Historical Perspectives And Technology Overview Of Loudspeakers For Sound Reinforcement

412 J. Audio Eng. Soc., Vol. 52, No. 4, 2004 April

INTRODUCTIONHorns and direct-radiating systemshave provided the basis for sound rein-forcement for more than a century.Both technologies have benefited fromengineering and manufacturing im-provements as well as demands forpushing the performance envelope.Trends of fashion have often inter-sected with engineering development,economics, and even marketplaceopportunism. A survey tutorial of thesignificant developments in transduc-tion, signal transmission, and systemsynthesis is presented here and dis-cussed in historical perspective.

We begin with an overview of soundreinforcement and the technologiesthat have supported it. This is followedby more detailed technical discussionsof both direct radiating and horn sys-tems, leading to a discussion of mod-ern loudspeaker array techniques. Thepresentation ends with a comprehen-sive bibliography.

HISTORICAL PERSPECTIVESIn the early days of transducer develop-ment, horn systems offered the onlymeans possible for achieving suitable

levels for speech reinforcement. Earlypower amplifiers were limited to about10 watts output capability, and horn-driver efficiencies on the order of 20%to 30% were necessary to reach thedesired sound pressure levels.

The direct field level referred to adistance of one meter produced by oneacoustic watt radiated omnidirection-ally from a point source in free space is109 dB LP [1, p. 314]. If we use a 10-watt amplifier with a horn–driver com-bination that is 30% efficient, we canproduce three acoustical watts. If thehorn has a directivity index (DI) onaxis of, say, 10 dB, then we canincrease that level to:

Level (re 1 meter) = 109 + 10 log (3) + DI = 124 dB LP

At a more realistic listening distanceof 10 meters, the level would be, byinverse square relationship, 20 dBlower, or 104 dB. If wider coverage isneeded, more horns can be added andsplayed as required.

There is little documentation of earlyexamples of general speech reinforce-ment, and that art progressed fairlyslowly [9]. The first example of large-scale sound reinforcement occurred onChristmas Eve, 1915, when E. S. Prid-ham, cofounder of the Magnavox com-

pany, played Christmas carols for anaudience of 50,000 using Pridham-Jensen rocking armature transducersconnected to phonograph horns [12].Western Electric set up a publicaddress system capable of addressing12,000 persons through 18 loudspeak-ers in 1916 [24, p. 24].

The first distributed system wasemployed in 1919; 113 balanced arma-ture driving units mounted on longhorns were strung along New YorkCity’s Park Avenue “Victory Way” asa part of a Victory Bond sale [24, p. 25][2], as shown in Fig. 1. The first suc-cessful indoor use of a public addresssystem was at the 1920 ChicagoRepublican Convention, which alsoemployed the first central cluster con-figuration [24, p. 25], as shown in Fig.2. On March 4, 1921, President Hard-ing’s inauguration was amplified [24,p. 24], and on November 11, 1921,President Harding’s address in Arling-ton, Virginia, was transmitted by West-ern Electric, using Edgerton’s 1918design of four-air-gap balanced-arma-ture units. For the first time 150,000people, at Madison Square Garden inNew York, in the adjoining park, and inthe Civic Auditorium in San Francisco,simultaneously listened to a personspeaking [2].

It was the cinema that paved the way

HISTORICALPERSPECTIVES AND

TECHNOLOGY OVERVIEWOF LOUDSPEAKERS

FOR SOUNDREINFORCEMENT*

*Revised and expanded from a presenta-tion at the Institute of Acoustics 12thAnnual Weekend Conference, Winder-mere, England, October 25-27, 1996.

J. Eargle1,2, Honorary Member, and M. Gander1, AES Fellow

(1) JBL Professional, Northridge, California, U. S. A.(2) JME Consulting Corporation, Los Angeles, California, U. S. A.

J. Audio Eng. Soc., Vol. 52, No. 4, 2004 April 413

for rapid development of professionalsound reproduction. Talking picturesrequired more than speech intelligibil-ity, however. The single horns of theday, as shown in Fig. 3, were limitedin response to the range from about125 Hz to 3 kHz. While this was ade-quate for speech, music requiredgreater bandwidth, especially at lowerfrequencies [7].

The first widely accepted cinema sys-tem used a two-way approach. A multi-cellular high-frequency horn with acompression driver was coupled to acone-driven, folded low-frequency hornassembly [3] as shown in Fig. 4. Itshigh level of performance and approvalby the Academy of Motion Picture Artsand Sciences, in the form of a technicalachievement award, led to its accep-tance as an industry standard [11].

The next step in low frequency (LF)response was to employ multiple large-diameter direct radiators in some sort of“directional baffle” that could both loadthe drivers for increased efficiency andgive them added forward directionality[20]. The best LF direct-radiating trans-ducers of the day were about 10 dBlower in efficiency than horn systems,but their use was mandated due to thesize and complexity of traditional basshorns. When employed in multiples,they could provide sufficient level andcoverage in large theaters. In time, thevarious directional baffles evolved intothe familiar front-loaded quasi-hornsthat became universally identified withthe cinema [16], as shown in Fig. 5.Field coil energized transducers alsogave way to permanent magnets fol-

lowing WWII [15]. The LF transducers

chosen for this appli-cation had relativelysmall moving massesand high (Bl)2/REratios. This enabledthem to efficientlyhandle the acousticalload transformed bythe horn and maintaingood response up toabout 400 Hz, at whichpoint the high fre-quency (HF) horn tookover. The HF hornitself was undergoingmodifications aimed atimproving its direc-tional response. RCAfavored the radialhorn, while Bell Labo-ratories favored themulticellular device[27]. Bell Laboratorieslater pioneered the useof the acoustical lensin similar applications [8, 14].

By the mid-1940s, HF horns hadestablished their primacy in the fre-quency range above 500 Hz, whilehybrid LF horns, which relied on reflexloading of cones below about 100 Hz,dominated the range below 500 Hz.These families of components formedthe basis of postwar sound reinforce-ment activities and maintained thatposition for nearly three decades.

By the early 1970s available ampli-fier power, which had been steadily ris-ing through the introduction of con-

sumer high fidelity during the mid-1950s and 1960s, reached the pointwhere beneficial tradeoffs could bemade among the three “eternal” loud-speaker variables of size, efficiency,and LF bandwidth extension. As earlyas the mid-1950s, consumers began toenjoy relatively small sealed systemsthat provided substantial LF output [25,26]. Additional analysis and synthesisof ported enclosure design by Thieleand Small [23], following the earlierwork of Locanthi [17], Novak [19], andBenson [31], led to the general

Fig. 1. First use of a distributed sound system,New York, Park Avenue (1919). Note trumpethorns in upper left hung above crowd aimingdownward. (Photo from Lester CowanRecording Sound for Motion Pictures, McGrawHill, New York, 1931.)

Fig. 3. Western Electric“Roxy” horn type 12Awith 555W dynamicdriver. (Photo, Cowan, p. 329.)

Fig. 2. First central array sound system, 1920Chicago Republican Convention. (Photofrom Frederick Thrasher, ed., Okay forSound … How the Screen Found its Voice,Duell, Sloan, and Pearce, New York, 1946.)

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Fig.4. Shearer MGM hornsystem, which won theAcademy of Motion PictureArts and Sciences scientificaward in 1936. Contributors tothis program included DouglasShearer, John Hilliard, JamesB. Lansing, Harry Olson, JohnVolkmann, and William Snow.(Photo from Research Councilof AMPAS, Motion PictureSound Engineering, VanNostrand, New York, 1938.)

