Subwoofer Box Design
To truly understand the methods employed in Subwoofer Box Design, one must first have a background in the physics of loudspeakers themselves. The dynamic cone type loudspeaker is a device that transforms electrical energy into mechanical, or acoustical energy. Speakers are electro-mechanical devices. The acoustical output of a loudspeaker is produced by the back and forth motion of the cone about its equilibrium.
The parts that make up the dynamic loudspeaker are, the cone, or diaphragm, the dust cap, the surround, the spider, the voice coil, magnet assembly, and frame. The selection of these parts create the operating parameters of a particular loudspeaker. A single change does not necessarily mean better performance. For example, a speaker with a larger magnet will not necessarily out perform a speaker with a smaller magnet. In general the larger the magnet the greater the power handling, this is caused partially because of better heat dissipation..
The loudspeaker has both electrical and mechanical specifications that are of interest to the installer. Also there are many different types of enclosures that may be used for low frequency reproduction in the automobile. These will be outlined with specific design criteria, as well as all the necessary formulas to determine system performance. Do not be overwhelmed by the math.
Closed Box Systems
Of all the enclosure designs, the closed box type is the simplest to design and implement. Closed box systems consist of an enclosed volume of air, and the loudspeaker. There are two basic types of closed box designs, infinite baffle and acoustic suspension. Both of these designs are analogous to second order high pass filters, with the associated 12dB per octave rolloff.
The infinite baffle system is one where the compliance of air within the box, is greater than the compliance of the loudspeakers suspension. By strictest definition, the infinite baffle would consist of a loudspeaker mounted on a plane of dimension. In this configuration we are not relying on the air spring (volume of air) to load the woofer, instead we are simply trying to avoid cancellation, by not allowing the front wave to come in contact with the rear wave and cause destructive interference.
In practical application, this system would consist of a woofer simply mounted on the back deck of a vehicle (or in a similar fashion) where no actual sealed box construction has been performed. There are several considerations for infinite baffle design in a vehicle. When mounting woofers and mids on the same plane, make sure the mids are sealed off from the woofers. If both speakers are using the same rear space, severe distortion may occur from interaction between the woofers back wave and the midrange. The stronger wave will modulate the weaker speakers diaphragm. Also make sure that none of the rear wave can can find its way back into the vehicle, this will cause cancellation. To avoid this problem make sure that the baffle is sealed between the front and rear.
A sealed box will become acoustic suspension when the compliance of the air inside the box, is less than the compliance of the loudspeaker, by a factor of three or more. This change in compliance acts as an added stiffness component. Because the sealed box is relatively easy to design and build, it becomes a very attractive type for automotive use. The acoustic suspension system became popular in the 1950’s when it used by acoustic research, the model AR-3 is still considered to be a classic design to many. The standard sealed design employs a speaker with a loose suspension, and a fairly tight enclosure. The fact that the suspension is loose is the reason that enclosures went from very large to fairly small. Because the volume of air inside the enclosure offers acoustical reference to the woofers movement, it stands to reason that a woofer with less mechanical resistance (a looser suspension) would alter the air requirement for the same response.
In order to understand the following, it will be necessary to reference the following definition of terms.
F3 = three dB down point, or half power point (the frequency that designates the beginning of rolloff on the low end)
Fs = the resonant frequency of the driver
Fc = the resonant frequency of driver/box (combined) system
Qtc = the total Q of the driver – box combination at Fc (sealed box only) (ratio)
Qts = the total Q of the driver at Fs (ratio)
Vas = a volume of air that has the same acoustic compliance as the drivers suspension
Xmax = the peak linear displacement of the driver cone
Sd = surface area of the driver cone (in inches squared)
Vb = the net internal volume of the enclosure
nO – reference efficiency
Sealed Box Design Criteria
When designing a sealed box, certain advantages, and disadvantages should be recognized. The main reason for placing a driver in a box is to control the response of the driver/enclosure combination. The Q factor of the box/driver is used to describe resonant magnification, or the relationship between gain, and Fc. Refer to the image below. For different values of Qtc, there’s a relative gain (peak) as the value is increased. A higher Qtc will yield a smaller Vb, and a higher Fc, with a boomy sound characteristic above certain values. A Qtc below .7 will generally have a bass output that may be described as weak, especially by car audio standards. Also from the chart it can be seen that a closed box will have a rolloff that approximates 12dB per octave. A sealed box will have more low bass, and better transient response than it’s vented counterpart, given the same F3.
