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 816A bins, 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
  14. Driver update

Latest blog entry

Horn Loudspeaker Simulation

Horn Loudspeaker Simulation

Many readers may be familiar with the free software Hornresp, which, given driver parameters and some geometrical parameters for the horn and cabinet, can simulate a wide variety of horn, direct radiator and bandpass systems. This may be enough for most people, while others (like me) are curious about the math and algorithms behind it

Simulating horns and horn loudspeakers has interested me for a long time. I found Hornresp back at the time when David McBean first made it available (around 2000 I think). At first you could only get the full functionality by paying a small fee, otherwise the throat area of the first segment was fixed. He later told me that he actually ended up giving the full version for free to those who asked, and if I had known that I'd probably started using it in earnest earlier. But my first midbass horns were designed using Hornresp (with the original limitation), as was my later horn subwoofer and other horns. But around 2005-2006 I got interested in horn theory and other methods of evaluating horn performance, like power factor (the cosine of the phase angle between resistance and reactance of the throat impedance). First I made a program that would read the data exported from Hornresp and plot the power factor. Later I started looking into wave fronts in horns, and combination of horn types (like multiple segment horns with Hypex segments), and for that I needed to write my own horn simulation software. 

I first made contact with David McBean in 2004, and we started corresponding regularly, discussing many aspects of horn simulation. This was extremely helpful when I started writing my own horn simulator, and I can't thank David enough for making Hornresp available, and for guiding me through the rough terrain of horn simulation. Although he never showed me more than a couple of snippets of code, through discussion and references I was able to make things work and learn things from the ground up. 

My horn simulator, HornCAD™, evolved into a complex program that could use the Mode Matching Method (MMM), simulate all types of segments, rectangular horn, and curved horns. It could use measured compression driver data, and export dxf files for CAD use. Thanks to the MMM, directivity simulations were quite accurate, and I used it extensively during my time at Celestion. 

But since HornCAD™ was born as a tool to learn horn simulation and to explore various ways to simulate horns, it is full of unfinished functionality and bugs that are hard to track down due to the size of the code base. Therefore it has never been released to the general public. That may change in the future, though... But enough about my background as a horn simulator writer!

Simulation Basics

The point of this article is to give an introduction to horn loudspeaker simulation. While it may seem like black art for most people, it is more similar to electrical circuit simulation. So in this little series, I plan to explain how to implement a simple "Hornresp-ish" code in Octave/Matlab. It will of course not have all the bells and whistles of Hornresp, but will be able to simulate the power response, electrical impedance and diaphragm displacement of a basic horn loudspeaker. 

Horn loudspeaker simulation typically consists of simulating:

  1. The radiation from the horn, especially radiation impedance, but also directivity.
  2. The horn itself: throat impedance as a function of mouth radiation impedance, and the output volume velocity as a function of the input volume velocity.
  3. The acoustical circuit apart from the horn: front and rear chambers, vents etc.
  4. How the loudspeaker driver behaves when connected to the acoustical load made up by the horn, chambers, vents etc and thereby the power delivered to the horn, the electrical input impedance of the system, diaphragm displacement etc. 

We will cover all of this, but also things like simulating multiple segment horns, horns with special profiles like the tractrix, and maybe even look at tapped horns. 

Glossary

The list above contains many words that may be unfamiliar, but if you want to learn horn simulation, you need to know what they mean. So here is a short glossary:

  • Radiation impedance: When something vibrates with a certain velocity, it pushes the air, and the air pushes back with a certain force. The ratio of this force from the air to the velocity of vibration is the mechanical radiation impedance. In this analogy, force is analoguous to voltage and velocity to current, and just like voltage divided by current gives electrical impedance, force divided by velocity gives mechanical impedance. 
  • Volume velocity: velocity times area, cubic meters per second.
  • Acoustical impedance: A similar analogy can be made in acoustics: with pressure analoguous to voltage and volume velocity analoguous to current, the ratio between them is acoustical impedance. It relates to mechanical impedance through the area of the vibrating surface (which may not be solid, but can be an imaginary surface, for instance the horn mouth). Mechanical impedance is acoustical impedance times area squared.
  • Acoustical circuit: an analoguous circuit of acoustical components like ducts, horns and volumes. It can be drawn like an electrical schematic, and we can calculate its performance based on electrical circuit theory. This is a fundamental method for simulating electroacoustic systems.