Fig.5. The Hilliard andLansing designed Altec-Lansing A-4 “Voice ofthe Theatre” system,1945. Utilizing a shortLF straight exponentialhorn with an acousticalpath length equal to thatof the HF horn to avoiddelay between the LFand HF sections.(Photo, Altec-Lansing)


adoption of ported enclosures as a LFbuilding block in professional soundsystem design.

Through the use of Thiele-Smalldriver parameters, LF systems could berationally designed for best responseand enclosure size. Gone were the daysof cutting and trying, and also gonewere the days of poorly designed LFtransducers. Thiele-Small analysispointed to the need for identifying theright cone mass, resonance, excursioncapability, Bl product, enclosure vol-ume, and tuning to achieve a targetedperformance goal.

During the 1970s and early 1980sported LF systems became the basis formost sound reinforcement LF design.For many music and speech applica-tions the horn HF crossover frequencywas raised from 500 Hz to 800 Hz andhigher, with cone drivers filling in themidrange [18]. This change from thetraditional two-way philosophy wasbrought on by modern programrequirements for generating increasedlevel. Higher power handling transduc-ers were substituted in the LF horns,but these new drivers forced the HFpower bandwidth of the horn down-ward. With the crossover frequencyraised to improve HF reliability, theresult was uniform on-axis response,but grossly uneven power response [6].

By the mid-1970s ported LF systemswere poised to take a commanding leadin the design of speech reinforcementsystems. Fig. 6 shows examples of theolder approach and the newer one. Thesystem shown in Fig. 6A makes use of

the previous generation of hardware(theater-type LF hybrid horns and HFmulticellular horns), while the systemshown in Fig. 6B makes use of portedLF systems and modern HF horn hard-ware. In terms of LF response andpower handling, both systems have sixLF drivers. With horn loading, the out-put capability of the system shown inFig. 6A will be higher in the 100 to 200Hz range than the system shown in Fig.6B. However, the LF system in Fig. 6Bis smaller and has been designed for

flat power bandwidth over its operatingspectrum in the range from 40 to 400Hz. It uses high-powered drivers andcan accommodate approximately fourtimes the amplifier power as the systemFig. 6A, but by the mid-1970s the costper watt of amplifier power had dimin-ished significantly.

For large-scale music reinforcementthere were other considerations. LFhorn systems had developed along linesunique to the music industry, sincefairly high mid-bass directivity was aprime concern. The older radial hornswere likewise favored for their direc-tionality, which increased at HF. Typi-cal usage is shown in Fig. 7.

The conservative motion pictureindustry continued with two-way solu-tions but eventually traded in its hybridbass horns for standard ported systemsand retired the old multicellular HFhorns of the 1930s [5]. The concept offlat power response in system designstated that not only uniform directarrival sound was important; reflectedsound (proportional to the total radiatedpower of the system) should also beuniform. This goal could be more eas-ily met with ported LF systems, alongwith uniform coverage HF horns.Hilliard [10] was well ahead of his timein bringing this concept to the attention

HISTORICAL PERSPECTIVES AND TECHNOLOGY OVERVIEWOF LOUDSPEAKERS FOR SOUND REINFORCEMENT

Fig. 6. Large systems for speech reproduction. Design using pre-1970 components,multicellular exponential horns with ported LF horns (A, J. Audio Eng. Soc., vol. 20,pp. 571); design using post-1970 components, constant directivity HF horns andported LF direct radiators (B, courtesy KMK Ltd.)

Fig. 7. Typical early-1970s horn-loaded system using ported LF horns, 90° radialhorns with large-format drivers, and 90° radial horns with small-format drivers foraugmenting the upper frequencies. A narrow coverage horn with a large formatdriver is used for long-throw coverage. (Photo, JBL)

A B

of the film industry, but his attempts atcommercialization failed.

The well-engineered ported LF sys-tem of the 1970s established its domi-nance at the low end of the frequencyspectrum. The combination of low-costpower amplification, low-distortion,high-power LF transducer development,and enclosure simplicity has given theported system an advantage at low fre-quencies that all but the very largesthorn systems could never match.

Keele [13] made an instructive com-parison between LF horns and directradiators, pointing out the virtual paritybetween them. For the same LF cutoff,the horn will have highest efficiency, alarge complex enclosure, and willrequire a small number of drive units.By comparison, a direct radiator multi-ple-driver vented box will have moder-ate efficiency, a small, relatively simpleenclosure, a large number of drivers,and higher power handling capability(because of the multiple drivers). InKeele’s words, “This roughly meansthat if one has a lot of space, not muchmoney to spend on drivers and ampli-fiers, and lots of cheap labor—build ahorn system. If labor is not cheap, andyou don’t have much space, and if youcan afford drivers and amplifierpower—build a direct radiator system.”In essence, the costs of labor and lum-ber had far outstripped those of driversand watts.

Through the late 1980s and 1990s,however, the professional sound indus-try saw a return to horn systems forcovering the range down to about 300Hz, especially for large-scale speechreinforcement. The reasons have to donot with efficiency per se but ratherdirectional control. These new systemshave taken the form of large formatcompression drivers, or cone transduc-ers designed for horn–driver applica-tions, and large horns optimized for therange from 100 to 300 Hz to 1 to 3kHz, with ported LF systems handlingthe range below. Rapid flare HF hornsare now employed, and their distortioncharacteristics, level for level, may beup to 10 dB lower than the older hard-ware [4]. New digital methods of signalcontrol have made multiway systemsmore acceptable than they were in thedays of passive dividing networks,through time alignment and steepcrossover slopes.

As we continue our discussion ofdirect radiators and horns, we willpresent a detailed analysis of theengineering fundamentals of bothmethods of transduction. This dis-cussion will cover basic operatingprinciples, directional control, anddistortion mechanisms associatedwith each method. We will followthis with a discussion of array con-cepts encompassing both kinds oftransducers.

DIRECT RADIATORS

Early Development

Ernst Werner Siemens’ 1874 U.S.Patent 149,797 was prophetic; hedescribed in detail a radial magnet struc-ture in which a coil of wire was placed.The coil was connected with a radiatingsurface that Siemens described as thefrustum of a cone. He had literallyinvented the cone loudspeaker—withnothing to play over it except dc tran-


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sients and other telegraphic signals. Heremarked at the time that it could beused “for moving visible and audiblesignals.”

Half a century later in 1925, Riceand Kellogg of General Electricdescribed “a new hornless loud-speaker” that resembled that ofSiemens—a similarity that promptedRice to say: “The ancients have stolenour inventions!” [37].

The key difference in the Rice andKellogg design was the adjustment ofmechanical parameters so that the fun-damental resonance of the moving sys-tem took place at a lower frequencythan that at which the cone’s radiationimpedance had become uniform. Overthis range, the motion of the cone was

mass controlled, and the cone lookedinto a rising radiation impedance. Thisin effect provided a significant fre-quency region of flat power responsefor the design. Details of this are shownin Fig. 8.

Region of Flat Power Response

Fig. 8A shows a section view of thecone loudspeaker with all electrical,mechanical, and acoustical parame-ters labeled. The equivalent circuit isshown in Fig. 8B; here the mechani-cal and acoustical parameters areshown in the mobility analogy.

