Subwoofer housing calculation

Calculating a housing for a subwoofer is not easy for every motorist, even one who is very passionate about music and understands various acoustic subtleties. A subwoofer is a complex and independent acoustic system designed to create high-quality sound inside a car.
However, few motorists know how to design a subwoofer housing correctly and without problems.

Hull and its calculations

So, directly the algorithm for calculating the subwoofer housing:

• There are four main types of subwoofer enclosures available today;
• Housing 3Ya is a closed type structure. This type, from the point of view of design and manufacturing, is the simplest. However, it has practically no efficiency. On top of that, it is leaky;
• The phase inverter (PI) has a complex calculation principle, but it has a high efficiency;
• The 4th and 6th order bandpass is the most difficult option from the point of view of design and practical manufacturing, but it has the highest efficiency within the range of low sound frequencies and at the same time completely suppresses high frequencies.

Note. Objectively, each of the options described above has a number of characteristic advantages and disadvantages, however, the choice must be made in accordance with the recommendations of the design program.

Program WinlSD 0.44

Before moving directly to the design process, you need to create an audio speaker in the database using the WinlSD 0.44 program:

• First, you need to move the computer mouse cursor to the New tab, after which you need to check Owndrivers and click on New again. After this, download the parameters selected in accordance with your own wishes and capabilities. At the end, just click OK, Close;
• Then you need to create a project based on the speaker and previously specified dimensions;
• Next, you need to repeat the above procedure many times, changing the type of case, having tried all four variations.

Direct algorithm for creating the housing itself for a car subwoofer

Here's what you need to know:

• The most optimal shape would be a truncated pyramid, since it is the most universal;
• The slope of the rear wall should be approximately 23 degrees, since the vast majority of modern passenger cars have an interior with the rear seat backs tilted at exactly this angle;
• It is imperative to calculate the volume of the case in accordance with the dimensions of the free space of the trunk (see).

Creating a closed enclosure

Begin:

• All walls of the 3Ya case (closed type case) must be made of chipboard, and the front wall must be 23 mm thick, and the side wall must be 220 mm thick;
• Now you just need to cut out the walls of the specified size from chipboard with an accuracy of a millimeter, and then you can proceed to the direct assembly of the body;
• The connection should be made using glue and specialized screws with their further screwing in at a distance of 5 cm from each other;

• For the self-tapping screws, you need to create holes exactly 3 mm in size using drills, and for the heads of the self-tapping screws, you will need to create the corresponding recesses using a 10 mm drill;
• Now it's time to mark the holes for the acoustic terminal using a simple compass;
• Next you need to create the corresponding holes using an electronic jigsaw.

Note. If the acoustic terminal is constantly under high pressure conditions, then various kinds of overtones will regularly emanate from it. In order to avoid the effect described above, it is necessary to simply shield the acoustic terminal using a small box.

Let's continue:

• Before proceeding to screwing the pre-prepared screws, it is necessary to coat the entire surface of the joints with glue;
• The parts of the body that protrude after gluing just need to be carefully cut off using a plane;
• In a similar way, it is necessary to mark and cut the corresponding holes already on the front wall in order to ensure high-quality installation of the car speaker;
• Nitrolacquer for furniture must be applied to a wooden body in order to preserve the properties of anti-moisture and anti-condensation processes;
• To create a beautiful appearance, it is recommended to cover the outer part of the body with carpet (see);
• Now all that remains is to simply connect the acoustic terminal and the subwoofer speaker.

Note. It is extremely important to familiarize yourself with all stages of the instructions and understand the design program, as this will allow you to perform independent installation and individually design the box directly to the dimensions and capabilities of the luggage compartment of your car. Also, during absolutely all stages of work, a high degree of attentiveness and accuracy is important, because any inaccuracy will certainly affect the final result.

Self-construction instructions in combination with photo and video materials will allow you to complete the work quickly and efficiently. The price of the issue is minimal and is ten times different from the operation performed in the workshop.
It is quite possible to build a housing with your own hands. The main thing, we repeat, when creating and constructing for the first time, is to carefully read the detailed practical instructions.

