High Performance Loudspeakers

By Martin Colloms

High Performance Loudspeakers, Sixth Edition is a fully revised and updated version of the highly successful guide to the design and specifications of high quality loudspeakers and loudspeaker systems. Each chapter has been substantially revised reflecting the many changes in the technology of loudspeakers. These revisions take the form of much new research and accompanying illustrations, with a radically new theoretical section, allied to in-depth coverage of the most important advances in the art of loudspeaker design. By clearly and practically analysing these many developments the authors have produced an authoritative loudspeaker designer's bible.

Key features of the Sixth Edition include:

• Radically new chapter on acoustic theory, developments in home theatre and surround systems, in speaker system design. Also crossover networks with new digital synthesis methods, and extensive reporting on CAD software

• New measurement systems and techniques are complemented by recent psychoacoustic research data.

• Expanded material on sub-sat design, 2pi and boundary speaker design, further work on optimum low frequency synthesis for improved group delay.

• New materials technology including ceramic and diamond diaphragms, plus first publication of the theory of the BMR, a fascinating hybrid driver technology employing a synthesis of bending wave and pistonic action and which can approach the directivity of a point source.

• Glossary; a valuable view of electroacoustic terms and definitions to guide all readers.

Acknowledged industry-wide as the definitive work on speaker design and analysis, this book is essential reading for audio engineers, speaker designers, equipment designers and students of acoustic engineering, electronics and electro-acoustics. It will also prove invaluable to students of electronics, broadcasting and recording techniques, and be of interest to amateur loudspeaker builders, authors and journalists in audio.

• Language: English
• Publisher: Wiley
• Release date: May 29, 2013
• ISBN: 9781118691120

Book preview

1

General Review

Speech and music is noise with meaning. The recording and reproducing of sound is imperfect, the process reduces meaning and adds noise.

It is the art of the loudspeaker designer to use science to help increase meaning in reproduced sound. An understanding of music in all its forms is a vital criteria for the reasoned application of acoustical engineering to loudspeaker design.

It is now 80 years since the loudspeaker as we know it was first developed—an electrodynamic transducer of respectable loudness, of satisfactory and uniform amplitude versus frequency, reliable in use and with the potential for economic manufacture. Before this, there were only earphones of various kinds. Earlier, moving coil and cone speakers had been made; even Ernst Werner Siemens’ US patent of 1874 was one of these. Ironically, at that time, no electrical audio signals were available to drive it. The familiar moving-coil cone loudspeaker, whose principle is so effective that its key elements have remained essentially unchanged to this day, came with ‘the New Hornless Loudspeaker’ of 1925 by Rice and Kellogg of GE (US), which set the stage for the mass controlled, low-resonant frequency form we know so well, a driver where at least part of the frequency response is fundamentally uniform with frequency and may be predictably acoustically loaded at lower frequencies.

To create the motor of such a transducer, take an affordable magnet and add a simple arrangement of magnetically permeable ‘soft’ iron to help concentrate much of the available magnetic flux into a narrow radial gap formed with a cylindrical pole. A small light coil or solenoid is wound onto thin card or a similar low mass former and is suspended freely in the magnetic gap, allowing an overall axial motion of half a centimetre or so. Following Maxwell’s electromagnetic equations, an axial force is generated on the coil when a current flows through it. This force is the product of B, the magnetic field strength, 1 the length of the wire immersed in that flux field and I, the current flowing. The force relationship is fundamentally linear and there is no perceptible distortion, for the moment ignoring effects at high amplitudes of motion where the precision of the coil and flux field and of the suspension may ultimately affect performance. There is no lower resolution limit for a moving-coil transducer. An infinitely small electrical input will produce an equivalent and essentially infinitely small sound output. Another excellent feature of the moving-coil transducer, generally taken for granted, is that despite its operation as a moving mechanical device it is essentially noiseless. It does not grate, or scrape or whirr.

Apply a sub-audible 5 Hz sine-wave current and you can see the coil move, but silently. It is these fundamental strengths that make the moving-coil principle so effective, and so justly popular. Over 99% of all loudspeakers ever made are moving coil. The principle may be used over a very wide range, from low-power speech reproducers of just 2.5 octave bandwidth and a modest 75 dB of sound pressure output and built on a frame just 20 mm in diameter, up to low-frequency monsters of 600 mm diameter, capable of generating 20 Hz sound waves at body shattering 110 dB pressure levels. Used alone, the moving coil itself generates almost zero sound output as radiated sound level is proportional to the area of air load driven by the transducer element, and for the coil alone, this is merely a thin ring.

To couple the moving element to the air load, a rigid, light diaphragm is attached to the coil. Typically, larger diaphragms have their own flexible surround suspension, coupled to an outer, skeletal, non-reflective support frame or chassis, providing centration of the moving system.

Paper as a flat sheet is stiff in tension but is very weak in bending. However, curl it up to form a cone and this structure exhibits an extraordinary axial stiffness for its mass, a marvellous means of coupling a large area of air load to the moving-coil motor. The latter is bonded to the cone apex.

Acting as an impedance transformer, the cone matches the lower acoustical impedance of the air load to the higher driving force impedance of the coil, maximizing the energy transfer in the path from electrical input to mechanical force, leading to useful radiated sound pressure, highly effective in practice even if the actual conversion efficiency is quite low.

Specialized smaller drivers intended for higher frequencies may have the cone replaced by a light dome formed form a variety of materials, paper, moulded plastic foil, resin doped fabric, metal foil or even vacuum-deposited pure diamond. In sizes down to 19 mm effective radiating diameter, the frequency response may extend to beyond audibility, up to 80 kHz. By apportioning the audible frequency range, appropriate combinations of moving-coil driver sizes may cover a frequency range of 10 Hz to 80 kHz, a ratio of no less than 8000 : 1 in acoustic wavelength, 34 m to just 4.25 mm.

