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PoorManQ45 »
https://forums.nicoclub.com/poormanq45-u17729.html
Fri Oct 15, 2004 12:37 pm
There is a PDF file attached. It has all this information and a little bit more.
2
Drivers for Enclosures
Every enclosure alters in some way the performance of the driver placed in it. For best results it is therefore necessary to know the basic limitations of the driver.
Basic Information Table 2-1 illustrated some vital statistics that apply universally to cone-type woofer speakers. Rated cone diameter is the advertised size of the speaker. The three most common sizes are shown. While woofers as small as 3 inches and as large as 30 inches have been employed, good design criteria dictates one of the three sizes shown. If a woofer is smaller than 8 inches, it requires so many cones of that size to generate a usable acoustical power that phasing problems are encountered. This is due to their physical separation on the baffle board.
If the woofer is much larger than 15 inches, the mass of the moving parts becomes too great to retain effective control; and, therefore, poor transient response results.
Column B of Table 2-1 is actual cone diameter. This is the figure to be used in calculating the cone area of a standard size speaker:
A = (pi)D(D)/4 - 8
where,
A = actual cone area, pi = 3.1416, D = diameter of the circle.
Column C of Table 2-1 shows the effective piston areas. Column D shows the amount of peak-to-peak excursion (the distance from the farthest forward movement of the cone to its most rearward position) that would be demanded of any size of cone at 50 Hz if it were required to generate one acoustical watt. This figure has no fixed relation to electrical power required (which may from 2 watts to 500 watts) in order to drive the cone to such an excursion, but it is the acoustical power generated by the mechanical action of the piston moved that distance at that rate. It should be noted that 0.50 inch is the maximum excursion that can be considered without excessive loss of electrical-to-acoustical conversion efficiency. The final column in Table 2-1 shows how many cubic feet must be subtracted from the calculated interior volume of the enclosure due to the physical volume displaced by the driver itself.
Refer to PDF
Choosing The Number Of Drivers And Their Sizes
The following relations should be noted when one decides whether to use a larger or smaller driver versus a larger or smaller number of drivers:
A = cone area, E = cone excursion, F = lowest frequency desired, P = acoustical power desired.
1. If the cone area is doubled, the cone excursion is halved:
2A = E/2
2. If the cone area is halved, the cone excursion is doubled:
A/2 = 2E
3. If the frequency is halved, the cone excursion is increased by a factor of four:
F/2 - 4E
4. If the frequency is doubled, the cone excursion is reduced by a factor of four:
2F = E/4
5. If the cone excursion is halved, the acoustical power is halved:
E/2 = P/2
6. Conversely, if the excursion is doubled, the acoustical power is doubled:
2E = 2P
7. If the cone area is doubled and the cone excursion remains the same, the acoustical power increases by a factor of four:
AE = P 2AE = 4P
8. By the same token, if the cone area is halved and the cone excursion remains the same, the acoustical power is decreased by a factor of four:
(A/2)E = P/4
Using these parameters one can determine the number of drivers desired to ensure achievement of at least one acoustical watt at 50 Hz with low distortion and peak-to-peak cone excursion less than 0.50 inch: Refer to PDF
The maximum acoustical power each size can produce at 50 Hz without exceeding 0.50 inch peak-to-peak cone excursion is as follows:
Refer to PDF file
To mount multiple drivers as woofers, care should be taken to ensure that they are close together. They should operate as nearly as possible as a single diaphragm. The high-frequency drivers should also be mounted close to the low-frequency woofers to minimize phase differences that can occur at the listener's ear if the angle between high frequencies and low frequencies becomes too large.
Efficiency Of The Driver
Changes in cone mass affect efficiency above the point of cone resonance. Tripling the cone mass reduces the acoustical power output by one-half. Conversely, reducing the cone mass by one third would increase the acoustical power output by a factor of two to one, or 3 db.
While reduction of cone mass increases efficiency it also increases distortion. Cone mass is therefore chosen as a compromise between efficiency and distortion requirements. Magnet weight, or magnet mass, changes the efficiency of the driver. Magnet flux is directly proportional to magnet weight and/or volume. The efficiency of a speaker is directly proportional to the flux up to a limit of around 20,000 gausses where saturation of the magnetic circuit occurs. This means, if all other factors remained constant, that doubling the magnet size would approximately double the efficiency of the driver.
It is very possible in actually comparing different drivers to find, for example, that Speaker A has a magnet twice the size of Speaker B, and yet Speaker A has an efficiency one-half that of Speaker B. This could be because Speaker A may have a much greater cone mass, its voice-coil gap may be much larger, its voice-coil resistance may be higher, or it may have a mechanical suspension that is stiffer and more difficult to overcome.
All parameters of the driver-cone area, cone excursion, weight of moving system, magnet size, voice-coil material, size and gap, and the form of mechanical suspension employed-are interwoven with the enclosure design to obtain a speaker system.
Matching Driver And Enclosure
The designer of a successful speaker enclosure cannot change the characteristics of the driver chosen (unless he is also a speaker manufacturer), but must rely on the action of the driver in the enclosure to adjust those parameters needing change.
