“...Top class 3, second place bottom left, recommended by the ears of famous testers ...”
...or a customized do-it-yourself project
If you want a guarantee that your speaker will fall under one of the applicable “quality evaluation lists,” building your own speaker may not be a good idea for you. But if you have a little manual dexterity, enjoy technology and above all love listening to music, a speaker can become more than an “ominous,” unnecessarily mystifying creature.
In industrially manufactured speakers, most of the manufacturing costs come from the cabinet. Do-it-yourselfers have the opportunity to build a cabinet that meets their preconceptions and that can also offer superior acoustic properties compared to a ready-made speaker. That doesn’t mean it’s enough to outfit a well-built cabinet with “super-powerful speakers” and the commonly advertised “universal crossovers.” Appearances can be deceiving, and those things have very little to do with high-quality music reproduction. A good loudspeaker is distinguished not just by the high quality of its components – a little know-how is needed, too.
In order to understand a few fundamental things, unfortunately we can’t avoid getting into some theory. But the focus will always be on the practical application.
Copyrigth I.T. Intertechnik Kerpen GmbH
Music is one of the most beautiful things in life. Its many different forms make it unique, so playing an instrument or going to a concert can be a fulfilling, relaxing or even uplifting experience for human beings.
In our technically advanced world, listening to music and words via acoustic playback systems is becoming more and more important. Just consider the media landscape, with its constantly growing volume of audiovisual information. It’s no surprise that almost every household has some way of reproducing sound through speakers. Televisions, radios, stereos, etc. all use speakers to convey acoustic events to our ears.
Special value is placed on the quality of the reproduction. It needs to be neutral, as close as possible to the original. Speakers should neither add nor subtract anything when reproducing the incoming electrical signal. In this context, people always mention hi-fi (high fidelity) as the measure of true-to-nature reproduction. In the following sections, we will see why true-to-nature reproduction is an almost impossibly ambitious goal.
The weakest link...
How can it be that one and the same speaker is judged so differently by different people? Are the reviewing criteria so broad that Listener A can listen raptly to the music while Listener B turns away in horror?
Probably very few people are in a position to say whether the speaker is acting as a neutral link in the transmission chain.
By its very principle, as an electric-acoustical transformer, the loudspeaker is the weakest link in this chain. The biggest problem here is the speaker’s inadequate performance in the timing area.
First of all, the vibrating unit (membrane) of a speaker is not without mass, so it cannot instantaneously follow sudden changes in the music signal. Second, as a system with a finite spring excursion, the speaker has a limited membrane deflection and therefore cannot create equal pressure.
An example to illustrate this: if a direct current is applied to the brackets of an ideal speaker (which does not exist), it will respond with a steady increase in membrane deflection at a constant membrane acceleration. This would correspond to creating equal pressure, since the sound pressure created by a speaker is proportional to the membrane acceleration. But in a real speaker, the membrane is only deflected as far as allowed by the spring-like suspension. Then the membrane comes to a stop, which causes the sound pressure to drop again. Unfortunately, this behavior creates alternating sound pressure in the real speaker, rather than the constant pressure that would have corresponded to the input signal.
Abb.1.0 Input signal
Abb 1.0 Speaker response
These fundamental errors in the timing area (transient and decay behavior) cannot be seen in the most commonly used representation of the sound-pressure frequency response. The human ear does not hear a “frequency response,” but rather chronological changes in sound pressure as they are created by sound sources, such as instruments.
With the structural possibilities available to us today, we are able to compromise. In order to create a kind of equal pressure at least for a short time, we use speakers with wide membranes and large spring excursions to reproduce deep sounds. The reproduction of higher tones is left to speakers with small, lightweight membranes, which can follow chronological changes in the music signal relatively quickly. These structural limitations lead to combinations of at least two speaker systems, a woofer and a tweeter, that are assigned to the respective frequency ranges through an electrical filter (frequency crossover).
The dynamic loudspeaker (the principle of sound creation)
In order to understand how sound can be created, we must first ask ourselves, “What is sound?” Looking at a textbook gives us the following definition: “Any object vibrating in a medium creates sound waves.” Sounds simple. Just imagine a vibrating plate that moves the air molecules in front of it. This motion is transferred from air molecule to air molecule, so the sound energy is carried to the recipient (e.g. the ear).