Loudspeaker systems with such a wide range have been designed for costly high fidelity installations; the near 12 octave span may be achieved with typically four, size and frequency-dedicated moving-coil drivers. Such systems can cost as much as a luxury car, and yet the humblest moving-coil speaker driver for modest speech use only may cost tens of cents in typical trade order quantities.

When the diaphragm of a moving-coil driver is appropriately horn loaded, the horn may additionally improve the matching efficiency between air load and transducer. It is then possible to reach an efficiency of almost 50% compared with the typical 1% efficiency of a direct radiating high fidelity speaker. With horn designs, a fairly easily obtained 40 electrical watts will result in a seriously loud 20 acoustic watts, sufficient to effectively address large audiences at realistic volume levels.

Moving-coil drivers have proved to be remarkably durable with many examples of these operating for 50 years and longer. Alternatives have been proposed, but like the wheel, it reigns supreme.

It seems that new transducer inventions appear almost monthly in the loudspeaker field, with many claimed to supplant the essentially pistonic moving coil. However, no comprehensive rival has as yet emerged to challenge it, and it remains pre-eminent in terms of effectiveness, economy, wide performance range and application.

While this introductory review concentrates on the moving-coil principle as applied to loudspeakers, it is also widely used in precision actuators such as the high-speed focus and fine tracking mechanisms for laser optical heads, compact disc and optical data discs. It is also applied in the most popular form of microphone and, not least, for almost all headphones and earpieces, as well as for many related communication apparatus.

The worldwide acceptance and growth of the high fidelity market and the high standards achieved in recording and broadcast studios have given great impetus to high-performance loudspeaker design in the last 50 years. The loudspeaker, however, has remained the most argued-over device in the entire high fidelity chain; every aspect of its design and execution has been subject to lengthy and involved discussion. Although audio engineers like to deal in facts, much to their dismay, fashion plays a considerable part in the burgeoning consumer market and loudspeakers are no exception. Occasionally, a technically ‘unbalanced’ design, one which a consensus of practitioners would consider has a design error, will nevertheless find public favour. Such a model may be claimed to have a ‘new sound’, perhaps derived from a different bass loading principle, or a new transducer and sound dispersion method. Unfortunately, other important aspects of its performance may well have been neglected by the designer in his or her one-sided efforts to incorporate this ‘special’ feature. Usually, after a cooling-off period, the market generally regains its senses and a longer-term consensus is restored.

In the professional field, operators are also inevitably conditioned by past experience and are often suspicious of any change, even for the better. Those whose judgement is free of prejudice and who have frequent contact with live programme sources discuss reproduced sound quality more reliably.

Recently, there has been an encouraging development, in that a degree of rationalization of performance standards has occurred on both the domestic and professional fronts. Designers are beginning to agree on a common standard of performance based on factors such as a natural frequency balance, uniformity of response on and off axis, and for low distortion and colouration. This common ground has developed in spite of dissimilarities of design approach and philosophy, and it implies that a basis of objective and subjective data and opinion concerning speaker performance is at last becoming freely available. Such a situation presents a dramatic reversal of the state of affairs that prevailed some 50 years ago.

A marked divergence of opinion existed then over subjective sound quality. Indeed, this was so extreme that the individual products of the major manufacturers could be identified by a specific ‘in-house’ sound that pervaded all their designs. A typical domestic ‘hi fi’ speaker system then comprised a 250 or 300 mm chassis diameter bass unit, with a light paper cone fitted with a 33 or 50 mm voice coil wound on a paper former. A separate paper-cone tweeter covered the treble range and was often concentrically mounted on the bass unit frame. The drivers were rear mounted on the inside face of the front panel, the enclosure was likely to have a typical volume of between 50 and 100 litres, and probably employed reflex loading. Standards for distortion and colouration, unnatural ringing effects due to in-band resonances, and false tonal balance fell well short of the performance of even today’s low-cost models.

It is interesting to examine the ‘ideal performance’ a contemporary speaker designer then aimed at achieving, even though the typical speaker on sale, outlined above, in fact fell far short of this standard (Table 1.1).

The ideal specification was limited by the level of achievement then attained by designers (Table 1.2 and Figure 1.1). Relative to the typical commercial system of the time, the ideal efficiency is placed at 100 dB for 1 W input at 1 m, which is 6 dB more sensitive than the then typical specification. Presumably, this difference reflects the relatively low power output of contemporary amplifiers as 10–20 W models were commonplace. Only a mild improvement in response flatness or bandwidth was then thought possible; the typical speaker provided a 35 Hz point at 17 dB down, and a 15 kHz point 12 dB down, which contrasts with the –10 dB limit proposed for the ideal system.

Table 1.1 Idealized loudspeaker system specification, circa 1965

Table 1.2 Typical specification of domestic two-way system, circa 1965

Figure 1.1 Typical response curve of two-way domestic system in Table 1.2

While it is reasonable to view the specification in Table 1.2 in its proper context, that is, as an example of typical contemporary commercial practice, it is surprising to discover that the basic technology and theory essential to good, modern loudspeaker design was well known to advanced specialists in the field. Furthermore, such work was well documented in many papers, periodicals and books; for example, although designers were aware of colouration effects, they appear to have done little about them, despite the fine research that had been conducted almost 20 years earlier concerning delayed resonances by Shorter at the BBC. Much of the currently accepted loudspeaker technology and principles were rarely applied, and the overall approach to design was a rather haphazard exercise.

However, some companies were researching highly advanced designs and a few were even in production, albeit in limited quantities. In 1967, K.E.F. Electronics (UK) released a costly experimental system incorporating a highly developed mid-band transducer. Covering a 250 Hz to 4 kHz range, this latter driver employed a 65 mm hemispherical dome formed in a rigid polystyrene/neoprene co-polymer, was fitted with a double suspension, and was loaded by a 0.8 m pipe transmission line filled with long-fibre wool, for effective back wave absorption. The use of an aluminium voice-coil former provided a high power handling capacity (Figure 1.2).

