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Mastering Series Design-White-Paper

Why the coincident source, point source loudspeaker is one of the best designs for Stereo and Home Theater systems


Loudspeaker design is a holistic process that involves compromises and trade-offs. It is not how well a loudspeaker performs one importance performance criterion, but how evenly it performs on all the important performance criteria that makes it a good loudspeaker. The following discussion is intended to present our approach to loudspeaker design and to explain why we believe the point source loudspeaker is one of the finest instruments of musical reproduction.


How accurately a loudspeaker reproduces music depends on its amplitude response, its time coherence, and its phase response. Most conventional loudspeakers can reproduce the amplitude of music fairly accurately, where they fall short is in their ability to accurately reproduce time and phase information. Time and phase accuracy are critically important for reproducing ambient information and subtleties which are crucial for realistic portrayal of the spatial, tonal, and timbral characteristics of music.

Amplitude response refers to the output or volume of the loudspeaker over the entire frequency range. An accurate loudspeaker should uniformly reproduce all parts of the frequency spectrum. That is, an accurate loudspeaker should have flat frequency response.


Most consumers know that flat amplitude response over the entire frequency range is an important indicator of overall loudspeaker performance and use it as a shorthand when evaluating loudspeakers. While flat frequency response is a predictor of overall loudspeaker performance it is not perfect. The fact that the frequency response of a loudspeaker measures flat when a measurement microphone is placed directly in front of a loudspeaker on the tweeter's axis does not necessarily predict the loudspeaker's frequency response on the listening axis (which is never directly in front of one loudspeaker, see the figure above). Therefore the off-axis response of a loudspeaker is more critical in determining how the loudspeaker sounds in real life listening situations. This explains why some loudspeakers with absolutely flat on axis measured frequency response sound awful and why some with less flat on axis measured frequency response sound wonderful. Manufacturers know that consumers use flat frequency response to appraise loudspeaker performance. Therefore they ensure their loudspeakers have flat frequency response to the neglect of other important performance factors. Because most loudspeakers now have reasonably flat frequency response much of the discussion about loudspeaker performance is centered on the importance of time coherence and phase response as the critical factors affecting a loudspeaker's ability to accurately reproduce music.


Point Source, Time Coherent, First Order, Two-way Loudspeakers


Time coherence refers to how sounds radiating from different drivers in a multi-way loudspeaker arrive at the listener's ear. Since the different drivers in a multi-way system reproduce different parts of the frequency spectrum, and musical tones are reproduced by a range of frequencies that are often reproduced by more than one driver, if the drivers are not acoustically aligned, parts of the musical tone will not arrive at the listener's ear at the same time. This will result in smearing of tones and low level information, which conveys the realism, emotionalism, and spiritualism of the performance, will be lost. Most of the music will be reproduced but most of the subtleties will be lost and the reproduction will be inaccurate. Loudspeakers that can deliver all the elements of a tone to the listener's ear at the same time are time coherent and those that cannot are time incoherent.


Phase response refers to how synchronized the sound waves emanating from different drivers on the loudspeaker baffle are when they arrive at the listener's ear. If the sound waves are perfectly synchronized they complement each other to the maximum extent (they are in perfect phase agreement), if they are not synchronized they cancel each other to some extent (they are said to be out of phase). Phase response is intimately related to time coherence in that phase inaccuracies will affect time coherence negatively. Inaccurate phase response, and by extension, time response, are mostly a problem of crossover design. This makes crossover design arguably the most critical factor of loudspeaker design.


Illustration: flat baffle, slanted baffle and point source phase responses

Addressing Time and Phase Incoherence


Most loudspeaker manufacturers who address the issue of time and phase coherence do so by positioning multiple drivers on a sloped baffle purportedly to align the acoustic centers of the drivers. In theory this should make sound from all drivers arrive at the listener's ear at the same time (i.e. time coherently). However, as technical reports in such magazines as Stereophile reveal, often these sloped baffle speakers are less time coherent than conventional flat baffle loudspeakers. This is sobering proof that other design factors, such as crossover design, are crucially important for achieving time and phase coherence. If two drivers are mounted in the correct position relative to each other (not necessarily on a slanted baffle) and are in phase their output at their crossover frequency will sum to twice the amplitude, whereas the amplitude of two drivers that are not appropriately mounted will sum to less than twice their amplitude depending on how much they are out of phase. In the first case all the elements of a tone will arrive at the listener's ear at the same time. In the second case they will not. It is true that time alignment is important to phase coherence. However, it does not follow, that a slanted baffle is necessary or essential for time and phase alignment.


