connect a 1.5 V battery across the input terminals and watch which way the cone of the bass driver moves. If it moves forwards, then the positive terminal of the battery corresponds to the positive input terminal of the speaker. If it moves backwards as the battery is connected, then the positive terminal of the battery is touching the negative input terminal of the speaker. The terminals can then be labeled + and −.

Positioning

Loudspeaker positioning has a significant effect upon the performance. In smaller spaces such as control rooms and living rooms the speakers are likely to be positioned close to the walls, and ‘room gain’ comes into effect whereby the low frequencies are reinforced. This happens because at these frequencies the speaker is virtually omnidirectional, i.e. it radiates sound equally in all directions. The rear- and side-radiated sound is therefore reflected off the walls and back into the room to add more bass power. As we move higher in frequency, a point is reached whereby the wavelength of lower mid frequencies starts to become comparable with the distance between the speaker and a nearby wall. At half wavelengths the reflected sound is out of phase with the original sound from the speaker and some cancelation of sound is caused. Additionally, high-frequency ‘splash’ is often caused by nearby hard surfaces, this often being the case in control rooms where large consoles, tape machines, outboard processing gear, etc. can be in close proximity to the speakers. Phantom stereo images can thus be generated which distort the perspective of the legitimate sound. A loudspeaker which has an encouragingly flat frequency response can therefore often sound far from neutral in a real listening environment. It is therefore essential to give consideration to loudspeaker placement, and a position such that the speakers are at head height when viewed from the listening position (high-frequency dispersion is much narrower than at lower frequencies, and therefore a speaker should be listened to on axis) and also away from room boundaries will give the most tonally accurate sound.

Some speakers, however, are designed to give their best when mounted directly against a wall, the gain in bass response from such a position being allowed for in the design. A number of professional studio monitors are designed to be let into a wall such that their drivers are then level with the wall’s surface. The manufacturers’ instructions should be heeded, in conjunction with experimentation and listening tests. Speech is a good test signal. Male speech is good for revealing boominess in a speaker, and female speech reveals treble splash from hard-surfaced objects nearby. Electronic music is probably the least helpful since it has no real-life reference by which to assess the reproduced sound. It is worth emphasizing that the speaker is the means by which the results of previous endeavor are judged, and that time spent in both choosing and siting is time well spent.

Speakers are of course used in audio-visual work, and one frequently finds that it is desirable to place a speaker next to a video monitor screen. But the magnetic field from the magnets can affect the picture quality by pulling the internal electron beams off course. Some speakers are specially magnetically screened so as to avoid this.

Loudspeaker positioning issues affecting two-channel stereo and surround sound reproduction are covered in greater detail in Chapters 16 and 17.

THIELE-SMALL PARAMETERS AND ENCLOSURE VOLUME CALCULATIONS

Low-frequency performance of a driver/box combination is one of the few areas of loudspeaker design where the performance of the practical system closely resembles the theoretical design aims. This is because at low frequencies the speaker cone acts as a pure piston, and wavelengths are long, minimizing the effects of enclosure dimensions and objects close to the speaker. Nearby boundaries, e.g. walls and the floor, have a significant effect at very low frequencies, but these are predictable and easily allowed for.

It was A.N. Thiele and Richard Small, working largely independently of each other in Australia mainly during the 1960s, who modeled driver and enclosure behavior in terms of simple electrical circuits. They substituted, for instance, the DC resistance of the coil with a resistor, its inductance with an inductor of the same value, and the places where the speaker’s impedance rose with decreasing frequency could be represented by a capacitor of an appropriate value in the circuit model. The latter could also represent the ‘stiffness’ of the air enclosed in the box. Electrical formulae could then be applied to these models to predict the behavior of particular drive units in various sizes and types of enclosure. A series of ‘Thiele-Small’ parameters are therefore associated with a particular drive unit and they enable systems to be designed, the low frequency performance of which can be predicted with considerable accuracy, something which had previously been a largely empirical affair before their work. A host of parameters are specified by the manufacturers, and include such things as magnet flux density, sensitivity, diaphragm moving mass, mechanical resistance of suspension, force factor, equivalent volume of suspension compliance, mechanical Q, electrical Q, and free air resonance. The list is a comprehensive description of the drive unit in question, but fortunately only three need to be considered when designing an enclosure for the target low-frequency performance. These are the free-air resonance, represented by the symbol f_o; the equivalent air volume of the suspension compliance, V_AS; and the total Q of the driver, Q_T. They will be considered in turn.

f_o is the free-air resonance of the driver, determined by taking an impedance plot and noting the frequency at which a large, narrow peak in the impedance takes place. Such a rise can be seen in Figure 4.12 at about 20 Hz.