In using the information gathered here to select a suitable woofer-driver for an enclosure, the following material must be calculated or obtained from the manufacturer:
1.How great an excursion of the cone, for the size driver being contemplated, would be required at the lowest frequency and highest sound pressure level (spl) desired?
2.At the lowest frequency and highest spl desired, is the electro-acoustical efficiency of the driver high enough to allow?A. A commercially available amplifier to be used?B. The required sound pressure to be reached without exceeding the power capabilities of the speaker?
3.If a smaller diameter driver is chosen, does the number of drivers required for sufficient bass response lead to detrimental phase relations as the frequency is increased?
4.Does the driver chosen retain linear response, low distortion, and acceptable polar characteristics at least to the nominal crossover frequency?
In considering all these factors, realize that no single unit can possess all the qualities required. Engineering design consists of Balancing the choices available to achieve the greatest harmony between conflicting requirements.
A Low-Cost Example
An excellent example of a low-cost, small-size, wide-range 8-inch would have these features: a large magnet to help raise efficiency, a large cone excursion to allow useful amounts of air to be moved at low frequencies, a subdivided cone to allow minimum variations in amplitude response as frequency is increased, and a flat cone in order to avoid a restriction in the angle of coverage at high frequencies.
Importance Of Balances
An important factor to consider in speakers is balance. Regardless of whether or not the full range or less than the full range is to be reproduced, the multiplication of the highest frequency by the lowest frequency to be reproduced should equal a figure close to 500,000. For example, a really full-range unit operating from 25 to 20,000 Hz equals 500,000. A system that operates from 35 to 15,000 Hz equals 525,000. If the highest frequency to be reproduced were chosen as 10,000 Hz, then 50 Hz would be preferred as the lowest frequency, and 60 Hz the highest compromise at the low-frequency end of the system's response.
Multiple Arrays
In order to produce the same acoustical power at 50 Hz, a 15-inch speaker will have to move only about one-half the distance that a 12-inch cone has to move. Two 12-inch cones mounted closely together can produce the same acoustical power with one-half the cone excursion for each unit.
When speakers are used in multiples for the same frequency range, danger of phasing problems arise. Phase should not be confused with polarity. It is a simple matter to ensure that four 12-inch speakers on a panel have the same polarity (that they all move forward at the same time and all move backward at the same time), but the phase difference of the radiation from the far left cone on the panel compared to the radiation from the far right cone on the panel can be substantial at certain frequencies and at certain listening positions in the room. To minimize these phasing problems, multiple-cone arrays can be arranged in a few ways.
If two speakers are separated by an excessive distance, phase cancellation will take place when the listener is positioned at unequal distances from the two speakers (angular displacement). This phase cancellation will occur at those frequencies where the difference in distance from one speaker to the listener is one-half wavelength of the distance from the listener to the second speaker.
It is this problem that rules out the use of many small but inexpensive speakers to obtain a high-performance speaker.
Phasing Woofer And Tweeter
Still another aspect of phase relations has to be considered-time delays between drivers operating at the same frequency in the crossover region. Sound travels at approximately 1140 feet per second. This means about 1.14 feet per millisecond-a foot every 1/1000 of a second. It has been demonstrated that the ear can detect differences as short as three milliseconds on sounds such as castanets. This was strikingly illustrated when, in 1935, the movie sound track of the tap dancing of Eleanor Powell reproduced the taps with an added echo on the two0way speaker systems then in use. It was soon discovered that the low-frequency driver and the high-frequency driver used for there recordings were some eight feet apart due to the difference in the length of the horns employed.
When the high-frequency unit was moved back to the point where both drivers were in the same vertical plane, the echo disappeared. Subsequent study of the problem proved that a delay of less than three milliseconds was not detectable in systems using crossovers in the region of 350 to 800 Hz.
Efficiency
Just what is meant by efficiency In the final analysis it means the usable loudness in the listening space. A full symphony orchestra can reach an spl (sound pressure level) of 120 db at the listener's ear. If one wished to reproduce the original dynamic range of an orchestra, this is the level one would need to reach in the listening room.
The power required to produce this level in a concert hall of 600,000 cubic feet (such as Symphony Hall in Boston, Mass.) and the power required to reproduce a similar level in a living room 30 ft x 20 ft x 8 ft, or 4800 cubic feet, is quite different even though the spl is the same.
Assuming that one is willing to sit as close as eight feet from the speaker system, then the goal would be 120-db spl peak intensity at eight feet from the system as a maximum acoustical power output. At eight feet, 0.4 acoustical watt would be approximately 100 db; 120 db would be 40 acoustical watts.
The large, built-in system described in Chapter 3, on infinite baffles, has a measured peak efficiency, in the 50- to 400-Hz range, of 40 percent (plane-wave tube measurements). This means that an amplifier peak output of 100 electrical watts would give an acoustical peak output of 40 watts from the speaker. It should be noted that most of the sheer power present in a musical passage that would reach 120-db spl would be concentrated well below 100 Hz, and as the ear does not hear sounds in the bass regions as efficiently as it does in the midrange, the loudness of these sounds is more ?felt? than heard; but the power required is high. Yet there are on the market today, speaker systems with efficiencies as low as 0.1 percent. This means that for the same loudness at any given frequency, the less efficient system would require 400 times more power than the 40-percent efficient system.