Simulation: The Nitty Gritty Details

Here are links to the parts in the series (the links will go live as the parts are added):

  1. Part 1: Radiation and T-Matrix
  2. Part 2: Adding a driver
  3. Part 3: Multiple segments and more T-matrices
  4. Part 4: Other horn profiles and curved wave fronts
  5. Part 5: A simple tapped horn model

The Bass Transmission Index

The Bass Transmission Index

Evaluating the accuracy of low frequency reproduction isn't as straightforward as one may think. There is talk about "fast bass", and PRAT (Pace, Rythm And Timing) is sometimes mentioned as a description. In such a discussion someone will invariably point out that a 20Hz sine wave isn't "fast", and that the issue of fast or slow bass is meaningless. It may seem that way using these simple arguments, until you experience accurate, detailed bass reproduction. But how do we quantify it? Obviously not by measuring the rise time of a 20Hz sine wave! 

This is actually a very real problem. For the mix engineer, perhaps the biggest problem is how a loudspeaker with poor temporal response alters the perceived balance between rhythm section instruments like kick drum and bass guitar. Though not exclusively the case, loudspeakers with ported cabinets (bass reflex loading) are more likely to exhibit this type of problematic behaviour, due to the use of resonant elements to increase bass extension. An incorrect mix made on loudspeakers like this may not transfer well to other sound reproduction systems, and can't be corrected later during mastering, since the two instruments occupy the same part of the audio spectrum.

Lara Harris, Keith Holland and Philip Newell have done extensive work on quantifying bass reproduction accuracy, resulting in Lara's PhD work and the Bass Transmission Index (BTI). The BTI is an objective measure of a loudspeaker's ability to accurately reproduce low-frequency musical content. The metric aims to describe how well a loudspeaker reproduces the temporal envelope of a dynamic and harmonically-complex signal, something that cannot easily be evaluated from the usual frequency response (magnitude plots). 

Like the STI (Speech Transmission Index), as used in speech intelligibility measurements, the BTI is based on a metric called the Modulation Transfer Function (MTF). MTF-based methods such as these pass an amplitude-modulated signal through the system, varying the rate of the temporal fluctuations across a range of values that are likely to feature in the real-world signals that the system will encounter. The preservation of modulation depth between input and output is used as an indicator of how well the system can reproduce these temporal variations. The figure below illustrates the concept, showing modulation depth for input (mi) and output (mo) signal envelopes.

MTF

The BTI evaluates the MTF in 10 frequency bands from 16-160Hz, with 7 modulation frequencies from 0.8-11.7Hz. The algorithm computes a matrix of modulation index scores between 0 and 1 for each combination of frequency band and modulation frequency. This grid of numbers can be used to calculate an overall average score, and is visualised as a grayscale intensity image where white = 1.00 (perfect reproduction). As a rule of thumb for interpreting these BTI intensity images:

  • Inconsistent shading in the horizontal direction (left-right) indicates variation in the frequency response magnitude (this is variation across frequency bands).
  • Inconsistent shading in the vertical direction (up-down) indicates variation in the faithfulness of envelope transmission (this is variation across modulation frequencies).

The figure below shows an example BTI intensity image and mean score for a bass-reflex studio monitor. Frequency bands (centre frequencies) are on the x-axis, and modulation frequencies on the y-axis.

BTIplot

Recently I have worked with Lara to make her BTI research code production ready, and it has now been officially made available on GitHub. It runs in Matlab and Octave (although not all the advanced options are available in Octave, and some requires certain Matlab tooboxes), and demonstrates a reference implementation. Here are the links:

BTI Toolbox on GitHub

Lara's LinkedIn post about BTI

My LinkedIn post about BTI

 

Big Bend Bass Horn: Driver Update

Big BenD Bass Horn: Driver Update

[Previous: InstallationMain

This update is actually long overdue, and related to a project at Celestion I wasn't able to finish: a cone driver specifically designed for bass horns. It follows the ideas I outlined under My Approach to Bass Horn Design, and is a 12" driver designed for a compression ratio of about 1:2. As I wanted it to be easy for Celestion to put it into production, I used as many standard parts as possible, either directly or something that could be easily machined from standard parts. But I also added a feature that aren't easy to find in modern drivers: an underhung edge-wound voice coil. 

Here are a some of the features of this driver:

  • Underhung 3" edge-wound voice coil
  • Copper sleve on pole piece
  • Focused magnetic gap
  • Low moving mass
  • Vented pole piece and back plate
  • 250W power handling
  • Large ferrite magnet
  • Inverted dustcap to allow for phase plugs if desired

And for those who worry about the high power rating being detrimental to other qualities important for horn speakers, rest assured: this power rating was a result of the voice coil size and venting, not of "beefing up" the driver (which typically makes the moving assembly lighter) to take higher temperatures and forces. 

