Definitions

Loudspeaker

[loud-spee-ker]
'' For the Marty Friedman album, see Loudspeaker (album)

A loudspeaker, speaker, or speaker system is an electroacoustical transducer that converts an electrical signal to sound. The term loudspeaker can refer to individual transducers (known as drivers), or to complete systems consisting of a enclosure incorporating one or more drivers and electrical filter components. Loudspeakers, just as with other electroacoustic transducers, are the most variable elements in an audio system and are responsible for the greatest degree of audible differences between sound systems.

To adequately reproduce a wide range of frequencies, most loudspeaker systems require more than one driver, particularly for high sound pressure level or high accuracy. Individual drivers are used to reproduce different frequency ranges. The drivers are named subwoofers (very low frequencies), woofers (low frequencies), mid-range speakers (middle frequencies), tweeters (high frequencies) and sometimes supertweeters optimized for the highest audible frequencies.

The terms for different speaker drivers differ depending on the application. In 2-way loudspeakers, there is no "mid-range" driver, so the task of reproducing the midrange sounds falls upon the woofer and tweeter. Home stereos use the designation "tweeter" for high frequencies whereas professional audio systems for concerts may designate high frequency drivers as "HF" or "highs" or "horns".

When multiple drivers are used in a system, a "filter network", called a crossover, separates the incoming signal into different frequency ranges, and routes them to the appropriate driver. A loudspeaker system with n separate frequency bands is described as "n-way speakers": a 2-way system will have woofer and tweeter speakers; a 3-way system is either a combination of woofer, mid-range and tweeter or subwoofer, woofer and tweeter.

History

Alexander Graham Bell patented the first electrical loudspeaker as part of his telephone in 1876, which was followed in 1878 by an improved version from Ernst Siemens. Nikola Tesla reportedly created a similar device in 1881, but was not issued a patent. During this time, Thomas Edison was issued a British patent for a system using compressed air as an amplifying mechanism for his early cylinder phonographs, but he ultimately settled for the familiar metal horn driven by a membrane attached to the stylus. In 1898, Horace Short patented a design for a loudspeaker driven by compressed air, then sold the rights to Charles Parsons, who was issued several additional British patents before 1910. A few companies, including Victor Talking Machine Company and Pathe, produced record players using compressed-air loudspeakers. However, these designs were significantly limited by their poor sound quality and their inability to reproduce sound at low volume. Variants of the system were used for public address applications, and more recently other variations have been used to test space equipment resistance to the very loud sound and vibration levels that launching rockets produce.

The modern design of moving-coil drivers was established by Oliver Lodge in (1898). The moving coil principle was patented in 1924 by Chester W. Rice and Edward W. Kellogg.

These first loudspeakers used electromagnets because large, powerful permanent magnets were generally not available at a reasonable price. The coil of an electromagnet, called a field coil, was energized by current through a second pair of connections to the driver. This winding usually served a dual role, acting also as a choke coil filtering the power supply of the amplifier to which the loudspeaker was connected. AC ripple in the current was attenuated by the action of passing through the choke coil; however, AC line frequencies tended to modulate the audio signal being sent to the voice coil and added to the audible hum of a powered-up sound reproduction device.

The quality of loudspeaker systems until the 1950s was poor. Continuous developments in enclosure design and materials have led to significant audible improvements. The most notable improvements in modern speakers are improvements in cone materials, the introduction of higher temperature adhesives, improved permanent magnet materials, improved measurement techniques, computer aided design and finite element analysis.

Driver design

The most common type of driver uses a lightweight diaphragm connected to a rigid basket, or frame, via flexible suspension that constrains a coil of fine wire to move axially through a cylindrical magnetic gap. When an electrical signal is applied to the voice coil, a magnetic field is created by the electric current in the coil which thus becomes an electromagnet. The coil and the driver's magnetic system interact, generating a mechanical force which causes the coil, and so the attached cone, to move back and forth and so reproduce sound under the control of the applied electrical signal coming from the amplifier. The following is a description of the individual components of this type of loudspeaker.

The diaphragm is usually manufactured with a cone or dome shaped profile. A variety of different materials may be used, but the most common are paper, plastic and metal. The ideal material would be stiff (to prevent uncontrolled cone motions), light (to minimize starting force requirements) and well damped (to reduce vibrations continuing after the signal has stopped). In practice, all three of these criteria cannot be met simultaneously using existing materials, and thus driver design involves tradeoffs. For example, paper is light and typically well damped, but not stiff; metal can be made stiff and light, but it is not usually well damped; plastic can be light, but typically the stiffer it is made, the less well-damped it is. As a result, many cones are made of some sort of composite material. This can be a matrix of fibers including Kevlar or fiberglass, a layered or bonded sandwich construction, or simply a coating applied to stiffen or damp a cone.

The basket or frame must be designed for rigidity to avoid deformation, which will change the magnetic conditions in the magnet gap, and could even cause the voice coil to rub against the walls of the magnetic gap. Baskets are typically cast or stamped metal, although molded plastic baskets are becoming common, especially for inexpensive drivers. The frame also plays a considerable role in conducting heat away from the coil.

