A few basic DiY loudspeaker design considerations
When designing a loudspeaker, one has to take many factors into account. I summarize a few important technical issues below, regarding passive closed box and ported loudspeakers. I don't touch upon every important detail and I recommend that if you're a stark beginner, then design a low cost loudspeaker as your first project. For the understanding of the descriptions below, electronics, acoustics and loudspeaker design basics are essential. The latter can be acquired, for example, from the following books:
David B. Weems, Designing, Building, and Testing Your Own Speaker System, McGraw-Hill Professional, 4th Edition, 1997
Joseph D'Appolito, Testing Loudspeakers, Audio Amateur Press, 1st Edition, 1998
Vance Dickason, Loudspeaker Design Cookbook, Audio Amateur Press, 7th Edition, 2006
Or maybe
John L. Murphy, Introduction to Loudspeaker Design, True Audio, 2nd Edition, 2014
Ray Alden, Speaker Building 201: A Comprehensive Course in Speaker Design, Audio Amateur Pubns, 2004
Also, besides the books I recommend the following sticky thread on diyaudio.com: Designing your own speaker from scratch.
There is also a lot of information on the net about this topic, you can find some pieces of them through my Useful links page.
This page doesn't contain information about more exotic designs like dipole, horn, TL etc., neither does it deal with active crossovers. This page is meant for beginners, who are not experienced in DiY loudspeaker design and contains many oversimplifications. It's not so in-depth, it doesn't contain information about much of the specifics, for example on how to use some preferred free design or measurement software or how to solve the outlined problems like the baffle step in practice. It was only meant to provide some basic guidelines and call DiYers' attention to the basic principles that should be taken into account for the most often used and simplest loudspeaker designs. People who want to design non-orthodox, audiophile or high-end speakers should consult more sophisticated articles and more in-depth discussions.
The most important design principle
Don't start to design loudspeakers without (1) knowledge in electronics and acoustics, (2) a calibrated measurement microphone and a microphone preamplifier, (3) an impedance measuring jig, and (4) a loudspeaker measuring and design software with a suitable sound card.
Free loudspeaker measurement and design software
For loudspeaker design I recommend VituixCAD which is a very capable loudspeaker design software, and surprisingly it's free. It can be best used together with the ARTA or REW measurement software. Unfortunately the demo version of ARTA cannot save files and the fully functional commercial version costs 79 EUR. I myself still use the very old and discontinued Speaker Workshop for design to this day, because I'm used to it. Maybe it's time to change! Xsim looks like a good enough crossover design software. You can find the links of further free software on my Useful links page.
Power handling capacity
The rated power must be evaluated together with sensitivity and impedance, and it depends on room size and even on the listener's distance from the loudspeaker. A larger room generally requires a higher loudspeaker power for the same perception of loudness, when one listens the loudspeaker from afar. Sensitivity is generally measured with a 2.83 V RMS voltage, which imposes 1 W on a 8 Ω loudspeaker, 1.5 W on a 6 Ω loudspeaker, and 2 W on a 4 Ω loudspeaker. Therefore, if different impedance loudspeakers are to be compared "power proportionately", relative to a 8 Ω loudspeaker, the nominal sensitivity of a 6 Ω loudspeaker must be decreased by 1.8 dB, while the sensitivity of a 4 Ω loudspeaker must be decreased by 3 dB. In this way the sensitivity will be given in dB/W. After applying this correction, any loudspeaker with a 3 dB higher sensitivity needs half the electrical input power for achieving the same sound pressure (loudness). It works vice versa: a loudspeaker with 3 dB less sensitivity needs double electrical power to achieve the same loudness.
Taking the rated noise power of the IEC 60268-5(2003) standard for the basis, the normal listening demands in a 20-25 m2 room containing a usual amount of sound absorbing appointments and assuming a 87 dB SPL/ 1 W sensitivity loudspeaker listened at a distance of 2 m is more than adequately served by an only 10...20 W rated loudspeaker for almost any kind of music. Naturally, a loudspeaker with 3 dB higher sensitivity (90 dB/W) needs only half of this power, that is 5...10 W for the same max. loudness, and a loudspeaker with 3 dB less sensitivity (84 dB/W) will need 20...40 W. But beware! If the bass or treble needs to be boosted with the tone control, then a 3 dB boost may call for up to two-fold increase, a 6 dB boost may call for up to four-fold increase of the rated power, depending on the actual construction of the loudspeaker!
