horn loudspeaker

  • Big BenD Bass Horn: Design

    Big BenD Bass Horn: Design

    [Previous: My Approach to Bass Horn Design; Main; Next: Scale Model]

     The requirements for the bass horn was set up in the overview article, and some additional considerations are outlined in My Approach to Bass Horn Design. This article will outline the basic design of the Big BenD horn.

    Initial Idea

    I have wanted a bass horn ever since I moved from Øyfjell. In Trondheim I had to make due with an Altec 816A enclosure, which has a horn, but that's more of an upper bass/lower midrange horn that doesn't add much to the actual bass. Moving to England I didn't even have the Altecs, and the first house didn't have enough space to set up much more than the midrange horns with open baffles. The open baffles, using either Altec 515-8G or various drivers I built, had decent performance, which is probably one reason why I kept them for so long. Another reason is I didn't have time to work on a big horn while writing the Book. But I was of course thinking about various options. 

    I could easily fit a horn mouth of 70 by 100cm, this would take up similar space to my baffles. Using a J-folded horn with the driver near the ceiling, I could easily get about a 250cm horn length, and with a throat area of 300cm2 the horn cutoff would be about 35Hz. With an Altec 515-8G the response is quite smooth, if the horn is placed in the corner:

    Horn1SPL

    The throat impedance is also quite smooth:

    Horn1Z

    This is for the horn placed in a corner, i.e. eighth space. In practice, however, the horn will be out on the floor, since I live in a rented house and can't make horn-sized holes in the walls. We'll see the disasterous effects of this shortly. 

    Horn Bends

    There are many ways to fold and bend horns, as outlined in the Horn Book, chapter 26. Sharp folds cause powerful reflections, and typically the throat resistance falls to zero save for at the resonances, above a few hundred hertz. Gentle bends with a bend severity parameter (ratio of horn radius or half width to the bend radius) smaller than unity, on the other hand, have much less reflections, and less issues with loss of radiation resistance and peaks and dips in the response. 

    In order to make it easier to play around with the geometry, I rewrote the horn curving tool in my simulation software, so that bends could be specified in several ways. For variable radius bends, this included some math in order to find the length around the bend. I also wanted to be able to specify two out of three of the parameters bend length, bend radius (relative or absolute) and bend angle. For the one-dimensional simulations I had also implemented the 1D theory outlined in the Horn Theory chapter in the book. While an approximation, it would at least give an indication of the change in acoustic length at low frequencies. 

    New Design

    As mentioned, I was also considering building a midbass horn, but with the effect of the rear wall causing a loss of radiation resistance right above the corner frequency of the horn looked like it could be troublesome. So after some thought, I decided to build a bass horn based on the initial ideas. 

    In the meantime I had also looked into designing a dedicated bass horn driver. Many of the classic bass horn drivers, like Altec 515 and JBL 2220 are 15" drivers, and building something similar was of course an option. But there are some factors that suggest this is not optimum for domestic use. A domestic bass horn does not need the power capacity of cinema and PA speakers. Even a couple acoustic watts is plenty, easily producing 120dB SPL in a small room. With the high efficiency of bass horns (25-50%) there is very little demand on the driver. I am all for having plenty of headroom everywhere in the system, so that amplifiers and speakers are only coasting along at even the highest peaks. But even with my open baffles, with C-weighted average SPL of 112dB in the listening position, the peak instantaneous power to the woofers was in the order of 30W. The bass horns should be at least 10dB more efficient. 

    Therefore a 12" driver would be a better choice. Cone breakup would also be pushed higher, and considering I wanted this horn to behave nice way above the intended 300Hz crossover frequency, that sounded like a good idea. Diaphragm displacement could still be kept low. 

    A 12" driver has a piston area of about 550cm2. I would like to keep the compression ratio low, so I selected a throat area of 250cm2. With an RE of 6.5ohms, a Bl of about 18Tm would be suitable. Diaphragm mass should be fairly light, and the suspension soft, in order to use a relatively small rear chamber. While I didn't have such a driver at hand, I planned to build one. 

    Geometry

    The geometry went through several iterations. With the smaller throat area I had to make the horn longer. After some number crunching I also found that I could get a bit more deep bass out of it if I made it slightly longer, placing the cutoff at 30Hz. This became the base design. The mouth was kept at 7000cm2, 1m wide and 70cm tall. 

    The first part of the bending geometry to be worked out was the mouth bend. Making a bend often involves laminating thin plywood, or using bendable types. Or both. I therefore looked into having a constant width bend to simplify things: this way simple flat plywood side walls could be used. But this geometry has quite sharp discontinuities, and it's also not visually satisfying. 

