Enclosure Must Be Adaptable to Size of Listening Area
A requisite for any loudspeaker system is that it be able to fit into the area where the listener intends to use the system. Despite the fact that this requisite apparently does not concern itself with performance, and as trite as this statement may seem to be, acceptance of it may clear the air as far as system size and quality are concerned. As an example, if the user wants a hi-fi loudspeaker system for his rather small den, in which he has a desk in one corner, a stack of bookshelves along one wall, an easy chair in another corner, and a closet and a window on another wall, there is not much room left for a really massive system.
However, he may find that he can weed out a couple of dozen books from one of the shelves, and in their place install a "bookshelf" type enclosure such as those illustrated in Figs. 12-1 and 12-2. Now, many of these smaller enclosures are legitimate hi-fi systems. They are de signed around high efficiency speakers; they may be full two- or three way systems employing well engineered crossover networks; and great pains may have been spent in designing and building the enclosures so that the utmost would be obtained from the speakers these enclosures will accommodate. In many ways, the bookshelf system is a legitimate member of the high fidelity family. It will provide the den in question with remarkably good reproduction, far superior to that of the garden variety of speaker-console assemblies so often found in "big" radios that are frequently simple open boxes with inexpensive speakers.
8" WOOFER BRILLIANCE CONTROL TWEETER
Fig. 12-1. Although the application for an enclosure may limit its size,
its components may constitute a true hi-fi system as shown here, using
multi-speaker elements, crossover network, and brilliance control. ( Courtesy
University)
However, despite the remarkable performance of such small systems in this application, we would certainly be foolhardy to suggest they could therefore be used to provide the proper sound reproduction for a large open reception room. Large spacious rooms have the physical space to accommodate the more elaborate enclosures, such as the folded horn variety, from which considerably superior bass reproduction is possible. Yet, in spite of this, we could not categorically say it is the best system. It certainly would not fit the needs of the man with the small den. Thus it is a question not of superiority but of adaptability, both to environment and to the budgetary means of the user. All enclosures have some usefulness, depending upon the circumstances in which they are to be used.
Speaker Size Generally Determines Enclosure Size
Fig. 12-2. Another form of a "bookshelf" enclosure, utilizing
multi speaker system components to provide a two-way system. (Courtesy
Jensen)
There is one basic fact, however, that determines the size of the enclosure, and that is the size of the largest speaker of the system, for there is a definite relationship between speaker size and enclosure volume due to the general correlation between a speaker's size and its resonance frequency. This then is our first concern - the matter of enclosure size and speaker resonance. In Section 3 the question of the general performance characteristics of loudspeakers of different sizes was discussed. Figure 3-10 lists some average resonant frequencies of the three popular size speakers (8-inch, 12-inch and 15-inch); note that the larger the speaker the lower the resonant frequency. This results, of course, from the generally heavier diaphragms found in these speakers, for resonant frequency is inversely proportional to the mass of the moving system (other factors remaining unchanged). It is there fore, to be expected that the larger speakers will have better low frequency response than the smaller speakers; this condition is illustrated in Fig. 3-1. It will be observed that not only does the frequency ex tension of the response go lower for the larger speakers, but the level of output is also higher. This will in general be the case if the speakers have magnetic circuits of increasing strength to match the increasing weight of the moving system to be driven.
The larger speakers, being larger in diameter, present a higher order of radiation resistance (Fig. 9-1) for a given low frequency than do the smaller speakers. Therefore, for equivalent driving force, the larger speaker will produce better low frequencies. What happens, for instance, if two loudspeakers of different size have the same resonant frequency? If this be the case, the larger speaker will have a higher level of response at this frequency, because of its greater radiation resistance.
