Open Baffle Line Array Speakers

Author: Dmitry Nizhegorodov ( My other projects and articles


1.   Introduction

These speakers were designed for low-power singe-ended triode (SET) amplifiers. The design was iterative, with lots of prototyping and concepts tested and changed sometimes on a daily basis. The result is a system which to my ears has a distinct quality of making music enjoyable.

Each speaker can be described as a near-field, vertical, tall, concave line array dipole. Elements of arrays are small full-range drivers mounted on sectioned wooden baffles with open baffle wings pointing away from the listener at ~ 20..40 degrees, much like the mouth a rear-facing horn speaker. This terminology and the design are going to be explained in details in the rest of this document.

2.   History, Concepts, Theory, Details

An Open Baffle speaker is a variant of dipole enclosure type, where the front facing and the rear facing sides of a driver are acoustically connected to the listener. The physics of dipoles (and open baffles, for that matter) can be explained in terms of diffraction and interference. Suppose a driver is mounted in the center of a disk. If an instantaneous impulse (snap) is applied to the driver, the front and the rear planes of it will emit sound pressure outwards, out-of-phase. Sound pressure change travels towards the edges of the disk-enclosure and due to diffraction cause secondary emission at the edges - where the front (+) wave meets the rear (-) wave. The signal from the edge will reach the listener delayed, where the delay is the time of sound travel from the driver to the edges. If driver plays sound tones of various frequencies, interference between the direct signal and the edges will cause comb-like frequency-dependent peaks and lulls. A baffle of a different shape, such as a rectangle, will smooth out combing due to secondary emission of varying delay.

Dipoles radiate into the space (the room) in such manner that the listener and the rear wall get most signal and the side walls, the floor and the ceiling receive little.

When dipoles are placed away from rear walls, they are capable of producing sound distinct from sound of closed speakers. Not only dipoles excite less room modes, and suppress much unwanted floor/sides/ceiling reflections, they add, through back radiation, nice and pleasant ambience. Plus dipoles are 3 dB more effective than closed boxes.

Everything you want to know about theory of dipoles, dipole speakers and much else is described on Siegfried Linkwitz's excellent web site [1].

I arrived at dipoles not directly, though, but through listening to full range drivers in various configurations.

Listening to a full range, single source of sound is not much different from listening to a conventional multi-way speaker, however the situation changes radically with stereo. In terms of imaging, soundstage and spatial resolution, only the best, mega-$ multi-way speakers can match to holographic images rendered by the most simplistic single driver pairs. It is believed that our ears are very sensitive to phase shifts and sound disbalance in so called critical range of sounds - the range where nature equipped us with an ability to detect direction and distance to the source of sounds. Primates need that in order to get a chance not to be eaten by a lion or bitten by a snake, and also to locate peers. How wide this critical range is for the purpose of musical enjoyment? There is no clear answer, but it is narrower than HiFi 20..20K range and wider than Bell Lab's speech spec. Note we talk about range where coherence is optimized, not the total range of the system. I tend to agree with Thorsten Loesch [2] that this range is not 20...20K but somewhat around 100..10K. A 80...15K would be even better, but 160...8K is still pretty good.

My current belief is that coherency within critical range is much more important than linearity of frequency response. My experiments with a 31 band stereo equalizer clearly support that, and such experiments can be done by anyone with a descent equalizer. So what is the big deal about frequency response linearity? Trends in HiFi industry forced speaker manufactures during ~ 1970...1990 era and up to now to signify frequency linearity, offering products with claimed +-3, +-2 or +-1 dB for big bucks. In my view only large plateaus and valleys and slopes in response matter very much, narrow dips and peaks are less important because room modes change frequency response to a much larger degree anyways - often as much as +- 20dB. For good imaging it is important that narrow dips or peaks are essentially coherent in both speakers. Of course, peaks that are due to resonances in driver/speaker elements are bad, but these can be relatively easily treated with dampening materials. Finding these does not require equipment measuring waterfall models. Warble tones and microphone tests with a good sweep generator and impulse generator is all that is needed. One more observation regards coherence: Finding coherent drivers in a batch is easy, finding two coherent complex enclosures is very difficult.

Single-driver stereo speakers appear to be "masters" of imaging, mainly because the critical frequency range is covered by two coherent single sources, How wide is the range covered by them? Most 3 or 4 inch drivers can reproduce up to 10kh, and some go up to 18..22kHz. Yet extending spectrum below of the critical range by the same driver appears very difficult. Four and three inch drivers have difficulties below 120Hz. The situation differs for larger drivers, which can extend lower but have difficulties in the upper register. Even the best, kilo-$ eight inch drivers, claimed to cover 40...>20K, do that by combining low-resonant yet ultra light (hence expensive) cone with wizzler cones, which are concentric transducers in disguise. One problem of wizzlers is that they can cause interference *within* critical range, which is alas very audible. You may or may not like it, but there is even a name for it - Lowther Shout - honoring the name of one the best full-range drivers yet clearly suggesting that the effect may be as pleasant as a shout.