     

    Horn1CWbend

    I therefore went for a simply curved bend. This means that the side walls also twist around the bend, necessiating a somewhat complex jig for laminating. But there is no longer any sharp discontinuities. I also decided to use a constant instead of variable curve radius, together with a vertically asymmetric geometry. The inner curve is therefore quite close to a constant radius too. 

    The mouth segment was designed to be fairly flat on the top, to provide a "shelf" for the midrange horn. This also set the depth of from the horn mouth to the front of the upright part, so to make it possible to fit the length of the midrange horn there.

    The middle segment, which I call the spire since it goes straight up, is asymmetric. This is to push the horn into the corner, so it doesn't cover too much of the window. 

    The throat bend was designed last, and here I chose to use a constant width for most of the length. Initially I considered a 90 degree bend here too, but since this would place quite a strain on the joints from the lever action and the weight of the driver, I made it a 180 degree bend in the end. 

    At this point I basically had the geometry laid out. See 3D rendring below. 

    Horn1CWbend

    There is space below the horn, the reason for that will become clear soon. 

    Simulations

    The horn was first simulated using a 1D model, with the horn mouth flush mounted in a corner. This is the infinite baffle +  two reflecting surfaces boundary condition. It is easy to calculate the radiation impedance and SPL under these conditions. Here is the SPL response at 1m on-axis:

    On-axis SPL

     

     In the listening postion the response is not as extended, both due to directivity and interference from the floor and side wall reflections.SPL in listening position

    The throat impedance also looks pretty good:

    Throat impedance

    Under these conditions, I also made an FEA simulation of the horn, to look at the wave fronts inside. Using gmshfor meshing, and Pafecfor simulations, the geometry was exported, meshed ans simulated. Symmetry planes were used to create a corner boundary condition. 

    Wave Fronts

    The geometry was simulated before I had settled on the 180 degree throat bend, but the rest of the geometry matches the final design. The wave fronts heave well inside the frequency range I intend to use the horn (up to 300Hz). At 460Hz we start to see mode formation in the mouth bend, and the wave fronts are somewhat rough even at 355Hz near the mouth. This is to be expected. Adding a lumped parameter driver model to the horn, we get the on- and off-axis results shown below (2m distance). There are no great peaks or dips in the working range. 

    FEA simulation

    Rear Wall

    But the horn will not be flush mounted in a wall. The mouth will be about 1.25m in front of the rear wall. The SPL in this case is shown below. There is about 5dB loss in bhe low frequencies due to the rear wall reflection. 

    Listening position SPL with rear wall

    The reason can be seen in the throat impedance, which is much more peaky compared to the flush mounted condition:

     

    Throat impedance with rear wall

    And the reason for this is the effect of the rear wall reflection on the radition impedance.

    Radiation impedance with rear wall

    There isn't really any practical way around this. Possible solutions would be

    1. Knock a hole in the wall and flush mount the horn
    2. Make the horn mouth a lot bigger
    3. Move the bend nearer the mouth
    4. Build a baffle in the wall, effectively making a partition

    None of these are very practical for me. In addition comes the complication of room modes, which I will return to later. However, there is an option that could be worth investigating: making the reflection weaker, for instance by using a Helmholtz resonator near the rear wall, under the horn (this was the reason for the space underneath the horn). I will investigate this using a scale model. Possibly an active solution could help too. But regardless of this, an impedance matched driver will give the smoothest possible response in any situation, so this must be implemented. 

     

     

     

  • Big BenD Bass Horn: Scale Model

    Big BenD Bass Horn: Scale Model

    [Previous: Design; Main; Next: The throat bend]

    One way to test aspects of horn design which are hard to simulate, is to make a scale model and measure it under similar conditions. A friend with a small CNC machine cut some plywood sheets based on exported on-the-flat profiles of a simplified version of the horn, having only the mouth bend. The scale is 1:5.

    Kit

    The mouth bend is the most important in this case, as this sets the footprint of the horn, and therefore enables us to position the horn in the same way as it will be positioned in the room.

    ScaleModel2

    To drive the horn, a scaled down driver is also required. I used a Celestion AN2775 driver, as I had some at hand. 

    ScaleModel3

    The horn was then placed in a corner, and a few experiments were tried. 

    ScaleModel4

    Below are frequency response curves for the horn alone in the corner, and with a cardboard baffle flush with the horn mouth. There is a 5dB loss of sensitivity, similar to the simulated loss, so we may assume we will get a similar loss for the big horn in real life.

    I also tried making a Helmholtz resonator under the horn, but this only reduced the loss by 1dB. 

