Planar Horn/waveguide design (Help needed)

I've heard a number of good things about horn designs, like increasing low-frequency response on HF drivers, improvements in directivity, better efficiency, etc. But it seems to be difficult to find documentation on how to control these various parameters and how to design a waveguide with specific goals in mind.
I am planning on building a speaker with some planar drivers from parts express, but all of them seem to have a sloping FR; lower in lows, and higher in highs. Thus I am hoping waveguides would be the solution to make them flatter and easier to crossover.

I planned on just making horns using trial and error to determine some of the variables that can be used to tweak a driver's response, but there has to be someone out there who's already done that science.
Does anyone know of any design methodologies or readings to point me in the correct direction?
 
its kind of a big topic! you are correct that you can improve the low end response by providing a better acoustic impedance match. A basic horn that would work is a conic horn, the directivity is nominaly the included angles and a flare is required in the last 3rd of the horn to reduce diffraction effects from the mouth termination.

Akabak3 is a good tool for simulations
https://www.grc.com/acoustics/an-introduction-to-horn-theory.pdf

This is the book to get:
https://hornspeakersystems.info/

Example of a horn loaded AMT:
https://audioxpress.com/article/tes...sound-amt-and-xmt200-horn-from-eighteen-sound
(uses some kind of acoustic lense to drive a close to conic horn, lense could be to modify the wavefront shape to better match the horn)
 
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