Figure 1.2 KEF’s mid-range loudspeaker with absorbent load

At that time, very few mid-range domes were available, the other well-established example being that employed in the classic American design, the Acoustic Research AR3, which also set standards for extended, uniform bass from a compact sealed-box (IB) enclosure. AR founder, Villchur, also introduced one of the first types of wide directivity dome type units for mid and for treble, these 2″ and 3/8″ sizes being first disclosed in 1958. Villchur is acknowledged as the commercial designer of the box airvolume or compliance dominant sealed box, the successful AR-1 ‘acoustic suspension’ speaker. This was a radical development at that time developed in late 1953, with a patent granted in 1956 (later revoked), when most loudspeakers were much larger with generally rather less low-frequency extension and much less even frequency responses. A two-way, of 40 litres, it employed an 8″ mid-treble with a 12″ long throw, very low resonance bass driver.

One non-moving-coil loudspeaker system that has survived the passage of time is the Quad full-range electrostatic loudspeaker by Walker and Dinsdale that dates from 1957. While it was by no means the first electrostatic with examples dating back at least 60 years, its push-pull constant charge design gave low distortion. Accepting that moderate power handling and low practical efficiency are its specific limitations, its subjective performance continues to bear favourable comparison with many current designs. Its successor, the ESL 63, a design that dates from 1963, has also survived; this is still in production and is largely unchanged. (Peter Walker has also noted the sale of a UK acoustic suspension loudspeaker, the ‘Audiom 8’, pre 1940)

The conservative atmosphere pervading the consumer market in the mid-sixties may be judged from the following example. At that time, the best systems were relatively large (50–100 litres), and when a new high-performance model of compact dimensions became available on the market, it was viewed with considerable suspicion. This was the Spendor BC1 by Spencer Hughes, which benefited from the latest BBC research, and was just 40 litres. It sounded quite different from the weighty systems currently available and, in fact, was rather nearer the live source than its contemporaries. The listener became aware after some experience that the ‘difference’ between the sound and regular speakers was in fact due to a rather closer approach to reality. This compact design represented a skilled balance of the important factors responsible for realistic sound quality, and yet it took almost a decade for this and its compatriot (BBC/Rogers LS 3/7) to become widely accepted.

By the mid-1960s, the BBC’s work on a new generation of monitoring loudspeakers incorporating co-polymer synthetic cones (Bextrene) was well advanced. It proved to be of great significance as it was clear that a major improvement in loudspeaker quality had been achieved. The high standards set by these designs acted as a stimulus to the industry, and through attempts to attain this standard at a commercial level, many new developments and designs have appeared, some strongly related to the BBC originals.

The performance of today’s typical high-quality domestic systems would have been unbelievable in 1965, for they exceed the majority of requirements of the 1965 ideal specification by a handsome margin (Figure 1.3, Table 1.3). This particular example is a bass reflex design, employing a plastic-coned 160 mm diameter bass–mid-range unit in conjunction with a 25 mm diameter soft fabric dome tweeter. However, system sensitivity/efficiency is much lower by some 12 dB than the mid-1960s target.

Figure 1.3 Typical response curve of good quality two-way domestic system

Table 1.3 Typical specification of domestic two-way loudspeaker system, circa 1984

This is the inevitable outcome of the modern requirement for wide bandwidth from a compact enclosure and also its attainment of vastly lower subjective colouration. The narrower amplitude response tolerance is also important; simultaneously, these qualify a far greater response range, serving to illustrate a considerable improvement in uniformity and consistency of response. The standards achieved for distortion and polar response are both vastly improved, and the power rating of 100 W programme (see Table 1.4) is 6 dB higher than the typical equivalent for 1965. This is necessitated by the reduced efficiency of the system as well as the considerably higher power capacity of modern amplifiers. In the light of this current level of attainment for contemporary technology, Table 1.4 suggests idealized specifications for a spectrum of high-quality loudspeaker systems.

The advance in quality is not confined to the high-performance end of the market: in fact, all loudspeaker systems have advanced, if not equally, over the same period. For example, many of the causes of colouration in both cabinets and drive units have been identified and can now be adequately suppressed. Further key factors concern a better understanding of diaphragm behaviour, and the successful application of synthetic materials to drive-unit manufacture. A sufficient variety of well-designed drivers are now available. These cover specific sections of the audio spectrum over a range of different power levels and allow the designer considerable latitude when determining the size and cost for a given system.

Table 1.4 Proposed loudspeaker specification

A key unit identified in the success of a number of original BBC and subsequent design derivatives was a high-frequency unit by Celestion, the HF1300. Designed around 1957, it was suitable for medium power applications and was in fact first used by GEC to augment their aluminium cone driver designs. Some 35 years later, it was a popular tweeter and was still employed in several high-performance systems. In design, it was primarily based on a 38 mm pressure unit for a mid-frequency horn, an internal cockpit loudhailer for a battle tank, and was later modified for use as a direct radiator, notably by the addition of the characteristic radially slotted, phase correcting front plate. It was pistonic over the working range and when in the right system it could provide very natural speech reproduction, something that still eludes many designs of recent vintage.

However, there still remains a major problem for drive-unit manufacturers, namely, suitable cone materials. Bextrene had proved highly successful for the manufacture of vacuum-formed cones and had gained wide acceptance among the major UK driveunit/speaker manufacturers. It was almost a chance discovery, as the material was originally designed for use in the production of low-cost moulded packaging. However, in the more critical loudspeaker application, experienced drive-unit manufacturers had discovered that Bextrene’s acoustical and mechanical properties showed variations from batch to batch. The chemical industry supplying the product is not particularly interested in solving these problems as the requirements of the loudspeaker industry are small compared to total sales. It is thus essential to carefully quantify the mechanical properties of the material to be used and to continue to do so for each batch ordered. Despite these technical difficulties, with careful design and manufacture, plastic cones can be superior to pulp/paper composition types in colouration, uniformity of response and sample-to-sample consistency. In recent years, varieties of polypropylene have largely displaced Bextrene and, like its predecessor, some characteristic sounds may remain, which are difficult to avoid entirely. Such polymers may be improved by suitable fillers. This and the pursuit of higher sensitivity have also led to experimentation with many composite or sandwich constructions and, in some cases, a return to both treated pulp and aluminium and other metal foil diaphragms.

