US 3308237 A
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United States Patent O 3,308,237 COLUMNAR LOUDSPEAKER SYSTEM .lames F. Novak, La Grange Park, Ill., assigner to The Muter Company, Chicago, lill., a corporation of Illinois Filed May 31, 1963, Ser. No. 284,517 11 Claims. (Cl. 179-1) The present invention relates to loudspeakers, and more particularly refers to a loudspeaker system designed to limit reverberation and equalize loudness at various positions when used in large auditoriums.
Many types of loudspeakers systems have been used for the reproduction of sound in large halls and auditoriums, which have been designed to limit reverberation, and other forms of distortion, as well as to equalize the loudness of the sound experienced at various parts of the auditorium. One such system is the large multicellular horn. Although this system functions well, its main disadvantage is that it is quite expensive.
Another type of loudspeaker system which has found some success for use in public address systems is the columnar type. This system comprises a plurality of small loudspeakers Amounted vertically in a column. This system has the advantage that the reproduced sound is directional. The directionality can be varied by varying the size of the loudspeakers used, their distance from each other, and their number. The columnar loudspeaker system, however, has two basic drawbacks. First, the directionality is a function of the frequency. Consequently, since even human speech has a frequency ratio between highs and lows of about to l, the directional pattern is very much different for the low pitched sounds than for the high pitched sounds. This results in considerable beam distortion.
A second disadvantage of the columnar loudspeaker system is that the angular pattern of sound intensity has side lobes which further contribute to beam distortion.
Attempts have been made to modify the columnar loudspeaker system into what is commonly termed a tapered column. The tapered column takes advantage of the fact that the greater the number of speakers employed, the greater is the directionality. Consequently, cut-off filters are utilized so that the higher frequency sounds are reproduced by a fewer number of loudspeakers than the lower frequency range sound. However, this arrangement only alleviates the frequency sensitivity problem to a small degree. Additionally, it offers no real solution to the side lobe problem.
It is an object of the present invention to provide a loudspeaker system for use in large halls and auditoriums which has a highly directional vertical sound intensity pattern.
It is a further object to provide such a system in which the directional pattern does not vary appreciably over the frequency range for which the system is designed.
It is still further an object of the invention to provide a loudspeaker system which minimizes the effect of side lobe distortion.
Other objects and advantages of -the invention will become apparent from the following description and drawings in which:
FIG. 1 is a diagram in perspective of a two array columnar loudspeaker system according to the invention.
FIG. 2 is a circuitdiagram of the electrical system of the loudspeaker system shown in FIG. 1.
FIG. 3 is a diagram showing a reference system for an array of 2N point sources.
FIG. 4 is a diagram showing a reference system for an array of (2N +1) point sources.
FIG. 5 is a diagram showing current distribution with frequency for each side of a ten element loudspeaker system, and
3,308,237 Patented Mar. 7, 1967 FIG. 6 is a polar graph illustrating the sound pattern of the two column array shown in FIGS. 1 and 2.
According to the invention, a loudspeaker system is provided in the form of a vertical column comprised of a plurality of closely spaced small loudspeakers. On each side of the center of the column the system is symmetrically tapered by means of filter networks having minimum phase shift characteristics, and which iilters are so designed that the signal current distribution across the column from center to each end is symmetrically arranged and is based on the properties of the Tchebyscheff polynomials, a well known mathematical expression. The loudspeakers arranged immediately at the center of the column may be driven with the unmodified signal current. As a result of this arrangement, the pattern of the sound beam projected by the system is highly directional and remains substantially uniform over a large frequency range.
As a further improvement of the invention, the present loudspeaker system is arranged in the form of two or more separate columns, one column comprising larger speakers and therefore having larger spacing between speaker centers, and the other column comprising smaller speakers, generally of equal number as the first column, and having smaller spacing between speaker centers and, consequently shorter over-all length. The electrical signal to be reproduced is divided into two or more parts by means of crossover networks, the lower frequency portion being applied to the column comprised of larger speakers, and the higher frequency portions being applied to the column or columns comprised of smaller speakers. Each column or array in turn has a system of filter networks designed to provide Tchebyscheff signal current distribution across the array, as described above. As a result, when the crossover frequency of the crossover networks are properly chosen, the number and intensity of side lobes are greatly reduced.
Directivity control in acoustic arrays is based upon wave interference. Radiation takes place in such a manner that the waves oppose each other in some directions and thereby pull the radiation pattern inward. In other directions, the waves aid each other and reinforce the radiation. A great deal of directivity (and gain) may be obtained by spacing the loudspeakers equally apart along a straight line and driving them with equal in-phase power.
