Design Limitations for Speakers
Introduction
There are many factors which determine the characteristics of a loudspeaker; to produce a successful design a careful balance of many factors must be achieved. Most of the challenges and considerations of loudspeaker design stem from the inherent limitations of the drivers themselves.
Desirable Characteristics & Real-Word Implementation
For a coherent approach to loudspeaker design to be established, one may elucidate the problem by considering two main sets of criteria; the desired characteristics of the finished system and the limitations which impinge on the achievement of these desired characteristics. The key desirable characteristics for the finished system are listed below.
Reproduction of all frequencies across input range
Flat frequency response across input range
Adequate Damping
Good Efficiency
Adequate SPL or perceived loudness
Minimal distortion
Minimal noise
Many of the above considerations are quite obvious. In terms of frequency response it is desired that the response of the system as a whole should be as flat as possible, since to truthfully reproduce a signal all frequencies across the input range should be represented equally. Weems (2000, p.14) notes that “smoothness of response is more important than range”. Naturally noise and distortion are undesirable for accurate signal reproduction. Damping is an important concern; when a signal is no longer applied to a loudspeaker there will be a natural tendency for the cone to continue to move under its own inertia. Thus damping must be employed in order to ensure that the SPL generated by such movement is sufficiently low and relatively inaudible. Rossing (1990, p.31) refers to damping as “loss of energy of a vibrator, usually through friction”. This is a simplification, however, the back EMF generated by the driver and the varying impedance seen by the amplifier of the crossover/driver network play an important role. As Weems (2000, p.17) rightly says “there are two types of damping, mechanical and electrical”.
Another quite obvious consideration is that the loudspeaker must indeed be loud enough. This is related to the issue of efficiency, since the more inefficient the speaker, the more power will be needed to drive it. The choice of enclosure design plays quite a significant role here, as will be seen shortly.
In terms of limitations, there are several immediate problems posed by the nature of the drivers themselves that must be addressed. Firstly, the sound from the back of the speaker cone is 180 degrees out of phase with the sound from the front. This phase separation means the sounds will cancel each other at lower frequencies, or interfere with each other in a more complex manner at high frequencies; clearly neither is desirable.
In some senses it would be ideal to mount the drivers in a wall with a large room behind, the so-called “infinite baffle”, having the sound from the rear of the cone dissipate in a large separate space, being thus unable to interfere with the sound produced by the front. In reality this is impractical; however some provision must be made to isolate sound from the rear of the cone. To this end, some sort of enclosure must be made for the drivers, yet this presents a new set of considerations.
Without an enclosure, a loudspeaker is very inefficient when the sound wavelengths to be produced are longer than the speaker diameter. This results in an inadequate bass response; for an 8 inch speaker this equates to anything below around 1700Hz[1]. So the infinite baffle is terribly inefficient in terms of the SPL produced at lower frequencies. Furthermore, the free cone resonance of the speaker works against the flat frequency response that is desired; input frequencies close to the resonant frequency will be represented too forcefully.
Another real-world complication is the fact that for high-fidelity applications, no one loudspeaker will be able to handle the entire range of input frequencies; “the requirements for low frequency sound are the opposite to those for high frequencies” (Weems, 2000, p.13). Higher frequencies require less power to be reproduced, but the driver must respond more quickly, whereas low frequencies require a larger driver and hence greater power to be effectively realised.
In view of the above, multiple drivers must be used, with each producing a certain frequency range of the input signal; at the very least a woofer and tweeter are required. In order to deliver only the appropriate frequencies to each driver, a device known as a crossover must be implemented. This can take the form of passive filter circuits within the speaker itself, or active circuitry that filters the signal prior to amplification. In the latter case, multiple amplifiers are needed, making this a more costly approach. The fundamentals of crossover design will be dealt with in a separate document and are hence not dealt with in detail here.
Enclosure Design
Faced with the reality that an enclosure is in almost all cases a practical necessity, perhaps the most important aspect of speaker design in the design of the enclosure itself. The first step in producing a successful design is to decide upon the drivers to be used and use this as a basis for choosing a cabinet design, or to decide upon the desired cabinet type first and allow this to inform the choice of driver. In general, most of the design work with regard to the cabinet is focused firmly toward the woofer, since the enclosure design is most critical with regard to midrange/bass performance. In typical 2-way designs, the tweeter is mounted in the same box as the woofer, but it is the latter which largely defines the cabinet dimensions.
In the past the design of enclosures was often something of a hit-or-miss affair, however the research of Thiele (1971) and Small (1973) has led to a much more organised design process. Most transducers today are accompanied by a comprehensive datasheet of Thiele-Small parameters, which allow most of the guess work to be taken out of enclosure design.
Ignoring more exotic enclosure designs, the first question is whether the enclosure should be ported or sealed (it should be noted that in reality even “sealed” enclosures are very slightly open or “leaky” in order to allow the internal pressure to equalise with the surroundings). If a driver has already been chosen, this can be determined from the Efficiency Bandwidth Product, which is defined as:
EBP = Fs / Qes(1)
Where Fs is the free air resonance of the driver and Qes the electrical Q or damping. In general, an EBP of 50 or less indicates a sealed box, whilst an EBP above 90 suggests a ported enclosure (Dickason, 2000). In between, the choice of enclosure lies more or less with the designer and a driver that falls in the middle should perform acceptably in either closed or ported situations.