The suspension system keeps the coil centered in the gap and provides a restoring force to make the speaker cone return to a neutral position after moving. A typical suspension system consists of two parts: the "spider", which connects the diaphragm or voice coil to the frame and provides the majority of the restoring force; and the "surround", which helps center the coil/cone assembly and allows free pistonic motion aligned with the magnetic gap. The spider is usually made of a corrugated fabric disk, generally with a coating of a material intended to improve mechanical properties. The name "spider" derives from the shape of early suspensions, which where two concentric rings of bakelite material, joined by six or eight curved "legs". Variations of this topology included adding a felt disc to provide a barrier to particles that might otherwise cause the voice coil to rub. Another German company currently offers a spider made of wood. The surround can be a roll of rubber or foam, or a ring of corrugated fabric (often coated), attached to the outer circumference of the cone and to the frame. The choice of suspension materials affects driver lifetime, especially in the case of foam surrounds which are susceptible to aging and environmental damage.

The wire in a voice coil is usually made of copper, though aluminium, and rarely silver, may be used. Voice coil wire cross sections can be circular, rectangular, or hexagonal, giving varying amounts of wire volume coverage in the magnetic gap space. The coil is oriented coaxially inside the gap, a small circular volume (a hole, slot, or groove) in the magnetic structure within which it can move back and forth. The gap establishes a concentrated magnetic field between the two poles of a permanent magnet; the outside of the gap being one pole and the center post (a.k.a., the pole-piece) being the other. The pole piece and backplate are often a single piece called the poleplate or yoke.

Modern driver magnets are almost always permanent and made of ceramic, ferrite, Alnico, or, more recently, neodymium magnet. A current trend in design, due to increases in transportation costs and a desire for smaller, lighter devices (as in many home theater multi-speaker installations), is the use of neodymium magnet instead of ferrite types. Very few manufacturers use electrically powered field coils as was common in the earliest designs. The size and type of magnet and details of the magnetic circuit differ, depending on design goals. For instance, the shape of the pole piece affects the magnetic interaction between the voice coil and the magnetic field, and is sometimes used to modify a driver's behavior. A "shorting ring" or Faraday loop may be included as a thin copper cap fitted over the pole tip, or as a heavy ring situated within the magnet-pole cavity. The benefits of this are reduced impedance at high frequencies providing extended treble output, reduced harmonic distortion, and a reduction in the inductance modulation that typically accompany large voice coil excursions. On the other hand, the copper cap requires a wider voice coil gap, with increased magnetic reluctance, reducing available flux, requiring a slightly larger magnet for equivalent performance.

Driver design, and the combination of one or more drivers into an enclosure to make a speaker system, is both an art and science. Adjusting a design to improve performance is done using magnetic, acoustic, mechanical, electrical, and material science theory, high precision measurements, and the observations of experienced listeners. Designers can use an anechoic chamber to ensure the speaker can be measured independently of room effects, or any of several electronic techniques which can, to some extent, replace such chambers. Some developers eschew anechoic chambers in favor of specific standardized room setups intended to simulate real-life listening conditions. A few of the issues speaker and driver designers must confront are distortion, lobing, phase effects, off axis response and crossover complications.

The fabrication of finished loudspeaker systems has become segmented, depending largely on price, shipping costs, and weight limitations. High-end speaker systems, which are heavier (and often larger) than economic shipping allows outside local regions, are usually made in their target market area and can cost \$140,000 or more per pair. The lowest-priced speaker systems and most drivers are manufactured in China or other low-cost manufacturing locations. Although the manufacture of drivers has become largely commoditized, the fabrication and subsequent sale of finished speaker systems still carries high profits. Partly for this reason, manufacturers are increasingly combining power amplifier electronics (a typically lower profit item) with finished speaker systems to create powered speakers with an overall higher market value.

Driver types

An audio engineering rule of thumb is that individual electrodynamic drivers provide quality performance over at most about 3 octaves. Multiple drivers (i.e., subwoofers, woofers, mid-range drivers, tweeters) are generally used in a complete loudspeaker system to provide performance beyond 3 octaves.

Full range drivers

A full-range driver is designed to have the widest frequency response possible, despite the rule of thumb cited above. These drivers are small, typically 3 to 8 inches (7 to 20 cm) in diameter to permit reasonable high frequency response, and carefully designed to give low distortion output at low frequencies, though with reduced maximum output level. Full range (or more accurately wide range) drivers are most commonly heard in public address systems, and in televisions, although some models are suitable for hi-fi listening. In hif-fi speaker systems, the use of wide range drive units can avoid undesirable interaction between multiple drivers, caused by non-coincident driver location, or crossover network issues. Fans of wide range driver hi-fi speaker systems claim a coherence of sound, said to be due to the single source and a resulting lack of interference, and likely to the lack of crossover components. Detractors typically cite the wide range driver's limited frequency response and their modest output abilities, together with their requirement for large, elaborate, expensive enclosures, such as transmission lines, or horns, to approach optimum performance.

