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- Introduction -
A study has been made combining acoustic simulations and topology optimization with a target of altering the horizontal directivity of a tweeter via adding a phase plug in front of it. This is a very complex setup as a single phase plug geometry needs to be found that across a wide frequency range changes the sound field across several angles in some desired manner, and so optimization with the computer leading the design is really the only way to go. This is not yet used in the loudspeaker industry, but I have done it for some clients now with great results, and I am sure that we will see companies in the coming years go down this route.
- Optimization Results -
With topology optimization a geometric body is assigned as a 'design variable field' domain in which the field represents a material distribution, and the optimization routine seeks out the best distribution associated with targets decided by a user via a mathematical objective function. There is a lot of mathematics involved in this computational setup, and I will refer to acculution.com/blog to see more details. Here, I will just show the tweeter before and after optimization, where after, a phase plug geometry has emerged.
The individual phase plug domains are for now disconnected, but could be connected via thin structures placed in the two symmetry planes. The phase plug is of course created in a way that prevents it from colliding with the moving parts of the tweeter.
The results are interesting in that the phase plug can give the tweeter an overall wider dispersion in the horizontal axis.
By focusing on a particular level, the directivity characteristics might be even clearer to see.
Such a result could not be achieved via DSP, as the off-axis trends would just follow the on-axis corrections, unless you are controlling several drivers and 'steering' the sound field that way, à la Beolab 90. And no textbook will help you in designing the phase plug. So topology optimization is a new tool that opens up to a whole new world of loudspeaker designs. The downside is that it is very difficult to set up with a lot of math and a lot of physics to consider, and it is still considered a research topic by many. However, I have now taken it into loudspeaker product development, and this is just the very start. You can imaging manipulating the acoustic radiation of transducers in cars, as they may not be physically oriented towards the ear. You could also think building the internals of headphones or smartphones using this technique. It is not well-suited for all problems, but sometimes it is the only way to go.
Also, what if different phase plugs come with your loudspeaker? Or that you can buy new phase plugs as they are being developed? Clip them on, and get a new sound field...
- About me -
René Christensen, Denmark, BSEE, MSc (Physics), PhD (Microacoustics), FEM and BEM simulations specialist in/for loudspeaker, hearing aid, and consultancy companies. Own company Acculution, blog at acculution.com/blog
A study has been made combining acoustic simulations and topology optimization with a target of altering the horizontal directivity of a tweeter via adding a phase plug in front of it. This is a very complex setup as a single phase plug geometry needs to be found that across a wide frequency range changes the sound field across several angles in some desired manner, and so optimization with the computer leading the design is really the only way to go. This is not yet used in the loudspeaker industry, but I have done it for some clients now with great results, and I am sure that we will see companies in the coming years go down this route.
- Optimization Results -
With topology optimization a geometric body is assigned as a 'design variable field' domain in which the field represents a material distribution, and the optimization routine seeks out the best distribution associated with targets decided by a user via a mathematical objective function. There is a lot of mathematics involved in this computational setup, and I will refer to acculution.com/blog to see more details. Here, I will just show the tweeter before and after optimization, where after, a phase plug geometry has emerged.
The individual phase plug domains are for now disconnected, but could be connected via thin structures placed in the two symmetry planes. The phase plug is of course created in a way that prevents it from colliding with the moving parts of the tweeter.
The results are interesting in that the phase plug can give the tweeter an overall wider dispersion in the horizontal axis.
By focusing on a particular level, the directivity characteristics might be even clearer to see.
Such a result could not be achieved via DSP, as the off-axis trends would just follow the on-axis corrections, unless you are controlling several drivers and 'steering' the sound field that way, à la Beolab 90. And no textbook will help you in designing the phase plug. So topology optimization is a new tool that opens up to a whole new world of loudspeaker designs. The downside is that it is very difficult to set up with a lot of math and a lot of physics to consider, and it is still considered a research topic by many. However, I have now taken it into loudspeaker product development, and this is just the very start. You can imaging manipulating the acoustic radiation of transducers in cars, as they may not be physically oriented towards the ear. You could also think building the internals of headphones or smartphones using this technique. It is not well-suited for all problems, but sometimes it is the only way to go.
Also, what if different phase plugs come with your loudspeaker? Or that you can buy new phase plugs as they are being developed? Clip them on, and get a new sound field...
- About me -
René Christensen, Denmark, BSEE, MSc (Physics), PhD (Microacoustics), FEM and BEM simulations specialist in/for loudspeaker, hearing aid, and consultancy companies. Own company Acculution, blog at acculution.com/blog
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