Reference: Multiphysics Simulation of a Low Frequency Horn Loudspeaker

September 17, 2021



Funktion-One Evaluates Acoustical Virtual Product Development

Simulation becomes a really attractive solution. The results from the simulation of the horn loudspeaker exceeded our expectations, considering this is a model of an existing speaker. This is not a product designed from scratch with simulation built in from the beginning. I am sure by integrating simulation into the product development process you can get the results even more accurate.”

James Hipperson, Acoustic Design Engineer at Funktion-One


Funktion-One – Innovative Manufacturer of Professional Loudspeaker Systems

Funktion-One, founded in 1992, is an innovative manufacturer of professional loudspeaker systems, with audio quality and resolution as the utmost priority. Over the past 10 years, Funktion-One has delivered systems to venues and projects as diverse as stadia in Russia for the 2018 World Cup and the Sochi Winter Olympics in 2014, as well as high-end clubs, restaurants and entire luxury casino resorts world-wide.

Developing professional speaker systems at the highest audio quality has always been the primary goal of Funktion-One’s R&D team. Not only maintaining this high level of quality but improving it with each new professional loudspeaker system is both a challenge and an incentive for Funktion-One’s acoustics experts.

Funktion One take pride in their empirical development approach of critical listening and real measurements from the very beginning of a product’s development. Nonetheless, simulation offers many attractive advantages to complement and augment this process.


Mvoid Group Selected by Funktion-One to Simulate Low Frequency Horn Loudspeaker

In spring 2021, Funktion One selected Mvoid for the simulation of an existing low frequency horn loudspeaker to learn more about Mvoid’s simulation methodology and to test the quality of the simulation results.

Early attempts at bass horn simulation were not accurate enough to be useful,” stated James. “We selected Mvoid for the simulation to be able to predict the coverage and directivity of bass horn arrays. Typically, you do this with a point source model, which is quite a good prediction for such a simple model. But there are a number of aspects that a point source horn model won’t predict. This was the motivation for the simulation,” James said. “And as you may be aware, you can’t really measure subwoofers in an anechoic chamber because you would need an impractically large chamber to have a low enough cutoff frequency, so you are left with some problems. Simulation could become a really attractive solution here”, continued James.


Functional DMU: CAD Based Geometry definition, Physics Attributes of Transducers, Enclosure and Air Domain

For accurate virtual measurements of Funktion-One’s horn loudspeaker, it was first necessary to build an electroacoustic Digital Mock-Up (DMU). The DMU is a virtual representation of the horn loudspeaker including the air space, which organizes and aggregates the components according to the design. The DMU allowed us to simulate the shape and spatial arrangement of the transducers and the enclosure. It is a 3D model with electroacoustics that functionally describes the design of the horn loudspeaker. Features that are not essential to the simulation, i.e. handles, bracing, are removed.

Mvoid: Functional DMU / Reference Funktion-One
Mvoid: Functional DMU / Reference Funktion-One


The image above shows the functional DMU. It is the CAD based geometry definition. The two transducers are shown in the core. We have excluded the elastic effects in this figure.

The functional DMU starts with a description of its geometry based on a 3D CAD model as shown in Figure 1. It models the simulation domain for electroacoustics, and hence differs from a traditional 3D mechanical CAD model. In addition to the transducers and the enclosure we had to model the surrounding air space in the near field as well. We were able to calculate the radiation to the far field, i.e. outside of the modelled near field in 3D, by means of a thick layer of special elements at the boundary of the near field domain, which is called Perfectly Matched Layer (PML).

Once we had defined the geometry of the DMU we needed to apply physics attributes to the geometry.

We have modelled the transducers as a 1D/3D coupled sub-system, where electromagnetics and structural dynamics are applied as a set of equations based on the Thiele/Small theory (1D) to the moving parts, while the coupling to the surrounding air is realized in 3D. We have modelled the enclosure as a boundary to the air space. While the enclosure has been assumed at this stage as being rigid and perfectly reflecting sound waves, we modelled the effect of damping foam in the rear cavity of the transducer as a porous material.

It is important to mention that the geometry, though it was modelled in an external CAD system, is bi-directionally linked to the simulation model. When geometry changes are applied to the CAD model the simulation model is automatically updated. Vice versa, it is also possible to apply changes to the geometry in the simulation model, e.g., by an optimization algorithm, and it will be updated in the CAD model. This approach guarantees an efficient way to assess changes to the electroacoustic design at an early stage and to re-use the CAD model for any additional mechanical design work.

The use of a PML led to an efficient way of including the effect of a baffle rather than a full-space radiation, and the generation of polar, directivity and balloon plots at arbitrary locations.