Full range drivers often employ an additional cone called a whizzer: a small, light cone attached to the joint between the voice coil and the primary cone. The whizzer cone extends the high frequency response of the driver and broadens its high frequency directivity, which would otherwise be greatly narrowed due to the outer diameter cone material failing to keep up with the central voice coil at higher frequencies. The main cone in a whizzer design is manufactured so as to flex more in the outer diameter than in the center. The result is that the main cone delivers low frequencies and the whizzer cone contributes most of the higher frequencies. Since the whizzer cone is smaller than the main diaphragm, output dispersion at high frequencies is improved relative to an equivalent single larger diaphragm. Limited-range drivers are typicall noted in compters, toys, and clock radios. These drivers are less elaborate and less expensive than wide range drivers, and they may be severely compronized to fit into very small mounting locations. In this application, sound quality is a low priority. The human ear is remarkably tolerant of poor sound quality, and the distortion inherent in limited range drivers may enhance their output at high frequencies, increasing clarity when listening to spoken word material.

Subwoofer

A subwoofer is a woofer driver used only for the lowest part of the audio spectrum: typically below 100-120 Hz. Because the intended range of frequencies in these is limited, subwoofer system design is usually simpler in many respects than for conventional loudspeakers, often consisting of a single subwoofer driver enclosed in a suitable cabinet or enclosure.

To accurately reproduce very low bass notes without unwanted resonances (i.e., from cabinet panels), subwoofer systems must be solidly constructed and properly braced; good ones are typically heavy. Many subwoofer systems include power amplifiers and electronic filters, with additional controls relevant to low frequency reproduction. These variants are known as "active subwoofers". Passive subwoofers require external amplification.

Woofer

A woofer is a driver that reproduces low frequencies. Some loudspeaker systems use a woofer for the lowest frequencies, making it possible to avoid using a subwoofer. Additionally, some loudspeakers use the woofer to handle middle frequencies, eliminating the mid-range driver. This can be accomplished with the selection of a tweeter that responds low enough combined with a woofer that responds high enough that the two drivers add coherently in the middle frequencies.

Mid-range driver

A mid-range speaker is a loudspeaker driver which reproduces middle frequencies. Mid-range drivers can be made of paper or composite materials, or be compression drivers. If the mid-range driver is cone-shaped, it can be mounted on the front baffle of a loudspeaker enclosure, or it can be mounted at the throat of a horn for added output level and control of radiation pattern. If it is a compression driver, it is invariably mated to a horn.

Tweeter

A tweeter is a high-frequency driver that typically reproduces the highest frequency band of a loudspeaker. Many varieties of tweeter design exist, each with differing abilities with regard to frequency response, output fidelity, power handling, maximum output level, etc. Soft dome tweeters are widely found in home stereo systems, and horn-loaded compression drivers are common in professional sound reinforcement. Ribbon tweeters have gained popularity in recent years, as their output power has been increased to levels useful for professional sound reinforcement, and their pattern control is conveniently shaped for concert sound.

Loudspeaker system design

Crossover

Used in multi-driver speaker systems, the crossover is a device that separates the input signal into different frequency ranges suited to each driver. Each driver, therefore, receives the frequency range it was designed for, so the distortion in each driver, and interference between the drivers, is reduced.

Crossovers can be passive or active. A passive crossover is an electronic circuit using a combination of one or more resistors, inductors and non-polar capacitors. These parts are formed into carefully designed networks, and placed between the amplifier and the loudspeaker drivers to divide the amplifier's signal into the necessary frequency bands before being delivered to the individual drivers. Passive crossover circuits need no external power beyond the audio signal itself. An active crossover is an electronic filter circuit which divides the complete signal into individual frequency bands before amplification, thus requiring one amplifier for each bandpass. The active crossover requires an external power supply.

Passive crossovers are generally installed inside speaker boxes and are by far the most common type of crossover for home and low power use. In car audio systems, passive crossovers may be in a small separate box, necessary to accomodate the size of the components used. Passive crossovers may be simple, or quite elaborate, although steep slopes such as 24dB per octave require components of unusually close tolerances. Passive crossovers, like the driver units that they feed, have power handling limits, and have a modest amount of insertion loss as theyconvert a small portion of the amplifier power into heat. So, when the highest output levels are required, active crossovers may be preferrable. Active crossovers may be simple circuits which emulate the response of a passive network, or may be more complex allowing audio adjustments. Active crossovers called Digital Loudspeaker management systems may include facilites for precise alignment of phase and time between frequency bands, equalization, and dynamics (compression and/or limiting) control.

Some hi-fi and professional loudspeaker systems now include an active crossover circuit as part of an onboard amplifier system. These designs are identifiable by their need for AC power in addition to a signal cable. This 'active' topology may also include driver protection circuits, and other features of a digital loudspeaker management system. Powered speaker systems are common in computer sound (for a single listener) and, at the other end of the size spectrum, in concert sound systems. Powered speaker systems for concert sound, by virtue of no external adjustments, have the potential to provide predictabile, if not necessarily good, sound quality by removing control of crossover, delay and limiter settings from the concert sound engineer.

Enclosures

Most loudspeaker systems consist of drivers mounted in an enclosure, or cabinet. The role of the enclosure is to provide a place to mount the drivers and to prevent sound waves from the back of a driver from interfering destructively with those from the front -- doing so typically causes cancellations (eg, comb filtering) and significantly alters the level and quality sound at low frequencies.

The simplest driver mount is a flat panel (ie, baffle) with the drivers mounted in a hole in it. However, in this approach, frequencies with a wavelength longer than the baffle dimensions are canceled out because the antiphase radiation from the rear of the cone interferes with the radiation from the front. With an infinitely large panel, this interference could be entirely prevented. A sufficiently large sealed box can approach this behavior..