I tested many inexpensive 3,4 and 5 inch, single-cone full-range drivers and found that often they sound better than most wizzler drivers, among which only the most expensive ones, like Lowthers, sound neutral enough (of course, 2, 4 or even 5 inch drivers can not reproduce enough SPL under 100 or even 140 Hz). I've been using open baffles - rectangular cardboard panels with holes for 4, 5, 6, 8 inches - to test and compare these drivers, even before knowing how far I can go with the dipole concept. Only later, after A/B comparing that to other types of enclosures, did I realize how revealing they are. After testing various inexpensive drivers my preferences were totally with now extinct Parts Express PE #269-469 for their neutral, natural tone. In comparison, other popular single-drivers choices such as other RadioShack favorites 40-1197, 40-1271, 40-1354, or 970-0551 (Pioneer B20FU20) or Fostex 103 sounded harsh. Cost/performance could not be theoretically better, as I was able to get a large number of these at 69 cents each.

Now a "collector's item", PE 269-469 has a nice tone. Some enthusiasts call them "69 cent wonders". Frequency range is ~ 110...18K, at 90.5..91 dB/W/m.

For full-range and single-drivers, many enclosure configurations can be tried. The main goal is to flesh out the bottom end, but the main concern is in preserving qualities of the critical range. Closed boxes are nice, but too dry for small full-rangers, ported enclosures offer more low-end volume but quality of port-resonant sound is questionable. Voight pipes are enormously popular among single-driver and full-range enthusiasts, and I spent a lot of time listening to Voight pipes with removable driver baffles and configurable flare. I tried other configurations as well, experimenting with front baffle size, etc. I moved the pipes around the room a lot and after a while found the best position close to the listening spot, approximately 7...8 feet (depending on a driver).

Near-field listening describes a setup where speakers are placed fairly close to the listener - 4..8 feet - and away from the walls. It is widely believed that near-field listening greatly reduces impact of a room. The tradeoff is that near-field listening reduces the size of a sweet spot. Note: this should not be confused with soundstaging. Near-Field listening does not worsen soundstage or imaging, in fact the width and the depth of soundstage and imaging are usually better.

Listening conditions outside of a sweet spot for most stereo systems are poor because frequency response is off, and also because imaging is gone. There may be some virtues in wide-dispersion home speakers (there are even radial ones, offering 360 degrees; however, remember that any wave sent not into a sweet spot will be reflected by something in your room) and in terms of dispersion "a speaker with large sweet spot" makes sense. However, what is a stereo speaker system that promises amazing imaging in a huge sweet spot? Marketing, I think. The laws of physics (interference) dictate that 2 transducers offer holographic resolution qualities only in a fairly restricted spot, at a junction of two narrow beams. Hence I believe that trying to achieve holographic imaging for groups of people listening to music in average rooms, or even sitting in a row on a couch is a bit pointless. On another hand, limiting this to a single person sitting in a chair is realistic. When a small spot is not a problem, near-field listening is very appealing. By the way, I think sometimes that for parties and casual listening around the house a Jukebox, not a pair of speakers is the right appliance.

Listening to a pair of single-driver Voight pipes in near-field was pleasant yet these did not produce much sound and much efficiency. An efficient driver, like Lowther, is very expensive primarily because it is so efficient. As I wanted to be free to experiment, I did not want to lock myself with expensive parts.

Now we are ready to arrive at the blessed shores of line arrays. If you have seen Brian May and other guitarists in front of stacks of Marshall amps you know that musicians combine speakers for a good reason. 16 Marshall amp, combos (an amp plus a speaker) sound 24 dB louder than 1 Marshall amp. Also, there is something very special about the sound besides to the volume - great dynamics and much fuller bottom end. This is the magic of speaker arrays.

Doubling guitar combos causes 6 dB volume gain. Doubling speakers that are fed from a single amp causes 3 dB of gain [3]. This is not very intuitive but my SPL meter shows it is true. Yet the diafragms in the drivers in each speaker travel only half of the distance (excursion in an array is inverse to the number of drivers. This means less distortion.

I mounted four 269-469, 2x2, on a baffle and liked the sound a lot, except this configuration in Voight pipes produced poor image. Lobbing - interference between drivers - is the reason. This is where line arrays help. Instead of mounting 4 speakers 2X2, I mounted them in a vertical array. The sound was fuller, imaging was still very sharp. I added 2 more drivers nd confirmed what I have already heard with 4-element array: high-frequency roll-off. Interference, again, was causing this. The drivers in the middle appear close to the listener than the top most and the bottom most drivers by more than an inch, which is enough to cancel out high-frequency waves.