As an example, some plots are shown below to give a small insight into the analyses:

Mvoid: Normalized directivity plot at 10 m 0° on-axis / Reference Funktion-One
Mvoid: Normalized directivity plot at 10 m 0° on-axis / Reference Funktion-One



Mvoid: Normalized Balloon plot at 10 m / 100 Hz / Reference Funktion-One
Mvoid: Normalized Balloon plot at 10 m / 100 Hz / Reference Funktion-One



Mvoid: Sound pressure level normalized at 2m in front of loudspeaker / 100 Hz / Reference Funktion-One
Mvoid: Sound pressure level normalized at 2m in front of loudspeaker / 100 Hz / Reference Funktion-One



Functional DMU: Postprocessing, Results and Validation

In the following a comparison of the virtual measurement coming from the fully coupled analysis of the low frequency bass horn loudspeaker and the physical measurements is given. Additionally, we will show balloon plots as a general postprocessing approach to visualize 3D-directivity data.

Even though the typical operating bandwidth of such a loudspeaker is from 20 – 200 Hz, we will show results up to 500 Hz to draw some conclusion on the effect of 2nd or 3rd harmonics coming from nonlinear effects when the system is driven at large signals.



Electrical Results

First, we will look at the total impedance. We can see two peaks in the response corresponding to the mechanical resonance of the transducer and the acoustical resonance in the horn. This impedance behaviour is very characteristic for such a low frequency horn loudspeaker. We also see in general a good agreement between virtual and physical measurements, meaning that the prediction of the voice coil physics is realistic.Mvoid: Electrial-Results / Reference Funktion-One

Acoustical Results

Acoustical results can be very diverse, especially when we think about directivity behaviour. An initial step is always to look at the on-axis frequency response. The following graph shows the sound pressure level response at a distance of 2 m when 2 V is applied to each of the transducers. An impressive sensitivity can be seen, which makes such a loudspeaker design outstanding. And it also shows a good agreement between virtual and physical measurements over the whole frequency bandwidth.Mvoid: Acoustical Results / Reference Funktion-One

Acoustical Results: Directivity

Due to the amount of data visualizing 3D high-resolution directivity results is quite challenging. Typically, it is done in an interactive way by means of a balloon plot as given in the following graphics.


Mvoid: Acoustical Results Directivity / Reference Funktion-One

Mvoid: Acoustical Results Directivity / Reference Funktion-One


The whole plot consists of four quadrants. In the upper left a 2D graph shows the sound pressure level plotted as a function of frequency (x-axis) versus direction (y-axis). You can select a specific combination of frequency and direction in this graph, while the other graphs show the corresponding frequency response in the selected direction (upper right quadrant), the corresponding polar plot at the selected frequency (lower right quadrant), as well as the sound pressure level distribution at the selected frequency on a sphere in a distance of 10 m (lower left quadrant).

Please note that this balloon plot is based on a virtual measurement including the effect of a baffle. Hence, only results on a half sphere are shown.



Reliable Predictions
The project demonstrates that multiphysics simulation can make accurate predictions of bass horns. The simulation covers both resonant and horn loading effects and covers also high-resolution directivity patterns.

The results show that multiphysics simulation can also help engineers to develop, improve or optimize loudspeakers. Any engineering targets the engineer has in mind can be implemented and analyzed in the virtual domain. All the geometry parameters that the engineers have defined in the CAD model are directly available in the simulation model. The engineer can change the parameters manually or by an optimization algorithm. Once he has found an optimal set of parameters it is available in the simulation model and the CAD model due to its bi-directional linking. Now the engineer can immediately move on to the detailed design work and do all the mechanical engineering work in the CAD system that is required to finalize the product.


What was most important to me was that the model correctly predicted both resonant and horn loading effects of the design which aren’t always correctly predicted in other types of modelling. It can do that with the lumped element simplified driver model bidirectionally coupled to the finite elements, meaning you don’t have to do a full multiphysics driver simulation. That is great because it’s quicker, and the directivity results are great as well. And it shows that we can get really useful data of modelling directivity via simulation. We validated that with real measurements outdoors”, said James.


Working with Mvoid has shown us how existing problems in loudspeaker development can be quickly solved and new ideas can be analyzed in the virtual environment, continued James.


Multiphysics simulation is an efficient tool and can be an essential part of a virtual product development process. It can serve as an efficient functional DMU for loudspeakers and can act as a Digital Reference for virtual product development.

Mvoid and Funktion-One are currently discussing an extension of the current simulation model to efficiently predict the SPL distribution of large arrays of bass horns.


About Funktion-One
Funktion-One, founded in 1992 by Tony Andrews and John Newsham, is based in the UK.

Funktion-One represent an unsurpassed pool of experience and expertise in the audio industry having been consistent innovators in audio design, concert touring and sound installation. The engineering team looks back on a multitude of innovations, including the 21” loudspeaker frame size, the turnkey package touring system, and numerous patents.




Picture credits

Header figure: Funktion-One
all other figures: Mvoid Group