Since panels of infinite dimensions are impractical, most enclosures function by containing the rear radiation from the cone. A sealed enclosure prevents transmission of the sound emitted from the rear of the loudspeaker by confining the sound in a rigid and airtight box. Techniques used to reduce transmission of sound through the walls of the cabinet include thicker cabinet walls, lossy wall material, internal bracing, curved cabinet walls or more rarely visco-elastic materials (eg, mineral loaded bitumen), or thin lead sheeting applied to interior enclosure walls.

However, a rigid enclosure internally reflects sound which can then be transmitted back through the loudspeaker cone, again resulting in degradation of sound quality. This can be reduced by internal absorption using absorptive materials (often called "damping") such as fiberglass, wool or synthetic fiber batting within the enclosure. The internal shape of the enclosure can also be designed to reduce this by reflecting sounds away from the loudspeaker diaphragm where they may then be absorbed.

Other enclosure types alter the rear radiation so it can add constructively to the output from the front of the cone. Designs that do this (including bass reflex, passive radiators, transmission line, etc) are often used to extend the effective low frequency response, and increase low frequency output of the driver.

To make the transition between drivers as seamless as possible, system designers have attempted to time-align (or phase adjust) the drivers by moving one or more drivers forward or back, so that the acoustic center of each driver is in the same vertical plane. This may also involve tilting the face speaker back, or providing separate enclosure mounting for each driver, or, less commonly, using electronic techniques to achieve the same effect. These attempts account for some unusual cabinet designs.

Any speaker mounting scheme (including cabinets) will also cause diffraction, causing peaks and dips in the frequency response. This is usually a problem at higher frequencies where wavelengths are similar to, or smaller than, cabinet dimensions. The effect can be minimized by rounding the front edges of the cabinet, curving the cabinet itself, using a smaller or narrower enclosure, choosing a strategic driver arrangement, or using absorptive material around a driver.

Wiring connections

Most loudspeakers use two wiring points to connect to the source of the signal (for example, to the audio amplifier or receiver). This is usually done using binding posts, or spring clips on the back of the enclosure. If the wires for left and right speakers (in a stereo setup) are not connected 'in phase' with each other (the + and - connections on the speaker and amplifier should be connected + to + and - to -) the loudspeakers will be out of polarity. Given identical signals, motion in one cone will be in the opposite direction of the other. This will typically cause monophonic material within a stereo recording to be canceled out, reduced in level and made more difficult to localize, all due to destructive interference of the sound waves. The cancellation effect is most noticeable at frequencies where the speakers are separated by a quarter wavelength or less; low frequencies are affected the most. This type of wiring error doesn't damage speakers but isn't optimal.

Specifications

Speaker specifications generally include:

• Speaker or driver type (individual units only) – Full-range, woofer, tweeter or mid-range.
• Size of individual drivers. For cone drivers, the quoted size is generally the outside diameter of the basket. However, it may less commonly also be the diameter of the cone surround measured apex to apex, or the distance from the center of one mounting hole to its opposite. Voice coil diameter may also be specified. If the loudspeaker has a compression horn driver, the diameter of the horn throat may be given.
• Rated Power – Nominal (or even continuous) power, and peak (or maximum short-term) power a loudspeaker can handle (i.e., maximum input power before destroying the loudspeaker. It is never the sound output the loudspeaker produces). A driver may be damaged at much less than its rated power if driven past its mechanical limits at lower frequencies (e.g., by bass heavy electronica or theatre organ music). Tweeters can also be damaged by amplifier clipping (lots of high frequency energy in such cases) or by music, or sine wave input at high frequencies. Each of these situations pass more energy to a tweeter than it can survive without damage.
• Impedance – typically 4 Ω (ohms), 8 Ω, etc.
• Baffle or enclosure type (enclosed systems only) – Sealed, bass reflex, etc.
• Number of drivers (complete speaker systems only) – 2-way, 3-way, etc.

and optionally:

• Crossover frequency(ies) (multi-driver systems only) – The nominal frequency boundaries of the signal division between drivers.
• Frequency response – The measured, or specified, output over a specified range of frequencies for a constant input level varied across those frequencies. It often includes a variance limit such as within "+/- 2.5 dB".
• Thiele/Small parameters (individual drivers only) – these include the driver's Fs (resonance frequency), Qts (a driver's Q (more or less, its damping factor) at resonant frequency), Vas (the equivalent air compliance volume of the driver), etc.
• Sensitivity – The sound pressure level produced by a loudspeaker in a non-reverberant environment, usually specified in dB, and measured at 1 meter with an input of 1 watt or 2.83 volts, typically at one or more specified frequencies. This rating is often inflated by manufacturers.
• Maximum SPL – The highest output the loudspeaker can manage, short of damage or not exceeding a particular distortion level. This rating is often inflated by manufacturers and is commonly given without reference to frequency range or distortion level.