The problems associated with acoustic arrays, such as columnar loudspeakers, are extremely complex because the sound column is a very wide-band device. The frequency range ratio covered is at least 10-1, and generally is greater. These wide-band requirements cause great variations in beamwidth and are apt to give rise to a large number of side lobes, both of which effects are undesirable for many applications.
From a practical viewpoint, it would appear that the ideal column should have (l) a constant beamwidth over at least a 10-1 frequency range, and (2) the side lobe level should be kept at a minimum. In order to illustrate the principles upon which such a column is based, it is best to consider first the reasons why a conventional column falls short of the wide-band uniformity requirements.
A conventional column of length L where all speakers are fed equal power has a directional pattern defined by the function sin me n sin :v
where r c=velocity of sound f=frequency of operation 6=angle from normal to the column nznumber of loudspeakers.
Although the beamwidth is usually defined as the angle between the half-power points, it is much simpler and no less valid for purposes of comparison to define the beamwidth as the angle subtended by the first nulls of the pattern. lf the length of the column is defined as L=(iz-l)d, it can then be shown that the beamwidth is where nznumber of speakers d=distance between speakers Equation b clearly illustrates that the beamwidth is dependent upon the product of column length and the frequency of operation.
Because the beamwidth is a function of the product of column length and frequency, a constant beamwidth would result if this product could be held constant over the entire frequency range. One method for achieving this is through the use of low-pass filters. The cut-off frequencies of these filters are progressively increased across the entire column length in such a manner that one-half of the remaining speakers are cut-off with each successive doubling of frequency. The starting frequency is that which yields the desired beamwidth with all speakers active. The result is that the beamwidth will not become less than the design value since column length is effectively shortened as frequency increases. The minimum frequency which will yield the desired beamwidth depends on the length of the column, and can be lowered by increasing column length. The column becomes essentially nondirectional below the frequency for which the column length becomes one wavelength.
One disadvantage of this method is that excessive beam tilting and/or beam distortion can occur since all filters have different cut-off frequencies and therefore different phase characteristics. An additional disadvantage is that the side lobe level is unaffected although the total number of side-lobes will be decreased. Side lobe generation in this case is dictated only by the spacing between speakers while the number of lobes depends upon the number of speakers.
The present invention utilizes the benefits of the tapered columnar system while avoiding its defects. In the present system uniform excitation is employed at low frequencies, since this type of excitation allows the specified beam width to occur at the lowest possible frequency. The column employs tapering provided by the use of a system of filter networks having minimum phase shift characteristics which cause the taper to increase as the frequency increases. The filter networks are so designed that the signal current distribution across the column or array on each side of center is based on the properties of the Tchebyscheff polynomials. As a result, the beam width of the column remains constant and the side lobe level is greatly reduced.
In order to obtain a correlation between the parameters of a columnar loudspeaker system and the Tchebyscheff polynomials, the derivation can be based on the theorem that every linear array of loudspeakers can be represented by a polynomial and every polynomial can be interpreted as a loudspeaker array. The total length of the array is the product of the separation between elements and the degree of the polynomial. The degree of the polynomial is one less than the number of elements.
The field pattern of arrays is given by the following equations, based on the reference systems shown in FIGS. 3 and 4:
The discussion of (l) and (2) can be reduced to the consideration of polynomials of a real variable, x=cos u, on the real interval -lxL Explicit polynomial representations in terms x=cos u for (l) and (2) result in the following expressions.
This invention utilizes a current distribution across the array based upon the properties of the Tchebyscheff polynomials which are defined by (5) TN(Z)=cos (n arc cos Z) Equation (5) is a polynomial of degree n in Z. By restricting the range of Z to -ZOZZO and introducing the scale contraction x=Z/Z0, polynomials of the form of (3) and (4) can be written in terms of x, Where -lxL TQN Z095) Z ZAQQQNZQMIQ (1:0
By equating (6) to (3) and (7) to (4), the resulting expression can be solved for the currents in each elerent.
If the first null of the pattern is specified as 00, the parameter Z0 can be obtained from The procedure now is to determine the beamwidth that is desired, 200, and plot the variation of Z vs. frequency over the rang-e of lZooo. One then plots the variation of currents, Ik, as a function of frequency over the resulting frequency range.
In FIG. is shown a graph of relative signal current as plotted against the value d/x as obtained from the Tchebyscheff polynomials for a element array, each half of the array being symmetrical with the other where:
d=distance between speaker centers kzwave length of sound.
This graph may be utilized to design a columnar speaker system as illustrated in FIGS. l and 2, as is described in greater detail below, by first determining what relative currents must be applied to each loudspeaker for various frequencies along the curve. Having determined these values, the respective filter networks may then be designed according to known principles to produce the respective currents over the desired frequency range.
