The majority of low frequency sound reproduction is from vented loudspeaker enclosures – that is, loudspeakers that have a port in the enclosure. Nearly all professional loudspeaker enclosures are vented to improve their low frequency output. Including a properly designed port in a loudspeaker enclosure is a straightforward way of gaining additional low frequency output over a simple closed-box enclosure. Unfortunately, port design is usually a compromise, and this affects how the port functions at high output levels. This article seeks to enlighten the reader about how the port in a vented box operates, and to provide some guidelines for identifying good port design.
Resonance
Technically speaking, a vented loudspeaker is an enclosure that exhibits resonance. Resonance is the characteristic of a system that causes it to produce additional output at a specific tone or frequency, and systems that exhibit resonance are called resonators. Common acoustic resonators include a Coke bottle, organ pipes, tuning forks and car mufflers. Vented loudspeakers have a resonance that is chosen in such a way that it reinforces the very lowest frequencies reproduced by the loudspeaker driver mounted in the enclosure.
The resonance of a vented box is caused by two factors. The first factor is that air in an enclosed space behaves like a spring. 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 you 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 our second factor that sets the resonance of a vented box. The port air is confined by the port walls and moves primarily as one big "slug" 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 slug 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 slug of air can change direction more quickly.
Combining the two factors above sets the resonance of a vented enclosure to a specific 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. Virtually any box resonance frequency can be chosen by careful selection of port volume and enclosure volume.
Ports Matter
The air in the loudspeaker port oscillates (i.e. moves in and out) most at the box's resonance frequency, Fb, where the port produces its maximum acoustic output. At frequencies near Fb, the air in the port also reduces the motion of the loudspeaker cone. Since 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! Figure 1 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 enclosure performance.
Air Speed Matters
The biggest influence on air flow in loudspeaker ports 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 this friction from the table, 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 the 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 the dryer. This condition is known as turbulent flow. The additional turbulent swirls mean acoustic energy is lost as air struggles to glide through the port. As the air speed increases, there is a transitional region where the flow is partially laminar and partially turbulent. This transition causes a dramatic increase in air's resistance to transmitting 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, it is time to investigate how that will compromise low frequency performance. The ports in pro audio cabinets routinely enter the transitional region between laminar and turbulent flow. In this region, the port acoustic output is 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.(1)
Eventually, air in the port becomes turbulent enough that the port nearly ceases operation, and the loudspeaker behaves almost as if the port was never there. 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
Since we now know that the air speed in the port matters critically for maximum output, 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. This volume of air depends on the area of the loudspeaker cone, how far the cone moves, and the frequency of sound being reproduced. 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.
Consider the comparison between two hypothetical loudspeaker enclosures that have the same box tuning frequency and port dimensions. Now imagine doubling the total port area of one of the boxes by duplicating the existing port. It can be shown that this doubled port area will allow for 6dB more SPL from the port before port choking becomes severe. As drivers grow ever more capable of high output, port area should increase to insure that port choking is not the limiting factor to enclosure performance.
No Free Lunch
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. The enclosure air volume, which does not include the volume of air inside the port, must remain constant. 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.
Improving Ports
An honest look at the simulation data for typical high power professional subwoofer enclosures shows that the port area should be about 80 percent of the driver cone area! Few, if any, boxes have ports that meet this criteria, as it is challenging to justify the practicality of a port that takes up nearly as much area as the driver. Thankfully, other methods to improve port performance have been investigated, and there are a couple of other tricks available.
The first trick is dividing a large port into several smaller ports. The onset of turbulence depends, in part, on the distance between the boundaries (i.e. port walls) that support the flowing air. The closer the supporting boundaries, the faster air can move before turbulent flow occurs. Dividing a large port into several smaller ports with the same overall area will result in an enclosure with a slower onset of port compression.
Another method to improve port air flow performance is "flaring" of the port ends. Some of the loss from the port results as air transitions sharply around the 90° bend where the port meets the cabinet face, or the 180° bend where the port terminates inside the box.(2) Rounding (or angling) these transitions can be shown to reduce port losses. Since air must flow in both directions through the port, the flare angle (or radius) chosen by the enclosure designer is a compromise between what is best for air leaving the port and air entering the port. Flared ports are commonplace in Hi-Fi applications, but unfortunately not in professional audio.
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 settle for handicapped port designs. The pro audio industry should increase the usage of segmented ports, flared ports and ports designed with aerodynamic profiles readily available from research literature. Improved port designs will help ensure that enclosure performance can match the ever-increasing SPL available from today's advanced loudspeaker drivers and in the years to come.
For more information, here are some excellent resources on the topic of loudspeaker ports:
(1) Button, D., et al., JAES, Vol. 50, No. 1-2, pp. 19-45, Jan./Feb. 2001.
(2)Vanderkooy, J., AES Preprint 4523, 103rd AES, Nov 1997.
Phil Graham is a principal of PASSBAND, llc in Atlanta, GA, a professional audio consultancy and a regular contributor to www.soundforums.net. Email him at: info at passbandllc.com.
