- by Phil Graham
in Speaking of Speakers
Over the past three issues of FOH, we have covered many aspects of loudspeaker horn behavior, so a fitting topic to follow this series is a discussion of the behavior of the devices that feed sound from the compression driver diaphragm into the throat of a horn. These devices are typically known as “phase plugs.”
Phase plugs, like horn flares, have many intricacies and are subjects of ongoing research in professional audio. The transition of sound from the diaphragm through the phase plug and into the throat of the horn heavily influences the sound reaching the listener. All of the idiosyncrasies within the compression driver are further magnified by the horn flare, making compression driver design one of the most exacting tasks in professional audio.
Let’s examine some of the principles behind the operation of phase plugs, beginning with the diaphragm inside the compression driver. We’ll discuss diaphragm behavior as it influences phase plug design, and then follow the sound pathway’s progression through the phase plug to the horn throat. Finally, we’ll briefly discuss how the wave behavior through the phase plug can cause problems downstream in the horn.
A Brief History
The compression driver’s genesis arguably starts before the Great Depression with Western Electric engineer Albert Thuras’ 1926 submission for a patent on an “Electrodynamic Device.” This patent was eventually issued in 1929 as U.S. patent number 1,707,544. Other than its use of electromagnets, Thuras’ creation would be readily recognizable to modern pro sound practitioners as a compression driver (Fig. 1). This driver has a throat, dome diaphragm, voice coil and phase plug, like the majority of modern compression drivers.
The intervening 85-plus years have seen compression drivers split into two major design categories. The first are the dome-based drivers that so clearly share DNA with Thuras’ work. The second group are similar, but instead use ring-shaped diaphragms. Both types have phase plugs tasked with bringing sound to the horn throat. In this article we will focus primarily on drivers with dome diaphragms. To grasp the complexities facing the phase plug, we first consider the behavior of compression driver diaphragms.
Project from the Diaphragm
The production of sound by a compression driver begins when the voice coil moves and transfers this movement to the compression driver’s diaphragm. This is true for both dome and ring diaphragm style drivers. As the voice coil moves, it sets up vibrations in the diaphragm, and those vibrations couple to produce sound in the air.
It’s important to understand that vibrations in the dome take time to travel across the dome’s surface, just as sound vibrations in air take time to travel to the listener. When the voice coil moves, the diaphragm does not instantaneously follow, but rather that vibration travels in waves across the diaphragm. There is a speed of sound in solid materials (i.e., the compression driver diaphragm) just as there is a speed of sound in air.
The speed of sound in a solid material depends on the nature of several of the material’s parameters:
• Density (ρ) is the mass (m) of a material per unit volume (V), where ρ = т ÷ V.
• Elastic Modulus (E) is how much a material deflects strain (ε), when you apply a force stress, (σ), where E = σ ÷ ε
• Poisson ratio (ν) – how a change in strain (Δε1), caused by deflecting a material in one direction, causes strain (Δε2) in another, perpendicular direction:
It can be shown that the speed of sound (с) in a block of material is equal to the square root of the elastic modulus divided by the density. The formula below shows that either increasing the modulus (E) or lowering the density (ρ)will raise the speed of sound in the material.
Typically, the compression driver designer desires the speed of sound in the dome to be as high as possible, as this means sound vibrations will reach the center of the dome in the shortest possible time. This led to the selection of stiff (i.e., high elastic modulus) and lightweight dome materials. The most common material is titanium, followed by aluminum and beryllium.
A reasonable question to ponder is why sound traveling through the dome quickly is desirable. To understand the benefit, it is helpful to imagine water rippling in a bathtub. The waves travel across the surface at a defined speed, reflect off the walls of the tub, and soon form a pattern of standing peaks and valleys across the surface. At very high frequencies, one would see a similar effect if they could visually observe the vibrations in the driver diaphragm as sound bounces across the dome. These various peaks and valleys are mathematically known as the “modes” of vibration in the diaphragm, and represent deviations from perfectly uniform diaphragm movement. They are analogous to the peaks and valleys in bass response one experiences in a venue due to “standing waves.”
As the speed of sound is high in solid materials, “modal” behavior only occurs at very high frequencies, typically above 7k Hz. Considering the behavior of a thin plate (similar to a dome diaphragm), the onset of the first bending mode is determined by:
Now, the realities of modes within a dome are more complicated than this equation, but can be simulated on the computer using numerical simulation methods. For a simple guideline, the modes of vibration in the compression driver only start to occur after a sufficient phase difference arises between the original and reflected wave. This phase difference depends on the frequency of sound, the size of diaphragm and the speed of sound in the diaphragm. Ultimately, if you raise the frequency high enough, all domes and ring diaphragms will exhibit modal behavior.