As far as frequency response is concerned, the fundamental analysis of loudspeakers at low frequencies was conducted by Thiele and was first presented by him in 1961. This analysis has been recognized for its true worth in later years, and the subsequent research on the subject by Small and others has also proved to be of great value to designers. Papers by these and other authors provide a remarkably complete theoretical analysis of the one area of loudspeaker design where the results are highly predictable. (A summary of this work is given in Chapter 4.) Armed with such theory and modern design software based on it, there is no reason why any loudspeaker designer worthy of note should fail to produce a loudspeaker with a less than optimal, objectively assessed low-frequency characteristic (see Figure 1.4).

Refined electronic crossover techniques are responsible for further improvements to the modern generation of active, power amplifier–equipped loudspeakers. Although the idea is not new, the early active filters were clumsy to execute with valve amplification and found little favour. In recent years, the development of active-filter theory and the availability of inexpensive operational amplifier circuits, together with the low cost of transistor power amplifier units, have given renewed impetus and many active designs have been produced, including some for domestic use. If their performance advantage is seen in full measure, then we may expect active ‘electronic’ speakers, especially those with a ‘digital’ content and input interface, to assume increasing importance in highquality applications. Advanced DSP solutions are increasingly economical and can deal with many design and room interface issues.

Another development supporting increasing sales for the speaker industry is the meteoric rise of the DVD and similar, multi-channel–capable media formats primarily for movies—Home Theatre replay for consumers. Where two channels sufficed for stereo, now there are typically 5.1 channels, extending to 7.1 for high-end arrangements. Controller/processor amplifiers of 200 W per channel, 7 channels are not uncommon and make significant demands on the more compact speakers favoured for multi-channel working, both for pure music recordings and for film.

1.1 Developments in System Design

Given the great difficulty that is encountered when attempting to satisfactorily cover the whole audible range with good uniformity and directivity with a single drive unit, a high-quality speaker will generally comprise a system. This is composed of an enclosure, several optimized drivers (frequency range specified), and a crossover network; this is generally a passive (non-powered) set of filters that direct the correct input frequency range and power to the appropriate drive units.

System design may be seen as the process of creating a speaker that meets the target specification for performance, both technical and subjective. The enclosure must provide the right non-resonant support and the required internal and external acoustic loadings, as well as the required style and finish.

Drivers must be chosen or custom designed to meet this system specification, not just for fundamental aspects such as sensitivity, power capacity and bandwidth but also with regard to the individual diaphragm characteristics and how the resulting natural acoustic ‘signatures’ are weighted and balanced in the final sound. In addition, driver size has a significant influence on frequency range, output power and also the directional properties according to frequency. Ideally, at the crossover point, there should not be too great a difference in effective acoustic size between adjacent drivers; otherwise, a step may occur in the off-axis frequency response and also in the related power response. This step is often seen through the crossover transition. Good off-axis frequency responses are important, and increasingly, the overall power response is taking its rightful place in the set of criteria controlled by the designer.

Figure 1.4 Exploded view of a modern multi-way loudspeaker system. Two 200 mm framed LF units drive the band-pass enclosure. Narrow fronted, the system has good uniformity in the lateral plane. Heavy damping is used on the panels of the front module while the rest of the enclosure is extensively braced (courtesy KEF Electronics: R104 II)

Some of the variables involved in system design are extraordinarily subtle and prove a source of continuing frustration for inexperienced designers. For example, long known but often overlooked is the surprising sensitivity of overall sound quality to small changes in high-frequency level relative to the mid-band. The upper crossover point between mid and treble is usually placed in the 2.5–3.5 kHz region. A truly natural timbre for the human voice, violin, acoustic guitar and the like can only be achieved when the high-frequency ‘energy’ is within 0.5 dB of the ideal target. This is rather smaller than the tolerances generally available both for measurement and for driver production.

If the treble range is set low, that is, ‘dull’, then the speaker system can sound too warm, veiled and muffled, lacking a sense of both air and atmosphere.

If set too bright, the result may be a sharper sound, perhaps attractive initially on percussive sounds and transients, but it is also likely to add a ‘nasal’ colouration effect to voice as well as impart a ‘harder’ closer sound with a degree of emphasis with sibilants. Violin often acquires a steely harshness with such a balance and may dominate the instrumental grouping. For spatial reproduction, the sense of depth in the image illusion is also impaired when the treble is set too bright.

Unfortunately, a touch of treble brightness may be heard to counter a possible lack of definition and clarity in the mid range and many designers resort to this damaging short cut for superficially better performance.

For critical applications, the production method may include matching for driver sensitivity and/or a means to closely align levels via selected attenuation.

Over the past decade, we have seen a shift away from a relatively inflexible textbook approach to system design, one where frequency ranges are neatly compartmentalized, to a point where designers now have a far greater awareness of the broad interaction of driver sound and power versus frequency, which for critical examples ultimately may only be judged subjectively.

Assessing sound quality is an important discipline, and despite an increased awareness of the many technical factors affecting sound quality, it is often very difficult to separate or filter them out sufficiently to give precise, individual definitions for the many associations between the objective and subjective quality factors.

For example, two views may be obtained for the overall frequency balance of a given speaker, and in this context, the word ‘tonal balance’ is of particular relevance. One critic may describe it as ‘bass light’, while another may describe it as ‘treble bright’. The measuring microphone has no trouble in making the correct identification of treble excess but it cannot take into account human perception. We try to seek a balance. In the latter context, what one critic perceives as a lack of bass weight or overall balance, the other directly identifies as excess treble.

