A few basic loudspeaker design considerations

When designing a loudspeaker, one has to take many factors into account. I summarize a few important technical issues below. Of course, I can't touch upon every important aspect, you know, all engineers have their own "secrets." For the understanding of the descriptions below, electronic and loudspeaker design basics are essential. The latter can be acquired for example from the following books:

Joseph D'Appolito: Testing Loudspeakers, Audio Amateur Press, 1st Edition, 1998

Vance Dickason: Loudspeaker Design Cookbook, Audio Amateur Press, 7th Edition, 2006

The most important design principle

Don't start to design quality loudspeakers without (1) a calibrated measurement microphone, (2) a microphone preamplifier, (3) an impedance measuring jig, and (4) a loudspeaker measuring and design software with a suitable sound card.

Power handling capacity

The rated power must be evaluated together with sensitivity and impedance, and it depends on room size, and even the listener 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 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 to 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!

Impedance curve

Loudspeakers must have an impedance curve that amplifiers can preferably drive with low distortion. The driveability for modern amplifiers is generally satisfied if the impedance of the loudspeaker nowhere drops below approx. 3.2 Ω (4 Ω speaker). Amplifiers 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, so I prefer to design 8 Ω loudspeakers, if possible.

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 is beaming 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 will 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 smaller 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

Since most loudspeakers utilize dynamic drivers, I will confine myself to discussing these. Distortion occurs in dynamic speakers when diaphragm excursion increases. 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 a 800 Hz sound at the same dB SPL. Harmonic distortion occurs because of many factors, to list only 4 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 (4) because the moving voice coil modulates the stationary magnetic flux in the air gap. To achieve low distortion of a loudspeaker design, the most important thing is to select a low distortion driver. Be prepared though that the manufacturer information available about driver distortion is very scarce. Ported loudspeakers have a lower low frequency distortion, since at the tuning frequency of such systems, the excursion of the woofer can be very little and this reduces distortion.

The designer must pay attention to not only the woofer, but also to the tweeter, which shouldn't be used at so low a frequency where it would distort at high volume levels. It's not recommended to allow the usual 25 mm diameter tweeters to go below 2...2.5 kHz with a 12 dB/octave crossover. If the crossover is 18 dB/octave or 24 dB/octave and/ or the tweeter is a chambered one with low resonance frequency, then you can decrease the crossover frequency to 1.5 kHz, but in this case the nonlinear distortion around the crossover frequency may be significant at high volume settings.

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 mid-woofer.

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 6 dB more sound pressure that is 2 times more loudly 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 mid-woofer. As you can see, the midrange of this driver is definitely very colored.

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 85...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 10...20 dB 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.

2 or 3-way loudspeaker (or maybe 2.5-way)?

There are mid-woofers 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) of tweeters is not an accurately repeatable manufacturing parameter, and differing Qts means differences in the frequency response 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 such a crossover has the following condition: the Qts of the tweeter should not be too high or too low (best is around 0.7), and the tweeter may need to be able to handle unusually high excursion and power levels. 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 mid-woofer 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 the 1/2 fraction of the surround). In the following table, let's summarize the result of the formula for a few popular diaphragm diameters:

 

Diaphragm diamater of mid-woofer, d

10 cm

13 cm

17 cm

Maximal crossover frequency fmax

2600 Hz

2000 Hz

1530 Hz

This is obvious that for good directional characteristics, the mid-woofer shouldn't be crossed over at such a high frequency where many designs have it.

To decide whether your preferred mid-woofer 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 so called baffle step. Without this compensation the sound pressure of mid and high frequencies would be 6 dB higher on average than the low frequencies, because low frequencies are radiated in full space (backwards, too) rather than half space. Baffle step indeed is not a step like change in sound pressure, it is more like a gentle slope of increasing SPL in the midrange toward high frequencies This is why loudspeakers that are designed for close to wall usage need a bass boost when they are placed far from walls. 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 one needs to make sure that the impedance peak is not too big.

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 for frequencies above 500 Hz, 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

At 2 kHz, the greatest group delay is caused by the 4th order inverted phase crossover (with the most common Butterworth characteristics, Q = 0.7). But even 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 time alignment errors, at least above 500 Hz. (Lower frequencies than 500 Hz were not investigated in the above scientific article.) High order crossovers up to 4th order applied between a midwoofer and a tweeter therefore don't cause audible group delay distortion.

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 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 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.

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 quality 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 need to be considered. 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 CCAW or copper speaker cables with at least 0.75 mm2 cross section for 8 Ω loudspeakers, and with at least 1.5 mm2 cross section for 4 Ω loudspeakers Note: CCAW (copper clad aluminum wire) cables are in fashion nowadays. The specific resistance of CCAW cables is about 60% higher than entirely copper cables.

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. Drivers made of hard material aluminum, aluminum/magnesium, titanium, kevlar, polycarbonate and in many cases paper, have a strong cone breakup resonance above their recommended passband, which may need to be treated with a suitable crossover, that is 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. Ferrorfluid also prevents the Helmholz resonance between the air gap and the enclosed air behind the diaphragm.

Enclosure

Unfortunately it's not the driver alone that determines the resulting sound, the enclsure also "has a say in it". Selecting a quality driver is in vain, when our 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 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 large panels as well. The next figure shows ring bracing, cross bracing and the combination of the two.

      

I have to mention standing waves that from between parallel walls. To prevent it, non-parallel walls and/ or sound absorping 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 fibre wool. For ported anclosures, cover the walls with at least 3 cm thick 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 fibre 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, 3 cm thick foam is not enough, therefore I recommend locating a small quantity of long fibre wool or similar synthetic stuffing material around the half of the length of the enclosure. 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 do make loudspeaker cabinets from cast stone and concrete, I myself made enclosures from concrete, and a dense, thick, non-resonating cabinet walls do seem to have effect on midrange clarity; the question arises though whether it's worth the invested money and energy.

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