Subwoofer Enclosure - Box Basics - Part 3

The damping of a TL is unlike the "air" spring of a sealed enclosure where the cone has to fight for motion. As a result, the efficiency is better than bass-reflex enclosures, the accuracy is better than acoustic suspension, and the frequency response and linearity is better than all systems.

Designing a transmission line enclosures requires thorough specifications and careful tuning. Suitable drivers for TL's usually have low QTS (0.2 to 0.4), low QES (0.3 to 0.4) and low Fs values. The distance the rear sound wave (of a subwoofer) travels in the enclosure is very specific. Determining the length is based a fraction of the wavelength of the woofers resonant frequency. For example, if the resonate frequency of the woofer used in a TL is 40 Hz, the wavelength of the frequency would be approx. 339 inches (see March 2002 issue, Box Basics II, for formula to determine wavelength). The channel inside the transmission line enclosure must be 1/4, 1/2 or 3/4 of this wavelength, resulting in a channel length of 84.75, 113 and 169.5 inches respectively. Because of the length of the channel, it is often common for a TL to be folded into a labyrinth, making it more compact. If stuffed properly with damping material such as wool, the actual length can decrease due to the resistive effect of the material on the air.

Both passive radiator and transmission line enclosures may not be completely suitable for the automotive industry, but they are great alternatives to the common enclosure. Give them a try- you may be pleasantly surprised.

Box Basics I - January 2002This issue touched on the design and history of infinite baffle, sealed, ported, and bandpass enclosures.Box Basics II - March 2002This issue guided you through the design process of a purely SPL enclosure.To order back issues call 714-712-2126.

Transmission LineThe origin of a transmission line (TL) has roots tracing back to the Stromberg-Carlson acoustic labyrinth, circa 1930. This labyrinth consisted of a long pipe, with the driver mounted at one end while the other end remained open, with a cross-sectional area about the same as that of the driver. In the early 1960's, Dr. AR Bailey experimented with different damping materials and techniques using the same basic concept in these folded labyrinth lines. His work has since become the standard for TL designs. In 1976, AT Bradbury used Dr. AR Bailey's density criteria of 0.5 lb/ft and published his paper describing changes in the speed of sound for different types of damping material such as fiberglass and long fiber wool.

So, what is a transmission line? As the name implies, a transmission line is a long chamber that expends from the back of the loudspeaker. At the opposite end of this line is a vent or opening (generally the size of the driver diaphragm) to the outside of the cabinet. Properly built TL's eliminate the phase cancellation of the driver in any form and make for a nearly perfect sub system. However, TL's are seldom found in car audio because of their size and complexity.

The design of a TL enclosure consists of a taper in the line, making it is possible to eliminate standing waves and resonance common to other speaker enclosures. Eliminating standing waves also protects the driver from harmful back waves that cause distortion and cone breakup. The length of the line does not allow time for air to travel through the chamber and cancel the front-wave. Because of its length, a tuned chamber, much like an open-ended pipe from a pipe organ, is created. This causes a phase shift. It is this phase shift to the rear sound wave (of the woofer) that reinforces the front-wave at the frequencies where the front-wave begins to decrease due to increased air resistance at lower frequencies, very much like a vented enclosure.

A PR is essentially made of two parts: a "weighted diaphragm" and a "spring". The weight of the diaphragm is a critical element the design and must be correct for the part to function properly. By changing the weight of the diaphragm, the resonance frequency will change, thus effecting the tuning of the enclosure. The spring is a combination of the stiffness of the suspension materials, and the air trapped within the cabinet. This too can change the tuning of the enclosure, much the same as the enclosure volume of a vented box changes its response.PRs are tuned, by the mass loading, to resonate at a frequency below the active woofer's linear response range. A passive radiator has a useful range about a 1/4 octave above and below its resonance. However, the typical roll off is a fairly steep 18 dB/octave. The combined response of the woofer and passive radiator should produce about a half an octave bass extension at low frequencies that add up to the level produced by the woofer on its own at higher frequencies, if the PR is tuned properly. In other words, a small amount of low frequency bass that the system would normally have difficulty reproducing now exists.

In a passive radiator system, both the cone of the active woofer and PR could move in phase with each other, or any combination of opposite motions, up to 180 degrees out of phase. Keeping both cones exactly in phase would be ideal in order to reinforce the output of the woofer, but as physics would have it, this sort of resonant system is not exactly possible.