Here's a side view of the driver, without the front segments. It's built on a Celestion FTR chassis. 

New driver

The magnet system:

bigBendDrivers3

The gap flux is slightly above 1Tesla, which is quite good for a gap this size. It takes a substantial amount of magnet to produce that, especially when you lose gap width to a copper cap. 

Comparisons with old DIY driver

Below are a couple of photos comparing the new driver to a DIY project I used to begin with, referred to as 12" DIY driver in the performance measurements. The DIY driver used the motor system from a pair of Celestion NTR08-2009D 8" woofers I found in the bin. They had the cones cut out, but the motor was salvageable (even the voice coil), and I used them to build a pair of 12" drivers using available parts. I used the lightest 12" by 2" cones I could find, and a fairly soft spider. They turned out to be quite good, with the BL^2/Re being a good match for my bass horns. But the new drivers are more robust, and also give a very good performance and produces very clean bass in the Big BenD horns. 

Comparision with old DIY driver

Comparision with old DIY driver (back)

 Parameter  Old DIY driver  New driver
 Re [Ohms]  4.46  5.8
 Le [mH]  0.065  0.086
 BL [N/A]  12.3  17.0
 Mms [g]  39.2  64.5
 Rms  [Ns/m]  3.4  0.63
 Cms [m/N]  4.36e-4

 1.88e-4

     
 

Now I just hope Celestion will finialize this project and put the drivers into production, as I think this would be a good driver for bass and midbass horn use, especially for domestic use.

[Previous: InstallationMain

Big BenD Bass Horn: Installation

Big BenD Bass Horn: Installation

[Previous: Performance MeasurementsMain; Driver Update

Finally, the last article about the Big BendD bass horn! This part will cover the installation and setup of the horn, with some comments on the subjective performance at the end.

Installation

Although the DIY 12" driver showed the most promise during outdoor testing, I still wanted to try the Altec 515-8G when setting up the horn. It was mounted in the rear chamber, the chamber was filled with wool, and the rear wall covered with pieces of an acoustic celing tile. 

RearChamberAltecWoolBackWallDamping

Then came the process of carrying all the parts into the living room, setting it up, adding gaskets, bolting it all together, installing the drivers, wiring it up and put the rest of the system back together. In the process I had help from my good friend Harry. This is really a two-person job, because carrying the big parts into the house isn't easy to do by oneself. The parts were all designed to fit through a standard door, but they are still a bit difficult to move around. 

Setup01Setup02Setup03

Setup01Setup05Setup03

Setup01Setup08Setup03

Setup01Setup11Setup03

With two people working, the setup was done in a couple of hours. There are a lot of bolts, about 70 per horn, so or ratchet spanners got a real workout. 

The complete setup is shown below. The white middle/throat sections blend in with the walls, making the bass horn less dominating in the room. It does work, some people have not recognised it as part of the bass horns.

Axi2050Proto1

The First Test: Where's the Bass?

Just setting up the horn and putting some music on, without any crossover or EQ, left us wondering: Where's the bass? Isn't this supposed to be a bass horn? There's a lot of lower midrange, but the sound was a bit thin. 

Altec95dBInRoomThe measurements made it obvious what the problem was: the output fell below 70Hz, and apart from a peak at 50Hz, the response was more like a midbass horn than a 30Hz bass horn. What was going on? 

We swapped the Altec for the DIY 12", and that helped significantly; the better impedance match between the horn and driver was definitely an issue in the presence of room modes. Which turned out to be the real problem.

Room Modes

 My living room is about 7m long and 3.5-4m wide. This means that the second mode in the length direction and the first mode in the width direction are both at about 50Hz, which is also clear from the measurement above. Between these two modes, energy transfer in the room is quite limited. A wider room would definitely be an improvement, but you have to work with what you've got. 

In the modal region in a room, the response can vary quite a lot from position to position. Some listening positions have a smoother response, while others place the listener at peaks or nulls of modes. To find the best starting point for EQing the response, I measured the response in the room at a 2.5 by 3m grid, every 0.5m. The results for all positions are shown below. 

RoomRespGrid

It turned out that the response was quite smooth about 3m from the horns mouths, somewhat behind the middle of the room. The responses at this line are shown below. Annoyingly, the response drops quite sharply below 45Hz, due to the lack of modes between 25Hz and 50Hz, but apart from rebuilding the room (which I'm sure the landlord wouldn't like), there's not much to be done. 

