Subwoofers are arguably the most popular and fun topic in all of pro audio. The majority of low frequency sound reproduction is from vented loudspeaker enclosures, which is to say loudspeakers that have a port in the enclosure. The vented subwoofer loudspeaker enclosure makes a great entry point into the world of building loudspeaker enclosures. Building a box, wiring it up and then hearing the beast rumble to life is an extremely rewarding experience.
Numerous programs are available to predict the frequency response of vented boxes. With the apparent ease of predicting vented loudspeaker response using software, it is tempting to blindly follow the software and start making sawdust. The reality of the performance of loudspeakers in vented enclosures is more complicated than the software lets on, and we unpack some of that in this article. Finally, at the article’s conclusion, I’ll provide a few practical construction tips to obtain maximum performance from vented enclosures.
Vented Boxes — The Basics
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 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., moving up and down) of the air in the bottle’s neck remains as long as one continues to blow across the bottle. The mass of air in the bottle’s neck, combined with the unique compression and expansion properties of air as a fluid, define the resonance.
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 the 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 port.
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.
Predicting Box Behavior
Using driver parameters commonly known as the Thiele-Small (T-S) parameters (click to expand view of sidebar, at left), one can calculate the acoustic response of the driver and enclosure together. Thiele and Small were Australian researchers who modeled vented box behavior, and then defined parameters that could be measured for real-world loudspeaker drivers and inserted into the models. This type of analysis is known as a “lumped element” model, and was used in other areas of science before being applied to loudspeakers and boxes.
The principle behind lumped element models is straightforward. Each mechanical behavior of a loudspeaker has an analogous description available in the world of electric circuit components (i.e., resistors, capacitors and inductors). Thus, the entire loudspeaker and box can be represented by electric circuit elements, and the performance analyzed with the same set of tools built to describe circuit behavior. Nearly 50 years ago, at the genesis of T-S parameters, this was an extremely powerful technique and is still broadly useful today.
There are two classes of parameters that describe the behavior of lumped elements in the T-S model. The first are the electromechanical parameters (click to expand view of sidebar 2, at left). These define physical aspects of how the loudspeaker driver operates. The derived parameters (sidebar 1) are then calculated from the electro-mechanical parameters and give insight into how the driver will perform in an enclosure.
One very key limitation of this model that people overlook is that the T-S parameters are “small signal” parameters, which means that they capture the performance of the loudspeaker at very low output volume. It is easy to crank up the power in the software, and the model will show the loudspeaker getting louder, but we shall see this oversimplifies the driver performance at loud volumes.
Six Speakers in the Same Box
Let’s start by designing 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 40 Hz. We used a 24 dB/octave Butterworth high-pass filter at 30 Hz to protect the drivers against over-excursion at low frequencies. We then select six 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 30 Hz 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 4 dB window. Second, the very low frequency response, below 35 Hz, is dominated by the response of the high-pass filter. Because of the influence of the high-pass filter, all six drivers have their -10 dB point at essentially the same frequency. Note that all six drivers exhibit similar frequency response in our simulated enclosure. Over time, the manufacturers have learned to tailor driver designs for vented enclosures tuned between 35 Hz and 45 Hz with dimensions that will fit in a truck.
Of course, there are meaningful differences between these six drivers that do not appear in this plot. 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. In a future article, we will talk about so-called “large signal” parameters, which quantify more deeply how drivers behave when pounding out the bass mid show.
Heat Changes Drivers
One “large signal” parameter effect we display briefly is how driver response changes when the amplifier pours on the power. The electromechanical parameters of drivers change during a gig. One of the primary sources of change is from heat generated by the driver voice coil. Unfortunately, loudspeakers are bad 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, physics dictates that the voice coil wire does not conduct as easily, and this 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 actually decreases the 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. A decrease in electrical damping offers less damping for cone motion, which results in changing frequency response of the box and driver combination.
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 Fig. 1 was originally calculated assuming a specific value of Qes, namely the datasheet value for a “cold” driver voice coil. By comparison, Figure 2 shows the simulated frequency response of the same six drivers with their voice coil temperatures set to 175-degrees C (347-degrees F). At 175 degrees C, we encounter the upper range of the long-term temperature handling capability for modern voice coils, and can be reached during a hard-hitting gig.
Note that while Fig. 2 could make it seem like the output level has increased, it obscures the fact that overall output has decreased due to power compression. What Fig. 2 does not obscure is that less electrical dampening causes the bumps in frequency response. This peaked response can lead to the impression of “flabby” or “tubby” sounding low frequencies after the drivers have warmed up. When you push the driver too hard, the total output is changed, as well as the tonal character. Prudent designers consider the box frequency response under extreme level conditions, including extensive voice coil heating, before committing to the design. Knowing how to simulate these changes, as well as knowing what the software is not telling comes with design experience.
Subwoofer Building Tips
- Now that we have discussed how vented boxes operate and some limitations on modeling, 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. For pro sound that means using Fb between 30 and 45 Hz.
- Always use a high pass filter of at least second order. Second order is the minimum needed to control the driver excursion.
- The box volume in most design software does not account for port volume. The total box volume will be driver volume + box volume + port volume.
- Brace the corners and walls of the inside of the cabinet. Flexing panels can slightly change or reduce the output of the enclosure. A simple brace that ties opposite walls together can be quite effective.
- Keep ports as straight as possible. Bends in ports cause losses.
- Leave at least 10 cm between the end of the port and the enclosure back wall, so air can move freely in and out of the port.
- Don’t be seduced into using small ports. The minimum cross sectional area of the port should be 35% of the driver area.
- 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.
- Pro sound drivers have very stiff suspensions and the parameters of the driver will settle to the values on the datasheet over the first few hours of use. Don’t be surprised if there are changes in your box’s sonic character as the drivers settle in.
Finally, prepare to modify the length of your final port from the value suggested by the box modeling software. Software port length predictions are almost never correct. For instance, ports that are built along the wall of an enclosure end up tuning the box to a lower frequency than the software predicts. Building a test port from MDF or other throwaway material is the best way to set the box resonance frequency of enclosures 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. Observe the amount of cone movement and find the frequency where the cone moves the least. The frequency where the cone movement is minimal is the box tuning frequency. Lengthen the port if the resonance frequency is too high; shorten if it is too low.
The Bottom Line
Simply stated, the larger the driver, the lower the box resonance frequency, and the greater the amplifier input, the more limitations of the vented enclosure itself will become apparent. 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.
Similarly, the small signal T-S parameters on a datasheet don’t tell the full story about driver performance when the gig is pounding away. For this, we need to consider the driver performance with large signal parameters that capture how things like driver temperature and control over excursion change as output increases. Tune in to this very column for a future article on large signal parameters and what they can tell us more about box behavior.