That is why experiencing the advantages of true tall line arrays for many is so troublesome. If anyone could build arrays as tall as listening distance, that would additionally raise the efficiency of the speakers, because tall arrays are known to radiate in cylindrical space, with sound decaying 3dB/d, which is better than 6dB/d a conventional point-source provides. There are commercial tall arrays but those do need driver selection to compensate for the loss, or use delay lines which are complex. There is another, much simpler and holistic solution - baffle curving. JBL professional sound papers describe curved line arrays. These are increasingly popular and can be seen at concerts. However, these curved arrays are to increase dispersion in a large hall.

I refer to another way of curving tall line arrays - concave curving. In this arrangement all drivers in a line are equidistant from listener ears. Two line arrays would be on a surface of a sphere, see a pic in [3]. When you sit in the listening spot, each driver is positioned straight at your face.

After I curved the front baffles of Voight pipes, each having 6 269-469 drivers, everything started sounding very nice. Still I heard the box - its resonances, perhaps, bothered me.

Knowing that open boxes are very neutral, one day I removed the back sides of my pipes - and the first prototype of my full range concave line array baffle speakers was born. A change to better was very apparent. The room behind the speakers was full with images of instruments. The stage-mapping tests on Stereophile CDs made much more sense. Thus I found that the baffle arrangement extended the soundstage deep behind, whereas back-closed Voight pipes presented comparatively more narrow stage in front and just a little behind. Also, once I opened the pipes, they "disappeared".

In my experience only planars and open baffles with dynamic drivers have an ability to completely disappear. There was also apparently a happy balance in tone: something between 269-469's Qts, making them a natural open-baffle performer, their overall sonic signature, and the distance of 8 feet where I positioned the speakers created nice synergy. These speakers offered ~ 97 dB/W/m, which was sufficient for listening with 3.5 W SET amps.

Two more versions of my line arrays prototypes:

laob5.jpg laob6.jpg

On the left is a tall closed-box line array. On the right is concave open-baffle array. You can see two additional rows of holes closed. When speakers were installed there, efficiency was +4dB but imaging was lost due to horizontal lobbing. Also you can see a supertweeter in the center, working in 16..40kHz range. The baffle is concave, but very wide; most likely because it is so wide and because its panels are not offset to the back, its soundstaging and imaging abilities did not match my open-back Voight pipes! A negative result is also a result, as it helps moving in the right direction.

With more experiments, more prototypes, I found that the front baffle must be narrow to avoid degradation of imaging and independently of that the sides should be facing slightly rear, not exactly sideways, to avoid "flat and shallow" soundstage.

These two factors influenced by current design featuring very narrow tall and concave front baffles and side panels opened backwards at 110...140 degrees. The angle can be adjusted as the side panels are on hinges.

Narrow front for better imaging, sides angled towards rear for deeper soundstage. Shown is an intermediate version that uses 9 drivers in the array.

Below is 15-element array, super tweeter is in the middle. This produces outstanding dynamics.

line-arrays16.jpg line-arrays16-2.jpg

The super-tweeter can be by a replaced by a full-range unit, In fact, this is my latest configuration. I've not yet found a super-tweeter that I like to keep permanently.

15 units is not the limit, but close to the maximum for the listening distance I use. Later I may add one or three more drivers which will elevate in-room efficiency of each speaker above 103 dB/W/m.

Upgrade from 9-unit configuration was very pleasant, with no noticeable reduction of sweetspot or onset of lobbing, but with noticeable improvement in dynamics and efficiency. One way of wiring the drivers is as shown on the right. The total impedance is Id * 5 / 3, which for Id = 8 gives 13.3.

With 15 drivers, I rarely need more than 0.2W total from the main amps, even to play loud passages! When baffles are placed in room and in near field, each can produce ~ 103dB SPL at 2m with 1W, 0.1W yields ~ 93dB and 10mW give ~ 83dB. Bob Katz [4] explains that 83dB is the ideal listening level for full-involvement listening, and that should correspond to the level of 0dB on a VU meter. In my room, this requires 10mW, or 1% of power, and still leaves 20dB of headroom. Note that 83dB on each channel can yield up to 86-89 dB with two; I get several dBs more in my room due to subs (two more channels). Way, way too loud for home! I personally prefer to set my O VU at 83 dBs with all channels combined. Some home audio experts recommend zero at 80dB combined; some refer to 77dB per channel. regardless of whether I choose 80, 83, 86 or even 89 combined, with 20dBs still reserved on top, I'm happy I can enjoy incredible dynamics of K-20 recordings [4] with just one watt per channel using my no-feedback SET amplifiers.