For the designer, there are some interesting options available to fix the problem. He or she could adjust the treble but might find the resulting sound less satisfactory, perhaps owing to clarity deficiencies in the mid range. Alternatively, the designer could look to augment the low-frequency performance and thus help to redress the overall balance if the treble excess was not too extreme.

In some designs, this is surprisingly easy and may involve no more than a percentage reduction in the amount of acoustically absorbent stuffing in the enclosure, and/or a reduction in the length of the reflex port duct, if such a low-frequency resonator is fitted.

For high-quality applications, there is no choice but to get the mid-range right and correct for the high-frequency excess.

Increasing awareness of the global scope of design parameters allows today’s designers to take a less dogmatic view of system design and to exploit more subtle methods of blending and balancing the outputs from multiple drivers.

Aware of the need for subjectively accurate timbre balancing in the face of insufficiently representative frequency responses, designers continue to use measurement as a development tool, but nevertheless rely on critical listening to help mould the various response curves to their overall intention.

To this end, drive units are now designed to operate more smoothly over wider bandwidths. Designers are taking advantage and many are reducing the complexity of their crossover networks. A decade ago, manufacturers proudly boasted of the high complexity of passive networks, highly toleranced and fully compensated for system input impedance as well as for driver acoustic variation. Conversely, it is now felt in some quarters that such complexity runs counter to perceived naturalness, and may interfere with the ability of a good recording to communicate the composer’s musical message to the listener.

Thus, those historic 40- and 50-element crossover filters are gradually being supplanted by much simpler arrangements offering a more direct link between amplifier and drive unit. In one exceptional example, a high-quality three-way speaker system, aided by natural, well-tailored intrinsic driver responses, was completed with only three elements in the crossover network. Ten years ago, the design would have used typically 10–12 elements without compensation for the driver’s motional impedance, and 30 elements with such compensation.

1.2 Performance Conflicts

With regard to physical and acoustical properties, loudspeaker designers are still busy trying to improve the uniformity of frequency response, not just at one, more or less arbitrary, axial point but over a range of angles and distances. Their aim is to generate a neutral energy balance over a forward directed solid angle, at least encompassing the listening area. Target beam shapes are 10 or 15 degrees in the vertical plane, and 25 or 35 degrees in the horizontal plane. There is a continuing requirement to reduce enclosure size to improve acceptability in the domestic environment, especially in view of the multi-system surround sound applications and for home cinema developments. This size reduction is in conflict with the quest for greater low-frequency extension and uniformity, one of the major factors that distinguishes genuine Hi Fi from Mid Fi. There is also a trend towards genuinely higher efficiency leading to higher maximum sound levels, but this is also in conflict with smaller enclosure sizes. The market expects speaker systems to operate at ever increasing loudness without commensurate increase in input power and, preferably, without adverse consequences, such as a compromised electrical loading on the amplifier or increased distortion or compression. On the face of it, this is clearly not possible but gains are being achieved in subjective performance through a better understanding of large signal non-linearity and corresponding improvements in power handing for smaller drivers.

1.3 The Stereo Illusion

Often referred to as ‘the stereo illusion’, two-channel recording and reproduction is far from perfect in creating an aural illusion of the spatiality of a recorded event. Indeed, for some listeners, its failure to convince leaves them wondering if what they hear is simply two channels sounding louder and more informative rather than one.

Primary experiments on spatial reproduction occurred in the 1930s with the US effort, in part, associated with the film business and the need for a stable, intelligible localized centre stage signal. A minimum of three channels, and preferably rather more, is required for this approach, and we see it being continued in the video associated, Home Theatre standards.

Some practitioners continue to support the importance of a discrete centre channel for clear localization, while the industry, cognizant of practical issues, settled on two-channel stereo reproduction long ago.

Blumlein, working at EMI in the 1930s, pioneered a UK alternative approach to the multiple-channel, multiple-spaced microphone idea. He advocated a lower cost and more effective two-channel method where the recording was encoded for both phase/direction and for intensity using, for example, a crossed pair of coincident dipole microphones. For this encoding, the optimal spatial illusion for sounds generated from a specifically located pair of loudspeakers, spaced for a 60° arc, is achieved for essentially one central listener position at the apex of the resultant triangle. Image stability is significantly impaired for small displacements away from the central location and as the spacing of one speaker to listener becomes significantly different from the other, the intensity differential results in a rapid collapse of the illusion. The sound image then appears to come almost exclusively from the nearest loudspeaker. Some aural accommodation will occur for most subjects helping the reconstruct some sense of an image, if now displaced from the centre. However, most recordings in fact rely on dominant intensity coding to convey stereo image information, generally missing out on the phase component heard in nature and the result is less natural, even if still entertaining, for many listeners.

1.4 Sensitivity and Impedance

One of the anomalies in specification concerns sensitivity. Objectively, sensitivity is accepted as a measured sound pressure level at a 1 m distance where the input voltage is 2.83 V rms, corresponding to 1 W into a standard 8 Ω resistance. By implication, there is an association with efficiency in its pure sense. However, very few loudspeakers have a uniform 8 Ω loading over their working frequency range. Even the industry standard allows for a range between 6.4 and 10 Ω such a variation is, by implication, associated with reactive regions where the load impedance passes through resistive, inductive and capacitative regions. In practice, loudspeaker systems exhibit impedance peaks well beyond 10 Ω, often to 50 Ω, but these are considered to be harmless since they do not prejudice the nominal sensitivity value. Frequency regions where the impedance falls significantly below the 8 Ω mean are prejudicial. First, designers may deliberately choose to ignore the standard and work to lower impedance, thereby taking greater current from the source amplifier (in practice, these are voltage sources of negligible output impedance and are thus capable, within limits, of providing greater current on demand). Greater current increases input power, provides higher sound levels and thus leads to superior ‘voltage’ sensitivity.