In order to achieve 120-db spl at eight feet, with a speaker of 0.1-percent efficiency, the peak electrical input power would have to be 40,000 watts; if the speaker were 1-percent efficient, then 4000 watts would suffice; and if 10-percent efficient, 400 watts would do the job.
One also has to bear in mind that even if amplifiers were free, and one had 40,000 watts available, the speaker that would require such an input never is capable of handling such power. It usually is rated at a maximum of 250 watts before burnout. If enough units are put together to withstand power-handling problems, then the same type speaker no longer exists, but instead, a new multiple-driver type comes into being with all its attendant phase problems.
Efficiency And Equalization
One of the major disadvantages of the low efficiency that often is not readily detected by the novice is the limitation it places on any chance to use a bass-boost control on the amplifier (often desirable because of a poor listening room and/or recording).
Consider a system that is 1-percent efficient. To produce 100-db spl at eight feet would require forty electrical watts from the amplifier (100-db spl at eight feet requires 0.4 acoustical watt from the speaker). Suppose still further that a 60-watt amplifier is being used-real continuous watts, not music power, peak, or other short-term values. In quality amplifiers, a 12-db bass-boost capability is usually considered conservative. A mere 6-db boost in bass response requires 160 electrical watts (40 watts times four), 100 watts more than the 60-watt amplifier can provide; 12-db boost would require 640 electrical watts. This means that the bass-boost controls are not really usable with the speaker selected.
Using a system that is 40-percent efficient would require one electrical watt for 100-db spl at eight feet; 6-db of bass boost would require four electrical watts; and if all 12-db bass boost available were used, the amplifier would be called on to produce 16 electrical watts. In this case the choice of speaker would allow full use of the capabilities of the amplifier chosen to power it.
If one either sits closer that eight feet (at four feet a 6-db increase occurs) or accept some compression of dynamic range, efficiency becomes an allowable parameter to compromise. For example, the listener who enjoys folk music and small jazz combos finds that such groups seldom, if ever, exceed 100-db spl. Let's imagine that this same listener lives in a quiet apartment. The ambient noise in the listener's apartment is about 45-db spl total reading. This means that with a top level of 100-db spl there is 55 db of dynamic range available. To achieve this degree of dynamic range, the 1.0-percent efficient speaker needs a 40-watt amplifier; the 10-percent efficient speaker needs four watts; and the 40-percent efficient speaker will need only a 1-watt amplifier.
The choice of a maximum level of 100-db spl permits the listener to consider a speaker with efficiency as low as 1 percent.
Unfortunately, little information is available on speaker efficiency. That which is available specifies one-watt electrical input to produce x number of db spl at a given distance. For example, a speaker with an efficiency specification of 95.5-db spl, at a distance of four feet, from one watt of electrical input. At 15 watts, the speaker can be expected to produce 107.2 db at four feet. If the speaker has an efficiency of 103 db from one watt at four feet, 35 watts would produce 118.5 db at four feet, 70 watts of power would yield 121.5-db spl at four feet.
In short, be sure to give consideration to the anticipated power requirements of the system at equalized settings as well as at ?flat? settings on the tone controls.
At this point still another factor enters the picture. It is a simple matter to get even a three-inch speaker to move back and forth within it's limits at 30 Hz, but the amount of air which it moves remains totally inaudible. A sound that is judged to be a given loudness and measures 60-db spl at 1000 Hz, a 30-Hz tone would have to be 90-db spl to be judged equally loud. At minimum audible frequencies (the quietest tones the ear can detect at a particular frequency) the softest tone the ear hears at 1000 Hz is about 5-db spl. However, a tone that is just audible at 30 Hz must be at least 60-db spl.
High-Frequency Drivers
High-frequency drivers do not normally require special housings; however, there are a few factors that relate to matching a suitable high-frequency unit to the woofer-enclosure combination chosen are:
1.The efficiency of the high-frequency unit should be close to that of the low-frequency unit so that the final exact match at crossover can be accomplished with a minimum or even a lack of attenuators.
2. The two units should be mounted so as to minimize differences in phase (distance form woofer diaphragm to the ear as compared to distance from high-frequency diaphragm to the ear).
3. The quality of tonal response, the polar pattern, and the impedance should harmonize with the low-frequency driver.
Coaxial and triaxial speakers solve all these problems inasmuch as they are mechanically, electrically, and acoustically integrated systems adjusted by the manufacturer.
If one is building his first enclosure, it is possible to greatly minimize the potential problems by choosing a coaxial or triaxial driver unit. For those who are ready to attempt simple measurements and are willing to do some experimenting on their own, the separate driver units offer a much wider latitude of performance.
Refer to the PDF file for charts and tables
Modified by PoorManQ45 at 7:05 PM 10/15/2004