Before you start designing and assembling the box, you need to decide on the choice of speaker. We recommend choosing 10-12 inch imported speakers, as they are most often used in car subwoofers and are best suited. We described in detail how to choose a speaker for a subwoofer in a previous article. The design of the box is also important: the quality and volume of low-frequency sound depends on it.

What types of subwoofer boxes are there?

There are several types of subwoofer boxes. The sound quality directly depends on the design of the box, which you will receive at the output. Below are the most popular types of subwoofers:

A closed box is the easiest to manufacture and design; its name speaks for itself. The woofer is housed in a sealed wooden housing, which improves its acoustic performance. Making a subwoofer in a car with such a housing is quite simple, but it has the lowest efficiency.

A 4th order bandpass is a type of subwoofer whose body is divided into chambers. The volumes of these chambers are different; in one of them there is a speaker, and in the second there is a bass reflex (air duct). One of the features of this type of subwoofer is the design's ability to limit the frequencies that the cone reproduces.

The 6th order bandpass differs from the 4th order by the presence of another bass reflex and another camera. There are two types of 6th order bandpasses - the first has one bass reflex, and the second has two (one of them is common to both cameras). This type of box is the most difficult to design, but produces maximum efficiency.

A bass reflex is a subwoofer with a special tube in the housing. It vents air and provides additional sound from the rear of the speaker. In terms of complexity in manufacturing and sound quality, this type is a cross between a closed box and a bandpass.

If you want to get the highest quality sound, you can opt for bandpasses. But this type of design has many details that must be carefully designed and calculated. All this can be done using a special program WinlSD, which will not only determine the optimal size and volume of the subwoofer, but also create a 3D model of it, and also calculate the dimensions of all parts.

Unfortunately, this program requires at least minimal knowledge in this area and the average car enthusiast is unlikely to be able to do everything right the first time. Moreover, in order for the program to work correctly, it needs some speaker parameters, which are also not known to everyone. If you do not plan to take part in car audio competitions, we advise you to discard the bandpasses.

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A bass reflex will be the most optimal solution for a homemade subwoofer. This type of box is good because the tube (bass reflex) allows you to better reproduce the lowest frequencies. In fact, this is an additional sound source that contributes to the sound of the subwoofer and increases efficiency.

What materials do we need to assemble the subwoofer?

The material for making the subwoofer box must be durable, dense and well insulating sound. For this Multi-layer plywood or chipboard is perfect. The main advantages of these materials are their affordable price and ease of processing. They are quite durable and provide good sound insulation. We will make a subwoofer from 30 mm thick multilayer plywood.

To make a subwoofer box we will need:

• Wood screws (approximately 50-55 mm, 100 pieces)
• Soundproofing material (Shumka)
• Drill and screwdriver (or screwdriver)
• Jigsaw
• Liquid Nails
• Sealant
• PVA glue
• Carpet, approximately 3 meters
• Klemnik

Subwoofer box drawings

In this article we will make a box for a subwoofer with a 12-inch speaker. Recommended box volume for one 10-12 inch speaker is 40-50 liters. Calculating a box for a subwoofer is not difficult, here is an approximate diagram with the dimensions of the panels.

It is worth paying attention to the minimum distance from the walls of the case to the speaker. It, like the volume of the entire box, is calculated based on the inner surface.

Video instruction: how to make a drawing for a subwoofer yourself

Assembling a subwoofer box with your own hands

You can start assembling. We use a 12-inch Lanzar VW-124 speaker.


Its diameter is 30 cm, and the first thing you need to do is cut a hole for the speaker. The minimum distance from the center of the diffuser to the subwoofer wall is 20 cm. We measured 23 cm (20 cm + 3 cm plywood width) from the edge of the panel and cut a hole with a jigsaw. Next, we cut a hole for the bass reflex slot; in our example, it has a size of 35*5 cm.


Instead of a slot, you can use a classic air duct - a tube. Now we assemble the bass reflex slot and attach it to the front panel of the subwoofer. We go along the joints with liquid nails and tighten them with self-tapping screws.