Another point of comparison between the low frequency characteristics of two speakers of different size but of the same resonant frequency is cleanness of response. If the same acoustic output is de-rived from both (that is, if they both sound equally loud) we may be reasonably sure that the large speaker is vibrating less severely than the smaller one. Acoustic power output of any vibrating diaphragm is proportional to its area and to its excursion; that is, the more air is pushed, the higher is the power output. If two pistons of different size are both pumping equal quantities of air (equal power output), the larger area piston will naturally have the smaller excursion. If this is the case, we may be reasonably sure that the larger piston is experiencing less nonlinearity in its motion, that diaphragm break-up is reduced (if any existed), and that less amplifier power is required. All in all, then, the larger speaker has a better low frequency response because of its lower resonance capabilities and its greater radiation resistance due to its size.
Enclosure Design Determined by Both High and Low Frequencies
Because larger speakers have better low frequency response, they generally are deficient in high frequency response. Their heavy moving systems preclude the same efficiency of reproduction of the high frequencies that smaller speakers enjoy. The smaller speakers present less of a moving mass to the small amplitude high frequency signal, hence these high frequencies are more efficiently reproduced. In general, the smaller speakers excel in the high frequency range. The enclosure size and design will be limited to a great extent by both low frequency and high frequency performance of the speaker. The size will be determined by the low frequency capabilities of the speaker. The design will be determined by the high frequency performance of the speaker, depending on whether it is a woofer or a full range direct radiator.
There are two ways of attacking the problem of the speaker enclosure combination. One method is to put a small speaker into as large an enclosure as possible in an attempt to get "large enclosure performance" from as economical a speaker as possible. The antithesis of this is to squeeze as large a speaker as possible into as small a space as possible in the attempt to get "large speaker performance" from enclosures of reasonable size. In both of these extremes there must be compromises, and somewhere in between is the middle ground of rational design.
Large Enclosure Response Determined by Speaker Size
EFFICIENCY RESONANT PO FREQUENCY
Fig. 12-3. The efficiency of a loudspeaker is highest at its resonant
point and then gradually drops off as the frequency rises.
In discussing baffles in general, it will be recalled that the wall baffle serves as an excellent means of preventing dipole action of the speaker; that is, it completely blocks the rear radiation and thus pre vents back-to-front low frequency cancellation. Under these circum stances, whatever low frequencies the speaker is capable of radiating are actually transformed into useful acoustic power. However, the speaker receives no assistance from the wall baffle other than to pre vent the dipole action. Once this has been accomplished, the speaker behaves essentially as if it were in free space; its resonance frequency remains virtually unaltered, its peak impedance remains virtually un changed (except for the free air loading). The wall baffle then is one in which speaker operation is completely independent of baffle dimensions. In extremely large enclosures, therefore, differences in the overall speaker systems for different types, sizes, and resonances of speakers are thus wholly dependent upon the speakers themselves, and not upon the combination of the speaker and the wall "enclosure." The same is true of the closet enclosure if the closet is big enough, or even of the closed box type of "infinite" baffle if the box is big enough. We have merely extended our thinking from the wall baffle to actual enclosures. If these are so large that they are essentially "unseen" by the speaker (except for the elimination of the dipole action), total performance will be a function only of the loudspeaker. If we put a 15-inch speaker in the closet door, we get more low frequency reproduction than if we were to put an 8-inch speaker in the same door, and the same difference in speakers will occur if we put them into box enclosures if the volume of the box is large enough.
Small Enclosure Response Determined by Both Enclosure and Speaker
As we decrease the size of the enclosure, however, the reduced volume becomes an important factor in the overall performance of the system. As the volume of the closed box gets smaller, the captured air within the box, against which the diaphragm has to work, exhibits an acoustic stiffness proportional to the size of the diaphragm, the motion of the diaphragm, and the volume of the box. If the diaphragm is large, and has a large degree of motion at the low frequencies, it will tend to compress the air within the box as it moves inward. This compression pushes back upon the diaphragm; thus the air appears "stiff." Since the cabinet and the loudspeaker are connected into one integral acoustic circuit, this stiffness reacts upon the overall resonant condition of the circuit.