Radically slanted baffle speakers are also susceptible to diffraction and re-radiation problems which adversely affect time and phase coherence. In general, while a large slanted baffle loudspeaker with time-aligned drivers may be time coherent and perform well on the measurement axis, the loudspeaker's performance may change as one moves away from the measurement axis and the distance between the listener and each of the drivers change. This results, in part, from diffraction which has to do with the bending of sound waves around objects, such as the edges of speaker cabinets, that are smaller than the length of the sound waves, and the relationship between the drivers and the baffle.


If the edges of the baffle form a right angle sound waves will re-radiate off the edge of the baffle and interfere with the sound. The direct and re-radiated sound waves will be in phase and out of phase at different frequencies and will interfere with the sound. Placing a large angled baffle in front of the tweeter also provides a large reflective surface to re-radiate the tweeter's sound waves. Re-radiation has an adverse effect on amplitude response but re-radiation also affects transient response because it causes a short delay for re-radiated sound waves to reach the listener's ear. This muddies the sound and postpones the decay of transients.


One solution to the multiple driver alignment problem is to use a single coincident point source driver array that is time coherent. In the coincident point source driver array, the tweeter is located in the throat of the woofer. This causes the woofer and tweeter in our driver array to have identical acoustic centers. In our design, the woofer and tweeter are time coherent, and low and high frequencies emanate from the same place. Because we use minimum phase first order crossovers that preserve phase coherence, our loudspeakers are also phase coherent. We minimize diffraction and re-radiation of sound waves by carefully positioning our point source driver array on a narrow vertical baffle and by rounding the edges of the baffle.




Directionality refers to how well a loudspeaker radiates sound throughout the listening area. Ideally, a loudspeaker should disperse sound widely and evenly throughout the listening area enabling all listeners to hear the same sound quality. In general, multi-way loudspeakers use large diameter drivers to cover low frequencies and small diameter drivers to cover the high frequencies. Because of the use of multiple drivers, if the dispersion patterns of the drivers are not complementary or if the drivers acoustic centers are not properly aligned, problems arise in directionality at the crossover point between drivers. How severe these problems are depend on how directional the drivers are at their crossover point, the placement of the drivers on the loudspeaker baffle relative to each other, and crossover design.


To the extent a driver is directional at the top of its pass band (where it crosses over to another driver), coloration of the reproduced sound will occur. That is, the drivers do not play the same note in a complementary fashion.


It is important that there is a seamless transition between how, for example, a large driver plays a part of the note and how a smaller driver, for example a tweeter, plays the rest of it. An abrupt transition from a large driver playing a note to a small driver playing the same note will result in discontinuites in the harmonic structure of the note. This is what happens in loudspeakers with steep slope crossovers. One way around this is to use high quality broad band drivers whose diaphragms are designed to flex in a controlled manner in their pass band (where the driver hands over the note, so to speak, to the other driver), reducing their effective radiating area, and hence their directionality, in their passband. Cone materials such as polypropylene and carbon fiber, that we use,  make effective controlled flexure diaphragms which reduce the problem of directionality.


Crossover Design and Time and Phase Coherence


Our opinion with regard to crossover design is that less is more. The more complex the crossover, the more current it soak's up, the more coloration it adds to music, and the more phase distortion it produces. Most of the really magical loudspeakers use only a few crossover components. It should be remembered that the crossover is a corrective circuit or at best a fine tuning devise. Through the judicious selection of drivers with the right driver roll-off and the design of the "perfect" matching cabinet the loudspeaker designer may find drivers and cabinet that complement each other to such an extent that there is no need for the attenuating or corrective effects of a crossover (except for the proponents of steep sloped crossovers). However, in the real world most designers only manage to come close to this ideal. When they do, they achieve very good results.


The frequency-amplitude curve for our Model 30M loudspeaker below shows the extraordinary level of performance that can be achieved in a well designed loudspeaker using only three crossover components. This is a real-life unsmoothed measurement taken 15 degrees off the tweeters axis. Note the loudspeaker's response is flat from about 30 cycles to 20, 000 cycles within the standard bandwidth of +/- 3 dB. The reader is encouraged to compare this level of performance with the measurements of other highly regarded loudspeakers reported in such magazines as Stereophile and Soundstage.



Crossovers, as attenuating circuits, are classified by their degree of attenuation, which is termed their "order." A first-order crossover attenuates the natural response of a woofer or tweeter by 6 dB per octave, progressively. Sound level is measured in decibels (dBs). An increase in sound level of 3 dBs leads to a perceived doubling of loudness. Therefore a 6 dB increase in sound level increases loudness fourfold, while a 6 dB decrease reduces loudness fourfold. An octave is a doubling or halving of frequency. A first-order crossover attenuates driver response by 6 dB for every doubling or halving of the frequency. A second-order crossover attenuates by 12 dB per octave progressively, and a third-order crossover attenuates by 18 dB progressively. In the case of the woofer, a crossover is attenuating its high frequency response and in the case of the tweeter a crossover is attenuating its low frequency response. Crossovers are also called filters. In that sense they filter out high frequencies in the case of woofers and filter out bass frequencies in the case of tweeters. Crossovers also attenuate the output of the woofer or tweeter so the output of both drivers are matched.