It is important to tighten the screws very tightly so as not to leave any voids. They will create resonant vibrations that will ruin the sound of the subwoofer.

Next, we assemble the side walls of the box, having previously lubricated them with liquid nails, and tighten them tightly with self-tapping screws.


On the back cover of the box you need to cut a small hole for the terminal block. We connect all parts of the body. We make sure that we cut and fastened all the parts correctly.


We insert the speaker. Let's look and admire.


Let's move on to the interior decoration of the box. The first thing you need to do is seal all the joints and cracks with epoxy glue or sealant. Next, using PVA glue, we glue soundproofing material onto the entire inner surface of the box.




Now we cover the entire outer plane of the box with carpet, including the bass reflex slot. You can attach it with epoxy glue or using a furniture stapler.


Next, insert and screw the speaker tightly. The subwoofer is almost ready, all that remains is to stretch the wires from the speaker to the terminal block and connect the amplifier.


We bought an additional amplifier, but you can also make it yourself. This is quite difficult, as it requires knowledge and practice in the field of radio engineering. You can also use ready-made kits and circuits for radio amateurs, like Master-KIT, and assemble the amplifier yourself. The only thing requirement for the amplifier - its maximum power must be less than the maximum power of the speaker.

See also a video report on making a homemade subwoofer for 2 speakers

Making a stealth subwoofer with your own hands

Tired of carrying a huge box in your trunk? Then the stealth subwoofer is just made for you. This unique type of case is more practical than the classic box. It doesn't sit in a square box in the middle of the trunk and takes up less space. Often, stealth is installed in the inner part of the wing, sometimes in a niche instead of a spare wheel. The minimum volume of the box that requires a 10-12 inch speaker for normal operation is 18 liters.

To make a passive stealth subwoofer we will need:

• subwoofer;
• protective grille and socket for connection to the amplifier;
• wire for connecting the speaker to the outlet;
• multilayer plywood or chipboard (thickness 20 mm);
• a small piece of fiberboard;
• epoxy adhesive;
• brush;
• fiberglass;
• mounting tape;
• polyethylene film;
• wood screws;
• drill, jigsaw.

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After choosing the place where the stealth will be installed, we empty the trunk and begin manufacturing the body. You can remove the trunk trim where the subwoofer will be installed to place it even closer to the fender. First of all, lay a plastic film on the floor of the trunk. It performs two functions at once: it protects the trunk lining from epoxy glue and allows us to make a mount to which we will screw the bottom of the subwoofer. Next, we cover the inside of the wing with mounting tape in two layers.


We cut the fiberglass into small pieces, approximately 20x20 cm. We place pieces of fiberglass onto masking tape and glue them with epoxy glue. It is better to overlap the fiberglass fabric so that there are no obvious joints and seams.


We sculpt layers of fiberglass on top of each other, simultaneously lubricating them with epoxy glue, until the thickness of the sheet reaches 10 mm (about 4-5 layers).


The material will harden in approximately 12 hours. To speed up the process, you can use a lamp. Now we cut out the bottom of the subwoofer and glue it to our body. The joint is treated with sealant or glued with epoxy resin.


In this particular case, the shape needs to be adjusted to the trunk hinges so that our homemade subwoofer does not interfere with its closing. After we cut off all the excess, we cut out the side walls and the top cover from chipboard. We make the rounded part from plywood, we did it “by eye”.

To make it easier to give the plywood a rounded shape, you must first wet it, give it the desired shape, secure it and let it dry.

Chipboard sheets must be glued with epoxy glue or sealant, and then fastened with self-tapping screws. We also glue the fiberglass box using epoxy resin, and when it dries, we fasten it with self-tapping screws.


For better sealing you can glue the seams again. We applied another layer of epoxy glue and pressed the structure with sand to help the glue adhere better.


Next we can measure the front panel and cut it out. Using a jigsaw, cut out a circle for the speaker. In order to securely attach the front panel to the body, you need to tighten it with self-tapping screws on all sides. That is, you need to install bars on the entire inside of the panel, at a distance slightly greater than the thickness of the plywood (in our case, we attached the bars at a distance of approximately 25 mm from the edge of the panel). Thanks to this, we will be able to secure the front part at the top, bottom, sides, and most importantly - securely attach it to the rounded element.