Electrical characteristics of a dynamic loudspeaker

The load a driver presents to an amplifier consists of a complex electrical impedance -- a combination of resistance, and both capacitive and inductive reactance, which combines properties of the driver, its mechanical motion, effects of crossover components (if any are in the signal path between amplifier and driver), and effects of air loading on the driver as modified by the enclosure and its environment. Most amplifiers output specifications are given at a specific power into an ideal resistive load. However, a loudspeaker does not really have a constant resistance across its frequency range. Instead, the voice coil is inductive, the driver has mechanical resonances, the enclosure changes the driver's electrical and mechanical characteristics, and a passive crossover between the drivers and the amplifier contributes its own variations. The result is a load resistance which varies fairly widely with frequency, and usually a varying phase relationship between voltage and current as well, also changing with frequency.

Electromechanical measurements

Fully characterizing the sound output quality of a loudspeaker driver or system in words is essentially impossible. Objective measurements provide information about several aspects of performance, so informed comparisons and improvements can be made. Examples of typical measurements are: amplitude and phase characteristics vs. frequency; impulse response under one or more conditions (eg, square waves, sine wave bursts, ...); directivity vs. frequency (eg, horizontally, vertically, spherically, ...); harmonic and intermodulation distortion vs. SPL output using any of several test signals; stored energy (ie, 'ringing') at various frequencies; impedance vs. frequency and small signal vs. large signal performance. Most of these measurements require relatively expensive equipment to perform and good judgement, but the raw sound pressure level output is rather easier to report and so is often the only specified value, sometimes in misleadingly exact terms. The sound pressure level (SPL) a loudspeaker produces is measured in decibels (dBspl).

Efficiency vs. sensitivity

Loudspeaker efficiency is defined as the sound power output divided by the electrical power input. Most loudspeakers are actually very inefficient transducers; about 1% of the electrical energy sent by an amplifier to a typical home loudspeaker is converted to the acoustic energy we can hear. The remainder is converted to heat, mostly in the voice coil and magnet assembly. The main reason for this is the difficulty of achieving proper impedance matching between the acoustic impedance of the drive unit and that of the air into which it is radiating. The efficiency of loudspeaker drivers varies with frequency as well. For instance, the output of a woofer driver decreases as the input frequency decreases.

Driver ratings based on the SPL for a given input are called sensitivity ratings and are notionally similar to efficiency. Sensitivity is usually defined as so many decibels at 1 W electrical input, measured at 1 meter, often at a single frequency. The voltage used is often 2.83 VRMS, which is 1 watt into an 8 Ω (nominal) speaker impedance (approximately true for many speaker systems). Measurements taken with this reference are quoted as dB with 2.83 V @ 1 m.

The sound pressure output is measured at (or mathematically scaled to be equivalent to a measurement taken at) one meter from the loudspeaker and on-axis or directly in front of it under the condition that the loudspeaker is radiating into an infinitely large space and mounted on an infinite baffle. Clearly then, sensitivity does not correlate precisely with efficiency, as it also depends on the directivity of the driver being tested and the acoustic environment in front of the actual loudspeaker. For example, a cheerleader's horn produces more sound output in the direction it is pointed, by concentrating sound waves from the cheerleader in one direction, and thus "focusing" them. The horn also improves the impedance matching between voice and the air, which produces more acoustic power for a given speaker power. In some cases, impedance matching (via careful enclosure design) will allow the speaker to produce more power.

• Typical home loudspeakers have sensitivities of about 85 to 95 dB for 1 W @ 1 m - an efficiency of 0.5-4%.
• Sound reinforcement and public address loudspeakers have sensitivities of perhaps 95 to 102 dB for 1 W @ 1 m - an efficiency of 4-10%.
• Rock concert, stadium PA, marine hailing, etc speakers generally have higher sensitivities of 103 to 110 dB for 1 W @ 1 m - an efficiency of 10-20%.

A driver with a higher maximum power rating cannot necessarily be driven to louder levels than a lower rated one, since sensitivity and power handling are largely independent properties. In the examples that follow, assume for simplicity that the drivers being compared have the same electrical impedance, are operated at the same frequency which is within both driver's respective pass bands, and that power compression and distortion are low. For the first example, a speaker 3 dB more sensitive than another will produce double the sound pressure level (or be 3 dB louder) for the same power input. Thus a 100 W driver ("A") rated at 92 dB for 1 W @ 1 m sensitivity will output twice as much acoustic power as a 200 W driver ("B") rated at 89 dB for 1 W @ 1 m when both are driven with 100 W of input power. For this particular example, when driven at 100 W, speaker A will produce the same SPL, or loudness, speaker B would produce with 200 W input. Thus a 3 dB increase in sensitivity of the speaker means that it will need half the amplifier power to achieve a given SPL. This translates into a smaller, less complex power amplifier and often to reduced overall cost.

It is not possible to combine high efficiency, especially at low frequencies, with compact enclosure size, and adequate low frequency response. One can, more or less, only choose two of the three parameters when designing a speaker system. So, for example, if extended low frequency performance and a small box size are important, one must accept low efficiency. This rule of thumb is sometimes called Hoffman's Iron Law (after J. A. Hoffman, the H in KLH).

Listening environment

The interaction of a loudspeaker system with its environment is complex and is largely out of the loudspeaker designer's control. Most listening rooms present a more or less reflective environment, depending on size, shape, volume, and furnishings. This means the sound reaching a listener's ears consists not only of sound directly from the speaker system, but also the same sound delayed by traveling to and from (and being modified by) one or more surfaces. These reflected sound waves, when added to the direct sound, cause cancellation and addition at assorted frequencies (eg, from resonant room modes), thus changing the timbre and character of the sound at the listener's ears. The human brain is very sensitive to small variations, including some of these, and this is part of the reason why a loudspeaker system sounds different at different listening positions or in different rooms.