There are many standards around about loudspeaker power handling and this created a chaotic situation. If you are interested, here you can read about why interpreting loudspeaker datasheets is so ambiguous.
Impedance curve
Loudspeakers must have an impedance curve that amplifiers can preferably drive with low distortion. The driveability for modern transistor amplifiers is generally satisfied if the impedance of the loudspeaker nowhere drops below approx. 3.2 Ω (4 Ω speaker). Amplifiers generally distort more heavily if they are to sound a lower impedance speaker. It is not considered safe to hook up a 4 Ω loudspeaker to an amplifier designed for 8 Ω load.
Frequency response and directivity pattern
Scientific research proved that both experienced and inexperienced loudspeaker listeners deemed loudspeakers with wide and uniform frequency response, and uniform directivity as being better. So it's not enough for the forward radiated (on-axis) sound to have uniform frequency response, a quality loudspeaker must retain its flat response at 30°, and 60° horizontal angles as well. The bigger the diaphragm, the lower the frequency is where the sound becomes directional, the radiated sound beams forward as frequency increases, deteriorating the nice spatial response. This means that drivers with bigger diaphragm shouldn't be allowed to operate at too high a frequency, they must be crossed over to a midrange driver, or a tweeter.
The figure below shows the frequency response of two good (P, I) a mediocre (B), and a bad quality (M) loudspeaker. In the test conducted with more than 300 listeners, people deemed loudspeakers P and I as being best, and M as being worst.
The designer must decide that the loudspeaker is to be operated alone or with a subwoofer. If the choice is with a subwoofer, then one need not make an effort for the loudspeaker to have deep bass, because that will be supplied by the separate sub. In this case one can use a smaller driver and a small enclosure. With smaller enclosures one has the possibility of attaining a clearer midrange, especially if it's a closed box, because standing waves are easier to tame in a small enclosure. It calls for a great enclosure volume to radiate the lowest frequencies with high efficiency.
Distortion
To achieve low distortion of a loudspeaker design, the most basic thing is to select low distortion drivers. Be prepared though that the manufacturer information available about driver distortion is very scarce.
Harmonic distortion
Since most loudspeakers utilize dynamic drivers, I will discuss these. Stronger harmonic distortion generally occurs in dynamic speakers when diaphragm excursion increases, or when the diaphragm produces cone-surround oscillation and partial oscillations.
Far enough from the characteristic resonance of the speaker, in the passband, diaphragm excursion is proportional to the reciprocal square of frequency. This means that to achieve the same sound pressure at 1/10 the frequency, a 100-fold increase of diaphragm amplitude is necessary. For example, it requires 100 times the amplitude to radiate a 80 Hz sound relative to an 800 Hz sound at the same dB SPL. Harmonic distortion increasing with diaphragm excursion occurs because of many factors, to list only 3 of them: (1) because of the asymmetry of the magnetic field, (2) because the diaphragm suspension acts a a nonlinear spring: the bigger the excursion, the bigger the distortion and (3) because the voice coil inductance depends on diaphragm position. Another source of distortion is that the moving voice coil modulates the stationary magnetic flux in the air gap.
Ported loudspeakers have a lower low frequency harmonic distortion, since at the tuning frequency of such systems, the excursion of the woofer can be very little and this reduces HD, but they generally have a much poorer low frequency transient response than closed boxes (bass reflex operation is basically sizing and utilizing a resonance phenomenon).
The designer must pay attention to not only the woofer, but also to the tweeter, which shouldn't be crossed over at so low a frequency where it would distort at high volume levels. As a general rule (excpetions exist) it's not recommended to allow the usual 25 mm diameter tweeters cross over below 2.5 kHz with a 12 dB/octave crossover. If the crossover is 18 dB/octave or 24 dB/octave, or the tweeter is a chambered one with low resonance frequency, then you can decrease the crossover frequency to somewhat below 2 kHz.
Group delay distortion
See below at the discussion of the order of the crossover.
The flatness of
frequency response
The resonances of diaphragms, that is standing waves forming in the diaphragm material, produce selective peaks and dips in the frequency response curve. Every diaphragm has a frequency above which it can't move like a rigid piston, and different portions of the diaphragm start "to have it their own way" (cone breakup). This has the effect that the frequency response curve of the driver gets uneven, parts of the response curve around the resonance get elevated and this gets the sound "colored." So if you observe that the frequency response curve of a driver shows a considerable (> 2...3 dB) peak or dip in the frequency interval you intend to use this driver for, then select a better quality driver.