Unfortunately, there is a price to pay. Higher currents lead ultimately to non-linearity in the magnetic components of the driver and thermal compression due to temperature rise in the coil. In fact, it is possible to generalize loudspeaker distortion as being strongly dependent on input current and not on the more obvious parameter, sound level. In addition, for lowered impedances, cables, contacts, terminals and, not least, amplifiers are subjected to higher stress; further, the complex nature of the electrical input impedance of many loudspeaker systems may evoke premature current limiting or protection in the driving amplifier. In addition, most amplifiers show a distortion characteristic that is essentially proportional to output current.

Honest voltage sensitivities, uncompromised by significant regions of low impedance, are thus to be encouraged in speaker design.

1.5 Enclosures

Advances in enclosure design have been numerous. Undeniably, the trend is towards a heavier, more rigid construction with a double purpose: (a) to control and minimize spurious resonances in the enclosure panels and structure, and (b) to provide an inertial platform against which the moving-coil drivers may reference themselves. If their foundation, the termination for their chassis/structure, is not rigid and has insufficient mass, then the wanted motion of the moving system will carry reaction errors. It is surprising how subtle those errors can be and still remain audible. For example, the tightness of the fixing bolts attaching a driver frame to an enclosure panel is a significant factor, affecting clarity, colouration and the subjective naturalness on dynamics, that is, those loudness contrasts so easily recognized as characteristic of live sound. The difference between ‘just tight’ and correctly torqued may only be a quarter of a rotation of a screw in a wood or wood composite panel, yet the resulting change is often audible and significant.

MDF board has generally eclipsed older plywood and chipboard panels for enclosure construction, while complex internal bracing, which may be arranged in several planes, is now commonplace. Bracing is intended to subdivide the panels into smaller unequal areas, thus helping to disperse the natural acoustic resonant ‘signature’ of the panels. The critical importance of this aspect can only be appreciated with the understanding that even in the case of costly speaker designs much of the false tonal ‘colour’ in the sound of a speaker system is still a result of the enclosure and not that of the drive units or the crossover design.

Treatments may also be applied to enclosure walls such as layering, for example, with tough phenolic laminates or with steel plates. Fibrous bitumen loaded pads offer a high mechanical resistance, and are effective in damping higher frequency modes acting as constrained layer damping, particularly for thin-wall enclosures which are allowed to bend.

More recently, catalytic polymer resins have become available, with useful properties for making loudspeaker enclosures. Heavily mineral loaded, such polymer mixes endow the easily cast material with a combination of stiffness, mass and resonance damping. The results are encouraging and good examples show a welcome absence of ‘woody’ panel sounds, hitherto a generally accepted component of loudspeaker sound. A good external finish may be more difficult to achieve.

Enclosures are now ideally keyed to the floor on which they sit via hardened steel spikes, with sufficiently narrow points to pierce the usual carpet (though not your best Persian!) and thus engage the floorboards beneath. Surprising improvements in overall system definition and stereo focus result from the resulting improved stability. For tiled or block floors, thin felt pads are optimal under feet of small area; any greater elasticity for the coupling may result in audible and measurable secondary resonances developing between enclosure and floor. For highly critical use, a few installations, fortunately at ground level, have apertures cut in the floor. The speakers are mounted on isolated brick piers supplied with their own foundations. It makes it hard to readjust the speaker location.

The appearance of enclosures is also changing. Reduced diffraction is important; edges are bevelled or rounded to reduce the impact of reflections at these acoustic boundaries, and overall shape may include tapered surfaces to maintain the smooth wavefront for the acoustic output and reduce secondary stray or parasitic sources such as re-radiation from sharp edges or corners. These impair stereo image focus and add audible roughness to the treble range.

A slant or angle to the front panel may help to compensate for the differential time delay between multiple drive units at the listener position, thus improving phase response and acoustic integration through the crossover regions.

1.6 Drive Units

The use of metal diaphragms is an obvious development in high fidelity loudspeakers. While paper or wood-based pulp cones are still popular and widely used at all quality levels, the goal of a resonance-free, pure piston performance for the cone still fascinates designers.

Distortions arise when a typical polymer or pulp cone material flexes in its naturally resonant regions. This is because these materials do not have the properties of linear springs. For these materials, often chosen for their good internal damping, deflection is not directly proportional to force. Several higher-order terms are required for the bending equation, these qualifying the non-linearity. This implies the generation of false sounds, together with some shift in energy from the fundamental up to the harmonic. Changes in perceived timbre may result, together with possible obscuring of other lower-level sounds in the harmonic masking range. Thus, distortion from mid-range sounds can mask quieter fundamental or formant information in the treble.

Certainly, there are other sources of distortion, but these can be satisfactorily dealt with through, for example, improvements in magnet and coil design.

The adoption of formed sheet metal for the diaphragm, usually a light alloy, typically based on aluminium or magnesium, provides such a high stiffness that the natural resonance modes (typically 700 Hz to 1.5 kHz for a conventional cone) are pushed up to the 5–7 kHz region, for example, for a 90 mm diaphragm diameter, which is usually beyond the crossover point for a multi-way speaker design.

When a metal cone does ‘break up’ and enter partial resonance, it does so with greater vigour because of the much lower mechanical losses compared with polymer or pulp constructions. What may be an amplitude ‘bump’ or ‘glitch’ of 1-3 dB for a high-quality plastic cone will now be seen as a severe resonance peak, 8-16 dB high (Figure 1.5). In return for a transparent, distortion-free linear performance in the range below resonance, the designer must suppress the resonant peak if it is not to interfere with the performance of the high-frequency drive unit, married to it via the system crossover network. It is thus customary to fit a filter to trap electrical input at the main cone resonance.

Figure 1.5 Comparison of polymer and metal cone frequency responses in a low diffraction enclosure (--- polymer —— metal)

While metal cones are often considered a recent development, and are increasing in popularity, light alloy cone drivers were in fact developed at the audio division of GEC as early as the late 1950s and also by Jordan in the 1960s in full-range form. Smaller pressure drive units for horn-loaded public address systems have also used metal foil diaphragms for many decades.