How dynamic loudspeakers work
The next two drawings are meant to illustrate how sound is created in practice. They show an electrodynamic speaker, which is the most common principle used in loudspeaker construction today.
The goal is to drive a two-dimensional membrane that will cause the air in front of it to vibrate.
The basic function of the membrane driver comes from the force exerted on an electrified conductor within a magnetic field. Ill.1.1 shows a conductor with electricity I flowing through it, with a length L moving in a magnetic field with flux density B (strength of the magnetic field). Due to the flow of electricity, a force F is exerted on this conductor. This force, also known as the Lorentz force, obeys the following law:
The following applies to the Lorentz force: FL = I·L x B ([F] = N )
Ill.1.2 shows a cross-section of a loudspeaker. The conductor is wound up into a coil, and the magnetic field is shaped like a ring. This construction creates a large effective conductor length in the magnetic field. Normally the coil is attached to a paper or aluminum bearing that is connected to the membrane. This unit is suspended resiliently with a centering spider and a seal. This produces a vibratory system. If the voice coil is connected to an alternating current, it creates attractive and repellent forces that cause the membrane to vibrate, along with the air in front of it.
Before digging a little deeper into the materials used for speaker construction, the do-it-yourselfer is probably wondering whether it’s a good idea to design the whole thing alone or to use a construction plan.
The speakers and construction plans in our product range give you both options. You might just decide to use the construction plans as inspiration for building a speaker box that fits your ideas about design and sound. If the theory is a little too dry for you, just skip Points 2.3, 3, 3.1 and 3.2.
[Graphic, clockwise from left: magnet system / voice coil / centering spider / membrane / seal edge]
The speaker: a mass-spring system
Mechanically speaking, the dynamic loudspeaker represents a mass-spring system, like a weight hung from a spring. If you were to pull on this weight and then let go, it would move up and down at a certain interval. This interval (vibrations per minute), which depends on the rigidity of the spring and the mass of the weight, is described as the resonant frequency or natural frequency of the vibration system.
Naturally, this system is not lossless. Otherwise, once it was set in motion, it would continue to vibrate further and further along with its resonant frequency. There are two main things that “brake” (dampen) the movement of the membrane. First there are the friction losses in the centering spider and the edge of the seal (mechanical damping); second is the electromagnetic braking function of the voice coil in the field of the speaker magnet (electrical damping). The mechanical and electrical properties can be described by a few pieces of data, known as the Thiele-Small parameters (TSP).
fs: resonant frequency [Hz] (natural frequency, determined by the membrane mass and the softness (flexibility) of the membrane suspension).
Vas: equivalent volume [liters] (measures the flexibility of the membrane suspension in relation to the membrane area).
Qms: mechanical value : (measures the mechanical damping (friction in the centering spider and the edge of the seal).
Qes: electrical value : (measures electrical damping)
Qts: free-standing value : (made up of Qms and Qes; describes the total damping of the speaker in its uninstalled condition).
The concept of a value is used here to measure the damping. The value is the inverse of the damping.
Often, only the electrical and mechanical values are given. Qts must then be determined using the following formula.
For the Qts value: Qts=(Qms·Qes)/(Qms+Qes)
The Qts value for a “usable” loudspeaker is between about 0.25 and 0.60.
The Thiele-Small parameters (TSP) are essential for the cabinet calculation. When buying woofers, make sure you are given a data sheet with these parameters. Every reputable manufacturer will provide this data.
The loudspeaker in the cabinet
Why does a speaker need to be installed in a cabinet, anyway?
The reason is that sound is dispersed from both the front and back sides of the membrane. When the membrane moves forward, excess pressure is created on the front side and low pressure on the back side. At low frequencies, at least (bass playback), this causes a reciprocal lift. Thus the front and back sides of the membrane must be prevented from having an acoustical connection. Normally, the solution is simply to build the back side of the speaker into a cabinet.
The basis for any adequate speaker box is a solid bass foundation. The goal of the development is to create as deep a bass reproduction as possible, combined with good impulse responses. To achieve this, it is important for the combination of the woofer and the cabinet to go together. The Thiele-Small parameters (especially the free-standing value Qts) can be used to determine which loudspeaker (driver) is predestined for a certain type of cabinet. The following table shows which speakers are suitable for which cabinet types.