With regard to phase coherence there are two classes of crossovers: phase linear crossovers and Linkwitz-Riley crossovers. Phase linear crossovers have a roll-off of 6 dB per octave for both the woofer and tweeter and are the only crossovers that do not introduce phase distortion into the loudspeaker's response. Linkwitz-Riley crossovers have 12dB or 18dB per octave roll-off and although they have some desirable properties, such as increased power handling, they introduce phase distortion. It does not matter that the drivers acoustic centers are time-aligned on a slanted baffle or that the woofer and tweeter outputs are in phase, or that the loudspeakers response is flat, Linkwitz-Riley and other high order crossovers add phase distortion to the drivers acoustic output.


First order crossovers versus higher order crossovers


We now come to an important question. If the first-order crossover is so superior why aren't all loudspeakers first-order? To be fair, as in any industry, different design principles have their adherents. But having said that, there are many other reasons for the current state of affairs. With the advent of computer assisted design, it is now possible to use less expensive drivers and to use complex, inexpensive corrective crossover circuits to shape their response.


To successfully execute a design using a simple first order crossover requires considerably more research, a judicious choice of expensive, high quality wide band drivers, and a well executed cabinet design. The drivers must have smooth roll-off characteristics in their pass band. And the cabinet must be designed to be free of resonances. Otherwise complicated crossover circuits will have to be devised to smooth out the driver and cabinet response aberrations. To call the complicated crossovers used to smooth the response of the now fashionable high-tech metal cone woofers first-order is a misnomer because while complex crossover circuits flatten and smooth amplitude response, the addition of each crossover component usually contributes more phase distortion. Metal cone woofers may be sexy and appear hi-tech and perform well in some situations (note metal cone woofers were first introduced by Bozak in the 1930s), however, they have horrible pass-band characteristics and are ill-suited for first-order designs. Hence, the use of metal cone woofers with "first order" crossovers usually requires using multi-element complex circuits to smooth the response of the loudspeaker.


Two-way Loudspeakers


As a class of loudspeakers, the two-way stands alone in its capacity to deliver sheer magical reproduction of a soundstage. From the dawn of the Stereophonic age, two-way loudspeakers have been the most successful designs. There are several reasons for this. First, two-way loudspeakers tend to have small baffles which help their radiation pattern. Second, because they are often implemented with a single woofer and tweeter it is easier to use a first-order crossover, which minimizes phase problems. Third, two-way loudspeakers often utilize small diameter woofers with shallow acoustic centers that are easier to time-align with tweeters. Forth, the combination of small baffle, first-order crossover, and time aligned close coupled drivers approaches a point source design. Fifth, the use of fewer drivers reduces the amount of Doppler effects between the drivers.


The major perceived limitations of the two-way acoustic suspension designs are limited bass response and an inability to move a large volume of air. With regard to bass response, the designer of the two-way loudspeaker is confronted with trade-offs between cabinet size, efficiency, and bass response. Bass extension can be achieved, but often at the expense of sensitivity and transient response. While bass extension is not strictly dependent on cabinet size, in general, the greater the cabinet, the greater the bass extension tends to be. Reflex designs provide more bass output. However, as a consequence of their more rapid roll-off, reflex designs have poorer transient response than acoustic suspension loudspeakers. And while the acoustic suspension loudspeaker may not produce bass volume on par with most reflex designs, the acoustic suspension loudspeaker is often capable of greater low bass output.


The ability to move a large volume of air or to play extremely loud is really an issue of matching the size of the speaker to the size of the listening area. Adding more drivers increases the ability of a loudspeaker to play louder and can increase the loudspeaker's power handling capacity but it most often leads to degradation of sonic performance. There is a way in which perceived bass performance and loudness are interrelated and it is through psycho-acoustics. Most listeners increase the loudness of their music systems to achieve more bass response. However, if the speaker has excellent bass performance the listener is often satisfied listening at a lower volume.


All our loudspeakers have excellent bass response. For those with large listening areas who require more volume and more bass output, we offer two solutions: transmission line bass loading in our Model 30M, for example, and our active subwoofers. Both of these solutions do not compromise the performance of our two way designs while they provide voluminous extended bass response. The innovative eighth wave transmission line design of the Model 30M produces bass response that is extended to 30 Hz and has the excellent transient response characteristics of acoustic suspension designs. The 15EXP is a compact and potent active subwoofer which is designed for use in both Stereo and Home Theater and Surround Sound systems. Judicious use and placement of our 20M monitors in conjunction with one or more of our active subwoofers will address almost any room response problem.