When mounted in a large baffle,the moving system looks into a com-plex acoustical load as shown in Fig.8C. The resistive component rises

with frequency to approximately ka = 2,above which point it is essentially con-stant (ka is equal to cone circumferencedivided by wavelength, or, 2πa/λ). Sys-tem response is shown in Fig. 8D, andsystem efficiency over the so-called pis-ton band is given [49] as:


Fig. 8. The cone driver. Section view (A); equivalent circuit (B); radiation impedance of a cone in a large wall (C); powerresponse of system (D).

Fig. 9. Illustration of mutual coupling of LFdrivers.


η = [ρ0(Bl)2SD2/RE]/2πcMMS

2

(1)

where ρ0 is the density of air(kg/m3), (Bl)2/RE is the electromechani-cal coupling coefficient (N2/W), c is thespeed of sound (m/s), SD

2 is the area ofthe cone, and MMS is the mass of themoving system (kg).

The larger the coupling coefficient,the lower the resonant Q at f0 and thehigher the piston band efficiency willbe. Likewise, the higher the Q at f0, thelower the piston band efficiency.Depending on the application, bothkinds of response may be useful to thedesign engineer.

It can easily be seen that, for maxi-mum extension of the piston band, thelower f0 must be, and the lower the sys-tem efficiency will be. The efficiency-bandwidth product, for a given conediameter and coupling coefficient, thustends to be constant over a relativelylarge range.

Mutual Coupling

In the LF range over which theirresponse is essentially omnidirectional(ka = 0.2 or lower), a doubling ofclosely spaced driving units will resultin an increase in acoustical output of 3dB for a fixed input power referencelevel [39, 48, 52, 53]. The progressionin efficiency increase is shown in Fig. 9for one, two, and four LF transducers,respectively. In each case, the electricalpower delivered to each ensemble ofdrivers is constant. Assume that the ref-erence power fed to the single driver isone watt; then for the set of twodrivers, the power per driver is 0.5watt, and for the set of four, the powerper driver is 0.25 watt.

One may imagine that, in the two-driver case with both drivers wired inparallel, those two drivers have, in asense, coalesced into a new driver—one with twice the cone area, twice themoving mass, and half the value of RE.Thus, by Equation 1, the efficiency willhave doubled. For the case where thetwo drivers are wired in series, theanalysis goes as follows: The newdriver has twice the cone area, twicethe moving mass, four times the (Bl)2

product, and twice the value of RE.Again, by Equation 1, there will be adoubling of efficiency.

Mutual coupling often appears to

give something for nothing, but thereare clear limits to its effectiveness.With each doubling of cone area, theka = 0.2 upper response frequencycorner moves downward approxi-mately by a factor of 0.7, since this isthe reciprocal of the value by whichthe effective cone radius hasincreased. As the process of addingdrivers is continued, in the limit it canbe shown that the efficiency of anensemble of direct radiators cannotexceed a value of 25% [38]. Becauseof these constraints, the approxima-

tion of power doubling for each two-times increase in drivers is accurateonly at very low frequencies and onlyif the efficiency values are low tobegin with.

Distortion

Mechanical Effects

The primary distortion mechanism incone transducers is due to mechanicalstress–strain limits. Small identified apractical mechanical displacementlimit from rest position in the axial ➥


Fig. 10. The ported system. Section view (A); equivalent circuit (B); port and conecontributions to total output (C).

Fig. 11. Power compression in a 380-mm-diameter LF driver. Curves for 1 and 100watts input are superimposed and displaced by 20 dB. (Data courtesy JBL.)


direction as the excursion at which10% harmonic distortion is reached.This limit is known as xMAX. While aloudspeaker may be operated beyondthis displacement limit, at least on amomentary basis, the 10% linearitydeparture is generally recognized as asafe limit for good engineering prac-tice. Since cone displacement tends toincrease as the inverse square of frequency down to the f0 region, it iseasy to see how the xMAX limitation may easily be encountered in normaloperation.

The onset of the cone displacementlimit at low frequencies can be allevi-ated by using ported LF enclosures. Thenature of this design is shown in Fig.10. A section view of a ported system isshown in Fig. 10A, and the equivalentcircuit is shown in Fig. 10B. The designrelies on controlling the Helmholtz res-onance of the enclosure to provide an“assisted output,” via the port, that min-imizes cone motion (and thus distor-tion) at low frequencies, as shown inFig. 10C. Thiele–Small parameters areuniversally used today to synthesizethese systems.

Virtually all commercial PC designprograms for ported systems will indi-cate transducer displacement limits sothat the design engineer will always beaware of whether a system, while stillon the drawing board, will go into dis-placement overload before it reaches itsthermal limit. Good engineering prac-tice demands that a ported systemremain thermally limited down to f0.

Below that frequency the electricaldrive signal is generally rolled off toavoid subsonic over-excursions of thecone.

A secondary mechanical distortioneffect will be seen when the voice coildriver is far enough out of the gap sothat there is a momentary loss of Blproduct at peak excursion values. Theeffect is asymmetrical and gives riseto both even and odd distortion components.

Port Turbulence in Vented Systems

In vented systems the ultimate output atlow frequencies may be limited not byconsiderations of maximum coneexcursion, but rather by air turbulencein the enclosure port when the systemis operating at the tuning frequency[34]. A tentative limit here is to restrictthe port air particle velocity so that itspeak value does not exceed about 5%of the speed of sound. In general, portsshould be designed with contouredboundaries to minimize turbulence andthe noise and losses it often produces.Significant studies of port turbulenceand its minimization through taperingthe port tube’s cross-section area havebeen carried out by Vanderkooy [50,51], Salvatti and Button [45], andRoozen et al. [44].

Thermal Effects

Modern cone transducers intended forheavy-duty professional applicationstake advantage of newer materials andadhesives to make them more immune

to thermal failure. Thermal failure isreached when the power dissipated inthe voice coil as heat cannot beremoved at a sufficient rate to maintaina safe operating temperature. A greatdeal of loudspeaker development hasgone into designing structures andmoving elements that are not onlyresistant to heat but aid in its removalfrom the transducer [32, 36].

For most applications in sound rein-forcement, the effects of loudspeakerheating are more likely to result incomponent failure than those associ-ated with displacement limitations.Dynamic linearity or power compres-sion are terms used to describe theeffects of heating on audio performance[34]. The data shown in Fig. 11 pre-sents the frequency response of a single380-mm LF transducer with inputs of 1watt and 100 watts. In each case thechart recording of the levels has beenadjusted to account for the 20-dB offsetbetween the curves. In this manner theresponse differences can be clearlyseen. If there were no dynamic com-pression, the two curves would lie oneon top of the other. As it is, the pro-gressive heating results in an increasedvalue of RE, which lowers the effi-ciency. In extreme cases, the increasein RE can result in changes in the LFalignment, which may be clearly audi-ble as such.

Another way of viewing power com-pression is shown in Fig. 12. Here, sev-eral 380-mm transducers have beendriven with a wide-band signal, and the


Fig. 13. Demagnetization plots for threeloudspeaker magnetic materials. Alnico V (1);ferrite (2); neodymium-iron-boron type (3).

Fig. 12. Power compression. Output level versus time for three LF driverdesigns. (Data courtesy JBL.)


effect of temperature rise has been plot-ted against time. For each transducerdesign, the reduction in output leveleventually reaches an asymptotic valuethat depends on how effectively heatcan be removed from the voice coil andmagnet structure. In general, largerdiameter voice coils remove heat moreefficiently than smaller ones; addi-tional measures, such as increasingconvection cooling and increasingradiation to outside mechanical partsof the driver, can be helpful as well.