How can you know a poor quality driver? Here's an example, below you see the factory frequency response curve of a driver marketed as a midwoofer.
It can be observed that the frequency response of this driver is non-uniform in its passband, there's a severe resonance around 1.2 kHz. This driver radiates 1.2 kHz with 5...6 dB more sound pressure that is with almost 2 times more sound pressure than it does 850 Hz! This means that this driver shouldn't be crossed over above 500 Hz, not really a nice thing from a supposedly midwoofer. As you can see, the midrange of this driver is definitely very colored.
The smoothness of the frequency response of the ready loudspeaker is influenced by the standing waves formed within the cabinet and in the cabinet walls. These can be reduced by proper cabinet design.
Sensitivity
The sensitivity of a loudspeaker has no direct influence on its quality save for the higher thermal compression of low sensitivity loudspeakers. A lower sensitivity loudspeaker simply needs a higher voltage (and consequently a higher power) output from the amplifier. The sensitivity of loudspeakers designed for home audio is generally in the range 84...91 dB SPL/ 2.83V RMS/ m. This means that even 1 Watt of amplifier power produces a loudness that the neighbors will complain of. Of course the music dynamics and the high crest factor of musical signals necessitates amplifier power much higher than 1 Watt to reproduce sound waves accurately (without clipping). To summarize: it's nice if a loudspeaker has higher sensitivity, because less electrical energy is wasted during listening to music, and there is less probability of driver overheating. But let's not sacrifice more important parameters (those mentioned before) on the altar of sensitivity.
Baffle step
The wavelength of low frequencies is long enough for them to wrap around the speaker baffle and so they are radiated in full space (in every direction; backwards, too). As soon as the wavelength becomes comparable to the front baffle dimensions, the sound will be radiated more and more into half space. This means that for finite size baffles there is always a transition of the sound pressure from full space (4π) to half space (2π) with a perceived increase of SPL at higher frequencies. This is the "baffle step", which on practical baffles is not as much a step, it is more like an gentler, elongated slope rising with frequency and flattening out at some point. Baffle step results in an average of +6 dB more sound pressure at higher frequencies. For example, here's the simulated baffle step of the two midrange drivers in the Euraudio Essentia loudspeaker, where the imaginary microphone was placed at 1.5 meters from the baffle at the height halfway between the two drivers:
The designer has to decide whether they correct the baffle step or not, and if they do, to what extent do they correct it. The vicinity of the back wall reinforces the SPL in the bass realm due to constructive interference, but causes an ugly dip in the lower midrange due to destructive interference. Loudspeakers that are designed for close to wall usage may not need baffle step compensation, but they need a bass boost when they are placed far from walls.
2 or 3-way loudspeaker (or maybe 2.5-way)?
There are midwoofers and tweeters that allow designing a 2-way loudspeaker. Using a third, midrange unit can be appropriate if this is not the case or if a higher power handling is needed, as the midrange unit can partially relieve the tweeter and/or woofer. Inspect the frequency response of the drivers you intend to use. It's not recommended to cross over the tweeter too close to its resonance frequency, especially because the total quality factor (Qts) and resonance frequency (fs) of tweeters are not accurately repeatable manufacturing parameter, and differing Qts and fs cause differences in the frequency response and phase around the resonance frequency. A practical formula for 2nd or higher order crossovers is fmin = 2fs, where fmin is the recommended minimal crossover frequency and fs is the resonance frequency of the tweeter. In some cases, e.g. with an acoustically 24 dB/octave crossover, which makes use of the 12 dB/octave sound pressure drop below resonance frequency (that's to say the crossover is only 12 dB/octave electronically), the fmin = fs condition is allowed. But let this be an exception rather than a rule, because using a tweeter with such a crossover imposes very serious requirements on the tweeter. In the following table, let's summarize the result of the fmin = 2fs formula for some tweeter resonance frequencies:
|
|
Tweeter
resonance frequency, fs |
||
|
850 Hz |
1200 Hz |
1700 Hz |
|
|
Minimal
crossover frequency fmin |
1700
Hz |
2400
Hz |
3400
Hz |
We have also set the goal that the loudspeaker should have good directivity, it shouldn't exhibit bigger dips even in the frequency response recorded at 60 degrees. Therefore the midwoofer shouldn't be operated above the frequency, where its radiation pattern (polar plot) becomes too directional. A good approximate value for the frequency where this happens is fmax = 26.000/d, where fmax is the recommended maximal crossover frequency and d is the diameter of the diaphragm in cm (this includes 1/2 of the surround). In the following table, let's summarize the result of the formula for a few popular diaphragm diameters:
|
|
Diaphragm diamater of midwoofer, d |
||
|
10 cm |
13 cm |
17 cm |
|
|
Maximal crossover frequency fmax |
2600
Hz |
2000
Hz |
1530
Hz |
This is obvious that for smooth directional characteristics, the midwoofer shouldn't be crossed over at such a high frequency where many designs have it.