Other developments include modern, high tensile strength low-mass fibres used in moving-coil driver cones, either as a woven formed matrix reinforced with a catalytic bonding resin or as a reinforcement to an existing diaphragm structure. Early trials with glass fibres have more recently been augmented by Kevlar and carbon fibre forms.

Another goal for the drive-unit designer has been realized in recent years. Conventionally, polymer cones were made by vacuum forming a sheet of thermoplastic Bextrene, vinyl or polypropylene. This technique tended to thin the diaphragm regions of greatest stretch, namely, the apex, leaving the cone rim near the original thickness. This is precisely the opposite of what is required, namely, a strong stiff driving point at the apex, the point of attachment to the moving coil, with a lighter, thinner more easily driven region leading out to the edge.

Only recent advances in moulding precision and the development of a free-flowing, mineral-reinforced, hard-setting grade of polypropylene have allowed the development of close-tolerance injection-moulded cones. These have a near-ideal mass and stiffness distribution. An additional bonus has been the successful addition of the surround suspension, simultaneously co-moulded in the same operation. The result has been higher-performance polymer cone assemblies of greater consistency and significantly lower cost (Figure 1.6).

Figure 1.6 Section through injection co-moulded polymer cone and surround

A whole range of materials have been used successfully for high-frequency units, the most popular being coated fabric or drawn aluminium foil for dome diaphragms.

1.7 The Room

Rooms vary considerably and there is good material on how to design optimal rooms. Domestic dwellings rarely have optimal rooms.

While domestic listening rooms have not really altered, our understanding of the way that this finite acoustic space is used has improved.

Designers are now aware of the effects of local boundaries close to a positioned loudspeaker system; for example, the immediate destructive interference in the lower mid-range resulting from out-of-phase reflected acoustic images from the floor.

The relative contribution of the floor, rear wall and side-wall reflections can be accounted for in a practical way and stable stereo images are aided by good left-right symmetry in placement, including the precise angling and positioning of the loudspeakers in the room. At a still lower frequency, the ceiling comes into play.

Then there is the quality of augmentation at still lower frequencies, where the reflection becomes increasingly in-phase and takes on a pressure character, thanks to increasingly larger wavelength.

Cognizant of a median ‘acoustic axis’ and location for a given speaker system, the most uniform low-frequency drive to the room will be obtained if the distances from that location to the three nearest boundaries are spaced in an inharmonic relationship. By this means, the worse combinations of standing-wave mode drive for spatially averaged room/speaker frequency responses of up to 18 dB may be subdued to a satisfactory +, −3 dB (assessed using third-octave band weighting) (Figure 1.7).

Figure 1.7 Placement versus location: Loudspeaker responses a, Axial, anechoic b, Room corner location (worst case) c, Optimum location, 0.5 m high, 0.3, 0.7, m to nearest walls (room curves are spatially averaged, traces are separated vertically for clarity)

Many system designers now take account of such room interface criteria, thus helping to achieve more uniform frequency response in real locations. The slavish following of the patently artificial, textbook-specified, low-frequency design conditions of 2π or 4π steradian acoustic spaces by designers is becoming less common.

Primarily, the past decade has seen a consolidation of speaker design and technology. Radical new inventions in the field of sound reproduction are rare. Such consolidation is primarily directed at the most enduring and effective sound transducer principle, that is, the moving coil, which continues to satisfy requirements in a wide range of applications, from the least to the most expensive. Indications of a useful breakthrough for the moving-coil driver are just emerging and are aired for the first time in Chapter 5.)

As to the future, we can only hope that through the application of both extant and future research material, loudspeaker designers will continue to support the common standard of performance that is beginning to emerge today. No car would find acceptance if it failed to meet basic requirements of handling, braking efficiency, acceleration and comfort, yet the existence of such standards has not prevented the automobile industry from producing a wide range of models of diverse styles and sizes. Similarly, there is no reason why an interesting range of speakers should not continue to be available, while aiming to meet or exceed a common standard of bandwidth, response uniformity, colouration and distortion.

Bibliography

Borwick, J., (Ed.), Loudspeakers and Headphone Handbook, 2nd edn 1994, Butterworth (1988), [Third edition Focal Press 2001 ISBN 0 240 51578 1]

Briggs, G., Loudspeakers, 5th edn, Wharfedale Wireless Works, Idle, Yorkshire (1958)

Briggs, G., More About Loudspeakers, Wharfedale Wireless Works, Idle, Yorkshire (1963)

Cohen, A. B., Hi Fi Loudspeakers and Enclosures, (1975)

Colloms, M., ‘Developments in loudspeaker system design’, Acoust. Bull., 20, No. 6 (Nov.–Dec. 1995), Institute of Acoustics

Geddes, E. and Geddes, L., ‘Audio Transducers’ (2002), ISBN 0-9722085-0-X

Hiraga, J., Les Haut-Parleurs, Editions Frequences (1981)

Jordan, E. J., Loudspeakers, Focal Press, London (1963)

Kelly, S., ‘Transducer drive mechanisms’, Loudspeakers and Headphone Handbook, (Borwick, J. Ed.), Butter- worth (1988)

Rice, C. W. and Kellogg, E. W., ‘Notes on the development of a new type of hornless loudspeaker’, J. Am. Inst. Electr. Eng., reprinted J. Audio Eng. Soc., 30, No. 7/8, 512–521 (1982)

Tremaine, H. M., Audio Cyclopedia, 2nd edn, Howard Sams, New York (1974)

* Note: A considerable number of the A.E.S. journal papers cited in this book have been published in four volumes by the Audio Engineering Society.