With the help of the Qtc chart it’s relatively easy to get an idea of subjective sound quality, (subjective being the keyword). As a general rule lower Qtc’s will have greater detail, since transient response is improved. Higher Qtc’s will sound more robust. or full sounding. For overall sound quality it is generally accepted that a Qtc of 1 is an all around good sounding enclosure. On the other hand for boom type cars one may choose a higher Qtc. simply to raise resonance. to a more usable portion of the frequency range. Bass lines in rap type music are usually in the 40 to 70 hz range. The following definitions of Qtc will help you realize the compromise between different values of Qtc. Once you get around 1.2 and above, it’s unnatural and doesn’t sound right.
Qtc = .5 Critically damped-best transient response
Qtc = .577 Maximum flat delay-Bessel response (D2) alignment
Qtc = .707 Max flat amplitude with minimum cutoff (B2) Butterworth
Qtc = >.707 Chebychev (C2) equal ripple-max power-max efficiency
You just choose a Qtc to tune the enclosure to how you want it to sound.
A higher Qtc you would use for rap, lower for rock or jazz.
Choosing A Subwoofer
When designing an enclosure there are certain driver characteristics that may be helpful in determining the best type of box to use with a particular driver. Woofers that work well in closed box systems are usually characterized by a low Fs, long voice coil, and a Qts greater than .3. A good rule of thumb is EBP or Efficiency Bandwidth Product. To calculate EBP use the formula
This should tell you if it goes in a sealed or ported enclore. EBP of 50 or less (approximately) typically indicates use in a sealed enclosure. EBP of about 100 or so suggests a ported enclosure. Remember when designing a sealed enclosure, the word sealed should be taken literally, this means there should be no air leaks.
Sealed Box Formulas
This is the logical format for calculating alpha, Vb, Fc, and F3. Alpha is used to determine Vb, it is simply the first in the equation. Practice these formulas with some real subwoofers. If Qts is higher than Qtc it won’t work.
Use the following example using brand x woofer
Vas = 4.7 Ft3
Qts = .508
Fs = 17hz
Qtc = 1
The volume of the box is 1.6 cubic feet and it’s tuned to 33hz.
Isobaric Box Design
The design for isobaric (constant pressure) enclosures is fairly straight forward. The advantages of this design are numerous and well worth it provided this design is practical in a particular install. The idea of compound loading woofers is not new, it was described initially in the early 1950s. There are two different configurations for isobaric. The first is where the two drivers ar mounted so the front of the rear driver is facing the rear of the front driver. The second is where the two drivers are mounted facing each other, and are wired out of phase.
In the first design, the main advantage is that the volume of the enclosure is half that of a standard sealed enclosure. Another advantage is that because of odd-order non-linear cancellation, the driver distortion is greatly reduced and response is lowered. The following applies to isobaric design
Qts is the same as a single driver
Vas is half that of a single driver
Fs is the same as a single driver
For parallel wiring impedance will be half that of a single driver
For series wiring impedance will be twice that of a single driver
Vb is half that of a single driver
Box volume should be calculated the same as for a sealed enclosure, only the Vas will be halved to get a Vb of half that of a single driver sealed enclosure.
Vented/Ported Box Design
The enclosure is a sealed box with the addition of a vent, or port used to tune the frequency of the box (Fb). The vent is used to augment the low frequency characteristics of the enclosure driver combination, and contributes to the overall output of the tuned system. This increase is achieved by additional loading at the rear of the woofer, which in turn reduces cone motion. In theory a +3 dB increase is noted, over the performance of a sealed enclosure of the same internal volume, although this is not only the case. In practicality the increase in output may be attributed in part to the design of the drivers used in this format. Because drivers used in vented enclosures typically do not have to exhibit large cone mass, and long voice coils, their magnet size may subsequently be smaller, hence they tend to be more efficient.
The loading effect caused by the addition of the port reduces cone motion, and along with this reduction comes lower modulation distortion, as well as higher power handling. One of the side effects caused by the port is a tendency for the system to unload at frequencies below resonance, this can be extremely harmful to life expectancy of the woofer. If the system unloads, the woofer will most likely destroy itself from excessive cone motion. This problem may be easily rectified by the addition of a subsonic filter. Another advantage of the vented enclosure, is a lower cutoff frequency as compared to a sealed enclosure with the same driver.
One thing to keep in mind when deciding on a system design, is that the vented enclosure is much more reactive to misalignment. This intolerance to design flaws makes the vented enclosure much more difficult to build correctly. Many standard alignments are defined for enclosures, these alignments are simply classifications that a system may fall into, with regard to frequency response verses box size and tuning frequency.