To decide whether your preferred midwoofer and tweeter can be used in a 2-way configuration, the condition fmax > fmin should be satisfied. If there is only a small discrepancy, let's say 100...200 Hz for the formula to be true, and you do with a little deterioration of quality, then you may accept the pairing of the two drivers.
2.5-way loudspeaker
The 2.5-way design uses 2 midwoofers. The lower one, which is farther from the tweeter, reproduces low frequencies only. This is aimed at compensating the baffle step. To better understand the principle of 2.5-way design, please refer to the following figure:
Crossover
Crossover frequency
The crossover frequency can be placed anywhere between fmin and fmax calculated above. If better directional characteristics are essential, then cross over at a lower frequency. If lower power loading of the tweeter and lower nonlinear distortion of the tweeter are your primary concerns, then cross over at a higher frequency.
The order of the crossover
Group delay is one kind of phase distortion. Only first order crossovers (6 dB/oct) have zero group delay. But these crossovers have a disadvantage in that they let too much low frequencies onto the tweeter, and too much high frequencies onto the woofer. This causes the frequency response to dip over a wide frequency interval, when the perceiver (measurement microphone or your ear) is not exactly positioned on-axis. Another disadvantage of the 1st order crossover is that it can't handle the impedance peak around the resonance frequency of the tweeter, causing an elevated sound pressure around there. Therefore it's advisable not to cross over the tweeter lower than 3 times its resonance frequency with a 1st order crossover (fmin = 3fs), but even in this case designers usually insert an RLC Zobel network to filter out the effect of the impedance peak.
The higher order crossovers, that is second order (12 dB/oct), third order (18 dB/oct), and forth order (24 dB/oct) have non-zero group delay. The audibility of group delay distortion is quite controversial. The researchers of the subject, Blauert and Laws found in their following article: Blauert, J. and Laws, P "Group Delay Distortions in Electroacoustical Systems" Journal of the Acoustical Society of America Volume 63, Number 5, pp. 1478-1483 (May 1978) that human hearing can sense this kind of distortion if it's large enough. The following table contains the audibility thresholds of group delay at the examined frequencies that were determined by the research:
|
Frequency |
Audibility threshold |
|
8 kHz |
2 ms |
|
4 kHz |
1.5 ms |
|
2 kHz |
1 ms |
|
1 kHz |
2 ms |
|
500 Hz |
3.2 ms |
The greatest group delay is caused by the 4th order crossover where the tweeter is inverted in phase (although this is unuseable because of a nulling at the crossover point). At 2kHz, assuming the usual Butterworth characteristics, the maximum of this group delay is less than 0.4 ms, and this is halved by each octave as we're going higher, and doubled each octave as we're going lower in frequency. Let's add to this the lack of time alignment found in most designs, that is the acoustic center of the tweeter is closer to the listener than the the acoustic center of the woofer, in most cases the offset is 5...7 cm, that means a further 0.15-0.2 ms delay of lower frequencies. Adding this to the 0.4 ms, we get max. 0.6 ms delay, which according to the table is still below audibility. The conclusion is that human hearing is not sensitive to group delays caused by even 4th order crossovers plus usual time alignment errors, at least above 500 Hz. (Lower frequencies than 500 Hz were not investigated in the above scientific article.)
If you're interested in more depth about the arguments and scientific test results behind whether group delay is audible and if so, on what conditions, then here's a nice overview about the scientific achievements: http://www.melaudia.net/zdoc/jml_crossovers_etf04.pdf
Passive crossover components
Many people buy expensive components for their crossover or expensive cables in expectation that sound quality will improve. Let's examine this question realistically.