So, what are the advantages and disadvantages of sealed vs ported enclosures? A sealed enclosure is very simple to build, whilst a ported enclosure requires some degree of tuning to ensure the port is matched correctly to the driver – in the ported or “bass reflex” design a tube extends into the cabinet allowing some air to escape from inside; if correctly tuned the air that leaves the port is delayed in phase by 180 degrees, hence reinforcing the sound from the front of the cone.
With a sealed enclosure the air inside acts as an approximately linear spring for the transducer cone and assuming the driver has a low Fs, a healthy bass extension with a gentle roll-off of -12dB per octave can be expected. The disadvantages are several; the enclosure may need to be quite large to achieve an acceptable Qtc (the damping value for a sealed system) and efficiency is poor. Further, with a sealed enclosure the driver reaches maximum excursion at resonance, which translates to greater distortion. Therefore a driver for use in a sealed enclosure requires quite a large linear throw to perform well. By contrast, in correctly tuned ported enclosures the driver is maximally damped at resonance, so a large linear throw is not critical and distortion is lower as a result. The basic methods of sealed and ported cabinet design shall now be explained.
Sealed Enclosure Design
To design a sealed enclosure the basic methodology is quite straightforward; the essential challenge is simply to find the optimum volume for the cabinet for the chosen driver. First one must decide on the value of the damping constant Qtc; the optimum value is 0.707 since it gives the lowest -3db break frequency and hence the best potential for bass extension, as well as good transient response. If the enclosure size is too large at this optimum value then Qtc may be increased, resulting in a trade-off between bass performance, transient response and enclosure volume. However, the more Qtc is increased, the more boomy and muddy the sound will become.
Depending on the application, the enclosure size may not be important; in this case an optimum Qtc is encouraged. Once Qtc is known, the constant ? may be calculated using the below formula, where Qts is the total Q factor of the driver at resonance (this may be obtained from the manufacture’s data sheet).
? = [Qtc/Qts]2 – 1(2)
Having calculated ?, the correct enclosure volume Vb is trivial to determine using the relationship below. Note that Vas is the equivalent volume of air that has the same acoustic compliance as the driver; again this may be obtained from the datasheet or experimentally. Note from equation (1) that a lower Qts will result in a higher ?, and hence a smaller enclosure. Thus for two transducers with equivalent acoustic compliance, a lower Qts will result in a smaller enclosure.
Vb = Vas/?(3)
Assuming the required box volume is acceptable, one may then also calculate the resonant frequency of the system (fs is the free-air resonant frequency of the driver):
(4)
Once fc is known the -3db break frequency may also be found:
(5)
Recall that below this frequency the roll-off is -12dB per octave and one can gain a fairly good impression of the bass performance to be expected. Naturally it is desirable for f3 to be low for maximum extension into the bass area, hence a low fs is a characteristic one should look for when choosing a driver for sealed enclosure use. If it is felt that the break frequency is too high, then a different driver must be selected for the sealed implementation.
Ported Enclosure Design
For ported cabinet design, the equations are more complex and it is generally not practical to attempt to design such an enclosure by hand. Instead there are a number of free and commercial software calculators available that simplify the process. One good freeware calculator is AJ Vented Designer[2]. Using such a program enables the designer to quickly ascertain what size enclosure and port is required for a given driver and whether this is feasible – for certain combinations the port may not physically fit within the enclosure for example. In addition, the program also plots the theoretical frequency response of the design, which simplifies matters greatly.
Acoustic Damping and Avoiding Resonance
In addition to the type of enclosure and the calculation of the required volume, diameter and size of ports (if ported), there are several other design considerations. Firstly, standing waves within the enclosure must be minimised. Thus enclosures are often stuffed with fibreglass, long-fibre wool or polyurethane foam.
In addition to standing waves and the resonance of the enclosure, one must also bear in mind the possibility of dimensional resonances with sealed designs. To avoid this it is prudent to ensure that length, width and height of the enclosure are all different and to not centrally mount the drivers.
The choice of cabinet material and thickness are also factors that require careful consideration; in general wood is the most appropriate material and a thicker structure is likely to be more rugged and be less susceptible to undesirable vibration. The structure should also be isolated from the floor since vibrations passed to a floor (especially a wooden floor) can cause the floor to vibrate which will muddy or colour the sound. Spikes or stands are commonly used to achieve this.
Conclusion
There are many factors that affect speaker design but perhaps the most important is that of the enclosure itself. More exotic enclosures such as band-pass and transmission line configurations are beyond the scope of this document, however it should be noted that there are many different approaches beyond the common sealed or ported methodologies. As with any engineering problem, successful speaker design requires a careful balance of many often opposing factors to be reached.
Sources
Borwick, John. (2001). Loudspeaker and Headphone Handbook, Focal Press.
Dickason, V. (1995). The Loudspeaker Design Cookbook, Audio Amateur Publications.
Rosenthal, M. (1979). How to select and use loudspeakers and enclosures, SAMS.
Rossing, T. (1990). The Science of Sound, Addison-Wesley.
Weems, D. (2000). Great sound stereo speaker manual, McGraw-Hill.
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