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Waveguides and horns

Ok. let's go with the driver...
 

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Well you need to review the patent again, because the concept of equal areas for all of the channels is critical, just as the concept of a Fresnel pattern also have equal areas. If the ares of the channels are not equal in area and equal in length the the wavefront at the aperature will not be constant, i.e. "flat". This is the central point of the patent.

So if you have three channels then the area of each channel must be exactly 1 / (3 * compression ratio) of the total area of the diaphragm.

The "centroids" tell you the locations for the channels, centroids match centroids, but nothing about their widths. The widths are defined such that each channel has an equal area and covers corresponding Fresnel areas of the diaphragm.
 
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