An additional feature of the invention resides in a means for the reduction of side lobes. The behavior of side lobes and their effect on reproduction can be illustrated by considering a specific array of, for example, ve point sources, that is, five separate loudspeakers. The directivity pattern of such an array is given by Equation a above. The directivity pattern is a function of n, the number of loudspeakers, and comprises a large central maximum in the direction of principal radiation followed by three smaller maxima of alternating phase, and, finally, by another maximum of the same amplitude as the first. The pattern then repeats itself in the same manner as frequency continues to increase. In the general case, the pattern with n point sources will be similar to this, with the quantity of small maxima ybetween the larger ones being equal to (1t-2) The effect of side lobe formation is as follows. At low frequency only the single central maximum or major lobe will be present. This gradually increases in sharpness as the frequency is increased and the smaller maxima (or minor lobes) begin to appear. When a frequency is reached such that spacing between speakers becomes a half wave length (about 1250 cycles per second, in the case of an array having a distance of about six inches between speaker centers), the entire pattern of major lobe, three minor lobes and ma-jor lobe will appear between 0 and 180. When a frequency is reached corresponding to a wave length -which is equal to the distance between speaker centers (2500 cycles per second), this entire pattern begins to appear between 0 and 90, and will repeat itself between 90 and 180. The process of pattern repetition continues to occur in smaller and smaller intervals as the frequency is increased.
The present invention greatly reduces the unwanted effects of side lobe formation by utilizing a plurality of columnar loudspeaker arrays, and limiting the frequency of the signal supplied to the first array so that the distance between loudspeaker centers is no greater than one wave length, and preferably no greater than about 0.8 wave length of the highest frequency sound. This is accomplished by means of a crossover network having the proper characteristics, the design of which may be determined by principles known in the prior art. A second columnar array, preferably having the same number of speakers, is provided having a smaller distance between speaker centers than that of the first array, and preferably about one-half that of the first array. For the reproduction of human speech two arrays are normnlly sufiicient. However, if desired, three or even more arrays may be utilized. Where three separate arrays are used, the distance between loudspeaker centers of the second array should be about one-half that of the first array, and the distance between loudspeaker centers of the third array should be about onelhalf that of the second array. Crossover networks should be used to limit the signal current applied to the first array so that the distance between centers of that arr-ay never exceeds 1.0 and preferably 0.8 wavelength of the signal current applied. The signal current which is applied to the second array is similarly limited with respect to the distance between loudspeaker centers of the second array. The last array generally is excited with the remainder of the signal current.
.Although the crossover frequency may be such that the distance lbetween speaker centers is equal to one wave length, it is preferred that the crossover frequency be such that the distance between speaker centers is only about 0.8 wave length of the signal current. This would normally correspond t0 a frequency of about 2,000 cycles per second utilizing a distance of about six inches between loudspeaker centers.
Each array is provided with filter networks designed to provide Tchebyscheff current distribution across each respective array, similarly as described above.
Referring to FIGS. l and 2, a practical arrangement embodying the principles of the invention is shown. A speaker enclosure 1, contains an array of ten equally spaced loudspeakers 2, ea-ch having a diameter of 5% inches, with a spacing of 5'1/2 inches between speaker centers. A second array is comprised of ten speakers 3 having a diameter of about one-half the size of the other speakers 2. A spacing of about 2% inches between centers is utilized for the small array.
The electrical circuit of the system is shown in detail in FIG. 2. Here the signal current 4 passes through a crossover network 5 and is separated into two components, a low frequency component having frequencies below 2,000y cycles per second, and a higher frequency component 7, having frequencies above 2,000 cycles per second. The first component 6 is utilized to excite the low frequency array comprised of the larger loudspeakers 2. The two central loudspeakers are excited with portions of the unmodified low frequency component. The remaining loudspeakers receive signal currents which first pass through pattern-shaping Ifilter networks 8-11 which are symmetrically arranged about the two center loudspeakers. Each filter network is comprised of electrical components such as inductances lf2-17, and resistors 18-21. If desired, separate filter networks may be used for each loudspeaker of the array. However, it has been found satisfactory to utilize a single filter network for each pair of symmetrically positioned loudspeakers.
The high frequency component of the signal current is applied to the array of smaller speakers 22 through filter networks 23, 24, 25 and 26.
In order to obtain the values of the current for each loudspeaker, the parameters for a system containing l0 loudspeakers were substituted into the Tchebyscheff polynomials as described above. FIG. 5 is a graph showing the calculated values obtained from the Tchebyscheff polynomials for the relative currents to be applied to each loudspeaker at any particular wavelength and spacing between speaker centers.
From the information which may be obtained from the graph of FIG. 5, the values of the components of each filter network may be readily determined by known methods.