Coils
An important coil parameter is serial resistance. Regarding this, stick to crossover specifications. The inductor in series with the woofer is usually designed to have a low resistance, while the inductor parallel to the tweeter can do with a higher resistance, cheap coil. Those aircore inductors that have identical inductance and serial resistance, the latter one mostly defined by wire cross-section, should work similarly within the audio frequency range. I don't think expensive, foil-type inductors are worth the higher cost. Another thing may be important though: the windings are usually glued together to reduce microphony. In mass production this is usually achieved by "baking" the coils (if they are bobbinless), this makes the insulation of the wires stick together. Home made coils can be soaked in lacquer and then dried, but I'm not sure if soaking works well without vacuum.
Capacitors
Regarding capacitors, an important parameter is ESR (equivalent serial resistance). Bigger and more expensive capacitors usually have lower ESR. The cheaper foil capacitors with PET (polyethylene) dielectric are said to produce less satisfying sound than their more expensive and bigger PP (polypropylene) counterparts. I can neither refute nor reassure this, since I have not dealt with capacitors in depth. As for me, I use PP capacitors in quality loudspeakers, except for the low frequency domain, where I think PET ones will also do. To the best of my current knowledge it's sure that all capacitors cause measurable distortion when there's a sufficiently large AC voltage across them. But the loudspeakers themselves probably distort much more than quality capacitors.
Never use polarized (uni-polar) electrolytics (those that have a lead marked with a minus sign) in passive loudspeakers. They will distort and will be damaged due to the AC voltage. I don't even use non-polarized electrolytics in loudspeakers. When the crossover frequency is very low though, one may be forced to use them, but in this case I strongly recommend the types designated for passive crossovers, because the ESR of run-of-the-mill non-polarized (bi-polar) electrolytics is too high and unstable.
Another important parameter of capacitors is their voltage rating. This is usually specified for DC voltage. Nevertheless you use them for AC in loudspeakers. The following table contains the minimal voltage rating to be used for loudspeakers of different impedances and rated power (capacitors with higher withstanding voltage than that listed are, of course, applicable):
|
|
Loudspeaker impedance, rated noise power |
|||
|
4 Ω,
50W |
4 Ω,
100W |
8 Ω,
50W |
8 Ω,
100W |
|
|
Min. voltage rating of capacitors |
100V- |
160V- |
160V- |
250V- |
Resistors
Regarding resistors, any type is suitable, even cheap ones, only the power rating needs to be considered. You must always calculate the power rating of the resistors according to the actual crossover network, but the table below shows rule of thumb values that you can't go wrong with in any case.
|
|
Loudspeaker rated noise power |
||
|
up to 30W |
up to 60W |
up to 120W |
|
|
Resistor power rating |
5W |
10W |
20W (2x10W) |
By simulating or calculating the actual crossover more precisely, in many cases, power ratings lower than those stated above are acceptable for certain resistors in the crossover circuit.
Internal cabling
Like I mention in Buying tips -> How to choose speaker cable, speaker interconnection cables don't need to be special or expensive ones. The same is true for internal cabling , too. Use simple copper speaker cables with at least 0.5 mm2 cross section for 8 Ω loudspeakers, and with at least 1.0 mm2 cross section for 4 Ω loudspeakers If the cable is CCAW, then increase the above said cross sections by 50%. Note: CCAW (copper clad aluminum wire) cables are in fashion nowadays. The specific resistance of CCAW cables is about 60% higher than that of entirely copper cables.
Computer aided crossover design
There are free software available for crossover design that you can find through my Useful links page. You'll need the impedance curves of all speakers with impedance phase (.ZMA files), as well as the frequency response magnitudes of all speakers with absolute phase (.FRD files). These curves must be acquired by measurement. If your measurement system or sound card isn't capable of keeping the timing unchanged between measurements (measurements are not "time locked"), then you won't have absolute phase information. In this case you'll have to restore the correct timing (delay) of your frequency response curves so that the loudspeaker phases relative to each other may be correct. If you use Xsim for crossover design, here's how you can readjust to absolute phase.