Phase Plugs and Tradeoffs
Our carefully engineered, thin, stiff, light dome diaphragms eventually succumb to modal behavior, no longer moving like rigid pistons, but more like the rippling head of a drum. The modal behavior causes local variations in the production of sound within the diaphragm. Much like how low frequency modes in a room can tremendously influence the evenness of the bass response based on location, the modes in the dome can also influence the sound that leaves the dome and enters the phase plug at different points on the dome. To complicate this effect even further, there is modal behavior of the air between the compression driver dome and the phase plug!
It is against the backdrop of these modal behaviors that the transducer designer must create a phase plug to bring sound from the compression driver diaphragm to the driver’s mouth. Phase plug designs for compression drivers have been pursued using two general classes of designs. The first class of phase plug is known as the radial phase plug, and is illustrated in Fig. 2. In a radial phase plug, thin slits that project towards the center of the dome allow for the entry of sound. The second class of phase plug is the circumferential phase plug. This phase plug consists of concentric circular rings that allow sound to enter the phase plug at a few discrete points across the diaphragm surface. Most compression drivers have phase plugs that fall into these two categories, or a combination of the two designs.
There are tradeoffs to both designs, of course. For instance, in a circumferential plug, the mode in the air between the dome and phase plug can produce a pronounced anti-resonance leading to a dip in the driver’s output. One can mitigate this by creating more concentric channels spaced closer together, raising the resonance frequency. This, however, complicates the manufacture of the circumferential phase plug, which is already a complicated, expensive piece to produce.
Radial phase plugs, while being simpler to manufacture and having a more gradual air cavity effect, expose the entire range of modal behavior across the dome’s full diameter. At higher frequencies, all of the modal oddities of the diaphragm are therefore on full display. In contrast, by using a circumferential phase plug with carefully chosen entrance points, the designer can help reduce the dome’s modal effects that make it to the horn throat.
Skilled designers have made choices to use both types of phase plugs, as well as changing the number, spacing, shape and path of the slots that lead from diaphragm to the compression driver mouth. Papers are commonly presented at the AES conferences that investigate performance tweaks in phase plug design. In a perfect world where diaphragms are infinitely stiff and light, the radial phase plug holds some theoretical advantages over the circumferential design. But the real world leaves plenty of room to build high performance designs with both.
Meeting the Horn
Ultimately, the compression driver phase plug’s core purpose is reducing the open area the driver diaphragm radiates into and then gradually transitioning that smaller area to the horn mouth’s cross section. The decrease in radiating area increases the local pressure and creates a better acoustic impedance match, which in turn increases output. Increasing output was the central consideration in the early days of loudspeakers.
Modern drivers are now less concerned with how much the phase plug can increase efficiency and more with improving compression driver extension and response smoothness. They are also concerned with the wave shape that enters the throat of the loudspeaker horn. Horns, especially the waveguides used for line array systems, make important assumptions about the nature of the waves that enter them. For instance, is the wavefront from the compression driver flat (i.e., plane), or does it have some curvature?
Path length differences to the driver mouth from the various phase plug slits will influence the curvature of the wave at the driver mouth. Modal anomalies from the diaphragm that are transmitted through the phase plug will also influence the wavefront as it enters the horn. This can result in changes to the coverage angle, or to variations in the sound intensity across the wavefront in the horn. Additionally, errant reflections in the phase plug can bounce their way down the horn flare.
If we are trying to “flatten” the wavefront as it expands, it is important to know the nature of the curvature of the incoming wave. Here the phase plug also plays an important role. If a line array waveguide assumes a plane wave entering from the compression driver, but the driver’s phase plug is curving the wave front, the very high frequency performance of the waveguide will be compromised. Different compression drivers can perform with great variability on the same waveguide or horn, depending on the shape of the wavefront they emit.
Even though they have existed since the dawn of compression drivers, phase plugs, and the diaphragms they support, always remain in the spotlight. Due to their high efficiency and output, any weaknesses in their design are clearly on display for the entire audience. The core design aspects of phase plugs have extensive pedigree, but manufacturers are constantly improving on the extension and smoothness of their output. The muted, splashy, shrill, or honky compression drivers of days past continue to give way to impressively clear modern designs.
Several of the most interesting AES papers in my personal library are on phase plugs. Multiple pages of mathematics or computer modeling work lead towards subtle tweaks in design that can yield impressive performance improvements. Compression drivers have come a long way, but still fall short in comparison to the best hi fidelity tweeters. This stands in contrast to professional cone drivers, which have largely surpassed the world of hi fidelity loudspeaker drivers. I’m excited for future innovations that improve phase plugs and compression drivers.