Closed and bass-reflex cabinets are the most common cabinet forms whose calculations we will discuss here. It should be said in advance that bass reflex constructions (assuming that speakers with the right parameters are used) have significant advantages in terms of reproducing bass tones.
The woofer works with a closed volume. Here, the air volume in the cabinet affects the speaker like an additional spring. All this means is that its parameters (resonant frequency and value) change when it is installed. The linearity of the frequency response in the bass range is determined by the value of the installed loudspeaker: the total value Qtc.
Ill. 3.0 shows that a Qtc of 0.707 can be considered good. In Ill. 2.0 you can see how various total values Qtc affect the frequency response in the area of resonant frequency.
If you have found a speaker whose free-range value Qts is between about 0.33 and 0.70, it is now very easy to determine the necessary cabinet volume. You will need the loudspeaker parameters fs, Vas and Qts. First, the total value Qtc of the installed loudspeaker must be established. (We had already established that a value of 0.707 is considered good here.)
We then use the following formula to calculate the cabinet volume Vb:
Vb= Vas / (( Qtc2/Qts2)-1)
Loosely filling the cabinet with insulation material will create an apparent increase in volume, so about 10% can be subtracted from the calculated volume.
Usable values for Qtc are between 0.6 and 1.0. A value higher than 1.0 will lead to a clear sound-pressure exaggeration in the area of the resonant frequency as well as poorer impulse responses.
By way of illustration, here is a short sample calculation using the GRADIENT TPC 145 RX/8 bass mid-range speaker.
First, we will obtain the necessary calculation parameters Qts and Vas from the speaker’s data sheet.
Parameters for TPC 145 RX/8:
Qts = 0.35
Vas = 16 liters
Total installed value:
Qtc = 0.707
Volume calculation for the cabinet:
Formula: Vb = Vas / (( Qtc2 / Qts2 - 1)
VB = 5.19 liters
If the cabinet is filled with insulation material, subtracting 10% produces a volume of 4.70 liters.
The resonant frequency fc of the installed speaker, due to the “air cushion” behind the chassis, is higher than the free-standing resonance; this naturally somewhat limits the transmission range for low frequencies. The installed resonant frequency is an interesting value because below this value, no sound radiation worth mentioning takes place. The installed resonant frequency can be calculated as follows:
Installed resonant frequency fc = sqr (fs2 •(Vas/Vb + 1))
(sqr=square root of...)
It takes a long time to do all these calculations with a pocket calculator. Nowadays there are computer programs that can do the work for the home builder.
Here we should mention a program called BOXCALC (see also page 71), which was used to determine all of the calculated frequency responses. With BOXCALC, you can quickly and easily do calculations for bass-reflex and band-pass cabinets in addition to closed cabinets, and create graphical representations of their frequency responses.
The bass range can be expanded with bass-reflex boxes, which we will learn about in more detail below.
The function and calculations of a bass-reflex box are slightly more complicated. The slightly greater effort in terms of calculation and cabinet building is made up for by the advantages in bass reproduction. Some of the prejudice against the reflex-box principle probably comes from the publication of fairly ominous-sounding tuning methods..
In contrast to the closed cabinet, the energy radiated from the back of the speaker is not left unused. The cabinet has an opening that is usually designed as a tunnel with a square or circular cross-section. The speaker works on this system, which is also known as a Helmholtz resonator. The back of the membrane is coupled to the air mass in the tunnel via the air cushion ( spring ) in the cabinet. Thus we have connected the vibratory speaker system with a second vibratory system, the resonator.
III. 3.1 shows this principle using a model.
The indicated force F, which corresponds to the signal sent by the amplifier to the speaker, causes the system to vibrate. Now we can differentiate three different cases, depending on the frequency applied to the system.
Case 1 –High frequency, fast movements in the membrane are caught by the spring; the mass remains at rest. The system acts like a closed box.