Low Resonance Speaker in Small Enclosure
It is now a question of proportioning the enclosure size to the resonance characteristic of the speaker for the desired response. Although it is ordinarily impossible to realize this in practice, let us assume that we have an 8-inch loudspeaker with zero resonance. This is a practical impossibility because if the speaker has any substance at all, it must have some weight of diaphragm and some compliance in the suspension of the moving elements; therefore, from the inexorable laws of physics, it must have a specific natural resonance. Let us, there fore, attribute to the speaker some resonance figure below the audible range, say 5 hz. Like any speaker, it is most efficient at its resonant point, and its efficiency drops gradually but constantly as the frequency goes up from its resonant point. This is indicated in Fig. 12-3.
Small Enclosure Raises Speaker Response
If this speaker is now put into a reasonably small box, it will be stiffened in proportion to the decreased volume of the box, and the resonant frequency of the combination will be increased. We can continue to make the box smaller and smaller, continually causing the resonance of the combination to go up in frequency. The point of maximum efficiency will move up with the resonant frequency. At first glance this may seem like a very simple way of getting good low frequency response from a small enclosure with a small speaker. It would seem that all we have to do is to get a small loudspeaker with a very low resonance (below audibility) and put it into a box that will stiffen it to the extent that its point of maximum efficiency will come within the range of usable sound output, say above 50 hz as shown in Fig. 12-4, and we have the panacea for all the problems of small speaker size and large performance. However, it is not quite that simple.
While it is true that the point of maximum efficiency may be moved up from the non-usable frequency to the usable frequency range, it is nevertheless true that the final efficiency may still be far below what might have been obtainable if we started with a speaker of the same size, but of a higher resonance (in the audible and usable area and with correspondingly high initial efficiency in that area). As indicated in Fig. 12-5, the initial efficiency of the higher resonance speaker for the same driving force will be considerably higher than that of the low resonant speaker even after it has been stiffened. This occurs because the overall operating range of the higher resonant speaker is more restricted, and its overall power capabilities are distributed over a narrower range, giving higher overall efficiency in that range.
It will also be realized that if a very low resonant system, such as our theoretical one, were to be constructed with the thought in mind of "creeping up" into the musical spectrum by making the box smaller and smaller, the size of the box would become quite small. Now too small a box will not provide the proper diffraction characteristics for these low frequencies. Furthermore, it is not very beneficial to the reduction of internal reflection of low frequencies, because of the close walls. It may become necessary in such a system to utilize a great deal of internal damping material to free the small enclosure of these internal reflections.
Efficiency Considerations in Small Damped Systems
A large amount of such resistive damping will cause the system efficiency to drop even lower. This secondary drop in efficiency, due to heavy internal damping, will reflect itself in poor amplifier power utilization. The amplifier will have to be overdriven to push enough power into this low resonance small enclosure system to make it pro duce useful sound. If the amplifier, after being turned up high enough to satisfy normal listening requirements, still has enough power reserve to handle the sudden heavy peaks and sustained loud passages without distorting, the system will be usable. If, however, the amplifier used with the system is one of low power output, only low level reproduction will be realizable from this system. It will thus be seen that, al though this system may have certain advantages as far as frequency extension is concerned, there are other factors in its design that are disadvantageous.
Fig. 12-4. When a very low resonance speaker is put into tight acoustic
volume, the resonance of the system is raised and the region of maximum
efficiency is raised to a higher frequency and the efficiency to a higher
value.
Fig. 12-5. Initial efficiency of high resonance speaker in tight enclosure
will be higher than ultimate efficiency of the low resonant speaker stiffened
by the tight enclosure.
In making an A-B listening test of this type of enclosure in com parison with similar small types, the listener should be aware of this question of overall efficiency. If the test is made simply by switching the amplifier from one speaker to the other without compensating for the differences in efficiency between the two systems, he may get a feeling that the lower efficiency system is deficient because it does not sound nearly as loud as the alternate systems. His ears will, in fact, be telling him the technical truth. However, he should also listen to each of the systems individually for some time, at the loudness that will be most comfortable to him, as well as comparing them at equal input, before he comes to a conclusion as to the merits of one small system over the other.