V_AS can be explained as follows. Imagine a bass driver with an infinitely compliant suspension, its cone being capable of being moved to and fro with the fingers with no effort. Now mount the driver in a closed box of say 70 liters internal volume. Push the cone with the fingers again, and the spring of the enclosed air now supports the cone, and one feels an impedance as one pushes against that spring. The suspension of the drive unit is thus specified as an equivalent air volume. The enclosure volume of both closed-box and reflex systems is always smaller than the drive unit’s V_AS in order that the air stiffness loads the cone of the speaker adequately, as its own suspension system is insufficient to control low frequency excursion alone.

Q_T, the total Q of the driver, is the average between the electrical Q, Q_E, and the mechanical Q, Q_M. Briefly, Q_E is determined using a formula containing total moving mass of the diaphragm, the resistance of the coil and the B1 factor (flux density multiplied by a length of coil wire immersed in the magnetic field, indicating the force with which the coil pushes the cone for a given input level). Q_M is determined by calculating the Q of the low-frequency peak in the impedance plot, dividing the center peak frequency by the bandwidth at the −3dB points each side of this. Q_T is always quoted, so one does not need to calculate it from the other parameters.

Before moving on to discuss how the above is used in calculations, system Q must be looked at. This is explained in Fact File 4.6.

For the following discussions, a Q of 0.7 will be assumed. Different Q values can be substituted by the reader to explore the effect this has on enclosure volume.

For a closed box (‘infinite baffle’) system, a three-stage process is involved. The following formula is used first:

where Q_TC is the chosen system Q (assumed to be 0.7), and f₃ is the resonant frequency of the system. x is the ratio between the two quantities. For example, if the driver’s Q_T is 0.35, then x is 2. If the driver’s f_o is 25 Hz, then f₃ is 50 Hz. Therefore, such a driver in a box giving a Q of 0.7 will have a resonant frequency of 50 Hz.

The next stage is to calculate the box volume required to achieve this performance. For this, x needs first to be converted into α, the compliance ratio. This is the ratio between the drive unit’s V_AS and the box volume.

The latter is always smaller than the former. This is done using the simple formula:

In the present example, this gives an α of 3. To calculate box size, the following formula is used:

where V_B is the box volume. If the driver has a V_AS of 80 liters, this then gives a box size of about 27 liters. These results are quite typical of a medium-sized domestic speaker system.

The bass reflex design is rather more complex. This consists of a box with a small port or ‘tunnel’ mounted in one of its walls, the air plug in the port together with the internal air volume resonating at a particular low frequency. At this frequency, maximum sound output is obtained from the port, and the drive unit’s cone movement is reduced compared with a closed box system. First, we will look at the formula for the enclosure:

where R is the port radius (assuming a circular port), L is the port length, and V_b is the enclosure volume. All dimensions are in meters; V_b is in cubic meters. f_c is the resonant frequency of the system. 344.8 is the speed of sound in meters per second at normal temperatures and pressures. The port can in principle have any cross-sectional shape, and more than one port can be used. It is the total cross-sectional area combined with the total length of the port or ports which are required for the calculation. Note that nowhere does the drive unit in question appear in the calculation. The box with port is a resonant system alone, and the design must be combined with drive unit calculations assuming a closed box system with a target Q rather lower than is customary for a closed box, usually much nearer to 0.5 so that the driver has a slow low-frequency roll-off as the output from the port rises, producing a smooth transition. The reflex enclosure volume is therefore typically in the order of about 80% of the drive unit’s V_AS. Looking again at Figure 4.12, we see two low-frequency peaks in the impedance with a trough in between. The lowest one is the free-air resonance of the driver (altered slightly by air loading), the trough is the reflex port resonant frequency, and the upper peak is the box/driver resonant frequency. The designer must ensure that the design arrived at with the particular chosen driver ensures these conditions. One does not, for instance, design for a port resonant frequency of 30 Hz when the drive unit’s free-air resonance is 40 Hz.