Case 2 –The frequency is reduced, the mass begins to vibrate. At a certain frequency, the movement of the mass will be very large in comparison to the movement of the membrane. This resonance case is distinguished by the fact that the movements of the masses counteract each other; however, this means that the membrane and air mass in the tunnel are simultaneously moving outward and inward. This frequency is also known as the tuning frequency fb.
Case 3 –At even lower frequencies, the membrane and air mass move in the same direction, in other words the membrane moves inward and the air mass moves outward.
The relationships between the directions of the movements are often described in vibration theory by using the concept of phasing. To illustrate this, let’s look again at the resonance case (Case 2). The membrane and the air mass are both moving outward. The phase difference here is 0°. In other words, the sound components from the tube and the membrane are added together. If we look at Case 3, there is a phase difference of 180°, which means the sound components cancel each other out.
In the area of resonant frequency, the sound components from the membrane and the tunnel are in-phase, so the sound pressure is amplified in this area (up to +6 dB compared to closed constructions). The transmission area can be significantly expanded into the lower frequencies by using reflex boxes. (see Ill. 3.2)
In order to avoid delving deeper into the mathematics, let’s look at some tables by Australian physicists Thiele and Small to calculate the bass-reflex cabinets. These tables summarize their findings about calculations for reflex boxes. They can be used to easily determine the cabinet parameters based on the speaker parameters.
In order to precisely describe the reflex cabinet, the following values must be determined:
Net cabinet volume Vb [liters]
Tunnel cross-section area Sv [cm2]
Tunnel length Lv [cm]
The following loudspeaker data is needed for the calculation:
Resonant frequency fs [Hz]
Free-standing value Qts 
Equivalent volume Vas [liters]
Since bass-reflex cabinets have greater cabinet losses than closed cabinets, these losses must be taken into account in the calculation. The cabinet loss factor Q1 must be estimated before the calculation is performed. Based on experience, small cabinets use (Vb < 40 L) Ql = 10, medium-sized cabinets use (Vb= 40-100L) Ql = 7 and large cabinets use (Vb= > 100 L) Ql = 5.
A rough volume calculation is first used to determine the expected cabinet size so that the values from the “correct” table can then be used to establish the precise cabinet size.
The table is explained as follows: The heading Qts shows the free-standing value Qts for the loudspeaker to be used. The row following the Qts value contains the tuning factors h, a and b..
Cabinet 40-100 liters
The easiest way to understand the procedure is by looking at an example. As a demonstration, let’s go back to the familiar Gradient TPC 145 RX/8 speaker from the “Closed cabinets” chapter..
Parameters TPC 145 RX/8:
For an approximate volume calculation, go to row 0.35 under the Qts column in the middle table. This volume tuning factor is used to determine the approximate volume. Now we use the following formula to determine the temporary cabinet volume Vb::
Vb = Vas / a
When we plug in these values, we find: Vb = 16 Liter/1.80 = ca. 8.9 Liter
As you can see, the cabinet belongs to the cabinet < 40 liters group, so we will use the right-hand table. We then repeat the volume calculation process with the values from the “correct” table.
Parameters TPC 145 RX/8:
Volume calculation for the cabinet:
Now the tunnel dimensions need to be determined. Normally you use tunnel constructions that end as a tube with a square or round cross-section area Sv, flush with the outer wall of the cabinet. We will limit ourselves to this design.
First, we determine the cross-section area Sv of the tunnel. The cross-section area must be adapted to the acoustic energy that the speaker can emit from the back side of its membrane. If the tunnel cross-section is too small, it can produce rushing noises. The table below shows which cross-section area Sv needs to be met for a specific speaker-basket size (approximately corresponding to the outer diameter of the chassis).
It is a good idea to choose a slightly larger cross-section if the required length needs to fit into the speaker cabinet. Since the TPC 145 belongs to the genre of the 140 mm chassis, according to the table it will receive a tunnel with a cross-section area of about 16 m2, which corresponds to a diameter Dv of 4.5 cm for a circular cross-section.
The following formula is used to calculate the tube length Lv::
Lv = ((30000·Sv)/(Vb·(h·fs)2))-0.82·sqr(Sv)
(sqr = square root of....)