Higher Resonant Speaker in Small Enclosure
What can we do now with the same relatively small sized en closure utilizing an 8-inch speaker of more conventional resonance characteristic, say in the 90-hz region? The first thing that becomes obvious is that we certainly do not want to put this speaker into any sort of enclosure that would raise its resonance. If possible, we would like to lower the resonance characteristic of the system. It follows then that for this higher resonance speaker, we should steer clear of the completely closed box. It would seem logical, therefore, to use some sort of enclosure that does not stiffen the speaker and that, if anything, will bring it down to a lower resonance point.
This, of course, we can do by means of the simple bass reflex enclosure. In the bookshelf size enclosure, it may well be possible to convert this 90 hz peak of the speaker into the two other straddling peaks on either side of it, one at 110 hz, and the other at 70 hz. Now, while it is true that 70 hz is not as low as we would like to go in the best system, there are particular advantages to this mode of operation for smaller speakers, despite the fact that the low frequency performance does not reach down to the lowest note on the piano. Of great importance is the fact that this sort of speaker-enclosure system is of the high efficiency type. In consequence, greater linearity of overall response will be obtained because of the conservative demands made upon the amplifier by the speaker, and because of the moderate excursion of the cone for good listening level. When the cone has to move large distances in order to produce the desired listening level in low efficiency enclosure systems, these large excursions may run into regions of nonlinearity of motion of the suspension system. In the higher efficiency systems, the excursion of the cone need not be as severe, and more linear motion will result. Thus, "power-wise" and "efficiency-wise," the higher resonance system outperforms the lower resonance system.
Now let us discuss for a moment the matter of those very low frequencies. It was with good reason that we used the phrase "reach down to the lowest note on the piano." The fact of the matter is that very seldom indeed do we hear music played that contains a note this low. Notes this low are ready and waiting to be sounded on the piano, the bass violin, the harp, and one or two other instruments, but they are elicited only when called for by the composer. Fortunately for the acoustic hobbyist, composers have shown their good taste in that they realized there was a whole gamut of notes to work with, and not just low frequencies. We find therefore, if we take the trouble to do some statistical research that perhaps for 90 percent of the time, music falls in the range above 60 to 70 hz. Perhaps the one big exception to this statement is the pipe organ that can produce a note low enough and heavy enough to shake the timbers of the ordinary auditorium. It seems that the composers for this instrument delight in showing off these low massive notes, and it is unfortunate if the acoustic system cannot reproduce them. However, even with this shortcoming, the smaller systems can give quite satisfactory reproduction over an exceedingly wide useful range for their size and application.
Tunable Enclosures are Adaptable to Either Large or Small Systems
We have examined the effect of an infinitely large (wall) baffle and the infinite (closed box) baffle upon the response of a loudspeaker.
We are ready to deal with the middle ground between the two - the vented box or bass-reflex cabinet. We have seen from Section 9 that one characteristic of the bass-reflex is that the low frequency resonance impedance of the system is spread out over an area considerably broader than the original single response peak. This serves to produce a wider band of low frequency reproduction. In the case of the bass-reflex enclosure, the question of the size of the structure is not as critical in affecting response as in the case for the completely closed box-type enclosure. The reason for this is that the bass-reflex system is a tunable one in which the two elements of internal volume and port opening may be juggled into many combinations and the desired resonance condition still maintained. The general conditions that govern this tuning procedure are based on the principles of the Helmholtz resonator. They are as follows. For a given volume of box, the resonance frequency increases as the opening in the box increases; for a given size of opening the resonance frequency increases as the volume de creases. Thus we can have a large volume with a large opening, or a small volume with a small opening, both with the same resonant frequency. These conditions are illustrated in Fig. 12-6. The various combinations in which volume and port opening may be arranged for a selected number of resonant frequencies have been given in Fig. 9-10.