Drivers for 2-way or
2.5-way systems
Midwoofer
Don't listen to generalizations, like "speakers with aluminum cone sound metallic." Choose quality drivers, which doesn't exhibit peaks or dips higher than 2...3 dB in the frequency range you intend to use them. This can be determined by looking at the frequency response curve. Driver cones made of hard materials like aluminum, aluminum/magnesium, titanium, kevlar, polycarbonate and in many cases paper, have a strong cone breakup resonance above their recommended passband, which need to be treated with a suitable crossover, that is either a high order crossover or a notch filter must be used.
Tweeter
Choose a quality dome tweeter. The directional characteristics of cone tweeters is worse because of the bigger diaphragm diameter and non-ideal shape of the diaphragm. Furthermore, dome tweeters generally have a smoother and more extended frequency response curve than that of cone type tweeters. I have no experience with ribbon tweeters, but apparently there must be good quality and also poor quality units among them. Affordable dome tweeters are generally made from textile, aluminum or silk. I like chambered tweeters, they are suited for lower crossover frequency. Up to the present, I have always used ferrofluid filled tweeters. They have better power handling capacity and lower thermal compression. Ferrorfluid also prevents the Helmholz resonance between the enclosed air behind the diaphragm and the air gap.
Cabinet
Unfortunately it's not the driver alone that determines the resulting sound, the cabinet also "has a say in it". Selecting a quality driver is in vain, when the enclosure is not on the ball. The woofer radiates backwards just as much as forward, but ideally the backward radiated sound should be totally absorbed. Now the internal pressure changes induce flexing vibrations in enclosure panels. This secondary sound is frequency and position dependent and spoils the sound delivered by the driver. On top of that, part of the sound within the enclosure seeps through the walls of the enclosure in a frequency dependent manner, too. These faults deteriorate the transient behavior of the loudspeaker and to prevent them, it's necessary to make the enclosure from thick enough material and it's necessary to employ internal bracing on larger panels as well. The next figure shows ring bracing, cross bracing and the combination of the two.
Resonance can occur on certain shallow basket woofers and midranges if the driver can't ventilate freely into the cabinet. This is prevented by chamfering the inside perimeter of the speaker cutouts.
I have to mention standing waves that from between parallel walls. To prevent it, non-parallel walls and/ or sound absorbing materials within the enclosure should be used. The cost of angled cabinets may be high due to the sophisticated joiner work and non-parallel walls may not eliminate the standing waves as much as one hopes for. Therefore I reckon fitting parallel walled enclosures with sound absorption as a more cost effective method. The inside of a closed box may be filled with absorbers, e.g. with long fiber wool. For ported enclosures, cover the walls with at least 2.5 cm thick sound absorbing material, e.g. acoustic foam. Closed cell materials are not suitable. The air-space of ported enclosures must not be filled with sound absorbers, because this adds a resistive component to the compliance of the air-spring, which can significantly degrade the bass-reflex operation. Long fiber wool and similar stuffing materials, furthermore acoustic foam is good only in taming mid to high frequency sound, its efficiency degrades toward low frequencies. In the long direction of floorstanders, a standing wave in the range of 150-200 Hz appears. To mitigate this, 2.5 cm thick foam is not enough, therefore I recommend locating a small quantity of long fiber wool or similar synthetic stuffing material around the half of the length (at the speed belly) of the cabinet. Do not place stuffing in the vicinity of the port tube.
A routinish material for enclosure panels is MDF (medium density fiberboard), 18 mm, 22 mm, or maybe 28 mm thick. Ask the parameters of the MDF before buying and choose one with density exceeding 700 kg/m3. Plywood may be also adequate, especially for smaller enclosures, but other materials are generally avoided. The density of particleboard (chipboard) is too low, real wood panels change their size due to air humidity, may warp and crack. Hi-fi enthusiast make loudspeaker cabinets from cast stone and concrete, I myself made enclosures from concrete, and a dense, thick, non-resonating cabinet walls seem to have effect on midrange clarity; the question arises though whether it's worth the invested money and energy.
The gluing of the cabinet panels should be made carefully, no air leaks should occur. Air leaks in vented boxes may degrade the Q of the system.
Sizing of the cabinet
For now I have added no information about Thiele/Small parameters which are important for the low frequency tuning of loudspeakers. They are used to determine box volume and port tube dimensions. Wikipedia has an article about them. As for the sizing of closed box or ported cabinets, there are free spreadsheets and free design software on the net. You can find some of them through my Useful links page.