As the temperature of a ferrite mag-netic structure increases, both flux den-sity and efficiency are reduced. Theeffect is similar to the resistanceincrease caused by voice coil heating.If the temperature rise in the ferritematerial has been moderate, normalperformance may be restored uponcooling.

Distortion in Transducer MagneticSystems

Many aspects of the direct radiator’smagnetic system can affect the distor-

tion performance of atransducer [33]. Theprimary effect is thevariation in the mag-netic operating pointthat comes as a resultof signal current inthe voice coil as itmodulates the mag-netic structure’s oper-ating point. This hap-

pens to some degree in all designs,but the effect on acoustical perfor-mance depends on the degree of fluxmodulation of the static magneticfield. The general result of flux modu-lation is to increase the level of sin-gle-ended distortion, which is largelysecond harmonic.

Fig. 13 shows the demagnetizationcurves for three magnetic materials,Alnico V, ferrite, and neodymium-based systems. With the Alnico V sys-tem, the flux curve has a moderateslope in the operating region, which isnear the intersection with the B-axis; atthat position there is little tendency forflux modulation to be a problem. How-ever, a strong input signal can result inpermanent demagnetization if the oper-ating point is forced downward on thesteep portion of the curve to the left ofthe normal operating point.

With the ferrite magnet there is a cer-tain amount of flux modulation due tothe uniform slope of the curve. Withthe high-energy neodymium materials,the demagnetization curve is normally

located high enough in the secondquadrant of the B-H graph that themagnetic circuit is very likely to beoperating at or near saturation. In thiscase the degree of flux modulation willbe minimal.

Fig. 14 shows how a typical problemwas solved. The distortion data shown inFig. 14A is that of an older 300-mm-diameter LF transducer operating withan Alnico V magnet structure. Keepingthe same moving system but changing toa typical ferrite magnet structure yieldsthe data shown in Fig. 14B. Note thesignificant increase in mid-frequencydistortion.

The data in Fig. 14C shows theeffect of a ferrite magnet system out-fitted with undercut polepiece geome-try and a large, low-resistance alu-minum flux shorting ring placed at thebase of the polepiece. The significantreduction in second-harmonic distor-tion results from the setting up of aninduction current in the shorting ringthat counteracts the normal tendencyof voice coil current to shift the mag-netic operating point.

Other magnetic distortion effectsinclude: the generation of eddy cur-rents in local iron structures, whichresults in an increase in third-har-monic distortion and I2R losses; andinductance modulation of the voicecoil, due the varying amount ironinstantaneously surrounded by thevoice coil, which results in increasedsecond-harmonic distortion. ➥


Fig. 14. Performance with same moving system in threedifferent motor assemblies. Alnico V (A); traditional ferrite(B); ferrite with undercut polepiece and aluminumshorting ring (C). (Data courtesy JBL.)

Fig. 15. The Altec-Lansing Duocone. Section view of cone (A);equivalent circuit (B).


Thermodynamic and FM DistortionEffects

Thermodynamic distortion, or air over-load, is present in relatively smallquantities in direct radiator systems andmay be disregarded in the normal oper-ation of cones and domes.

Frequency modulation (FM) com-ponents are more likely to occur,especially at low to mid frequencies,where high cone excursions at lowerfrequencies may modulate higher fre-quencies as the cone’s velocity attainsa significant percentage of the speedof sound. The effect is quite notice-able in single-cone systems but isminimized in multiway systems.Beers and Belar [30] and Klipsch [40]were among the first to describe thisphenomenon in detail.

Another aspect of thermodynamicdistortion present in sealed direct radia-tor systems is due to the nonlinearity ofthe enclosed air spring. In general, ifthe maximum instantaneous change inan enclosed volume can be limited toabout 0.5%, the effect of the nonlinear-ity can be ignored [34]. The type andamount of enclosure damping materialin a sealed enclosure has the additionaleffect of increasing the actual enclosedvolume. The work of Leach [41] is sig-nificant in this area.

The Decoupled Cone

Over the years loudspeaker designershave observed that, at high frequen-cies, the cone ceases to move as a sin-gle unit, but rather breaks up into morecomplex motions. These result in aneffective lighter moving mass at highfrequencies, extending the HFresponse of the system. This was firstcommercialized by the Altec Duoconeloudspeaker [28]. Fig. 15A shows asection view of the cone profile used inthe Duocone loudspeaker, and a mobil-ity mechanical circuit is shown in Fig.15B. The modern soft-dome HF unitexploits this effect more predictablythrough high damping of the movingsystem. Finite element analysis (FEA)provides a means of analyzing in detailthe directionality of loudspeaker conesand domes, taking into account multi-ple breakup effects. Many low-costdrivers intended for ceiling installationin distributed systems make good useof decoupling for attaining wider cov-erage at HF.


Fig. 16. Polar plots for a piston mounted in a wall. (Data after Beranek, 1954.)

Fig. 17. Polar plots for a piston mounted at the end of a long tube. (Data afterBeranek, 1954.)


In recent years, the notion of decou-pling has resurfaced with the dis-tributed mode loudspeaker (DML).Here, a panel of light, stiff, and fairlylossless material is driven by a mass-loaded transducer. When operated inthe frequency range over which thepanel exhibits a dense array of higher-order two-dimensional bending modes,the resulting power output and disper-sion are uniform over a frequencyrange defined by:

Upper frequency limit, fmax = RP/2πMc

(2A)

Lower frequency limit, fmin = RP/2πMm

(2B)where RP is the radiation impedance ofthe panel and Mc and Mm are, respec-tively, the masses of the driven systemand the magnetic actuator.

Due to its random, diffuse nature, theresponse of a typical DML paneldeparts from that of a typical dynamicdriver in several regards: the modulusof electrical impedance is quite uniformover the normal system passband; thesolid-angle radiation pattern is quiteuniform over the normal system pass-band; the impulse response for a typicalpanel is fairly long, upwards of 25msec, however it is free of ringing atany specific frequency; commensuratewith the long impulse train, the ampli-tude response will exhibit, in all direc-tions of radiation, many fine responsedips on the order of 6 dB [29].

With its unique combination ofacoustical properties and relatively lowcost, the DML offers great promise inthe area of distributed system design.

Directional Properties of DirectRadiators

Assuming that the moving systemshave only a single degree of freedom,the polar data in Fig. 16 shows thetheoretical directionality of a pistonmounted in a large baffle as a func-tion of ka. The on-axis directivityindex (DI) of each directional patternis also shown in the figure [1, 42].Similar data is shown in Fig. 17 for apiston mounted at the end of a longtube. These two conditions simulatenormal 2π and 4π mounting condi-tions for loudspeakers. For many rou-tine system design applications, thisdata is sufficiently accurate.

Gradient Loudspeakers

The simplest gradient loudspeaker is anunbaffled cone transducer operating asa dipole. The natural directionalresponse for a dipole is a cosine pattern,or a “figure-eight” [43]. Dipoles arevery inefficient and have not beenwidely used in sound reinforcementapplications; however, there are certainapplications where their specific radia-tion pattern could be very useful. Dur-ing the early 1970s, Altec produced amodified gradient loudspeaker in which

one side of the dipole operated in serieswith an acoustical delay path. The delayproduced a hypercardioid pattern inmuch the same manner as a typicaldynamic microphone does.

Fig. 18A shows a section viewthrough the hypercardioid loudspeaker.The output from the rear of the trans-ducer is sent through a constant delay,provided by the path length and theresistive elements in that path. The resultof the delay is that, at 135°, output fromfront and back of the transducer will ➥


Fig. 18. The Altec Extenda-Voice gradient loudspeaker system. Section view (A);physical circuit (B); nominal off-axis response curves (C).