This relationship may bear some analysis. A small volume is a stiff volume. It has small "capacity" to absorb acoustic vibration, and its acoustic capacitance is therefore small. To cause it to resonate at a low frequency, we must provide it with a large value of acoustic inductance, for in the resonant circuit the frequency of resonance is inversely proportional to the square root of the product of capacitance and inductance. In order to obtain this small acoustic capacitance with a necessarily large inertance, we must provide an opening that will make it difficult for air pulses to get through. Obviously, the smaller the hole the more difficult it is for the pulses to get through. There fore, a small hole represents a high inertance. Thus, the combination of a small volume and a small opening resonates at a low frequency.
Fig. 12-6. Graphic representation of relationship between bass-reflex
volume, port area, and resonance.
Conversely, a large volume, which can absorb large values of acoustic pulsations, has a large acoustic capacitance, and requires a small inertance to resonate it at a low frequency. A large hole allows sound pulses to get through quite readily, and represents a small acoustic inertance. Consequently, a large volume with a large opening will resonate at a low frequency just as well as a small volume with a small opening.
It now becomes a matter of evaluating the two different structures for qualities other than their resonance capabilities. One very easy way to examine a set of conditions is to go to the extreme values of the set, for at the extremes some of the component factors drop out and analysis becomes easier. Let us examine the bass-reflex enclosure in this manner, taking it first to an extremely small size. As the enclosure is made smaller and smaller, the port necessarily becomes smaller and smaller, until theoretically we are left with no port at all. We have a small tight closed box that is not a reflex enclosure at all. There fore, there must be a lower limit for the size of a reflex enclosure.
Looking at the other extreme, as the enclosure gets larger and larger the port size becomes larger and larger until we have the large room type of enclosure (wall baffle) with a very large auxiliary hole some where in the wall. Under these conditions of operation, the bass-reflex principle completely deteriorates, because the large dimensions allow standing waves to be set up in the structure, and the capacitance as such ceases to exist. Anything large enough to permit the setting up of standing waves belongs to the family of transmitting and receiving devices and not simple circuit elements. The room will act as a "sink," absorbing the rear radiation rather than behaving as an active circuit element in a resonant circuit. The end result of this "king sized" bass reflex enclosure will be operation as a simple wall baffle with some back to-front cancellation at some frequency where the distance from the speaker to the hole in the baffle is equal to a wavelength of the sound being radiated. Between these two extremes lies the proper size for the bass-reflex enclosure for a given size of speaker.
Enclosure Port Must be Compatible With Diaphragm Size
We must start with the premise that the purpose of the bass reflex speaker is to allow radiation from the port at some low frequency region. The port must then have a radiation resistance characteristic compatible with the frequency it is to transmit. It would therefore be logical to assume that the port area should be at least as large as the speaker itself. This would give the port radiation resistance the same value as the speaker radiation resistance. If the port were made very small, there would be poor low frequency radiation resistance for the port, and the low frequency reproduction of the system would suffer.
It is therefore general practice to make the port area equal to at least three-quarters of the effective area of the speaker itself.
The word effective is important here in that the area of the diaphragm should not be calculated on the basis of the advertised diameter of the loudspeaker. This is the measurement that spans the very out side of the speaker housing. From that must be subtracted that section of the diaphragm that is taken up by the rim compliance of the speaker.
In a 12-inch speaker, this reduces the diameter of the speaker by at least another 1- 1 / 2 inches. Then there is a somewhat more subtle effective reduction of the diaphragm because of inability of the diaphragm to vibrate completely as a piston. All in all, if we consider the effective area of a 12-inch loudspeaker to be that of a 10-inch piston, we have a fairly good conservative approximation of its active diameter. Using this figure for the diameter of the speaker, we arrive at an area of approximately 75 to 80 square inches for the area of the port. If we want to go down to three-quarters of the effective area of the diaphragm, the port area should be at least 60 square inches. This figure places the average limit to the lowest value of port area for a bass-reflex enclosure for a 12-inch speaker. In like manner, the smallest port suit able for an 8-inch speaker (effective diameter, about 7 inches) is 28 square inches, and for a 15-inch speaker (effective diameter, about 13 inches) about 95 square inches. These figures (tabulated in Fig. 12-7) give the smallest port size practical, from which the enclosure may then be designed.