A significant factor in the sound of a loudspeaker system is the amount of absorption and diffusion present in the environment. Clapping one's hands in a typical empty room, without draperies or carpet, will produce a zippy, fluttery echo which is due both to a lack of absorption and to reverberation (that is, repeated echoes) from flat reflective walls, floor, and ceiling. The addition of hard surfaced furniture, wall hangings, shelving and even baroque plaster ceiling decoration, will change the echoes, due primarily to the diffusion caused by somewhat reflective objects with shapes and surfaces having sizes on the order of the sound wavelengths being diffused. This somewhat breaks up the simple reflections otherwise caused by bare flat surfaces, and spreads the reflected energy of an incident wave over a larger angle on reflection.

Placement

In a typical rectangular listening room, the hard, parallel surfaces of the walls, floor and ceiling cause primary acoustic resonance nodes in each of the three dimensions: left-right, up-down and forward-backward. Furthermore, there are more complex resonance modes involving three, four, five and even all six boundary surfaces combining to create standing waves. Low frequencies excite these modes the most, since long wavelengths are not much affected by furniture compositions or placement. The mode spacing is critical, especially in small and medium size rooms like recording studios, home theaters and broadcast studios. The proximity of the loudspeakers to room boundaries affects how strongly the resonances are excited as well as affecting the relative strength at each frequency. The location of the listener is critical, too, as a position near a boundary can have a great effect on the perceived balance of frequencies. This is because standing wave patterns are most easily heard in these locations and at lower frequencies, below the Schroeder frequency - typically around 200-300 Hz, depending on room size.

Directivity

Acousticians, in studying the radiation of sound sources have developed some concepts important to understanding how loudspeakers are perceived. The simplest possible radiating source is a point source, sometimes called a simple source. An ideal point source is an infinitesimally small point radiating sound. It may be easier to imagine a tiny pulsating sphere, uniformly increasing and decreasing in diameter, sending out sound waves in all directions equally, independent of frequency.

Any object radiating sound, including a loudspeaker system, can be thought of as being composed of combinations of such simple point sources. The radiation pattern of a combination of point sources will not be the same as for a single source, but rather will depend on the distance and orientation between the sources, the position relative to them from which the listener hears the combination, and the frequency of the sound involved. Using geometry and calculus, some simple combinations of sources are easily solved; others are not.

One simple combination is two simple sources separated by a distance and vibrating out of phase, one miniature sphere expanding while the other is contracting. The pair is known as a doublet, or dipole, and the radiation of this combination is similar to that of a very small dynamic loudspeaker operating without a baffle. The directivity of a dipole is a figure 8 shape with maximum output along a vector which connects the two sources and minimums to the sides when the observing point is equidistant from the two sources, where the sum of the positive and negative waves cancel each other. While most drivers are dipoles, depending on the enclosure to which they are attached, they may radiate as monopoles, dipoles (or bipoles). If mounted on a finite baffle, and these out of phase waves allowed to interact, dipole peaks and nulls in the frequency response result. When the rear radiation is absorbed or trapped in a box, the diaphragm becomes a monopole radiator. Bipolar speakers, made by mounting in-phase monopoles (both moving out of or into the box in unison) on opposite sides of a box, are a method of approaching omnidirectional radiation patterns.

In real life, individual drivers are actually complex 3D shapes such as cones and domes, and they are placed on a baffle for various reasons. A mathematical expression for the directivity of a complex shape, based on modeling combinations of point sources, is usually not possible, but in the farfield, the directivity of a loudspeaker with a circular diaphragm will be close to that of a flat circular piston, so it can be used as an illustrative simplification for discussion. As a simple example of the mathematical physics involved, consider the following: the formula for farfield directivity of a flat circular piston in an infinite baffle is $p\left(theta\right) = frac\left\{p_0 J_1\left(k_a sin theta\right)\right\}\left\{k_a sin theta\right\}$ where $k_a=frac\left\{2pi a\right\}\left\{lambda\right\}$, $p_0$ is the pressure on axis, $a$ is the piston radius, $lambda$ is the wavelength (i.e. $lambda = frac\left\{c\right\}\left\{f\right\} = frac\left\{text\left\{speed of sound\right\}\right\}\left\{text\left\{frequency\right\}\right\}$) $theta$ is the angle off axis and $J_1$ is the Bessel function of the first kind.

A planar source will radiate sound uniformly for low frequencies whose wavelength is shorter than the dimensions of the planar source, and as frequency increases, the sound from such a source will be focused into an increasingly narrower angle. The smaller the driver, the higher the frequency where this narrowing of directivity occurs. Even if the diaphragm is not perfectly circular, this effect occurs such that larger sources are more directive. Several loudspeaker designs have been built which have approximately this behavior. Most are electrostatic or planar magnetic designs.