Cut a hole in the end for the socket.


In the end, it was decided to add two more layers of fiberglass and epoxy glue to the curved part of the body for the stealth subwoofer.


We carry out the final assembly: install the socket and connect the speaker to it, but do not screw it yet. Further There are two options - paint the subwoofer, or cover it with carpet. Painting is a little more difficult, since you must first level the surface. For this we used universal putty.


We level everything with sandpaper, prime and paint. The subwoofer is ready!

Calculation of the subwoofer housing - ZYa ( Z covered I shield). It is not difficult to calculate and make a sound element for a specific subwoofer speaker; it is a very simple acoustic design to calculate and manufacture. The task is to determine the required volume of a closed box in which the subwoofer speaker will create a relatively flat frequency response in the car interior.

To calculate the enclosure, you will need a program for calculating subwoofer enclosures - JBL SpeakerShop or another similar one. We find a datasheet with the technical characteristics of the subwoofer speaker, we are interested in the Thiel-Small parameters, the minimum that you need to know about the dynamics: Fs(resonant frequency of the speaker), Vas(equivalent volume) and Qts(full quality factor). If more parameters for the speaker are known, then good, you can enter them all, but to calculate the body of the ZY and even the FI, the three above parameters are quite sufficient.

Calculation of the subwoofer housing - ZYa.

Button Plot, shows the frequency response curve. By changing the volume, it is necessary to obtain the smoothest possible curve, without dips in the working area. If something is wrong, check whether this subwoofer is suitable for the PL.

Once the optimal frequency response curve is obtained, it will become known how large the subwoofer enclosure needs to be made.

This is considered in the following way:

Calculated volume 1000 ÷ length ÷ height = width. In more detail, with an example, is described at the end of the article on calculating the bass reflex box.

I recommend making the case with a beveled back or front wall, this will reduce the impact of reflected waves from the back wall. To correctly calculate such a case, you need to make the bottom of the case longer by several cm, and the top, on the contrary, a few cm shorter, from the original calculated width, in the end the volume of the case will not change. Or use damping material in the body, but in this case, this must be taken into account when calculating the volume in the program.

Subwoofer box

How you design your subwoofer is how it will sound. Of course, there are ready-made options - cabinet-mounted woofers, but you shouldn’t demand real performance and vibrations from them. This is the “middle”, designed for the average consumer, and is far from an audiophile and creative format.

The most popular types of acoustic design for low-frequency speakers are closed boxes and bass reflexes. A lot has been written about them, the advantages and disadvantages are described in detail, there are reviews, examples and much more.

The subwoofer box requires precise calculation; there is even a special program for calculating the volume of the subwoofer box. If you are faced with this issue for the first time, it is better to turn to professionals. Otherwise, the result will be disastrous: money down the drain and the lack of sound we are striving for.

What box volume is needed for a closed box?

• Subwoofer 8 inches - box 8-12 liters in its pure form
• Subwoofer 10 inches – box 13-23 liters
• Subwoofer 12 inches – box 24-37 liters
• Subwoofer 15 inches – box 38-57 liters

It is impossible to indicate the exact volume, since each woofer has its own characteristics and installation requirements; setting is also important here. If the volume of the box is larger than necessary, then the low frequencies will be blurry and not clear. If it is less, the bass will become “fast” and harsh, this is too much for human hearing.

What volume of box is needed for a bass reflex?

• Subwoofer 8 inches – 20-33 liters in pure form
• Subwoofer 10 inches – 34-46 liters
• Subwoofer 12 inches – 47-78 liters
• Subwoofer 15 inches – 79-120 liters

Unlike a closed box, a bass reflex enclosure can operate even at lower values, although here it is important not to overdo it. If the volume is too increased or decreased, you will not get sound; in the worst case, the result will be a loss of power and failure of the woofer.

