Phase Plugs

Most of the papers tend to concern compression driver phase plug design, but here are a few.

An Investigation of the Air Chamber of Horn Type Loudspeakers by Bob H. Smith.

Phase Plug Modelling and Analysis: Radial vs. circumferential Types by Clifford A. Henricksen.

There are a number of papers by M. Dodd and J. Oclee-Brown including.

Loudspeaker Compression-Driver Phase-Plug Design.

New Methodology for the Acoustic Design of Compression Driver Phase Plugs with Concentric Annular Channels.

Is there any reason why you need to use a 10” drive unit up to 4KHz? It is probably not the best solution. Plus the modern trend is for horn loaded compression drivers to be used to increasingly low frequencies.

JBL used to do a device called CMCD, which stood for cone mid-range compression driver. It might be worth searching for the term as JBL were pretty good at releasing tech documents.

Which cone based systems are you comparing with which compression driver based systems, that leads you to conclude that compression drivers are harsh at 2KHz? With a well designed system they shouldn’t be.

Getting a 10” horn loaded drive unit to have a smooth unprocessed response above 1KHz is tricky. If the point of the exercise is a reduced output at 2KHz they should fit the bill.

All loudspeaker drive units have an upper roll off point, sometimes referred to as the mass break point (because the upper limit is mainly due to the coil/cone mass). Above that frequency the power available efficiency starts to drop off.

The on-axis sensitivity can remain flat above that point, because the directivity increases, so the power is radiated into a smaller volume. A 10” drive unit will have a directivity index of about 12dB at 1.5KHz. That is, the sound level will be 12dB higher on axis than if the acoustic power was radiated omni-directionally. If the on-axis SPL is still flat at that frequency it is actually putting out less than 0.1 of the power compared to lower frequencies.

If you manage to make a horn with constant directivity, you will lose the extended response, which comes from increasing directivity, and it will require additional eq to regain the flat response. This is why high frequency boost is needed on compression drivers fitted to constant directivity horns, because they have a falling power response.

With 1” compression drivers the hf roll off happens at around 4KHz, with 2” compression drivers it is about 2.5KHz. There is a lot more variation in cone design, but a 10” driver could start to roll off well below 1KHz. There maybe outliers that perform differently, but chances are such a device will have been designed for a specific purpose.

With a horn, there is also a volume of air between the diaphragm and horn throat. This air has a compliance which at low frequencies behaves like an incompressible fluid, so all the air displaced by the diaphragm passes into the throat of the horn. At high frequencies the mechanical reactance of this air space becomes sufficiently low (i.e., the air becomes compressible) so that all the air displaced by the diaphragm does not pass into the throat of the horn. As the compliance tends to zero the roll off tends to 6dB/octave (determined by mass alone). By careful choice of compliance, the space can be caused to resonate with mmd (moving mass) which extends the response upwards, but the roll off then tends to 12dB/octave.

A final nail in the coffin, is that at higher frequencies the cone doesn’t move as a single, solid diaphragm. Parts of the cone can be moving forwards at the same time as other parts are moving backwards. This does not help maintain a smooth response.

However, to quote Beranek:

It has been remarked that if one selects his own components, builds his own enclosure, and is convinced he has made a wise choice of design, then his own loudspeaker sounds better to him than does anyone else's loudspeaker. In this case, the frequency response of the loudspeaker seems to play only a minor part in forming a person's opinion.