Acoustic Loading Optimized William Neile Horns – Part 1

It is quite a long time ago since I wrote my last article about William Neile Horns. There was definitely considerable progress exploring and refining this new type of horns, but unfortunately the lack of spare time did not allow it to be documented. The attentive reader will certainly not have missed the fact that one of my fundamental goals is to achieve a good acoustic horn loading almost down to the desired cut-off, but the William Neil horns presented so far behave more or less like classic waveguides with regard to horn loading as there is no visible cut-off, instead of this a very slight roll off of the radiation impedance towards low frequencies happened. Although, some people might in fact prefer the loading properties of my first William Neile horns. 

This article series will deal with acoustic loading optimized (ALO) William Neile horns which means that acoustic loading should be pushed to the most reasonable level down to the desired cut-of frequency but at the same time keeping the resonances / reflections of a classical exponential wave front surface area expansion to a minimum. I am aware that there is a controversial view about horn loading in the community. Some say that horn loading is almost unimportant as you can simply push the driver where you need the output. Directivity control should be the major design objective of a horn . I have a different view on this issue as generally without proper horn loading you need to push the driver more and more towards lower frequencies where it hurts most as the excursion doubles with each octave towards lower frequencies and when there is any need to push the driver even more – it might work technically – the excursion needs are even larger, so this is never the best solution.  Horn loaded compression drivers are an ideal combination with low power single ended tube amplifiers using a passive crossover – well, usually there is almost no output power left to push anything. The speaker has to sound great with the first Watt of output power and even with much less. So with more low frequency loading from the horn you get more SPL in that region and less output power means less excursion for lower frequencies. My experience is that a compression driver used within the acoustic loading optimized frequency band of a horn (resistive loading) will give you much better micro dynamics with an open and effortless sound. What I intend with new ALO William Neile horns is to combine good acoustic loading characteristics and good directivity control especially for the horizontal plane. This is not an easy task but as we will see that it is possible.

The BEM simulations of the final ALO William Neile horn designs were indeed so promising that is is planned to have the first prototypes made since the inherit property of the Neile parabola obviously provides the capability to obtain very good directivity control especially with smooth transitions along the frequency pass band of the horn. This property combined with an exponential throat section and an appropriate mouth termination flare there is a valid prospect of an excellent horn design.

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PETF Applied to JMLC Horns – Simulation Results

In two previous posts I presented my PETF algorithm and JMLC inspired horn calculator. Assuming that many of my readers are familiar with the native JMLC horn performance like loading or radiation polar it should be a common acceptable consensus that JMLC horns do not belong to the so called constant directivity (CD) category. Towards higher frequencies they tend to slightly beam which is because of the curved horn walls. This might not be an issue for some applications or some people might even like this behaviour but as general rule of thumb the lower the horn cut-off value the longer the horn profile will be and the smaller the initial opening angle both causing an increasing tendency to narrow the dispersion of higher frequencies. A more focused dispersion of higher frequencies might be an advantage in small environments if it is fairly constant or if the intention was to compensate the natural roll-off of most compression drivers but generally a design goal of wider dispersion is one of my personal preferences. More precisely, one of my main goals is to find a good compromise between good horn loading and good directivity control.

There can be found some BEM simulation examples for round JMLC horns in the web that clearly show the increasingly more narrowed dispersion towards higher frequencies especially for the lower loading versions with 350Hz or lower cut-off. On the opposite JMLC horns shine if the target design intention was mainly a nearly perfect horn loading down to the desired cut-off frequency or by looking at the smoothness of radiated wave fronts when the formalism inherited roll-back is present.

I already presented that the PETF algorithm produces a faster opening of a horn profile while straightening the horn walls. In this article I will investigate what horn properties we can expect by applying PETF to a given profile. 

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Progressive Expansion T-Factor Horns

In this post I would like to describe a method that I have been using since some time to get more flexibility with regard to different horn profile slopes. The fact that slow expansion profiles like the exponential or spherical wave horn provide very good loading but suffer somewhat with respect to directivity control inspired me to look for an algorithm that influences the given specific horn expansion function. I ended up with a modification of the well known wave front surface area expansion formula for hyperbolic (hypex) horns which is given by:

\tag{1a}S_z = S_0\cdot \left( cosh(\frac{m}{2}\cdot z) + T \cdot sinh(\frac{m}{2}\cdot z) \right)^2
\tag{1b}m=\frac{4\pi \cdot f_c}{c_s}

I will not go into more detail but with T=1 we get exactly the well known exponential horn for a two dimensional surface area expansion. This formula can also be used for the spherical wave horn with it’s assumed spherical wave fronts and will put out the same SWH profile already described on this site. Equation (1) is extremely flexible because when  T \lt 1 an hyperbolic profile is the result and when T \to \infty the horn profile becomes conical. This is the reason why I switched to this formula as it gives me the flexibility to produce horn shapes with different slopes only by changing one parameter. Up to here nothing new but what if we make T a variable function that depends on a reference point somewhere on the horn axis z_{off} and the distance from or to this offset?

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