For this example, we then see:
Parameters TPC 145 RX/8:
Tunnel cross-section area:
Sv =15.9 cm2
Length calculation for the tunnel:
Plugging this into the formula for Lv, we get:
Lv = 30000·15.9 cm2 - 0.82·sqr (15.9 cm2) = 13.5cm
(8.7 L· (1.12·51 Hz)2
Whether the reflex tunnel is designed with a round or a square cross-section is not important for the functioning of the loudspeaker.
As with the closed cabinet, you can also calculate a limit frequency f3 for bass-reflex boxes, below which no noteworthy sound deflection takes place. This frequency can be calculated using the tuning factor b:
f3 = b·fs = 1.24·51 Hz = 63.24 Hz
Let’s compare the limit frequency for the bass-reflex construction with the limit frequency of the closed box from Chapter 3.1. The same loudspeaker was used, with a limit frequency of 103 Hz, so a difference of 40 Hz in this case clearly speaks for the bass-reflex box.
Bass-reflex boxes should also be filled loosely with insulation material (polyester wool; sheep’s wool) in order to reduce standing waves inside the cabinet. The area around the inner end of the reflex tunnel is left open so that air can move freely through the tube. (Further information about damping and insulation can be found in the chapter on cabinet construction.))
Finally, we just want to make a brief “practical” observation. What happens if the tunnel length is changed within certain limits, in deviation from the calculated ideal length?
Ill. 3.3 shows the effects that shortening or lengthening the tunnel by 30% has on the frequency response in the bass area, again using the example of the TPC 145 RX/8. An extension of the tunnel causes a flat bass decay and a narrower bass reproduction. Shortening the tunnel creates an increase in sound pressure in the area of the resonant frequency and a more strongly emphasized but less in-depth bass reproduction.
In this chapter we look at various aspect of cabinet construction, from suitable materials to insulation methods.
Fundamentally, any material that comes as a board can be used to build a cabinet. However, depending on the density and stability, every material influences the tonal characteristics of the loudspeaker box.
The energy radiated from the back of the speaker causes the cabinet walls to vibrate. However, vibrating cabinet walls act as sound sources, whose sound components are added to the sound emitted by the loudspeaker. This leads to a corruption of the sound. Ideally, the sound would only be emitted by the speaker membranes.
In order to reduce the cabinets’ sound emanations and their susceptibility to vibration, materials with high density and high internal damping are used.
Wood in the form of particleboard or medium-density fiberboard (MDF) is very common, not just because of its lower weight. In contrast to solid wood, fiberboard and MDF boards demonstrate more neutral acoustic behavior without any distinctive resonances. In addition, pre-cut boards are available from hardware stores at quite reasonable prices. Normally, very good results can be achieved with a cabinet made of 19 mm-thick fiberboard that is then reinforced.
For the sake of completeness, we will list the most common materials here, describe their advantages and disadvantages and give some information about working with them.
Pressboard (well suited)
Compressed into a board made from wood chips and glue, this material has a relatively smooth surface. However, the cut edges are very porous. The boards are glued with normal wood glue. The surface is usually veneered, glued with film or painted. In order to create a flawless finish when painting, it needs to be treated with sandpaper, putty and filler first.
Smaller boxes with volumes up to about 10 liters should use a wood thickness of 16 mm; larger houses should not be less than 19 mm. Interior reinforcements are helpful.
MDF board (well suited)
Compressed into board format and made from fine wood fibers and binding agents, this board has a denser structure and a much smoother surface than the pressboard. Glue the boards with wood glue. The surface treatment is easier, but involves the same steps as for the pressboard. Again, the thicknesses call for 16 mm for a small cabinet, at least 19 mm for larger cabinets. Interior reinforcements are helpful, as with the pressboard.
Stone (moderately suitable)
Marble, granite and slate are the most common natural stones that can be used for building unusual cabinets. They are hard to work with, and they require the machinery and skills of a stonecutter. The low internal damping of the material is also somewhat problematic, which leads to a relatively strong “natural resonance” in the cabinet within the noticeable middle frequency range. Gluing bitumen plates at least 3 mm thick on the cabinet walls can largely eliminate this effect.
Plastic (well suited, not as easy to work with)
Of all the plastics, Plexiglass is probably the best. A cleanly built cabinet that doesn’t hide its inner value is something special. But please note that to process these materials, you will need special tools and experience in working with plastics.
