The majority of low frequency sound reproduction is from vented loudspeaker enclosures — that is, loudspeakers that have a port in the enclosure. Nearly all modern professional loudspeaker enclosures are vented to improve their low frequency output, and numerous programs are available to predict the frequency response of vented boxes.
In the early days of audio, though, none of the modern prediction tools existed. Vented box loudspeakers were patented by Albert Thuras, a Bell Labs researcher, in 1932. Earlier this year, during Winter NAMM 2014, Thuras was inducted into the TECnology Hall of Fame for this invention. His patent, number 1,869,178, not only outlined the enclosure configuration, he also developed early mathematical models to predict vented box performance. Fig. 1 shows the fruits of his labor, comparing his predicted and measured responses.
This month, in honor of Thuras’ work, we take stock of the current state of vented boxes. We’ll investigate how they operate, and look at their limitations in the face of modern high performance drivers.
Vented Box Basics
To conceptualize how a vented loudspeaker cabinet operates, first consider a common Helmholtz resonator: the cola bottle. Nearly everyone has blown across the mouth of a cola bottle and heard a specific tone. This tone is known as the bottle’s resonant frequency. The narrow neck of the bottle acts like the port in a vented loudspeaker enclosure, and the wider body of the bottle is like the air inside the loudspeaker cabinet. Blowing across the bottle is analogous to the loudspeaker cone moving the air inside a vented enclosure.
As one blows across the cola bottle, some of the breath is caught by the lip of the bottle, and this presses down on the narrow column of air in the bottle’s neck. The air in the neck then bounces downwards against the air that fills the rest of the bottle, compressing it. The compressed air in the bottle springs back, pushing up on the air in the neck, forcing it slightly outside the bottle. This creates a partial vacuum inside the bottle, and that vacuum then pulls the air from the neck back inside. The oscillation (i.e., up/down motion) of the air in the bottle’s neck remains as long as one continues to blow across the bottle. The specific mass of air in the bottle’s neck, combined with the unique compression and expansion properties of air, create the resonance. The resonance frequency is defined by the amount of air in the bottle and the geometry of the bottle’s opening.
In a related fashion, the resonance of a vented box is caused by two factors. The first is the “springiness” of the air in the box. Anyone who has played with a beach ball, sat on an air mattress, or pressed on a balloon will realize that after pressing against an air-filled object, the object will spring back to its original shape. Ultimately, the air molecules want to remain a certain distance apart, and when you temporarily squeeze them together, or pull them apart, they will quickly return to their preferred spacing. The air inside a vented enclosure behaves similarly to sitting on an air mattress; it acts as a spring, pressing against the driver’s cone and also pressing against the air in the loudspeaker port.
The loudspeaker driver exerts force on one end of the spring, and the spring, in turn, exerts force on the air in the port, which brings us to the second factor that sets the resonance of a vented box. The port air is confined by the port walls and moves largely as one big charge of air. This volume of air moves in and out of the port as it is pushed and pulled upon by the spring. The larger the volume of air in the port, the heavier it is. A heavy charge of air changes direction more slowly, from moving into the box to moving out of the box, when the spring pushes on it. A lighter charge of air can change direction more quickly.
Like the cola bottle, vented loudspeaker enclosures have a specific resonant frequency, called the box resonance frequency, commonly abbreviated Fb. The box resonance frequency is defined by the combination of the volume of air in the port and the springiness of the air in the box. A large enclosure volume makes for a soft spring, and a small enclosure volume makes for a stiff spring. We use a large box (i.e., a soft spring) with a heavy (i.e., large volume) slug of port air to produce a low Fb. Using driver parameters commonly known as the Thiele-Small parameters (see sidebar), one can calculate the acoustic response of the driver and enclosure together. The Theile-Small parameters are the completed realization of the modeling predictions Thuras undertook some 85 years ago.
Heat Affects Vented Boxes
The Thiele-Small parameters of drivers change during a gig. This change primarily results from heat generated by the driver voice coil. Unfortunately, loudspeakers are inefficient at turning electricity into sound, and the majority of energy input is dissipated as heat. This heat raises the temperature of the driver voice coil and magnet structure. As the voice coil temperature rises, the voice coil wire does not conduct as easily, and that causes the driver voice coil resistance, Re, to increase.
When voice coil heating causes Re to rise, the overall output of the subwoofer enclosure decreases. As Re increases, less current flows in the voice coil for a given amplifier voltage input. This effect is commonly known as power compression. Power compression can become so severe that any additional increase in input from the amplifier produces essentially no increase in output from the loudspeaker.
In addition to power compression, the increase in Re also affects the frequency response of a vented box. Qes — the measure of the driver’s electrical damping capability — increases as a consequence of rising Re. Lower values of Qes mean more electrical damping, and higher values indicate less electrical damping. Re and Qes are related linearly: double Re, and Qes will double. A decrease in electrical damping offers less overall damping for cone motion, which results in changing frequency response. The flabby bass that one experiences towards the end of a gig is usually the result of this rise in Qes.
Ports Matter
The air in the loudspeaker port oscillates (i.e., moves in and out) most at the box resonance frequency, Fb. Consequently, the port produces its maximum acoustic output at Fb. At frequencies near Fb, it can be shown that the air in the port also reduces the motion of the loudspeaker cone. As the loudspeaker cone is moving very little near the box resonance frequency, the energy of the driver is instead strongly coupled to driving air in and out of the loudspeaker port. Near Fb, the port is effectively acting as the loudspeaker, producing nearly all the acoustic output. Fig. 2 illustrates this by showing the relative output of the driver and port, assuming the port functions properly. Because the port output is so important to the enclosure’s overall SPL at low frequencies, compromised air movement in the port can tremendously impact a vented enclosure’s performance.