Subwoofer with inverted speakers

Typically installed on demo cars for SPL competitions, where maximum sound pressure is particularly valued. Plus - savings in housing volume, the ability to install several subwoofers on one box. The speaker diffuser “pumps” volume in both directions. This is how SPL drivers achieve that very “wind” when everything around the cabin vibrates, including upholstery, “long hair,” and people. Such boxes are made by real professionals, relying on experience and knowledge in the subject of car audio.

Material requirements

Multilayer plywood, wood or chipboard are used as materials for the subwoofer box. You will also need sound insulation, sealant, screws, glue and tools. In the technical documents for each woofer there are instructions indicating the required volumes of the housing for good sound. Drawings are developed in accordance with the box volumes recommended by manufacturers.

If you want to buy a box for a subwoofer, you can consult directly in the store; MVA specialists know a lot about this and will advise the required volume and type for the existing low-frequency speaker.

It is engraved in stone: one of the fundamental dependencies of electroacoustics prohibits simultaneously increasing sensitivity and decreasing the lower limiting frequency of the loudspeaker and the volume of design. And if it’s not knocked out, then you have to knock it out...

RULES OF THE GAME

This is for sculptors. I have long wanted to clarify how exactly this dependence is realized. These notes are devoted to the results of these clarifications. First, a couple of preliminary notes. The sensitivity of a loudspeaker throughout this material (unless otherwise stated) will mean the so-called reference sensitivity, that is, sensitivity at those frequencies where the amplitude-frequency response of the system has a more or less linear horizontal character, or, as they say acoustics, the normalized frequency response has a single (more or less) value. The actual sensitivity of the system in a certain band can be both higher than the reference one (if acoustic amplification is observed in this band) and lower than it (if there is a decrease in the frequency response). In most formulas, however, instead of sensitivity, the value of the efficiency (reference efficiency) of the loudspeaker η (this is in Greek, in ours - “this”) appears, which is related to the sensitivity SPL by a simple dependence:

(1a) η = 6.026 10 -12 10 SPL/10 ,

(1b) or SPL = 10log(η/6.026 10 -12)

One of the options for writing the formula for calculating the efficiency of an electrodynamic converter looks like this:

(2a) η = 4π 2 Fs 3 Vas/(c 3 Qes)

Here, as always,
Fs - frequency of the head's own resonance (Hz),

Vas - equivalent volume of air (m3),

Qes - electrical quality factor of the head,

c is the speed of sound in air (334 m/s).

The first and simplest conclusion that follows from consideration of formula (2) is that one of the Thiel-Small parameters is related to the other two through the efficiency of the converter, in particular, for an equivalent volume we can write:

(2b) Vas=c 3 Qes η/(4π 2 Fs 3)

So, for a head with a fixed Qes value, we can obtain the dependence of the equivalent volume Vas on the arguments (or SPL) and frequency Fs. To move from Vas to the volume of the box Vb (at this stage we are considering only a closed box - ZY), we will need the value of the target quality factor of the head in the box Qtc and the total quality factor of the head in air Qts. The Qtc parameter is the main characteristic of the “setup” of the software. (We are accustomed to the fact that only the phase inverter (PI) is tuned, but the combination of the Qtc parameters and the lower frequency limit of the VJ can also and is even commonly called tuning.) In particular, for Butterworth tuning Qtc = 0.707, for Bessel 0.577. Chebyshev settings also exist; depending on the amount of permissible overshoot on the frequency response (0.5 or 1 dB), the quality factor Qtc can be 0.86 or 0.95. It can be shown that the volume of the box Vb is related to the equivalent volume Vas by the relationship:

(3) Vb = Vas Qts 2 /(Qtc 2 - Qts 2).

Now we need to relate the resonance frequency of the head in the box Fc with the natural resonance frequency (in air) Fs. There is also a corresponding formula for this:

(4) Fc = Fs Qtc/Qes.

Finally, the value of the frequency corresponding to the lower frequency limit of the loudspeaker at a level of -3 dB (denoted as F3) is strictly related to the frequency Fc through the constant k, which is known for each setting:

(k can be either greater or less than one, in particular, for Butterworth k = 1.0.)