Fig. 19. Radiation resistance for conical, exponential, and hyperbolic horns.


effectively cancel. For useful outputfrom the front of the transducer, the sig-nal fed to the system must be equalizedwith a 6-dB-per-octave rise for eachhalving of frequency to compensate forthe diminishing gradient. The equivalentphysical circuit of the loudspeaker isshown in Fig. 18B, and off-axis polardata is shown in Fig. 18C. A systemsuch as this would normally be used forspeech purposes in highly reverberantspaces where the loudspeaker’s DI of 6dB at LF would work to its advantage.Vertical stacks of the device canincrease total output capability as well asincrease the on-axis DI.

HORNS AND COMPRESSIONDRIVERS

Early Development

Many engineers and physicists havecontributed to horn and compressiondriver development over the years.Early versions of the horn were used bymany tinkerers who basically did notunderstand how the horn worked—theyknew only that somehow the horn

increased acoustical output [58]. Thefirst example of thorough engineeringwas carried out by Bell Telephone Lab-oratories [83], working from the modelof horn impedance described by Web-ster [81]. Significant later developmentwas carried out by Klipsch [66], whodesigned a remarkably compact basshorn, and Salmon [76, 77], whodescribed the impedance characteristicsof several important horn flares, includ-ing the hyperbolic, or Hypex, profile[68]. Geddes [55] sought to positionWebster’s model as a special casewithin a broader context.

Fig. 19 shows the real part of theradiation impedance for hyperbolic,exponential, and conical horn profiles.Here, only the exponential and hyper-bolic profiles provide useful output atlow frequencies. In our discussion wewill restrict ourselves to the exponen-tial profile, since it has found almostuniversal application over the years.

Fig. 20A shows the real and imagi-nary parts of throat impedance for along exponential horn. For a horn ofpractical length, we might observe

impedance components such as thoseshown in Fig. 20B. The slight peaksand dips in response are due to reflec-tions from the mouth of the horn backto the throat. There is an optimummouth size for a horn of specific cutofffrequency to minimize reflected wavesfrom the horn’s mouth [63].

Theoretical Modeling

The compression driver is designed tomatch the impedance of the electrome-chanical system to the throat of the horn,and the radiation impedance, reflected tothe electrical side of the circuit, is:

RET = [ST(Bl)2]/ρ0cSD2 (3)

where ST is the area of the driver throatand SD is the area of the driverdiaphragm. The phasing plug in thedriver is the means by which the ratioof the two areas is adjusted for best HFresponse.

When the driver is attached to thehorn, the efficiency in the range wherethe horn’s radiation impedance isessentially resistive is:

η = (2RERET)/(RE + RET)2 (4)

where RE is the voice coil resistance.When the voice coil resistance is madeequal to the radiation resistance, theefficiency of the driver over its normalpass-band will in theory be 50%. Inpractice, efficiencies of the order of30% can be achieved in the mid-range—and this is only about 2 dB below the theoretical maximum.

Region of Flat Power Output

The data of Fig. 21 shows the normalpower response for a compressiondriver/horn combination when thehorn’s throat impedance is resistive.The LF limit is due to the primary reso-nance of the driver; for a typical HFcompression driver this may be in therange of 500 Hz.

The principal midband rolloff com-mences at what is called the mass breakpoint, fHM, given by:

fHM = (Bl)2/πREMMS (5)

where MMS is the mass of the movingsystem. For most HF compressiondrivers the mass breakpoint takes placein the range of 2500 to 4500 Hz. It is


Fig. 20. Real and imaginary components of horn impedance for a long exponentialhorn (A) and a short exponential horn (B).

Fig. 21. Plane wave tube measurements of a compression driver showingamplitude response and impedance.


considered a fundamental limit in HFdrivers, inasmuch as today’s magneticflux densities are normally maximizedin the range of 2 tesla, and low-movingmass is limited by metals such as tita-nium and beryllium that are not likelyto be replaced in the near future.

Two additional inflection points areoften seen in the HF driver responsecurve: one is due to the volume of thefront air chamber in the driver, thespace between the diaphragm and thephasing plug. Its effect on responsemay be seen as low as 8 kHz in somedrivers. Voice coil inductance maycause an additional HF rolloff at highfrequencies. This may be compensatedfor through the use of a silver or cop-per shorting ring plated on the pole-piece in the region of the voice coil.(See Distortion in Transducer Mag-netic Systems, page 419.)

Cone-Driven Horns

From the earliest days, cone transduc-ers have been employed as horn drivers[71, 72]. The theoretical principles thatgovern the design parameters for horndrivers apply equally to the adaptationof cone drivers as well as to purpose-designed compression drivers. Keele[60] presented a straightforward anduseful analysis of LF horn design usingboth Thiele–Small and traditional elec-tromechanical parameters. Leach [69]summarized Keele’s work, togetherwith Small’s approach to the subject[78], and addressed other factors suchas reactance annulling.

Reactance Annulling

In some compression driver designs, amechanical stiffness in the form of asmall air chamber is located behind thedriver’s diaphragm. The mechanicalreactance resulting from the stiffnesscancels in part the mass reactance por-tion of the radiation impedance, result-ing in a more resistive impedance in theregion of the cutoff frequency. Theeffect of this is greater acoustic outputin the horn cut-off frequency range fora given drive signal [73, 74].

Reactance annulling is not normallyused in HF compression drivers, but itis used in the design of bass horns, mostnotably in the case of the Klipschorn,where the normal response associatedwith a 47-Hz flare rate is extendeddown to about 40 Hz [66].

DistortionThe dominant cause of distortion incompression driver-horn systems is dueto thermodynamic, or air, overload[75]. This comes as a result ofextremely high pressures that exists atthe horn throat:

LP = 94 + 20 log (WA(ρ0c)/ST)0.5 (6)

where WA is the acoustical power gener-ated and ST is the throat area (m2).

For example, in plane wave propaga-tion, an intensity of one watt per squarecentimeter will produce a sound pres-sure level of 160 dB LP. For levels inthis range, successive pressure peaksare tilted forward as they propagatedown the horn due to the increase in

sound velocity at elevated temperaturesunder adiabatic conditions.

Thuras, Jenkins, and O’Neil [80] andGoldstein and McLachlan [57] ana-lyzed the problem, leading to a simpli-fied equation that gives the percentsecond harmonic distortion in hornsystems:

% 2nd HD = 1.73(f/fC) √IT x 10-2

(7)

where IT is the intensity in watts persquare meter at the horn’s throat, f isthe driving frequency, and fC is the cut-off frequency of the horn.

Fig. 22 presents measurements of thesecond-harmonic distortion producedby two horns of differing flare rates. ➥


Fig. 22. Second-harmonic distortion in two horn systems, using a compressedfundamental. (Data courtesy JBL.)

Fig. 23. Plane wave tube amplitude response of three compression drivers.


The fundamental output in each casewas held constant at a level of 107 dBat a distance of one meter, and the sec-ond-harmonic distortion has beenraised 20 dB for ease in reading. Thescale on the right ordinate indicates thesecond-harmonic distortion in percent-age. The cutoff frequency of the hornused for the data shown in Fig. 22A is70 Hz, while that of the horn used forthe data shown in Fig. 22B is approxi-mately 560 Hz. The average differencein distortion is 8 dB.