In Table I which follows is contained a listing of the values for the various components utilized in the filter networks shown in FIG. 2. Values for the components of the filter networks 23-26 which are associated with the array of small speakers 22 may be determined from the Tchebyscheff polynomials or from the graph of PIG. 5 in similar manner. As a practical matter, the values may be determined for the smaller system shown by dividing each of the corresponding values given in Table I for the larger system by a factor of 1.83.
7 Table I Component: Value 12 mh 1.86 13 Inh 0.90 14 mh-- 0.93 15 mh 0.45 16 mh 0.93 17 mh 0.28 18 ohms 79.0 19 do 39.4 20 ido 39.4 21 do 6.7
The impedance of each loudspeaker is l2 ohms.
The columnar loudspeaker system, as shown in FIGS. 1 and 2, was tested to determine its directional pattern over a wide range of frequencies. The frequency ranges utilized were 30D-600 cps., 600-1200 c.p.s., 1200-2400 c.p.s., and 2400-4800 c.p.s. The patterns obtained are illustrated in the polar graph of FlG. 6. As can be seen, the beam is extremely uniform over the entire frequency range for which it was designed and tested. Moreover, the side lobes have been greatly reduced from those which would normally result from a traditional columnar array. The columnar speaker system of the invention clearly represents a significant advance in the directional loudspeaker field.
Although the loudspeaker system of the invention has been described and shown in only a limited number of embodiments, variations thereof will occur to those skilled in the art and are to be considered as falling within the spirit and scope of the invention as defined by the claims which follow.
Invention is claimed as follows:
l. A loudspeaker system comprising a linear array of a plurality of loudspeakers and an electrical system associated therewith, said electrical system comprising a plurality of filter networks so modifying the individual signal currents applied to said loudspeakers that the signal current distribution across said array from center to each end substantially conforms to the properties of the Tchebyscheff polynomials.
2. A loudspeaker system comprising a plurality of arrays each comprised of a plurality of linearly arranged loudspeakers, and an electrical system associated therewith, the electrical system of each array comprising means for so modifying the individual signal currents applied to said loudspeakers that the signal current distribution across each array from center to each end substantially conforms to the properties of the Tchebyschei polynomials, the distance between the centers of adjacent loudspeakers of each succeeding array being smaller than that of the preceding array, said electrical system having means for so limiting the frequency range of the signal current applied to the first array that the distance between the centers of adjacent loudspeakers thereof does not eX- ceed one wave length of the signal current applied to said array.
3. A loudspeaker system according to claim 2, wherein the means for modifying the individual signal currents applied to the loudspeakers comprises a plurality of filter networks.
4. A loudspeaker system according to claim 2, wherein each pair of loudspeakers symmetrically positioned on each side of the center of the respective arrays is supplied with a signal current from the same filter network,
5. A loudspeaker system according to claim 2 wherein the signal current applied to each respective array is applied to the loudspeakers immediately adjacent the center of the array without further modification.
6. A loudspeaker system according to claim 2, wherein the frequency range of the signal current applied to each array but the last is so limited that the distance between the centers of adjacent loudspeakers does not exceed a value of one wave length of the signal current applied to said respective array.
7. A loudspeaker system according to claim 2, wherein the frequency range of the signal current applied to the first array is so limited that the distance between the centers of adjacent loudspeakers does not exceed a value of about 0.8 wave length of the signal current applied to said array.
8. A loudspeaker system according to claim 2, wherein the distance between the centers of adjacent loudspeakers of each succeeding array is about one-half that of the immediately preceding array.
9. A loudspeaker system according to claim 2, wherein the loudspeakers of each array are equally spaced.
10. A loudspeaker system according to claim 2, wherein the distance between the centers of the loudspeakers of each succeeding array is about one-half that of the immediately preceding array, and the frequency range of the signal currents applied to all but the last array are so limited that the distance between the centers of adjacent loudspeakers of each respective array does not exceed about 0.8 wave length of the signal current applied to said array.
11. A loudspeaker system comprising two arrays each comprised of a plurality of equally spaced linearly arranged loudspeakers, and an electrical system associated therewith, the electrical system of each array comprising a plurality of filter networks for so modifying the individual signal currents applied to said loudspeakers that the signal current distribution across each array from center to each end substantially conforms to the properties of the Tchebyscheif polynomials, the distance between the centers of adjacent loudspeakers of the second array being about one-half that of the rst, said electrical system having a crossover network for dividing the signal current into two components, a first component applied to the first array the maximum frequency of which is so limited that the distance between the centers of adjacent loudspeakers of said first array does not exceed about 0.8 wave length thereof, and a second component applied to the second array comprising the remainder of the signal current.
References Cited by the Examiner UNITED STATES PATENTS 6/1964 Avedon 179-1 KATHLEEN H. CLAFFY, Primary Examiner.
R. MURRAY, Assistant Examiner.