RoomResp3m

I have applied some EQ to lift the response a bit, but one should be very careful with EQing dips caused by room modes. And I'm not going to spend the rest of my life in this house, so hopefully my nest home will have a more beneficial distribution of modes int eh listening room!

Listening Tests

So, after all this work, how does it sound? The lack of output below 45Hz is only noticable on music where you know there should be something down there. Apart from that, the response in the listening position is quite smooth, and it has the traits of bass horns that I have been missing for so long: proper impact - even at low volumes -, and responsive, detailed and tight bass. Low frequency details in the recordings are quite easy to hear, and there's no overhang or resonance. It sounds effortless even at very high volumes too. The horn integrates well with the fast and detailed midrange of the Axi2050, making it a good combination. I also tried a delay-derived subtractive crossover, as described in the Horn Book, and it made a worthwile improvement to the coherence and naturalness in the lower midrange.

All in all, I'm very satisfied with the performance. 

[Previous: Performance MeasurementsMainDriver Update

Big BenD Bass Horn: Performance Measurements

Big BenD Bass Horn: Performance Measurements

[Previous: Belts and braces pt. 4Main; Next: Installation

 With one horn finished, I took it outside to do some frequency response measurements. First thing to do is to measure the horn under conditions similar conditions to the simulations. This is a very important part of designing speakers, if you want to use simulation tools in the process. You need to verify that your simulation is correct, and if not, in what way. It is especially important if you are writing your own simulation software. I think people are getting better at it, but there have been many cases on DIYaudio of people complaining about their simulations being wrong, when the actual problem is that they have not simulated what they have actually built. 

Corner

The actual condition of a horn built into an "infinite corner" (3 infinite baffles perpendicular to each other) isn't easy to achieve in practice. The best I could do was to use the walls of my house and garage:

Testing1

And then put some extra sheets of plywood between the buildings to try to close the gap.

Testing2

So, finally the first measurements, with and without baffles. The difference isn't huge, This may be because the garage is still close enough in terms of wavelengths to contribute to the baffle effect. (I'm not sure if the levels are actually correct, trying to do the calibration in ARTA gave some confusing results.)

MeasuredCornerTxt

So how well does this fit with the simulations? Actually pretty good, see below. The Response below 200Hz is almost spot on, the  response at higher frequencies deviates, probably because of the simple model used for simulating the curving, and because I used a different driver than in the measurements. 

What I'm quite happy with is that the curving approach worked as intended: there are no sharp dips and peaks or suckouts in the response, and it doesn't roll off until about 500Hz. This creates a nice overlap with the midrange horn. At the lower end, the response starts to fall off rapidly below 30Hz, which was the intended lower limit. The response is a bit uneven, but we'll see that this changes with a different driver.

OutdoorResp

Wall

The second test condition is in front of a wall. Neither of the two are fully representative of the operation conditions in actual use, but it will show the effect of placing the horn in front of, instead of flush with, a wall.

Testing3

The effect of one missing side wall and the increased distance to the back wall is evident: a loss of level at low frequencies that was predicted by both the simulations and scale model measurements. 

MeasuredWallTxt

Driver Tests

The next measurements were done with REW as I found it easier to do a level calibration there than when using ARTA. Four different drivers were tested:

Altec 515-8G, a 15" driver built in a Celestion FTR-3070 chassis, A 12" guitar speaker, and a 12" high efficiency woofer built using various parts available. The results are shown below. 

There is a clear difference between the drivers; the guitar speaker clearly fails and has a very peaky response (not all musical instrument drivers are suitable for bass horn use, even if Dr. Bruce Edgar had good results with EVM-12). The 15" drivers perform about the same. The best results comes from the 12" driver I built. This isn't actually very surprising, since it has the best impedance match with the horn of all the drivers. 

The dips in the response at 483Hz and 870Hz are from standing waves in the empty rear chamber.

FR105dBWall

Distortion

Following is some distortion meausrements of the drivers tested. I measured at 95, 105 and 115dB SPL at a 2m distance. Only the results for 115dB (114dB for the 12" prototype) are shown.
Altec115dB

15inDIY115dB

Guitar115dB

12inDIY115dB

The 15" drivers are quite similar in response, but the Altec clearly has lower distortion. The guitar driver has very high distortion (not surprisingly, since it has a stiff paper surround and only 1mm overhang on the voice coil), and is best left to what it was designed to do: create distortion for electric guitars. 

The 12" DIY driver has the smoothest response, and while the distortion is slightly higher than the Altec, they are both quite at "sane" listening levels.  

Altec95dB

12inDIY95dB

[Previous: Belts and braces pt. 4Main; Next: Installation