Acoustic Horn Design – The Easy Way (Ath4)

I don't get what you're aiming at. Once you get a spherical wave, it's radius should not be crucial - it's only expanding. You can do it on a 1.75" or 3" diaphragm, that shouldn't really matter (suspecting smaller diaphragms to behave better, as usual).

sorry for bad explanation
 

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The point here is that a conical waveguide seems better suited for a dome tweeter than an OS waveguide - I tried some, those weren't that nice, I just didn't show that. I will release the new (much updated) version soon so everyone can test whatever combination.

Whether a specific waveguide works with a specific dome tweeter depends on the shape, construction and materials used, both of the dome, suspension and (integration of the) voice-coil.
 
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Of course, I'm talking about the first (ideal) approximations here.

It really surprises me - this is a 44 mm (!) dome piston in a conical throat - not bad at all. Pretty wide constant directivity, isn't it.
 

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The same for OS throat.

In the Appendix of my book, I did an analysis of an axially vibrating source at the throat of a cone. In that solution, I predicated that as long as only the lowest mode propagates the source curvature doesn't matter much. BUT, as the second mode comes in things get much more complicated, usually a widening. In the 1" case this would be around 7-8 kHz. Seems confirmed by your analysis.
 
Throat conical extension - beta 5

I've always wanted to know what happens for a conical throat extension. Now you can try it yourself:

ThroatExtension = 20 ; [mm] (default = 0)

Download link: ath-4.4.3-beta-5.zip

This isn't working for me. When I select this option, with any length greater than zero it yields a waveguide that's a cylinder.

I am using supershapes, not sure if that's part of the problem.
 
Interesting! By using a non-zero value for "ThroatAngle", I got a working waveguide.

Earlier today, when using a value of zero, I wasn't getting a functional waveguide.

Here's where things get confusing:

When using a throat angle of zero, it now works. But it didn't work earlier.

I'm guessing that the wall angle that I was using earlier may have been at the edge of what can work. We see that certain extreme wall angles will cause the program to go into a loop.

Or at least, that's my best guess.

Nonetheless, everything is working now.