A horn with a high cutoff frequencyhas a rapid flare rate and as such maylack good directional control at low fre-quencies. This is a tradeoff that thedesign engineer has to reconcile for avariety of applications. For example,sound-reinforcement applicationsrequire specific pattern control in therange from 300 Hz upward, whilemusic-monitoring applications mayrequire horn pattern control no lowerthan about 800 Hz.

If the exact mechanism for a given

kind of distortion can be defined mathe-matically, a model can be implementedand used to predistort the signal, result-ing in reduced distortion in the system’soutput over a given power operatingrange. Klippel [65] describes some ofthe techniques for accomplishing this.

The Role of SecondaryResonances

As shown earlier in Region of FlatPower Repsonse (page 416), the powerresponse of a horn driver is flat up to itsmass break point, above which theresponse rolls off 6 dB per octave. How-ever, beneficial secondary resonancesmay be used to increase the driver’s out-put above this point [64, 70]. These res-onances generally occur in the surroundsections of the diaphragm and aredecoupled from the diaphragm itself. Asin the case of decoupled resonances incones discussed earlier, the lowering ofmoving mass at higher frequencies canresult in a considerable increase in use-ful HF response. Fig. 23 shows theresponse for three compression drivers,all with 100-mm-diameter diaphragmsand mounted on the same horn. DriverA has an aluminum diaphragm and half-roll surround. The secondary resonanceis about 9 kHz. Response is maintainedfairly flat to that frequency, falling offrapidly above. Driver B has a beryllium


Fig. 24. Directivity of various exponential horns. (Data from Olson, 1957.)

Fig. 25. Beamwidth and directivity data for typical radial horn (A) and slant-plate lens system (B).


diaphragm with a half-roll surround.Note that, due to the greater stiffness andlower mass of the material, the sec-ondary resonance has shifted out toabout 17 kHz. Driver C has an alu-minum diaphragm with distributed sur-round geometry that moves the sec-ondary resonance to beyond 20 kHz,resulting in smooth, extended responsewithin the normal audio band with nopronounced peaks [70].

Directional Response

The basic exponential horn exhibitsdirectional response as shown in Fig. 24. From the earliest days it wasrecognized that directional characteris-tics were a key element of loudspeakerperformance [84]. Over decades ofdevelopment, numerous methods havebeen used to improve directional per-formance at high frequencies for sound

reinforcement applications. For multi-cellular horns, in the early days [83],groups of exponential cells, each about15° wide in each plane, were clusteredtogether to define a specific solid radi-ation angle; this produced excellentresults at mid-frequencies, but therewas pronounced “fingering” of theresponse along the cell boundaries athigher frequencies. For radial horns, inthis application, the horn’s horizontalprofile is conical, with straight, radialsides defining a target coverage angleand the vertical profile is tailored tomake a net exponential profile alongthe horn’s primary axis; the nominalhorizontal and vertical -6 dBbeamwidth of a radial horn is shown inFig. 25A [71]. For acoustical lenses, aslant-plate acoustical lens can beplaced at the mouth of an exponentialhorn to diverge the exiting waves in

one dimension, as shown in Fig. 25B[54, 67].

Constant Directivity Horns

Also known as uniform coverage orconstant coverage horns, these designsdate from the mid-1970s to the early1980s [59, 62, 79]. The basic designcommon to a number of manufacturersuses a combination of exponential orconical throat loading, diffraction waveguide principles, and flared termina-tions to produce uniform nominal cov-erage angles in the horizontal and verti-cal planes. The general shape of thebeamwidth curve is shown in Fig. 26A,as it applies to the horizontal and verti-cal planes independently. Fig. 26Bshows the measured beamwidth and DIof a typical constant directivity hornwith nominal 90°-by-40° pattern con-trol. Within certain limitations, ➥


Fig. 26. Directivity of a uniform coverage horn. Basicdirectivity regimes (A); beamwidth and directivity for a 90°by 40° uniform directivity horn (B).

Fig. 27. Attenuation of sound with distance from point, line, andplanar sound sources.


acoustic waveguide theory has pro-posed an alternate approach to achiev-ing similar goals [55, 56].

ARRAYSBoth horns and direct radiators maybe treated the same in terms of array-ing. In this section we will examinesome useful concepts. Single-ele-ment, line, and planar arrays differ intheir radiation characteristics overdistance, as shown in Fig. 27. At longwavelengths, the simple inversesquare relationship of a point source

A is modified by a line array asshown at B, and a very large planararray will show little attenuation withdistance up to limits proportional tothe array dimensions [98]. A finiteplanar array will have the characteris-tics shown at D. Long horizontal linearrays have been placed aboveprosceniums in performance spacesto extend the range of a high direct-to-reverberant ratio toward the rear ofthe space; large planar arrays are themainstay of mega-event music rein-forcement [87].

The Simple Line Array

Kuttruff [95] describes the polarresponse of a line array of omnidirec-tional sources in the plane of the array as:

R (θ) = (sin [1/2 Nkd sin θ])/(N sin[1/2 kd sin θ]) (8)

where N is the number of elements inthe array, k is 2πf/c, d is the spacing ofthe elements in the array, c is the speedof sound, and θ is the measurementangle in radians. For four elements asshown in Fig. 28, the polar response


Fig. 28. Directivity of a four-element vertical line array with 0.2 meter separation between driver centers. 200 Hz (A); 350 Hz(B); 500 Hz (C); 1 kHz (D); directivity factor for arrays of 4, 6, 8, and 10 elements (E).

Fig. 29. Tapering of arrays. Electrical tapering (A); acoustical tapering (B); tapering through component rotation (C).

➥

A B C


is shown in A through D. The directiv-ity factor is shown at E.

The four-element array will exhibitgood pattern control over the rangefrom d/λ 0.5 to 2.0. At higher frequen-cies the pattern will exhibit narrowingand lobing, and simple arrays of morethan six elements will generally haveunsatisfactory characteristics.

Tapering the Line Array

The accepted method of extending theuniform coverage range of a line array

is through frequency tapering, orshaping, to allow the array to, ineffect, reduce in size with rising fre-quency. Some techniques are shownin Fig. 29. Electrical frequencytapering is shown at A, and acousti-cal frequency tapering is shown atB [94]. A unique “barber-pole”array is shown at C [93].

The Product Theorem

The product theorem [91] states thatan array composed of uniform direc-tional elements will exhibit the samefar-field response as a like array ofomnidirectional elements multipliedby the directional properties of oneof the single directional elements.This is another way of stating theprinciple of superposition, and isuseful in estimating the directionalresponse of complex arrays.

The Bessel Array

Franssen [88] describes an array ofelements whose amplitude drive char-acteristics are derived from Besselcoefficients [90, 92]. A simple 5-ele-ment array is shown in Fig. 30A, andsimplified wiring diagrams to derivethe drive coefficients are shown at Band C. The far-field response of thearray, modeled with omnidirectionalsources, is shown at D. Note that theresponse is essentially omnidirectional

over a 100-to-1 wavelength ratio.Via the product theorem, each omni-

directional element could be replacedwith a directional element, all orientedin the same direction, with the resultingresponse of the array exhibiting thechosen directional characteristic overthe same 100-to-1 wavelength ratio.

The Bessel array has potential forspeech reinforcement in live spaces. Itsphase response varies with angle andfrequency, however, and thus it may bedifficult to integrate the concept into asystem that includes standard radiatingelements.