With this port area figure available and the resonant frequency of the speaker either known or determined, the enclosure volume is readily selected from the chart of Fig. 9-10. The set of conditions thus determined will provide the optimum resonance impedance compensation for the chosen speaker by being matched to it in frequency, and by acting as a good radiating source itself (through the port). If the constructor is building his enclosure from the ground up, it is possible for him to follow these precepts quite literally. However, the user often finds it necessary to use an already existing piece of furniture. He will then find it necessary to work backwards from the fixed enclosure size to the port size. If, because of a fixed small cabinet size, the port turns out to be too small to produce the proper radiating characteristic for the desired low frequencies, there is not too much that can be done except to make a compromise. The best compromise that can be made in this case is to provide a port of at least one-third to one-half the effective area of the diaphragm so that reasonable low frequency efficiency of radiation from the port will be obtained. This will result in an enclosure volume that will resonate somewhat higher than the speaker requires and the area of bass compensation will be moved up in the frequency scale.
In the case of enclosures that are originally large, like built-in wall cabinets, it is possible and desirable to build the full-size port into the structure as called for by the chart. However, the port should not exceed twice the effective diaphragm area, even though theoretically the enclosed volume calls for a larger port than this. By this last expedient of making the port larger than the diaphragm requires, but still smaller than the resonance condition calls for, we effectively reduce...
Fig. 12-7. The effective diaphragm area of a speaker is smaller than
its rated size. This table gives the effective areas of speakers for use
in de signing bass-reflex enclosures. (See also Fig. 9-10.)
...the resonance frequency of the enclosure. The overall effect of this low resonance cabinet is to permit the cabinet to function at a lower frequency than the original speaker resonance frequency, with consequent boosting of the output in those areas below resonance. The effect of the larger port is to produce better radiation characteristics from the opening for the low frequencies. However, in this mode of operation, the section of the response immediately at and above the speaker resonance area will not benefit by the reflex action to the optimum degree, and the response in that area will be compromised. Further more, too large an enclosure may cause actual deterioration of the bass reflex function as described above. In large fixed enclosures it is of course possible to make changes to the internal volume by simply closing off as much space as is necessary to bring the port area down to a respect able size, so that proper tuning may be realized.
In laying out the volume of the enclosure, some thought must be given to the proportions of height to width to depth. It is not generally desirable to proportion the enclosure to a symmetrical cubic form. The uniformly equal lengths of such a structure make it easy for standing waves of one particular frequency to be set up. The box will tend to exhibit a "normal mode" of vibration because of its symmetry, and this normal mode of vibration will not be related to the bass-reflex resonance condition. Where volumes of cubical form must be used because of already available structures, it is necessary to pro vide a lot of internal wall damping material so that the internal waves ...
CUBICAL VOLUME SHELF TO MINIMIZE NORMAL MODE VIBRATION
Fig. 12-8. Where nearly cubical volumes are used, the interior should
be well padded and broken up by a shelf placed midway in the structure.
This will minimize the strong normal resonance modes characteristic of
cubical structures.
... are well absorbed by the reflecting layers. This will greatly reduce the normal mode resonance. In such structures, it is also common to place a well-padded shelf along the middle of the cabinet, reaching about halfway to the rear wall. Such a structure is shown in Fig. 12-8. This will further reduce the internal standing wave condition and minimize the normal resonances of the box. Practice has shown that good results will be obtained if the height-to-width-to-depth ratio is 4 to 3 to 2.