Air Speed Matters
The most dominant influence on air flow in a loudspeaker port is the speed of the air molecules. At low speeds, the air molecules slide smoothly past each other. To visualize this, imagine that the “layers” of air in the port are like a stack of playing cards on a table. The bottom card, which contacts the table, experiences substantial friction from rubbing against the table surface. The next card up the card stack experiences less of the “table friction,” because the bottom card does not fully transmit the friction from the table to the second card. Each successively higher card in the stack experiences a little less of the table friction.
The behavior of air in the port, at low speeds, is similar to our stack of cards analogy. The air layer near the port walls experiences the most friction, and the air in the center of the port the least. Each layer of air slides smoothly past each other. The speed of air in the port near the wall is near zero, and at the center of the port reaches a maximum value. The flat layers of air slide smoothly against each other, like a stack of the world’s thinnest playing cards. When air moves at low speeds, the majority of the molecules stay in their respective layers and move orderly in and out of the port. Air movement under these low speed conditions is known as laminar flow.
At higher air speeds, though, all is not so smooth with molecule movement. Rather than sliding past each other like playing cards, the air molecules create all manner of swirls and loops. The air is no longer orderly moving in and out of the port, but rather tumbling about inside the port like clothes in a dryer. This condition is known as turbulent flow. As the air speed increases, there is a transitional region where the flow is partially laminar and partially turbulent. This transition causes a dramatic decrease in air’s ability to transmit acoustic output through the port.
Performance Compromises
Now that we realize that air flows differently at different speeds, and that this influences how much acoustic output our loudspeaker port will produce, let’s consider how that will compromise low frequency performance. The ports in pro audio cabinets routinely enter the transitional region between laminar and turbulent flow. There, the port acoustic output can be substantially reduced, as is control over loudspeaker cone movement. The combined effects of this reduced performance are called port compression. Port compression typically hurts overall output by several decibels.
Eventually, air in the port becomes turbulent enough that the port nearly ceases to function. The benefits of box porting then disappear, but only at high SPL. The loudspeaker driver therefore experiences level-dependent enclosure behavior, and the port performs most poorly when the loudspeaker driver needs the most help. The best designed loudspeakers avoid this port “choking,” and therefore perform better at maximum output level.
Controlling Air Speed
We now know that the air speed in the port matters critically for maximum output. So how do we control this speed? The simplest manner for reducing port air speed is increasing the cross-sectional area of the port. The loudspeaker cone in a vented enclosure can move a specific volume of air in a given length of time. Because the area of the port is almost always smaller than the loudspeaker cone area, air must flow through the port faster to move an equivalent amount of air in the same length of time. The smaller the port area relative to the cone area, the higher the air speed in the loudspeaker port must be for a given acoustic output.
Unfortunately, increasing the port cross-sectional area also requires increasing the port volume, typically by lengthening the port, to retain the same Fb. One cannot simply “steal” air volume from the enclosure and give it to the port. Any increased port volume must therefore be added to the enclosure’s overall physical size. Since enclosure size, weight, and cost are always at a premium, there is strong competitive pressure to skimp on port cross-sectional area. At low output, an undersized port performs adequately and produces graphs that look fine on a data sheet. It is only at high output levels that the enclosure performance suffers.
Simply stated, the larger the driver, the lower the box resonance frequency, and the greater the amplifier input, the larger the port area should be. When comparing two loudspeakers of comparable size, driver quality, and cone area, the enclosure with the larger port cross-sectional area is likely to be the stronger performer at high SPL levels.
Conclusion
Perhaps the most important assumption about vented boxes is that the air moving in the port behaves the same way independent of the enclosure output SPL. Unfortunately, this assumption is easily violated. Designs that appear to function well at low output levels may behave poorly when required to produce the extreme output levels commonplace in professional audio.
As loudspeaker drivers grow to ever-larger diameters (e.g., 21-inch subwoofers) and ever-longer excursions, port performance places increasing output constraints on the stalwart vented box. Low frequencies, and the vented boxes that reproduce them, are a cornerstone of excitement in live sound, yet we are increasingly handicapped by port performance.
Thankfully, manufacturers are rising to this challenge by utilizing larger ports, fluid modeling, and by shaping port geometry to create better aerodynamic behavior in the port. At the end of the day, though, the most straightforward way to improve vented box performance is to increase port size. The audio professional looking for high performance vented boxes is well advised to look for cabinets that provide the most generously sized ports.
The Theile-Small Parameters
First proposed by Neville Thiele and later expanded and brought to prominence by Richard Small, what are now known as the “Thiele-Small parameters” are attributes that can be used to define and predict a speaker’s response in a ported enclosure. These include:
• Re: The DC resistance of the voice coil wire.
• Le: The inductance of the voice coil. Inductance is a measure of the energy stored by a magnetic field.
• Mms: The mass of the speaker cone and the nearby air that moves with it.
• Sd: The surface area of the cone.
• Cms: The compliance of the driver suspension. A loudspeaker with high compliance moves easily when the cone is pressed.
• Rms: A measure of the damping of the driver suspension.
• Bl: Characterizes the strength of the electromagnetic force the voice coil can exert on the cone.
• Fs: The driver’s natural resonance frequency, it comes from Mms and Cms.
• Vas: The volume of air that has the same compliance as the driver’s Cms.
• Qes: A measure of the electrical dampening of the driver at Fs.
• Qms: A measure of the mechanical dampening of the driver Fs.
• Qts: A combined term that describes the overall driver dampening at Fs.