The design procedure is normally to calculate for a closed-box system with a chosen drive unit, the target Q being closer to 0.5 than to 0.7. (Reflex systems are larger than closed-box systems for a given driver.) One notes the driver/box resonant frequency, and then chooses port dimensions which give a port resonance which is midway between the driver/ box resonance and the driver’s free-air resonance. Final dimensions will be chosen during prototyping for optimum subjective results in a real listening environment.

Above port resonance, the output from the port falls at the rate of 12dB/octave, and the design aim is to give a smooth transition between the port’s output and the driver’s output. The port gives a useful degree of bass extension. Below resonance, the speaker cone simply pumps air in and out of the port, and the latter’s output is therefore 180° out of phase with the former’s, producing a rapid 24dB/octave roll-off in the response. Furthermore, the drive unit is not acoustically loaded below resonance, and particularly in sound reinforcement use where very high powers are involved care must be taken to curtail very low-frequency drive to reflex enclosures, otherwise excessive cone excursions combined with large currents drawn from the amplifiers can cause poor performance and premature failure.

The abrupt 24dB/octave roll-off of the reflex design means that it interfaces with room boundaries less successfully than does a closed-box system with its more gradual roll-off. However, some reflex designs are deliberately ‘de-tuned’ to give a less rapid fall in response, helping to avoid a ‘boomy’ bass quality when the speaker is placed close to walls.

Drive units with Q_T values of 0.2 and below are well suited to bass reflex use. Drivers with Q_T values of 0.3 and above are better suited to closed-box designs. If one runs calculations for bass reflex designs using drive units with high Q_T values, one finds that the drivers’ free air resonances and the driver/box resonances are uncomfortably close together, leaving little room to place the port resonances in between. If one runs calculations for closed box designs with drivers having low Q_T values, one finds that the system resonances are disappointingly high even though the drivers’ free air resonances may be encouragingly low.

In the above discussions, no mention has been made of sound absorbent material in the box, either in the form of foam lining or wadding filling the volume of the enclosure. This should not be necessary for low-frequency considerations, and it is usually included to absorb mid frequency energy from the rear of the speaker cone to prevent it from re-emerging back through the cone and the enclosure walls, coloring the sound. However, the presence particularly of volume-filling material has the effect of reducing the speed of sound in the enclosure, making it apparently larger, sometimes by as much as 15% for some types of filling. This must be taken into consideration in the final design. An over-dense filling tends to behave in a manner more like a solid mass, and the box volume is apparently reduced. There is no reason in principle to include sound absorbent material in a box intended purely for low-frequency use, unless one wishes to increase its apparent acoustic volume for economic or space-saving reasons.

The website www.thielesmall.com provides a large data base for drive unit parameters, both obsolete and current, and it helps one to find replacement drivers with closely matching specifications which will give comparable performances in given enclosures.

DIGITAL SIGNAL PROCESSING IN LOUDSPEAKERS

Digital signal processing (DSP) is used increasingly in loudspeakers to compensate for a range of linear and non-linear distortion processes that typically arise. DSP can also be used in crossover design and for controlling the spatial radiation characteristics of loudspeakers or loudspeaker arrays. With the help of such technology it may be possible to get better performance out of smaller loudspeaker units by using electronics to counteract physical inadequacies. Some such processes can make use of psychoacoustical phenomena, such as a means of extending the perceived bass response without actually reproducing the relevant low frequencies, and it may also be possible to modify the way in which the loudspeaker interacts with the listening room. Finally, there are various ways by which it may be possible to engineer an ‘all-digital’ signal chain, even using digital forms of representation right up to the point where the binary data is converted into an acoustical waveform.

RECOMMENDED FURTHER READING

Beranek, L., Mellow, T., 2012. Acoustics: Sound Fields and Transducers. Academic Press.

Borwick, J. (Ed.), 2001. Loudspeaker and Headphone Handbook. Focal Press.

Colloms, M., 2005. High Performance Loudspeakers, sixth edition. Wiley.

Eargle, J., 2003. Loudspeaker Handbook. Kluwer Academic Publishers.

Toole, F., 2008. Sound Reproduction: The Acoustics and Psychoacoustics of Loudspeakers and Rooms. Focal Press.

USEFUL WEBSITES

www.thielesmall.com: Among other things, has a valuable drive unit database which helps one to compare parameters of obsolete drivers with current ones.

www.xlrtechs.com/dbkeele.com/papers.htm: Contains papers covering a wide variety of design and performance issues, with further information about Bessel Arrays.