When beginning the design sequence for a vented enclosure, remember to choose a woofer according to the EBP. This is not to say that a woofer with a different EBP will not work, this is more of a rule of thumb to follow, and generally yields satisfactory results. Designing vented enclosures becomes a little more complicated than their sealed counterpart, mostly because the value of Qtc is not one that can be manipulated through the use of simple math equations. It is for this reason that the formulas used to determine box size and response shape are quite different.
As with the sealed enclosure, all of the terminology used, F3, Vas, etc., remain the same and will be needed for the following calculations. You will use the same speaker parameters as used for sealed, this will help you relate the different response characteristics between sealed and vented.
Vented Box Formulas
The following formula will calculate for optimum enclosure volume, this will yield the smoothest response with a minimum amount of ripple.
As mentioned this is volume for an optimum enclosure, in reality, working in a car you will most likely be forced to use anything but optimum. The following formulas will allow you to calculate backwards from the available amount of space you have to work with in the car. From these formulas you may determine if the response from the available space you have to work with is acceptable.
The last equation is used to determine the amount of deviation from a flat magnitude response, the value is expressed in dB, and the answer will be given as a positive value (peak), or a negative value (dip).
Calculating Vent Dimensions
For a tubular type vent mounted flush on the baffle use the following formula to calculate for length.
R = radius of the vent
Fb = frequency of the box
Vb = volume of the box in cubic inches
Lv = length of the vent in inches
The last part of the equation (- 1.463R) is used to compensate for end correction, this is assuming the vent is mounted flush with the baffle.
When mounting the port on the baffle, to avoid interaction between the vent and the driver, keep a distance of 3 to 6 inches between the vent and the driver whenever possible. The distance of the port from any wall or the speaker, inside the box, should be approximately 3 to 4 inches.
When deciding on a certain diameter of vent, there are formulas used to derive what is considered to be the minimum acceptable diameter. The fact of the matter is that none of the formulas given are any better than a poor approximation, and by following these to closely you may be apt to make a bad judgement call in terms of vent size. As mentioned earlier, a more practical technique is to simply make the vent as large as possible without exceeding the diameter of the driver. Since a vent is expected to operate in a linear fashion, the vent velocity must be controlled. In actuality this is much harder to do than it might seem, at some point the vent will no longer work correctly, and depending on the amount of input, the vent will experience power compression. This means that the more power input to the system, the less likely the vent will operate within it’s deign parameters. If you want to use an absolute minimum vent diameter calculation, simply divide the diameter of the speaker by three, and use that figure as the vent diameter.
It should be mentioned that the reason bass reflex enclosures approximate fourth order filters is that, because the vent works at a certain frequency and Q (which determines bandwidth), below the frequency of the vent, radiated energy from the vent is 180 degrees out of phase with the diaphragms radiated energy. This out of phase condition causes cancellation, hence changing the slope of attenuation below that point. This is also what causes excessive cone motion at these low frequencies. Below the tuning frequency of the vent, it can no longer load the rear of the driver, and allows all of the rear rear wave to cause destructive interference with the front wave, very similar to what happens when you try to use a speaker without a baffle.
So far we discussed the technical aspect of enclosure design. We can’t ignore the practical side of what many would call an art form that is enclosure cosmetic appeal, as well as certain functional characteristics that change the way the enclosure may perform.
The shape of the enclosure is the first thing that you should decide on, of course many times this will be decided for you by the car. Yet there are certain rules that should be followed whenever possible. One of the worst shapes for an enclosure would be a square box, because every wall in a square box has an equal size parallel wall, they generate a large number of standing waves. These standing waves reflect back into the woofers cone and cause non-linear response problems.
The next shape of interest, and the most common is the rectangular shaped box. While this is not dramatically better than a square, it is better, and it is most likely the shape you will use the most. One of the ways you may minimize this standing wave problem is to locate the woofer somewhat off center on the front baffle.
Certain materials minimize the problem of box resonance. As a general rule most installers use medium density fiberboard (MDF) as the best suited material for enclosure design, MDF is readily available at most hardware stores. Internal bracing is of paramount importance to the proper construction of subwoofer enclosures. Always use some form of internal bracing in the enclosure, not only will this minimize resonance but it will ensure a strong long lasting enclosure as well. Always use wood glue. The glue is what actually holds the enclosure together, while the screws only hold the wood in place until the glue dries. You can use Bondo Fiberglass to strengthen the inside corners and it will ensure an airtight enclosure.
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