    ScaleModelFR

     

  • The Big BenD Bass Horn

    The Big BenD Bass Horn

    Those who have followed the evolution of my system, will have noticed that I haven't had proper bass horns since 2010, before I moved to Trondheim. In Trondheim I had Altec 816Abins, but they don't count as bass horns. They have a cutoff of about 160Hz, and create a bump at about 200Hz, which made them a bit challenging to cross over to my midrange horns. 

    Proper bass horns is something different. Having experienced horn loaded bass down to some 35Hz before, I miss the physical impact, detail and texture you get with proper horns. So after the Horn Book was completed, and I had recovered from the experience and enjoyed some spare time (although most of it in lockdown), it was time to bring a bass horn into the Kolbrek household again. 

    Having coauthored the book on horn speakers, I knew I couldn't take shortcuts. Like building someone else's design! There are many clever and experienced horn designers out there, but in addition to using the knowledge gained while researching the book, I also wanted to make a horn that would match my room and system. 

    First Ideas

    I started thinking about this several years ago. Some quick calculations showed that a 2.5m long horn with a 7000cm2 mouth, using an Altec 515-8G driver, would produce decent bass down to about 40-45Hz. It could also be built in the form of a J, with the mouth at the floor and the throat near the ceiling. But at this stage I was still workig on the book, and had neither the time nor the tools to start such a project. 

    A second idea was to build a midbass horn covering down to about 100Hz, and making a subwoofer for the frequencies below 100Hz. The concept I was toying with was using two 12" drivers in a straight midbass horn, with about the same mouth size as the bass horn outlined above, and some sort of Slot Loaded Open Baffle (SLOB) built into a platform the horn could stand on. This would make the horn design fairly straightforward, but had the complication that I needed another amp and two more DSP channels. While I plan to upgrade my DSP, this approach required too many changes to the system to be convenient. Another problem was also showing up.

    When the first lockdown started in 2020, with furloughs and working from home, I was asked to worked reduced hours. The extra time was spent extending my horn simulation software to approximate the reflections from a rear wall. Hornresp assume a corner horn to be placed in the actual corner, essentially the horn is built into one of the walls. In my PhD I extended this modelling to allow the horn to be moved away from the corner, but still being mounted in one of the walls. This does some rather unpleasant things to the radiation impedance, creating dips that create larger impedance ripple and reduced output. 

    Using the image source method and a simple low frequency approximation for diffraction, I was able to model the horn in front of a rear wall in a way that matched reasonably well with BEM. All good so far. Except this placement had the same shortcomings as when a horn is moved away from the reflecting surfaces. The added time delay and phase shift creates dips in the radiation impedance and response. For the placement I had planned for the midbass horn, the dip came right at the lower end of the band, effectively pushing the lower 3dB frequency up by a significant amount. 

    So after some simulation and thinking, I abandoned that idea too, and began looking at the J-curved horn again. And I realised that to make a horn like that, I had to upgrade my curving tool. That took a few months, but then I was ready to design my new bass horn.

    Requirements

    Before starting a project, it's good to make a list of requirements. Then work from the requirements towards a design that will fulfill them. In my case, I wanted the following:

    • Bass down to at least 40-45Hz
    • Not (too) undersized mouth
    • Not critically dependent on driver parameters
    • Easy to cross over to the midrange horn at about 300Hz
    • Modular
    Low Frequency Extension

    The low frequency extension depends on the horn lenght and mouth size. Essentially we want the throat impedance of the horn to follow that of the infinite horn as closely as possible, but this is impractical for bass horns. We should still try to avoid impedance peaks. The lenght also needs to be sufficient, so that the first impedance peak isn't placed too high. This becomes more critical the smaller the mouth becomes. 

    Not Undersized Mouth

    This is important for to reduce the impedance ripple. A good match between driver and horn (set by driver parameters and throat area) will minimise response variations in the face of impedance variations, but the horn can often end up fairly narrowbanded, especially of it is folded. 

    But mouth size is also set by practical limitations. In my case a mouth size of about 100 by 70 cm was the largest I could allow. This is a fairly substantial mouth size, nearly the size of the baffles I currently use, but still relatively small for a 40Hz horn. I would have to accept a compromise here. 

    Driver Dependency

    If throat impedance ripple is reduced, so is sensitivity to driver parameters. This means that several drivers are possible, and that I can experiment without having to do major modifications. 

    Crossover

    Crossovers in horn systems can be tricky. Direct radiators may have some bandwidth outside the crossover frequency, but are still often pushed quite far. Textbook crossovers require the response of the drivers to be flat way past the crossover frequency, otherwise the response of the drivers have to be factored in when designing the network. Or, if using an active crossover, EQ applied to flatten the response so that the acoustic slopes are as desired. For horns, things often seem to be pushed even further. Horns need to be a certain size to be usable down to a given frequency, and although they have high group delay near cutoff, people often want to use as much of that hard-earned bandwidth as possible. Bass horns are often extra tricky to cross over, as they may be folded and have response irregularities, sharp dips and peaks that makes the phase go haywire. 