The quality factor Qts is related to Qes through the quality factor Qm of mechanical losses in the suspension and in the box by the known relationship:

(6) Qts = Qes Qm/(Qes + Qm).

Let us first assume that there are no mechanical losses, Qm >> Qes, and then Qts = Qes. (This assumption can be considered reasonable for heads with Qes of no more than 0.3, having a mechanical loss quality factor of at least 3.0.) Later, we will see how the volume of the box changes when the loss quality factor becomes comparable to the electrical quality factor. As always, we take the ZY with Butterworth quality factor as a starting point. The first figure shows graphs of the obtained dependence for Qes equal to 0.2, 0.4 and 0.6.

Rice. 1. Ground cell with full quality factor Qtc = 0.707:

For you and me, there is not much practical use from such graphs - what is the point of talking about boxes with a volume of 1 - 5 cubic meters, when we have a cabin volume of, at best, about three cubic meters? Indeed, the volume of the box is calculated in cubic meters, if we set a sensitivity of 100 dB and a lower frequency limit of 16 Hz, we don’t set such tasks for ourselves, and now it’s clear to see why we don’t need to set them. We'll get to practical results later. In particular, we see that the function is monotonic with respect to each argument (SPL and F3), that is, there is no such range of argument values ​​where it would be possible to reduce the volume of the box without losing in the length of the bass band or in the sensitivity of the system.

But now you can ask the question: how will the volume of the box change in the presence of mechanical losses? Since consideration of all possible combinations of electrical and mechanical quality factors goes far beyond the scope of any journal article, it was necessary to choose some typical value of the mechanical quality factor Qm. As a result of processing the statistics we collected during numerous tests, an average value of 3.3 was obtained. Approximately the same (3.333) value of mechanical quality factor can be obtained by using a head with a mechanical quality factor of 5 and a box loss quality factor of 10. The value Qm = 3.333 was adopted for further calculations. In Fig. 2 you can see the dependences for the volume of the cell, taking into account the quality factor of losses.

Rice. 2. Ground cell with loss quality factor 3.33 and total quality factor Qtc = 0.707:

Calculations have shown that taking into account mechanical losses leads, as a rule, to an increase in the volume of the box. But this dependence is nonlinear, and in those cases when the electrical quality factor Qes approaches the “box” quality factor Qtc (in our case - 0.6 and 0.707), the presence of losses allows for a slight gain in volume. True, even in this case the boxes turn out to be much more voluminous than for heads with low Qes, and if we want to find out the sizes of the minimum possible boxes for each value of quality factor Qes, the presence of losses will need to be taken into account. We will move on to practical implementations a little later, but now we can draw some preliminary conclusions.

1. Heads with a high total quality factor (Qts > 0.5) are unsuitable for work in a compact design.
2. When the cutoff frequency changes by 1/3 of an octave, the required volume of the box changes by half (well, that is, as if by an octave).
3. The same thing happens with the volume of the box when the required sensitivity changes by 3 dB.

Now you can leave the Butterworth setting behind and ask: how will the volume of the box change if the values ​​of all arguments are preserved, but when the quality factor of Qtc changes? Calculations gave a simple answer: the higher the quality factor, the more compact the box. This means that in order to obtain the parameters of the “minimum possible” box, you need to set some restrictions. And here we can’t do without using the “standard” interior transfer function (also known as the “AutoSound function”). With the involvement of this function, the following interesting patterns arise (we continue the numbering).

1. With increasing quality factor Qtc and minimal unevenness of the frequency response, the volume of the box decreases.
2. In the range of total quality factor Qtc values ​​from 0.4 to 0.67, the unevenness of the frequency response in the cabin can be maintained no higher than 0.4 - 0.6 dB.
3. With higher and lower quality factors Qtc, the unevenness of the frequency response in the cabin increases.