* LOUDSPEAKERS VOL.1 edited by Raymond E. Cooke. Sixty-one papers, covering the years 1953 to 1977, written by the world’s greatest transducer experts and inventors on the design, construction, and operation of loudspeakers. 448 pages

* LOUDSPEAKERS VOL.2 edited by Raymond E. Cooke. Forty-nine papers from 1978 to 1983 by experts in loudspeaker technology, extending the work initiated in Vol. 1. 464 pages

* LOUDSPEAKERS VOL.3–Systems and Crossover Networks edited by Mark R. Gander. Forty-two papers with comments and corrections published on this specific area of loudspeaker technology from 1984 through 1991. With a companion volume on transducers, measurement and evaluation, this publication extends the work of the first two volumes on the important topic of loudspeakers. An extensive list of related reading is included. 456 pages

* LOUDSPEAKERS VOL.4–Transducers, Measurement and Evaluation edited by Mark R. Gander. Thirty- eight papers with comments and corrections covering this specific sub-category from 1984 through 1991. A bibliography of related reading lists essential titles in this field. 496 pages

2

Theoretical Aspects of Diaphragm Radiators

In this chapter, we introduce the fundamental theory of direct radiating loudspeakers, with reference to a hypothetical driver typical of the low-frequency units used in domestic loud-speaker systems. The discussion begins with that frequency range where the loudspeaker may be approximated by a ‘lumped parameter’ model—specifically, one in which all moving components of the loudspeaker have equal velocity.

We shall not rely upon the equivalent circuit methods that have dominated loudspeaker textbooks for the past half a century. We shall also seek to avoid those objects of higher mathematics, such as Bessel functions, which arise in analytical treatment of radiation from sources.

Instead of using an equivalent circuit, we introduce a ‘TwoPort’ model of the loudspeaker. This technique, borrowed from electrical network analysis, generates a fixed general model of the loudspeaker, which may be ported to different operating conditions. Although reasonably compact to describe on paper, the real power of the TwoPort formulation becomes apparent when used on a computer. Instead of appealing to analytical treatments of radiation from complex sources, we shall use the numerical method of summing the response of an array of simple sources that represents the complex object.

It is our hope that this treatment will be accessible to a new generation of readers who have never seen an analog computer yet are comfortable with the numerical methods applied on a digital computer.

The radiation of sound by loudspeaker systems is a complicated phenomenon controlled by the interaction of a range of electrical, mechanical and acoustical effects. In order to develop an understanding of this complex system, it is useful first to consider the radiation of sound from a simple elemental object, which shall form a building block for a more complete understanding of practical loudspeakers.

2.1 Radiation from Simple Sources

Treating sound radiation from a loudspeaker as a synthesis of sound radiation from simple elemental sources is useful for at least three reasons. Firstly, it is an effective means of developing understanding. Secondly, it is in accord with classical analyses of the acoustics of idealized loudspeaker diaphragms, which were based on analytical methods that sum the contributions of infinitesimally small components, using the methods of calculus. Finally—and most importantly—the numerical methods that today dominate the computer modelling of loudspeaker systems use exactly the same method, modelling the interactions of elemental subsystems and summing their combined effect.

While hardly practical, the simplest conceivable sound source might consist of a sphere, whose radius can be changed such that the whole object swells and contracts. The movement of the surface of the sphere is impressed upon the air in contact with it and this disturbance causes sound to radiate away from the sphere. Such a source has been described in many texts on theoretical acoustics [1,2], where it is named, appropriately, the simple source. These texts place the simple source in an idealized environment in which there are no reflecting boundaries or other objects, and show the resulting sound to be a wave having spherical wavefronts, which propagate away from the source. The situation is sketched in Figure 2.1, and equation (2.1) describes the relationship between movement of the sphere and the resulting sound.

(2.1)

Equation (2.1) reveals some important properties of sound radiation from the simple source. The pressure p and the source velocity u are related by a function of properties of the air (the mass density ρ0 and the speed of sound c) and of the size of the source (the source radius a). The ratio p/u is also seen to be complex (note the presence of j = √ − 1), which allows the expression to encode time and phase delays between the source velocity and the pressure. It is, however, two other aspects of the equation (2.1) that deserve closest attention at this point.

Firstly, notice that the expression is a function of frequency, f. This dependence upon frequency is seen both in the presence of the factor f, which scales the magnitude of the pressure, and in the complex exponential e−j²πfr/c, which controls the phase of the pressure. The dependence upon frequency reveals that radiation from the simple source has a frequency response, an attribute of system behaviour fundamentally important to loudspeakers. This frequency response embraces both the dependence of magnitude and phase upon frequency. For the sphere the frequency response is a simple linear function of frequency—a doubling of frequency giving rise to a doubling of pressure for the same surface velocity.

Figure 2.1 The simple source

The pressure is also a function of measurement radius r, both in magnitude and phase. The magnitude of the pressure is inversely proportional to the radius, while the phase shift is proportional to the radius. The magnitude result is fundamentally important—the tendency of freely propagating sound to decay in amplitude proportional to the inverse of the distance from the source shall become a general limiting behaviour of radiation from any source of sound.

The deciBel

Biologists have observed that sensory systems tend to operate such that sensation is approximately proportional to the logarithm of the intensity of the stimulus (this observation was embodied in Fechner’s Law, proposed in the nineteenth century). In auditory terms, the intensity of the auditory stimulus is proportional to the squared pressure, such that there is a psychophysical motive to describe sound in terms of the logarithm of the squared pressure. Such a description is offered by the deciBel, which represents 10 times the base 10 logarithm of an energy ratio and derives its name from the telecommunication pioneer Alexander Graham Bell.

Applied to acoustics, the deciBel can be used to describe any ratio of squared pressures or—with a standardized choice of a reference pressure—any pressure level. For example, the sound pressure level, Lp, associated with a RMS pressure of p is defined as

(2.2)

where pref is the reference acoustic pressure: pref = 20 μPa.

To give a rough guide, when listening to a single tone, an amplitude change of one dB is a barely audible change while a change of 10 dB is perceived as an approximate doubling of loudness.

In terms of radiation from the simple source moving with constant surface velocity, a doubling of frequency causes a 6 dB