The only motto here is “Do what you like.” You don’t need to use the standard square box that everyone else has already. An unusual cabinet shape is not just an eye-catcher – it can also have technical advantages. Cabinets with walls that are not parallel (e.g. pyramids) tend to have fewer cabinet vibrations than square shapes.
So far we have calculated the net cabinet volume for our loudspeaker, which now needs to be put together in a technically sensible and visually attractive way. What is important is for the frequency range of about 500 Hz to 8000 Hz, where the human ear is most sensitive, to be reproduced as optimally as possible..
A few ground rules for building cabinets
1. Position the mid-range speaker and the tweeter closely on top of each other, along a vertical line.
2. Arrange them in such a way that the speakers used for reproducing mid-range and high tones will be at ear height once they are installed. (Ill. 4.0)
3. Bass-reflex openings should be placed in such a way that they do not hinder the air movement.
4. Avoid (even partially) cube-shaped cabinets.
Wood cutting and assembly
Most hardware and home improvement stores will cut MDF or pressboards to size for you according to a list (with the individual dimensions of the boards). You can also buy wood glue or “express” wood glue (dries more quickly) there to glue the boards together later.
Nails and screws are not needed to assemble the wooden boards. A well-glued cabinet will be completely stable. Nails and screw-heads mar the surface of the cabinet and will need to be puttied over later.
Pre-fabricated baffle boards are available for some construction plans; you should use these, since it is almost impossible to make a baffle board with speaker cutouts without using a router.
Once the rough cabinet construction is finished, any surface irregularities (slightly uneven edges, etc.) can be fixed with a block and sandpaper. A little bit of putty is also helpful for creating a flawless surface. Two-component putty (a polyester putty used in the automotive industry) is easy to work with. It sticks well, dries quickly and is easy to sand. Before applying putty, make sure the surface is clean and free from dust.
The stability of the cabinet can be improved significantly by adding reinforcements to the inside. Upright slats or struts glued between two walls are simple but very effective measures to reduce wall movements. (III.5.0)
[Graphic: side view / slats on the wall / top view]
For many do-it-yourself speaker builders, the practically endless surface design options are a huge advantage. The self-built box becomes a one-of-a-kind item. In the following, we describe just a few of the many options.
Paint allows for countless colors, which lets you match it to any kind of décor. We started with a puttied, sanded cabinet shell. Before the final coat of paint, the cabinet receives one or two coats of primer, which is applied with a brush, foam roller or spray can. Each layer should dry completely before being sanded with fine sandpaper.
For the final colored coat, you can use acrylic or synthetic enamel paint. You can use a wide, high-quality brush to apply the paint, but it’s not especially easy. The results will be better with foam paint rollers. The smoothest results come from spray paint, which is a good alternative especially for smaller speaker cabinets.
Films, fabrics, etc.
One simple option is to glue a layer on top of the surface. Self-adhesive films are available by the meter and by the roll in many different designs, from shiny to matte to rough and velvety. They are relatively easy to use, although you do need a little coordination for the cabinet edges.
Original surfaces are also a possibility, for instance gluing on an unusual carpet, a fabric with an interesting print or even tiles or mirrors.
Damping and insulation
First, a brief explanation of the difference between the two. Damping is a measure to reduce sound emanation along with the cabinet wall’s tendency to vibrate. In other words, a damping measure is applied directly to the wall of the cabinet. A few options are the abovementioned reinforcements, and bitumen plates or soft-fiber boards glued onto the wall surfaces.
Insulation is the conversion of sound energy into thermal energy. One example as an illustration: imagine a swinging pendulum that you want to bring to rest. One way of doing this would be to dip the pendulum in a thick “porridge” that takes the kinetic energy away from the pendulum and converts it to heat. However, sound is nothing but vibrating air particles, so we can also remove its kinetic energy with porous materials like polyester wool, sheep’s wool or mineral wool. Therefore it makes sense to fill the entire cabinet interior with insulation material. Once energy is converted in this way, it can no longer cause the cabinet walls to vibrate.
In practice, the entire interior is loosely filled (not packed) with insulation material (Sonofil). For reflex boxes, the area around the tunnel end extending into the box must be left open.
We wish you lots of fun putting together your box!