When testing subwoofers, we proceed from the fact that frequency response unevenness of less than 2 dB (in the range of 25 - 100 Hz) is sufficient to obtain the highest rating for the shape of the frequency response (this recommendation itself was obtained on the basis of practice). Then, for a box with a minimum volume, we will set the unevenness to 1.9 dB and get a setting with the following parameters:

Qtc = 0.80; Fc = 70.1 Hz (F3 = 63 Hz).

For this we can already build graphs for practical use. Please note that for a head with a quality factor of 0.6, mechanical losses in the moving system and box are also taken into account (Fig. 3).

Rice. 3. Graphs of distribution of cell volumes with Qtc = 0.80and Fc = 70 Hz

For convenience, Table 1 is provided below, which includes all those values ​​on the basis of which the graphs shown above were constructed.

Table 1. Volumes of ground cells with uneven frequency response in the cabin of 1.9 dB

As you can easily see, in the table it would be enough to provide values ​​for a range covering only 10 dB of the SPL sensitivity spread; the remaining values ​​are obtained by moving the decimal point. Let's say the box volume for an SPL of 90 dB is ten times larger than for an SPL value of 80 dB. This pattern, however, is directly related to the statement that was given above under number 3.

With the box closed, everything seems clear. With the bass reflex design, as usual, it is somewhat more complicated. Let's start with the fact that it is not so easy to understand which setting is considered the most compact. During the mathematical experiments, the following dependencies emerged.

1. The higher the quality factor of the head in the Qtc box, the smaller the gain in bandwidth is given by the FI compared to the ZY. For this reason, settings with a quality factor Qtc > 0.707, in our opinion, do not make sense.
2. Design with FI at the same cut-off frequency F3 is always more compact than ZY, sometimes by tens of percent, and sometimes by three to four times.

The last statement seems at first glance somewhat unexpected - in our experience, a box with FI is always more voluminous than a ZY. We will see how this contradiction is resolved a little later, but for now we move on. The same mathematical experiments showed that almost all settings known from classical literature (for a free field) do not perform well in the conditions of a car showroom. The only exception is the tuning known from Mr. Thiel's work as the fourth-order Butterworth "maximum flat tuning" (B4). With proper selection of the box tuning frequency Fc (not the tuning frequency of the phasic Fb, but the resonance frequency of the head in the box, on the impedance curve this is the upper hump of the double-humped curve), the resulting frequency response in the cabin becomes suspiciously similar to our “normalized” frequency response, which we strive to build with testing subwoofers, albeit with a bandwidth slightly larger than “our” 4/3 octaves. So, to calculate the reference setting for the calculations, we took as a basis our “standard” frequency response with an average acoustic gain of 4.0 dB. More precisely, the task was the opposite: to find such a setting (a combination of Qtc, Fc and Fb), in which the frequency response in the cabin would have a maximum of 35 Hz, and the bandwidth at the -3 dB level would be 4/3 octaves. Where did the 4 dB gain come from? The fact is that when analyzing the preliminary results, the following rule was formed.

1. The less acoustic amplification a design with FI provides, the more compact the box becomes.

Well, 4 dB is practically the minimum value of acoustic gain from what we get in our tests. (The streamlined expression “almost minimal” means that we encountered indicators that were slightly lower, but it was obvious that this head was not at all suitable for working in FI.)

So, the “minimal setting” has the following parameters. Qtc = 0.58, Fc = 53 Hz, Fb = 32.6 Hz. The F3 frequency measured by free field is 37.3 Hz.

This is where a terrible secret was revealed: our boxes with FI yield more because their lower limit frequency in the free field must be significantly lower than that of the ZY - in order to obtain comparable results in the cabin.

Now, using all the same dependencies, we can construct similar dependencies for FI (Fig. 4).

Rice. 4. Graphs of distribution of volumes of boxes with FI: with Qtc = 0.58, Fc = 53 Hz, Fb = 32.6 Hz

Please note that the dependences for the design (and heads) with losses were chosen as the basis for constructing the last two graphs, since the boxes turned out to be a little more compact. And also for ease of use, we have summarized all the data in Table 2. The range of function values ​​not exceeding 85 l (three “cubes”) is highlighted in color.

table 2. Volumes of a box with FI having a standardized frequency response form

From a comparison of the data in Tables 1 and 2, it is easy to conclude that all boxes with FI, without exception, have a larger volume than the corresponding SF. Then, one might ask, why fence a garden? To find the answer to this question, let's try to take into account the acoustic amplification and add those same 4 dB to the data in the first column. And we will summarize the results for FI and ZY in a general table 3.

