Advice on matching a HE 12" mid and tweeter

[RobWells]

Plot1

[RobWells]

plot2

[RobWells]

plot 3

I wish I'd done one at 45 degrees aswell, maybe next free weekend...

[rcw]

A rule of thumb given by Art Ludwig, is that a drivers radiation angle is approx.
a=29*Lambda/r
Where, a=angle in degrees, Lambda=wavelength, r= effective cone radius,
From this a 12inch driver can be expected to have 90degree beaming at around 1kHz., 60 degrees at around 1200Hz.
These correspond to the crossover frequencies one finds in the p.a. systems that use a single l.f. driver and a cd horn.

[paulspencer]

RCW, I did a excel spreadsheet based on that formula, shown below.

Does it apply to all driver diameters?

I'm guessing not since it shows a 1" driver as omnidirectional below 2k.

(if anyone wants a copy of the spreadsheet, send me an email)

I've set it up to show both that table, and a calculator, where you enter in desired angle, and it returns the frequency, or you enter in the frequency and it returns the angle.

This is quite interesting. If I want 40 degrees, with a 10" driver I get this at 1.9k and 1.6k with a 12".

With the 12" I get about 33 degrees at 2k, which was the point at which i was considering a good xo point.

EDIT: something's not right since I get 65degrees for a 12" @ 1k.

Are the units in metres?

Rob, thanks for the measurements. Still trying to digest it all...

[rcw]

That formula is an approximation that is valid over the drivers piston range Paul, above that it depends upon the details of how the outer parts of the cone decouple with increasing frequency, but should be O.K. up to 1.5-2 times the piston range in most cases.

[paulspencer]

RCW, are the units in metres? We seem to have a discrepancy in calcs ....

Another question - so by adding a waveguide on the top end you can match the polar response at the xo point and get say 40 degrees dispersion (which I think is a good goal for home use). This seems like it is good for the top end. What about the midrange? Suppose we went dipole to improve the polar response in the midrange by increasing directivity down lower, this would be an improvement would it not? It seems to me that a 12" low distortion PA driver could in fact be ideal for this ... thoughts anyone?

[rcw]

All dimensions are in meters Paul.
The major problem with the 40degree idea is that by that time significant sidelobes have developed, for a single radiator the practical limit withought significant sidelobes is around 60 degrees.
In diploe radiators the pattern is to do with the baffle width, Linkwitz's site has the details.