Subwoofers are arguably the most popular, visceral, and fun topic in all of pro audio. The classic vented loudspeaker enclosure makes a great entry point into the world of building loudspeaker enclosures. Building a cabinet, wiring it up and then hearing the beast rumble to life is an extremely rewarding experience. We will help prepare you to "make sawdust" with the drivers in this month's Buyers Guide.
Our three-pronged attack first provides some background on vented box operation and modeling. Then we simulate and discuss the performance of six different loudspeaker drivers in a vented, truck pack-compatible subwoofer. Finally, we provide practical construction tips to obtain maximum subwoofer performance. After reading this, you'll know more about vented loudspeaker cabinets, and be better equipped to build your own!
Understanding Vented Boxes
The most precise name for a vented loudspeaker cabinet is a Helmholtz resonator, named for Hermann von Helmholtz, who first described the effect scientifically in the 1850s. To understand how a vented loudspeaker cabinet operates, first consider another common Helmholtz resonator: the Coke bottle (I'm in Atlanta). Nearly everyone has blown across the mouth of a 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 you blow across the bottle's mouth, some of the breath is caught by the lip and 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. moving up and down) 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 in the rest of the bottle, create the resonance. The resonance frequency is defined by the amount of air in the bottle, and the geometry of the bottle's opening.
Predicting Box Behavior
Like a bottle, vented loudspeaker enclosures have a specific resonant frequency, called the box resonance frequency. The box resonance frequency is defined by the combination of the port area, port length and the internal enclosure volume. Using driver parameters commonly known as the Thiele-Small parameters, one can calculate the acoustic response of the driver and enclosure together.1 Thiele and Small developed mathematical models of vented box behavior and then defined parameters that could be measured for real loudspeaker drivers and inserted into the models. Their work is accessible in numerous software packages that predict the low frequency response of loudspeakers in enclosures. One major reason vented loudspeakers are so popular arises from our ability to accurately predict their acoustic response.
The parameters shown on data sheets for drivers are divided into two categories. The electro-mechanical parameters (Re, Le, Mms, Sd, Cms, Rms, and Bl) define physical aspects about how the driver operates (see Glossary 1 for more details). The derived parameters (Fs, Vas, Qes, Qms, and Qts) are calculated from the electro-mechanical parameters and give insight into how the driver will perform in an enclosure (see Glossary 2 for more details).
These derived parameters are the minimum needed to design an enclosure. Plugging the derived parameters into one of the box modeling programs demonstrates how the enclosure volume and box resonance frequency affect the frequency response. A popular free program for modeling enclosures is WinISD Pro.2 After downloading WinISD Pro, you may want to follow the passbandllc.com link to download a zip file that has the Thiele-Small parameters for every driver in the product showcase.3 These two files will allow you to experiment and compare the response of vented boxes.
Six Speakers, One Box
While software allows successful modeling of virtually any enclosure size and port tuning, the majority of users are constrained by the typical truck pack dimensions. A common, truck friendly subwoofer configuration is 22.5 by 30 by 45 inches. We designed a virtual subwoofer enclosure out of 18mm plywood that fits comfortably in the truck pack dimensions. This enclosure holds two 18-inch woofers and has large rectangular ports tuned to 40Hz. We used a 24dB/octave Butterworth high pass filter at 30Hz to protect the drivers against over excursion at low frequencies. We then selected six top-shelf 18-inch drivers from a range of driver manufacturers and simulated them in our enclosure to see how their frequency response would vary.
Fig. 1 presents the simulated frequency response, including the 30Hz high pass filter, for all six drivers. From the graph, two things are clear. First, the frequency response of all six drivers falls within a 4dB window. Second, the very low frequency response, below 35Hz, is dominated by the response of the over excursion high pass filter. Because of the high pass, all drivers have their -10dB point at essentially the same frequency.
All six drivers exhibit similar frequency response in our simulated enclosure. Vented boxes have an extensive history in live sound; over time the manufacturers have learned to tailor their driver design for vented enclosures tuned between 35-45Hz with dimensions that will fit in a truck. Beyond their similar frequency response, there are meaningful differences between these six drivers. They have different suspension and magnet designs, different magnet materials, different diameter voice coils and a range of excursion capability. Not surprisingly, the longer excursion drivers are also more expensive. All of these drivers are excellent performers relative to drivers made a decade ago, with better venting for driver cooling and smaller enclosure volume requirements.