Very Large Arrays for Music

Concert sound reinforcement in verylarge venues, indoors or out, requireslarge arrays, and the accepted methodof assembling these arrays is to usebuilding blocks that are each relativelyfull-range units. Thus, the assembledsystem, normally resembling a largeplane, or sets of planes with curved sec-tions connecting them, has much incommon with the principles describedin Fig. 31 [87]. As an example of thiswe show in Fig. 32 an elevation view ofa typical large vertical array (A) alongwith the on- and off-axis response (B)measured in an arc along the listeningplane [89].

The great virtue of these systems istheir ability to deliver very high ➥


Fig. 30. The Bessel array. Layout (A);series wiring diagram (B); parallel wiringdiagram (C); polar response (D). (Datacourtesy Keele, 1990.)

Fig. 31. Grateful Dead “Wall of Sound” direct radiator system, 1974, using line,planar, and arc segment arrays. Individual discrete systems were employed foreach instrument separately from the vocal reinforcement. (Photo courtesyRichard Pechner.)



Fig. 32. A large array for music reinforcement. Physical layout (A); off-axis response on the ground plane (B). (Data courtesyGander and Eargle.)

Fig. 33. Performance of a continuous array 3meters in length. Attenuation with distance at10 kHz (A); polar response at 10 kHz (B).

Fig. 34. Performance of a spiral array. Side view of array (A); polar response ofarray at 500 Hz, 1, 2, and 4 kHz (B). (Data courtesy M. Ureda.)

AB


sound pressure levels at considerabledistances with relatively low distortion.The primary defect is the dense combfiltering (lobing) and “time smearing”that inevitably results from such a multi-plicity of sources covering a given lis-tening position. Actually, since therequired acoustic power cannot beachieved by a single source, the aimhere should be to keep the coverage ateach listening position as uniform aspossible. The greater the number ofeffective sound sources, the finer thelobing patterns and the more uniformthe received signal will be. Ideally, wewould like the interference peaks anddips among the elements to be wellwithin the ear’s critical bandwidths.

Continuous Line Arrays

A continuous line array is an approxi-mation of a uniformly illuminated “rib-bon” of sound, and its directionalbehavior in the far field can be deter-mined by equation (8). At low frequen-cies, the far-field for a straight linearray begins approximately at a dis-tance equal to the array length divided

by π [98]. For progressively shorterwavelengths, this distance increasesaccording to the following equation:

r = l2f/700 meters (9)where l is the array length, and r and lare in meters [99].

Fig. 33A shows the attenuation pat-tern with distance from a straight 3-meter array at 10 kHz, and the polarresponse in the far field of that array isshown at B. Note that the beamwidth (-6-dB) is 0.8°, as given by the equation:

θline array = 2 sin-1(0.6λ/l) (10)

where l is the length of the array and λis the wavelength [99].

The pronounced HF beaming ofstraight arrays is of course a liability,and articulation of the array is one wayof dealing with the problem

J and Spiral Arrays

Ureda [100] describes a J array as hav-ing two distinct portions: a straightupper section and a uniformly curvedlower section. Each segment of the

array will act independently, with theupper section producing a highly direc-tive HF beam for distant coverage andthe lower section producing broaderradiation for near coverage.

Ureda proposes the spiral array formore uniform overall coverage. Thespiral array is continuously curvedfrom the top down, beginning withsmall angular increments, whichincrease downward in arithmetic fash-ion. Fig. 34A shows a side view ofsuch an array with a total length of 5meters and a terminal angle of 45°.

The directivity function is remark-ably uniform with frequency over abouta decade. Fig. 34B shows a group ofpolar plots from 500 Hz to 5 kHz.

Steerable Arrays

The very large arrays for music dis-cussed earlier consist of elementsequally driven in terms of level andbandwidth, and the directional proper-ties are due entirely to the spatial rela-tionships among elements. A steerablearray is one in which the elements arefixed in space, with relative drive ➥


35. A programmable array. View of array (A); signal flow diagram (B); examples of variable polar response (C). (Data courtesyEastern Acoustics Works.)

A B C


levels, signal delay, and frequencytapering individually adjustable foreach transducer.

Relatively simple arrays can bereconfigured, through sequential tim-ing, to steer their beams as needed [85,86, 96, 97]. While far-field modelingmay be fairly simple, the fact that manylisteners are seated in the transitionregion between near and far fieldsmakes the problems of reconfigurationand uniformity of coverage fairly com-plex to estimate.

The relatively small system shown inFig. 35 can be configured via a PC bythe user as required. The system profileand signal flow diagram are shown at Aand B, and a family of typical far-fieldpolar plots is shown at C. Systems suchas these, large or small, are presentlyused to solve intelligibility problems ina variety of large reverberant spaces.

REFERENCES ANDSUPPLEMENTALBIBLIOGRAPHY

Historical Perspectives

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Horns and Compression Drivers

[54] Frayne, J. and Locanthi, B.,“Theater Loudspeaker System Incor-porating an Acoustic Lens Radiator,”SMPTE, 63:3, pp. 82-85 (September1954).

[55] Geddes, E., “Acoustic Wave-guide Theory,” J. Audio Eng. Soc., 37:7/8, pp. 554-569 (July/August 1989).

[56] Geddes, E., “Acoustic Wave-guide Theory Revisited,” J. AudioEng. Soc., 41:6, pp. 452-461 (June1993).

[57] Goldstein, S. and McLachlan,N., “Sound Waves of Finite Ampli-tude in an Exponential Horn,” J.Acoust. Soc. Am., vol. 6, pp. 275-278(April 1935).

[58] Hanna, C., and Slepian J., “TheFunction and Design of Horns forLoudspeakers,” Transactions, AIEE,vol. 43, pp. 393-404 (February 1924);also, abridged text in J. AIEE, vol. 43,

pp. 250-256 (March 1924); discussionpp. 1191-1197. Reprinted in J. AudioEng. Soc., 25:9, pp. 573-585 (Septem-ber 1977) and volume 26, number 3(March 1978).

[59] Henricksen, C. and Ureda, M.,“The Manta-Ray Horns,” J. AudioEng. Soc., 26:9, pp. 629-634 (Septem-ber 1978).

[60] Keele, D., “Low-FrequencyHorn Design Using Thiele-SmallParameters,” presented at the 57thAES Convention, Los Angeles, 10-13May 1977; preprint 1250.

[62] Keele, D., “What’s So SacredAbout Exponential Horns,” presentedat the 51st AES Convention, LosAngeles, 13-16 May 1975; preprint1038.

[63] Keele, D., “Optimum HornMouth Size,” presented at the 46thAES Convention, New York, Septem-ber 1973; preprint 933.

[64] Kinoshita, S. and Locanthi, B.,“The Influence of Parasitic Reso-nances on Compression Driver Loud-speaker Performance,” presented atthe 61st AES Convention, New York,November 1978; preprint 1422.

[65] Klippel, W., “Modeling theNonlinearities in Horn Loudspeakers,”J. Audio Eng. Soc., 44:6, pp. 470-480(June 1996).

[66] Klipsch, P., “A Low-FrequencyHorn of Small Dimensions,” J.Acoust. Soc. Am., vol. 13, pp. 137-144(October 1941). Reprinted in J. AudioEng. Soc., 27:3, pp. 141-148 (March1979).

[67] Kock, W. and Harvey, F.,“Refracting Sound Waves,” J. Acoust.Soc. Am., 21:5, pp. 471-481 (Septem-ber 1949).

[68] Leach, M., “A Two-Port Anal-ogous Circuit and SPICE Model forSalmon’s Family of Acoustic Horns,”J. Acoust. Soc. Am., 99:3, pp. 1459-1464 (March 1996).