Various manufacturers use different driver mounting arrangements to create a specific type of sound field in the space for which they are designed. The resulting radiation patterns may be intended to more closely simulate the way sound is produced by real instruments, or simply create a controlled energy distribution from the input signal (some using this approach are called monitors, as they are useful in checking the signal just recorded in a studio). An example of the first is a room corner system with many small drivers on the surface of a 1/8 sphere. A system design of this type was patented by, and actually produced commercially, by Professor Amar Bose -- the 2201. Later Bose models have deliberately emphasized production of both direct and reflected sound by the loudspeaker itself, regardless of its environment. The designs are controversial in high fidelity circles, but have proven commercially successful. Several other manufacturers' designs follow similar principles.

Directivity is an important issue because it affects the frequency balance of sound a listener hears, and also the interaction of the speaker system with the room and its contents. A speaker which is very directive (ie, on an axis perpendicular to the speaker face) may result in a reverberant field lacking in high frequencies, giving the impression the speaker is deficient in treble even though it measures well on axis (eg, "flat" across the entire frequency range). Speakers with very wide, or rapidly increasing directivity at high frequencies, can give the impression that there is too much treble (if the listener is on axis) or too little (if the listener is off axis). This is part of the reason why on-axis frequency response measurement is not a complete characterization of the sound of a given loudspeaker.

Other driver designs

Other types of drivers which depart from the most commonly used direct radiating electro-dynamic driver mounted in an enclosure include:

Horn loudspeakers

Horn speakers are the oldest form of loudspeaker system, having been used from very early on for cylinder recording players. They use a shaped waveguide in front of or behind the driver to increase the directivity of the loudspeaker and to transform a small diameter, high pressure condition at the driver cone surface to a large diameter, low pressure condition at the mouth of the horn. This increases the sensitivity of the loudspeaker and focuses the sound over a narrower area. The size of the throat, mouth, the length of the horn, as well as the area expansion rate along it must be carefully chosen to match the drive to properly provide this transforming function over a range of frequencies (every horn performs poorly outside its acoustic limits, at both high and low frequencies). The length and cross-sectional mouth area required to create a bass or sub-bass horn require a horn many feet long. 'Folded' horns can reduce the total size, but compel designers to make compromises and accept increased complication such as cost and construction. Some horn designs not only fold the low frequency horn, but use the walls in a room corner as an extension of the horn mouth. In the late 1940s, horns whose mouths took up much of a room wall were not unknown amongst hi-fi fans. Room sized installations became much less acceptable when two or more were required.

A horn loaded speaker can have a sensitivity as high as 110 dB @ 2.83 volts (1 watt @ 8 ohms) @ 1 meter. This is a hundredfold increase in output compared to a speaker rated at 90 dB sensitivity, and is invaluable in applications where high sound levels are required or amplifier power is limited.

Piezoelectric speakers

Piezoelectric speakers are frequently used as beepers in watches and other electronic devices, and are sometimes used as tweeters in less-expensive speaker systems, such as computer speakers and portable radios. Piezoelectric speakers have several advantages over conventional loudspeakers: they are resistant to overloads which would normally destroy most high frequency drivers, and they can be used without a crossover due to their electrical properties. There are also disadvantages: some amplifiers can oscillate when driving capacitive loads like most piezoelectrics, which results in distortion or damage to the amplifier. Additionally, their frequency response, in most cases, is inferior to that of other technologies. This is why they are generally used in single frequency (beeper) or non-critical applications.

Piezoelectric speakers can have extended high frequency output, and this is useful in some specialized circumstances; for instance, sonar applications in which piezoelectric variants are used as both output devices (generating underwater sound) and as input devices (acting as the sensing components of underwater microphones). They have advantages in these applications, not the least of which is simple and solid state construction which resists the effects of seawater better than, say, a ribbon based device would.

Electrostatic loudspeakers

Electrostatic loudspeakers use a high voltage electric field (rather than a magnetic field) to drive a thin statically charged membrane. Because they are driven over the entire membrane surface rather than from a small voice coil, they ordinarily provide a more linear and lower distortion motion than dynamic drivers. They have the disadvantage that the diaphragm excursion is severely limited because of practical construction limitations; the further apart the stators are positioned, the higher the voltage must be to achieve acceptable efficiency, which increases the tendency for electrical arcs as well as the increasing the speaker's attraction of dust particles. For many years electrostatic loudspeakers had a reputation as a generally unreliable and occasionally dangerous product. Arcing remains a potential problem with current technologies, especially when the panels are allowed to collect dust or dirt, or when driven with high signal levels.

Electrostatics are inherently dipole radiators and due to the thin flexible membrane cannot be used in enclosures to reduce low frequency cancellation as with common cone drivers. Due to this and the low excursion capability, full range electrostatic loudspeakers are large by nature, and even so are not outstanding performers at the lowest frequencies. To reduce the size of commercial products, they are often used as a high frequency driver in combination with a conventional dynamic driver which handles the bass frequencies.

Ribbon and planar magnetic loudspeakers

A ribbon speaker consists of a thin metal-film ribbon suspended in a magnetic field. The electrical signal is applied to the ribbon which moves with it, thus creating the sound. The advantage of a ribbon driver is that the ribbon has very little mass; thus, it can accelerate very quickly, yielding very good high-frequency response. Ribbon loudspeakers are often very fragile -- some can be torn by a strong gust of air. Most ribbon tweeters emit sound in a dipole pattern; a very few have backings which limit the dipole radiation pattern. Above and below the ends of the more or less rectangular ribbon, there is less audible output due to phase cancellation, but the precise amount of directivity depends on ribbon length. Ribbon designs generally require exceptionally powerful magnets which make them costly to manufacture. Ribbons have a very low resistance that most amplifiers cannot drive directly. As a result, a step down transformer is typically used to increase the current through the ribbon. The amplifier "sees" a load that is the ribbon's resistance times the transformer turns ratio squared. The transformer must be carefully designed so that its frequency response and parasitic losses do not degrade the sound, further increasing cost and complication relative to conventional designs.