    I usually cross my midrange horns at around 300Hz, so the horn should behave well up to at least 400Hz, preferably higher. When testing horn folding methods for the Horn Book, I noticed that a fold typically creates a sharp loss of resistive loading above about 200Hz in typical bass horns. This would not be good for a wide band bass horn. 

    Curving, on the other hand, while having its own challenges, doesn't create the reflections and cancellations of a folded horn. Therefore the horn would need to be gently curved, not too sharply. 

    Modular Build

    In order to get the horn into the house, it would have to be divided into sections. This also makes it possible to experiment with inserting other sections, removing sections and so on. It creates more possibilities for problems, like leakage, but the flanges also act as bracing. 

    The "Blameless" Concept

    In his articles, and later books, on power amplifier design, Douglas Self describes the concept of a "blameless amplifier". The concept is, in his own words,

    "...the concept of what I have called a "Blameless Amplifier", the name being chosen to emphasise that the remarkably low THD comes from the avoidance of errors rather than from fundamental advances in circuitry."

    I have a great deal of respect for Mr. Self and his approach to audio design, and especially the blameless concept is something well worth adopting for more than amplifiers. Oftentimes we want to make "the best" speaker or amplifier or turntable by applying some new and inventive concept, while very good results can be had by identifying problems in old and "boring" technology and fixing them. Self identified a series of distortion mechanisms in a classic, standard amplifier topology, and through simulations and practical tests reduced or eliminated these mechanisms. 

    In the same way, I will try to eliminate or reduce as many problems as possible in this bass horn. Since it is my first design using this approach, and since the thought came up after I had started building the actual horn, it will not be completely blameless. But I will, as far as possible, do scientifically and rationally guided choices, backed up by simulations and measurements. 

    The Horn

     Since this design will take some time to complete, I will post updates in my blog, using this article as an index page to the blog entries. 

    1. My Approach to bass horn design
    2. The design
    3. Scale model
    4. The throat bend
    5. The middle section and rear chamber
    6. Belts and braces pt. 1
    7. Belts and braces pt. 2
    8. The mouth bend
    9. Belts and braces pt. 3
    10. The mouth section
    11. Belts and braces pt. 4
    12. Performance measurements
    13. Installation
  • The Big BenD Bass Horn: Throat Bend

    Big BenD Bass Horn: Throat Bend

    [Previous: Scale ModelMain; Next: Rear chamber and Middle Section]

    One of the first things I started building was the throat bend. Basically because it was a fairly small part, that was easy to build before the garage got filled up by the large mouth bend and mouth sections. But as you will see in the background on some of the pictures, some of the other sections were also under way during the building of the bends. 

    In laying out the bend, I had first drawn everything up in CAD. At the centre of the arc I drew lines every 15 degrees, and measured the inner and outer radii. On the plywood I similarly used ruler and compass to divide the circle into 15 degree segments, and used the dimensions from CAD to draw up the outer curve. The aluminium ruler was (ab)used as a spline ruler to get a smooth curve. 

    Bend dimensions

    With the curves drawn, the four side walls were cut and sanded to match each other. As mentioned previously, I decided to go for constant width most of the way around this bend. 

    ThroatBend2

    For the part nearest the throat, I changed the profile from constant width in order to make the throat more square. Using a router table, I got the angles right so that everything matched up without gaps. 

    ThroatBend3

    The throat bend is built on a sheet that serves as a flange for both ends: one end connects to the spire/middle section, the other end to driver box. This stabilises things and puts less stress on the bend itself. 

    ThroatBend4

    The throat end and the bend sides are connected using wooden dowels. 

    ThroatBend5

    The sides are then glued to the flange, also using wooden dowels for support. These are drilled and hammered in from the outside, leaving the inner surface untouched.

     ThroatBend6

    For the inner curve, three layers of 5mm bendable plywood were used. The curve was too steep to use other types of plywood without steaming.

    ThroatBend7

    The inner surfaces are then painted to reduce absorption.

    ThroatBend8

    The "ceiling"/outer wall has an innner skinn of aluminiumm. A groove is routed in the side walls. 

    ThroatBend9

    Laminating the outer sides was a bit tricky. I Used two layers of 3mm hardwood plywood and 2 layers of 5mm bendable plywood. Getting things properly aligned took some practice, and I found it was easiest to nail each layer using small nails, instead of using clamps. 

    ThroatBend10

    A view from the bottom, showing the aluminium "ceiling".

    ThroatBend11