[69] Leach, M., “On the Specifica-tion of Moving-Coil Drivers for Low-Frequency Horn-Loaded Loudspeak-ers,” J. Audio Eng. Soc., 27:12, pp.950-959 (December 1979). Com-ments: J. Audio Eng. Soc., 29:7/8, pp.523-524 (July/August 1981).

[70] Murray, F. and Durbin, H.,“Three-Dimensional Diaphragm Sus-pensions for Compression Drivers,” J.Audio Eng. Soc., 28:10, pp.720-725(October 1980). ➥



[71] Olson, H., “A New High-Effi-ciency Theatre Loudspeaker of theDirectional Baffle Type,” J. Acoust.Soc. Am., pp. 485-498 (April 1931).

[72] Olson, H., “Recent Develop-ments in Theatre Loudspeakers of theDirectional Baffle Type,” SMPTE(May 1932).

[73] Plach, D., “Design Factors inHorn-Type Loudspeakers,” J. AudioEng. Soc., 1:4, pp. 276-281 (October1953).

[74] Plach, D. and Williams, P.,“Reactance Annulling for Horn Loud-speakers,” Radio-Electronic Engineer-ing, pp. 15-17, 35 (February 1955).

[75] Rocard, M., “Sur la Propaga-tion des Ondes Sonores d’AmplitudeFinie,” Comptes Rendus, p. 161, 16January 1933.

[76] Salmon, V., “Hypex Horns,”Electronics, vol. 14, pp. 34-35 (July1941).

[77] Salmon, V., “A New Family ofHorns,” J. Acoust. Soc. Am., 17:3, pp.212-218 (January 1946).

[78] Small, R., “Suitability of Low-Frequency Drivers for Horn-LoadedLoudspeaker Systems,” presented atthe 57th AES Convention, Los Ange-les, 10-13 May 1977; preprint 1251.

[79] Smith, D., Keele, D., and Ear-gle, J., “Improvements in MonitorLoudspeaker Design,” J. Audio Eng.Soc., 31:6, pp. 408-422 (June 1983).

[80] Thuras, A., Jenkins, R., andO’Neill, H., “Extraneous FrequenciesGenerated in Air Carrying IntenseSound Waves,” J. Acoust. Soc. Am.,vol. 6, pp. 173-180 (January 1935).

[81] Webster, A., “AcousticalImpedance and the Theory of Hornsand of the Phonograph,” Proceedingsof the National Academy of Sciences,vol. 5, pp. 275-282 (May 1919).Reprinted in J. Audio Eng. Soc.,25:1/2, pp. 24-28 (January/February1977).

[82] Wente, E. and Thuras, A., “AHigh Efficiency Receiver for Horn-Type Loudspeakers of Large PowerCapacity,” Bell System TechnicalJournal, VII:1, p. 40 (January 1928).Reprinted in J. Audio Eng. Soc., 26:3,pp. 139-144 (March 1978).

[83] Wente, E. and Thuras, A.,“Auditory Perspective—Loudspeakersand Microphones,” Electrical Engi-neering, vol. 53, pp. 17-24 (January

1934). Also, Bell System Technical J.,XIII:2, p. 259 (April 1934). Reprintedin J. Audio Eng. Soc., 26:7/8, pp. 518-525 (July/August 1978).

[84] Wolff and Malter, “DirectionalRadiation of Sound,” J. Acoust. Soc.Am., vol. 2, pp. 201-241 (October1930).

Arrays

[85] Augspurger, G. and Brawley,J., “An Improved Collinear Array,”presented at the 74th AES Conven-tion, New York, 8-12 October 1983;preprint 2047.

[86] Augspurger, G., “Near-Fieldand Far-Field Performance of LargeWoofer Arrays,” J. Audio Eng. Soc.,38:4, pp. 231-236 (April 1990).

[87] Davis., D and Wickersham, R.,“Experiments in the Enhancement ofthe Artist’s Ability to Control HisInterface with the Acoustic Environ-ment in Large Halls,” presented a the51st AES Convention, Los Angeles,13-16 May 1975; preprint number1033.

[88] Franssen, N., “Direction andFrequency Independent Column ofElectroacoustic Transducers,” Philips“Bessel” Array, Netherlands Patent8,001,119, 25 February 1980; U.S.Patent 4,399,328, issued 16 August1983.

[89] Gander, M. and Eargle, J.,“Measurement and Estimation ofLarge Loudspeaker Array Perfor-mance,” J. Audio Eng. Soc., 38:4, pp.204-220 (1990).

[90] Keele, D., “Effective Perfor-mance of Bessel Arrays,” J. AudioEng. Soc., 38:10, pp. 723-748 (Octo-ber 1990).

[91] Kinsler, L., et al., Fundamen-tals of Acoustics, third edition, Wiley,New York, 1980.

[92] Kitzen, J., “Multiple Loud-speaker Arrays Using Bessel Coeffi-cients,” Electronic Components &Applications, 5:4 (September 1983)

[93] Kleis, D., “Modern AcousticalEngineering,” Philips TechnicalReview, 20:11, pp. 309-348 (1958/59).

[94] Klepper, D. and Steele, D.“Constant Directional Characteristicsfrom a Line Source Array,” J. AudioEng. Soc., 11:3, pp. 198-202 (July1963).

[95] Kuttruff, H., Room Acoustics,

Applied Science Publishers, London,1979.

[96] Meyer, D., “Multiple-BeamElectronically Steered Line-SourceArrays for Sound ReinforcementApplications,” J. Audio Eng. Soc.,38:4, pp. 237-249 (April 1990).

[97] Meyer, D., “Digital Control ofLoudspeaker Array Directivity,” J.Audio Eng. Soc., 32:1, pp. 747-754(1984).

[98] Rathe, E., “Note on Two Com-mon Problems of Sound Reproduc-tion,” J. Sound and Vibration, vol. 10,pp. 472-479 (1969).

[99] Ureda, M., “Line Arrays: The-ory and Applications," presented at the110th AES Convention, Amsterdam,May 2001; preprint 5304.

[100] Ureda, M., “‘J’ and ‘Spiral’Line Arrays,” presented at the 111thAES Convention, New York, Decem-ber 2001; preprint 5485.

SUPPLEMENTALBIBLIOGRAPHY:

[101] Borwick, J., ed., Loudspeakerand Headphone Handbook, third ed.,Focal Press, Oxford, UK, 2001.

[102] Colloms, M., High Perfor-mance Loudspeakers, fifth ed., JohnWiley & Sons, New York, 1997.

[103] Dickason, V., The Loud-speaker Cookbook, sixth ed., AudioAmateur Press, Peterborough, NH,2000.

[104] Eargle, J., ElectroacousticalReference Data, Van Nostrand Rein-hold, New York, 1994.

[105] Eargle, J., Loudspeaker Hand-book, 2nd ed., Kluwer Academic Pub-lishers, Boston, 2003.

[106] Eargle, J. and Foreman, C.,JBL Audio Engineering for SoundReinforcement, Hal Leonard Publica-tions, 2002.

[107] Langford-Smith, F., ed.,Radiotron Designer’s Handbook,Amalgamated Wireless Valve Co,Sydney, and Radio Corporation ofAmerica, Harrison, NJ, 1953 (avail-able on CD ROM).

[108] Merhaut, J., Theory of Elec-troacoustics, McGraw-Hill, NewYork, 1981.

[109] Olson, H. Solutions of Engi-neering Problems by DynamicalAnalogies, second ed., D. Van Nos-trand, Princeton, NJ, 1958.


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