Needless to say, if you build less efficient system that is a bit shy of K20, it still can do k14 flawlessly, which is great.

By the way, a few words w.r.t the math involved. Doubling of drivers adds 3 dB to speaker's efficiency. The formula is

   S = Sd + 3 * log2(N)

   where S  .... speaker's efficiency, dB/W/m
         Sd .... single driver's efficiency on infinite baffle,  dB/W/m
         N  .... number of drivers in the array
in my case Sd = 90.5 (conservatively) and we get

   for 1 unit ....  90.5 dB/W/m
            2 ....  93.5
            4 ....  96.5
            6 ....  98.3
            8 ....  99.5
            9 .... 100.0
            10 ... 100.5
            12 ... 101.3
            15 ... 102.2
            16 ... 102.5
            18 ... 103.0
            32 ... 105.5

for Sd=91, which is the norm for most PE 269-469 mounted on baffles after break-in, we add .5. Running a pair of speakers with separate amps adds 3..6dB, more often ~5, and sitting in the near-field sweet spot of a tall array pair at 2m distance subtracts ~3 dB (as opposite to 6dB for a point source) and influence of the room (1/4 space radiation, modes at <200Hz, reflections) adds 3-4dBs. With these assumptions, I get pretty high SPL levels at very low wattages and lots of headroom:


Here is rather very conservative Excel sheet, providing 90.5 for the driver sensitivity, 5dB due to channel coupling, complex formula S + 5 - 6 + (3 * N/18) for tall array effect, and no room boost:


still the numbers are very good for 12+ units in each array.

If you decided to replicate the design, here is the plan.

Drivers are mounted on 5 3-unit baffles made from white fir. The vertical posts are made from redwood.

Pine side baffles are on hinges allowing to adjust the angle for best-sounding combing and for depth of presentation.

These speakers are supported at the bottom by woofer speakers with separate amplifiers. I use the *same* 269-469 drivers on the bottom. Loaded below Fs, they are equalized at 12 dB in closed box configuration or at 18 dB in dipole (open box) configuration. Loading drivers below Fs is not very common but works very nice when done correctly. I use *lots* of drivers to limit cone excursion. Open boxes, despite less efficiency, excite room modes (and fireplace :) much less and produce much cleaner warble tones. Not surprisingly, dipoles are superior musically, adding much subtlety and articulation to kick-drums as well as much punch. The closed boxes can be seen behind the 9-unit arrays; each driver receives 6 liters of volume; the open-box configuration and the EQ can be seen behind the 15-unit prototypes. The boxes with back baffle removed and wooden shelfs on top form an H-frame tuned at 80-90Hz. At the moment I use 36 drivers (2 rows by 9 drivers per side). Within acceptable displacement, this gives enough SPL down to 20Hz (the upper range can be arbitrary and is determined by the Fs-induced pole and the sub baffle 6dB pole, and the -3dB point is currently at around 100..120Hz with the slope reaching 18dB/octave angle at ~ 200..250Hz. The production system will use twice that much, with drivers mounted on a dense 3-row grid. This configuration will reproduce enough SPL in 15...100 Hz range.

Integration of the sub module with the mains is perhaps the most important and delicate issue in such two-way system, and deserves a separate article. For now, I'll mention that I tried various "scientific" methods involving group delay calculations and then verified them in practical tests involving music samples, sine waves, SPL metering, phase adjustments and mic-to-scope setup. The position shown on the pictures is the one that is not the best from theoretical standpoint but the one that gives the best transients and musically most satisfying. Here is LF-only system response, giving the idea about the baffle roll-off, sub performance and most importantly, mains/sub integration. Note that absolute SPL levels of the two modules, combined, would result in a hump of a few dBs in the crossover region (80..140Hz) which does not show up because of phase shifts. It is because of these shifts the "-6dB at crossover" math rarely works in practice.


Response of the "current prototype" system consisting of two 15-unit open-baffle vertical arrays and two 18-unit horizontal dipole subs. The subs are equalized with 12dB/oct low-pass and additionally corrected by 31-band equalizer to produce 18dB/oct slopes. In-room response has much spatial variance due to standing waves, hence measurements were done in several locations around the sweet-spot and each vertical bar on the plots defines the range of SPL values for given frequency.

Equipment: mains - 1W triode amps, subs - PE 300W sub amps + GEQ 3102 EQs, EICO Sine generator, modified RS SPL meter (20-20K mic + schematics mod)

3.   References

[1] Thorsten Loesch on critical range

[2] Linkwitz dipole models

[3] OrdinaThor on Line Arrays

[4] Bob Katz talking about Magic 83, death of CD format, headroom, K-20 and K-14 systems

Author: Dmitry Nizhegorodov ( My other projects and articles