Table 3. Comparison of volumes of ZY and FI

As you can see, taking into account this correction, the phasicist manages to win back a certain amount of volume (9 - 29%) from the closed box. The only exception is the option with a head quality factor of 0.50; As already mentioned, high-Q heads are not well suited for working in FI.

What happens if you choose a setting with an acoustic gain of not 4 dB, but less or, conversely, more? The lower the gain, the physically smaller the contribution to the radiation made by the phase inverter and the closer the volume of such design is to the volume of the ground cell. The greater the amplification, the larger the volume of the box with the FI, but the greater the gain in volume (compared to the ZY) it gives, taking into account the acoustic amplification. It turns out like this: if the designer of acoustics operating in a free field environment pays with the relative complexity of the design for reducing the lower frequency limit, then the creator of acoustics operating in a compression environment pays in the same coin for reducing the volume of the box. Simultaneously with the increase in acoustic amplification, of course, the unevenness of the frequency response increases. However, the increase in this unevenness is not so important, since it occurs outside the range (4/3 octaves) that interests us.

In our desire to identify patterns for establishing design volumes, we did not touch at all on the important issue of the feasibility of boxes in given specific volumes using certain heads. A detailed examination of these patterns is beyond the scope of any single journal article. However, if we introduce into consideration restrictions on the possible values ​​of the box volume Vb, as well as the parameters Vas and Mas (mass of the moving system) depending on the standard size, plus restrictions on the value of the force factor Bl (regardless of the standard size), then you can get interesting results.

Let's go from below. 8-inch heads allow you to cover approximately 2/3 of the SPL range from bottom to top (according to our table it turns out the other way around, from top to bottom), that is, from 80 to 94 dB/W. Moreover, for heads with a higher Qes, the “coverage area” is wider than that of “eights” with a powerful magnet and, accordingly, a low quality factor. By the way, this is a general pattern: taking into account design limitations, the area of ​​application of heads with low electrical quality factor shifts downward, that is, to the area of ​​​​higher sensitivity and larger box volume.

Now we move on to the most famous (albeit rare) 18-inch caliber in our industry. It is quite obvious that boxes on heads with such articles occupy the lower part of the table - with large volumes and corresponding sensitivity. Heads with a quality factor of 0.2, as it turned out, are generally unrealizable (you and I have noted more than once that the larger the caliber, the higher (per circle) the quality factor). Heads with a quality factor of 0.3 allow you to build a box with a sensitivity of at least 97 dB/W, but the volume there will also be serious. (If its sensitivity is lower, it means that subwoofers with the “correct” frequency response shape cannot be produced with them, but that’s probably not what they are created for, at least in our industry.) Heads with a quality factor above 0.4 and beyond allow work with reference sensitivity of 96 dB/W and higher.

“Fifteens” with a quality factor of about 0.20 are an extreme rarity; we recently came across one of these rarities “on the carpet”. They implement ground cells with a sensitivity of 92 - 94 dB/W, and that’s it. At least that's how it worked out for me. Heads with a higher quality factor cover a wider area - from the same 92 dB/W and beyond.

Finally, the 12" and 10" heads together cover 3/4 of the range, leaving only the 84 dB/W and below regions free, leaving free cells with a sensitivity of 100 dB/W and slightly below.

The question may arise: what will happen if the heads do not play according to our rules, in particular, their sensitivity is lower than it should be? This will mean that the head parameters do not allow the frequency response to fit within the specified tolerance of 1.9 dB for a given box volume. That is, either the box will be larger, or the frequency response will have higher unevenness. So the table above can be used as a universal determinant of the minimum volume of a box. True, what has been said applies only to a closed box; for a bass reflex, the dependencies are no longer so clear.