Heat Affects Vented Boxes
The Thiele-Small parameters of drivers change during a gig. The primary source of changes results from heat generated by the driver voice coil. Unfortunately, loudspeakers are inefficient at turning electricity into sound, and the remaining energy 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 Re, the driver voice coil resistance, 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: doubling Re will cause Qes to double. A decrease in electrical damping offers less damping for cone motion, which results in changing frequency response.
Instructive for understanding how a vented box will perform in the real world is simulating the driver performance after the voice coil heats up. The enclosure design in Figure 1 was originally calculated assuming a specific value of Qes, the datasheet value for a "cold" driver voice coil. With a "hot" voice coil, the Qes increases, and the frequency response of the enclosure changes.
Fig. 2 shows the simulated frequency response of the same six drivers with their voice coil temperatures at 175° C (347° F).
175° C is in the upper range of the long-term temperature handling capability for modern voice coils, and can easily be reached during a hard-hitting gig. Less dampening causes the bumps in frequency response seen in Figure 2. This peaked response can lead to the impression of "flabby" or "tubby" sounding low frequencies after the drivers have warmed up. It is prudent to consider the box frequency response under extreme conditions, including extensive voice coil heating, before committing to the design.
Subwoofer Building Tips
Now that we have discussed how vented boxes operate, how to model them, and how driver response changes over a gig, here are some practical tips for building your own subwoofer enclosures:
- Don't pick a box resonance frequency well below the frequency range to be covered.
- Always use a high pass filter of at least second order.
- The box volume in most software does not account for port volume. The total box volume will be driver volume + box volume + port volume.
- Build each driver into a separate chamber with its own porting. This ensures one driver will function correctly if the other fails.
- Brace the corners and walls of the inside of the cabinet. Flexing panels can slightly change or reduce the output of the enclosure.
- Build a brace supporting the magnet structure of the driver to protect it in the event of a drop.
- Keep ports as straight as possible. Sharp bends in ports cause losses.
- Leave at least 4 inches between the end of the port and the enclosure back wall, so air can move freely in and out of the port.
- Make sure the driver has sufficient excursion room to prevent the cone from hitting the speaker grill.
- Seal the inside seams of the box and input plate with sealant to make sure the box has no air leaks.
- Allow any sealants, paint or other box coatings to fully dry before installing the drivers. Leftover solvents can dissolve the glues that hold drivers together.
- A small amount of fiberglass or wool acoustic material can be used in the enclosure, but keep it away from the port and the driver magnet venting.
- Pro sound drivers have very stiff suspensions and should be broken in with low frequency sine wave tones for several hours. This will ensure that the Thiele Small parameters have settled to the values on the data sheet.
Finally, prepare to modify the length of your final port from the value suggested by the box modeling software. Port length predictions are almost never correct! For instance, ports that are built along the wall of an enclosure will almost always end up tuning the box to a lower frequency than the software predicts. Building a test port out of MDF, plastic, cardboard or other throwaway material is the best way to set the box resonance frequency of your enclosure before completing the final product. The easiest way to determine port tuning frequency is to play sine tones with 1 Hz resolution through the driver mounted in the enclosure. Visually observe the amount of cone movement, and find the frequency where the cone moves the least. The frequency where the cone movement is a minimum is the box tuning frequency. Lengthen the port if the resonance frequency is too high and shorten the port if it is too low.
Whether building your own loudspeaker design or upgrading the drivers in an existing cabinet, these cabinet-building tips will help you get the best performance from your project. WinISD can help you pick an enclosure and driver combination for your needs. You will find selecting drivers, modeling cabinets, and ultimately making noise will be a fun and rewarding experience.
For more information, here are some excellent resources on the topic of designing subwoofers:
1http://en.wikipedia.org/wiki/Thiele_Small_parameters
2www.linearteam.dk/default.aspx?pageid=winisdpro
3www.passbandllc.com/winisd.zip
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@passbandllc.com .
Electro-Mechanical Parameters
- 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.
Derived Parameters
- 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.