Point Source Loudspeakers


Theoretically, a point source is an infinitesimally small sound radiating source that radiates sound equally in all directions regardless of frequency. A point source has accurate amplitude, phase response, and time coherence. More importantly, theoretically, the off-axis performance of a point source is equal to its on-axis performance. While much of the technical measurement of loudspeakers is focused on the on-axis response of loudspeakers as indicative of their performance, the off-axis response of loudspeakers is a much better indicator of how a loudspeaker performs in a Stereo or Home Theater system. No one sits directly in front of, that is, on the measurement axis, to listen to a loudspeaker (except, of course, the center channel speaker, and there we are more concerned with a narrow band of frequencies that cover the human voice). Instead, we are always off-axis to each loudspeaker when we listen to our Stereo or Home Theater or Surround Sound systems.

For practical purposes, in loudspeaker applications, a loudspeaker is considered a point source if it radiates sound equally 180 degrees in all planes to the front of the loudspeaker relative to the loudspeaker's acoustic center. This is a holy grail, but the closer the loudspeaker gets to it, all things being equal, the more magical the speaker performs. And this explains why the well-executed two-way minimonitor design with closely time-aligned drivers sounds so magical. It is easy to see that the point source criterion is best approximated by a single full range driver. However, a full-range single driver loudspeaker is a rarity, and single driver loudspeakers have other problems such as inadequate frequency extension at both extremes of the frequency spectrum. Therefore, most loudspeakers use two or more drivers to cover the entire frequency range.


We use a time coherent, coincident point source, two-way driver array with highly complementary woofer and tweeter response in order to ensure that the woofer and tweeter used in our loudspeakers have identical acoustic centers and identical directivities at the crossover frequency. This driver array produces a stable symmetrical radiation pattern with smooth power response and has flat amplitude response, and it is time coherent. All our loudspeakers are outfitted with minimalist first order crossover to preserve the phase response of our driver array.


Below is an excess group delay curve measurement of our Model 30M taken at 15 degrees off axis. The excess group delay measurement is a measure of the time and phase coherence of the drivers in a loudspeaker system. While perfection is very rear, this measurement curve is flat between 225 cycles and 20,000 cycles, indicating the tweeter and woofer in the Model 30M are time and phase coherent. Note the downward slope in the lower part of the curve which shows some time delay in the bass. However this is innocuous.


Although coincident two way driver arrays have been in existence for some time, they are not well understood, and are difficult to implement. They should be distinguished from the more generic co-axial drivers because coaxial drivers do not have identical acoustic centers, in other words, in a coaxial driver the woofer and tweeter are not time-aligned. The coincident driver requires considerable engineering because it requires the use of a very small, high quality tweeter with excellent power handling characteristics, which has to be shoe horned into the throat of the woofer (i.e., where the dust cap usually is).


In a coincident driver array loudspeaker, the response on the listening axis is superior to the response on the measurement axis. Coincident source drivers, however, have a narrow band cancellation on the measurement axis. Although inaudible it has been the subject of debate. Some people perceive this as a fault in the design. However, it is mostly an artifact of the convention of relying on measurements taken directly in front of a loudspeaker as indicative of its performance at the listening axis.

Below is a frequency-amplitude curve measurement which is based on averaging five measurements taken across the front of our 30M loudspeaker. Notice this curve is less flat than the single curve displayed earlier which was measured 15 degrees off the tweeters axis. There is some evidence of cancellation right above 10,000 cycles, but few highly regarded loudspeakers can match the evenness of the 30M's response. The proof of the benign effect of the cancellation is that it disappears in the off axis measurements shown earlier.


Another criticism of the coincident source driver array is that it has the potential for Doppler distortion when driven too loudly. This is true to some extent, however any loudspeaker driven loudly begins to exhibit maladies, whether it is Doppler distortion, beaming, or cone break-up. Some people also question the wisdom of using a first-order crossover with the small tweeter used in our coincident driver array, because of concerns about the power handling capacity of the tweeter. This can only be an issue in loudspeakers that are poorly designed. Since we started using this driver array in 1994, we have not had a single incidence of tweeter failure. This is not only testimony to the quality of the drivers we use but it is a testimony to the soundness of our design.


As we mentioned at the outset, good loudspeaker design requires trade-offs and compromises to ensure consistent performance on all the important factors of loudspeaker performance. We believe the concentric array, point source, two-way loudspeaker represents one of the most judicious approach to producing a musical, accurate loudspeaker. It is an elegant and efficient way to address all the critical issues of accurate amplitude response, time coherence, phase accuracy, and diffraction. However, the proof of our design approach is in what you hear from our loudspeakers. We invite you to listen.