Planar magnetic speakers (having printed or embedded conductors on a flat diaphragm) are sometimes described as "ribbons", but are not truly ribbon speakers. The term planar is generally reserved for speakers which have roughly rectangular shaped flat surfaces that radiate in a bipolar (i.e., front and back) manner. Planar magnetic speakers consist of a flexible membrane with a voice coil printed or mounted on it. The current flowing through the coil interacts with the magnetic field of carefully placed magnets on either side of the diaphragm, causing the membrane to vibrate more or less uniformly and without much bending or wrinkling. The driving force covers a large percentage of the membrane surface and reduces resonance problems inherent in coil-driven flat diaphragms.

Bending wave loudspeakers

Bending wave transducers use a diaphragm that is intentionally flexible. The rigidity of the material increases from the center to the outside. Short wavelengths radiate primarily from the inner area, while longer waves reach the edge of the speaker. To prevent reflections from the outside back into the center, long waves are absorbed by a surrounding damper. Such transducers can cover a wide frequency range (80 Hz to 35,000 Hz) and have been promoted as being close to an ideal point sound source. This uncommon approach is currently being taken by only two manufacturers, in very different arrangements.

Flat panel loudspeakers

There have been many attempts to reduce the size of speaker systems, or alternatively to make them less obvious. One such attempt was the development of voice coils mounted to flat panels to act as sound sources. These can then be made in a neutral color and hung on walls where they will be less noticeable than many speakers, or can be deliberately painted with patterns in which case they can function decoratively. There are two related problems with flat panel techniques: first, a flat panel is necessarily more flexible than a cone shape in the same material, and therefore will move as a single unit even less, and second, resonances in the panel are difficult to control, leading to considerable distortions. Some progress has been made using such lightweight, rigid, materials as Styrofoam, and there have been several flat panel systems commercially produced in recent years.

Distributed mode loudspeakers

A newer implementation of the flat panel speaker system involves an intentionally flexible panel and an "exciter", mounted off-center in a location such that it excites the panel to vibrate, but with minimal resonances. Speakers using such techniques can reproduce sound with a wide directivity pattern (paradoxically somewhat like a point source) and have been used in some computer speaker designs and bookshelf loudspeakers.

Heil air motion transducers

Dr. Oskar Heil invented the air motion transducer in the 1960s. In this approach, a pleated diaphragm is mounted in a magnetic field and forced to close and open under control of a music signal. Air is forced from between the pleats in accordance with the imposed signal, generating sound. The drivers are less fragile than ribbons and considerably more efficient (and able to produce higher absolute output levels) than ribbon, electrostatic, or planar magnetic tweeter designs.

ESS, a California manufacturer, licensed the design, employed Dr. Heil, and produced a range of speaker systems using his tweeters during the 1970s and 1980s. Radio Shack, a large US retail store chain, also sold speaker systems using such tweeters for a time. At present, there are two manufacturers of these drivers, both in Germany, one of which produces a range of high end professional speakers using tweeters and midrange drivers based on the technology.

Plasma arc speakers

Plasma arc loudspeakers use electrical plasma as a radiating element. Since plasma has minimal mass, but is charged and therefore can be manipulated by an electric field, the result is a very linear output at frequencies far higher than the audible range. Problems of maintenance and reliability for this approach tend to make it unsuitable for mass market use. In 1978 Dr. Alan Hill of the Los Alamos National Laboratory designed the Hill Plasmatronics, an \$8000 tweeter whose plasma was generated from helium gas. This avoided the ozone and nitrous oxide produced by RF decomposition of air in an earlier generation of plasma tweeters made by the pioneering DuKane Corporation, who produced the Ionovac (marketed as the Ionofane in the UK) during the 1950s. Currently, there remain a few manufacturers in Germany, and a do it yourself design has been published.

A less expensive variation on this theme is the use of a flame for the driver, as flames contain ionized (electrically charged) gases.

Digital speakers

Digital speakers have been the subject of experiments by Bell Labs as far back as the 1920s. The design is simple; each bit to full amplitude; a value of "0" causes it to be completely shut off.

There are two problems with this design which have led to it being abandoned as impractical for the present. First, for a reasonable number of bits (required for adequate sound reproduction quality), the size of the system becomes very large. Secondly, due to analog digital conversion, the effect of aliasing is unavoidable, so that the audio output is "reflected" at equal amplitude in the frequency domain, on the other side of the sampling frequency, causing an unacceptably high level of ultrasonics to accompany the desired output.

The term "digital" or "digital-ready" is often used for marketing purposes on speakers or headphones, but these systems are not digital in the sense described above. Rather, this is a somewhat deceptive marketing tactic, in which the manufacturer is trying to capitalize on the popularity of digital sound recordings and equipment.