Other purpose of the phase-plug is to equalize the acoustic path lengths to thereby minimize high frequency cancellations caused by standing waves into phase-plug slots.
In order to achieve this two main goals, the phase plug has:

- to be designed to an accurate study of the slots positioning and topology

- to be easy to manufacture with tightly controlled dimensional tolerances

The slots design and the properly geometrical matching between phase-plug and diaphragm are the key points to put extreme attention during the compression driver acoustical development.

Figure 1 shown a typical circumferential slot phase plug with path length l d shown. It’s surface is spherical and the mating diaphragm sits above it at a distance h.

Figure 2 shows a simplification of figure 1. The air between diaphragm and phase plug possesses compressibility as well as inertia. As a result a single frequency resonant condition is possible, its vibration being parallel to the diaphragm an depend on the geometry of the phase plug l d and h diaphragm phase plug rated distance.

An electrical equivalent circuit of the compression driver can be introduced. We will put our attention only on the part regarding phase plug model. This study, introduced by Clifford A. Henricksen [1], illustrates the theoretical origin of the high frequency cancellations as a inherent physical consequence of this phase plug topology. The electrical compression driver model with concentric annular slot is showed below in Figure 3

Where:

At low frequency, (f < c/3.63ld ), Cp1 and Lp1 can be neglected and therefore the PP is modeled by a simple second order low pass filter constituted by Cp and Lp. At higher frequency the presence of Cp1 and Lp1 introduce a resonant circuit in parallel to the exit. By the directly proportionality between Cp and ld², it is can easily deduce that a smaller distance among adjacent slot is desirable with the purpose to increase the PP cut off frequency and consequently in order to move over the audible range the effect of the resonance. Therefore, we should design phase plug with ld as small as possible, necessitating a lot of air channel passages of high frequencies. This demand make phase plug complicate and expensive.

Figure 4 shows a radial phase plug where maximum ld being indicated. The radial slot differs from a circumferential type by having lddecrease toward the center. The effect of the spacing between the diaphragm and phase plug is the same for both type; the effect of the air reactance (Lp) is independent to ld; hence the only difference between radial versus circumferential should be the effective air mass Cp; if ld was zero, Cp would be zero and the air in the phase plug would be massless. For the inner portions of the diaphragm, the resonance frequency is high, but since the relative damping is constant, the “Q” of this section is low. The outer sections would be higher “Q” but resonate at lower frequency. The net result will be an aggregate of all these impedances. 

Altogether, it is possible to demonstrate, that radial phase plug is much lower “Q” with a more gradual roll-off and without a severe notch at the high end than circumferential topology. Theoretically, we would expect a 5dB gain at 20kHz and 1.2dB loss around 9-10kHz due to the radial lack of “bump” at these frequencies. This is attributed to the distributed nature of radial flow path, as opposed to the discrete single-path behaviour of the circumferential; the radial phase plug has an infinite variety of flow path lengths opposed to only one path of the circumferential. Lastly, the radial phase plug has a further advantage in its easy manufacturability in one piece.

Figure 5 shows 18 sound proprietary phase plug. By the carefully combinations of radial external slot and circumferential inner slot is clearly possible conjugate on the same phase plug the advantage of both radial and circumferential topology. In this case the inner part of the diaphragm has discrete nature with single flow path ld while the outer part would be consider as distributed flow path modulated on average value ld. In fact, for the outer part, if we calculate the average value of the variety of flow path, we will found ld. The effect of this topology is that, theoretically, we never have ld = 0 and Cp = 0 and consequently lower total “Q” responsible of the 1.2dB efficiency lost around 9-10kHz. Despite this the variable flow path is desirable in order to avoid the severe notch at the high end typical of single path phase plug. 

Lastly, the 18 sound phase plug topology has a further advantage in its easy manufacturability in one piece with tightly controlled dimensional tolerances.

[1] Clifford A. Henricksen “Phase Plug Modelling and Analysis: Radial Versus Circunferential Types” presented at 59th AES Convention