Abstract:
An improved Bessel array of electromagnetic transducers, in which the Bessel coefficients (phase and/or magnitude) are applied only in a high frequency range, where off-axis interference patterns between the outputs of respective transducers cause undesirable acoustic results. One improvement is in using an all-pass filter or the like in lieu of an inverter in the inverting Bessel coefficient path, to provide an in-phase signal in low frequencies and an opposite-phase signal in high frequencies. This achieves the improved off-axis result of a conventional Bessel array, with improved low-frequency maximum sound pressure and efficiency. Another improvement is in using a frequency-dependent voltage divider in the half-strength Bessel coefficient paths, to provide full-strength signals in low frequencies and half-strength signals in high frequencies. This achieves even more improved low-frequency maximum sound pressure.

Description:
BACKGROUND OF THE INVENTION  
       [0001]     1. Technical Field of the Invention  
         [0002]     This invention relates generally to transducers such as audio speakers, and more specifically to an array of transducers which operate as a Bessel array in higher frequencies and as a conventional array in lower frequencies.  
         [0003]     2. Background Art  
         [0004]     It is well known to organize two or more transducers together into a variety of array configurations. One popular configuration is the line array.  
         [0005]      FIG. 1  illustrates a conventional line array system  10 . A plurality of transducers  12  are arranged in a linear fashion. In some instances, the transducers may be substantially identical. Although five transducers are shown, line arrays may use any number of transducers. Commonly, the transducers are coupled to a single, common enclosure  14 . The transducers are driven in phase by a common signal (as indicated by the “+1” indication at the input to each transducer) from an amplifier  16 .  
         [0006]     As compared to a single transducer, a line array composed of multiple units of that same transducer offers the advantage of increased maximum sound pressure (sometimes referred to as loudness or volume), due simply to there being more transducers moving air, and also offers the advantage of higher efficiency, due to mutual air coupling between the transducers leading to improved impedance matching. However, line arrays can suffer from undesirable effects, such as interference patterns, which are observed at off-axis listening positions. In this context, “off-axis” refers to positions which are removed in a direction parallel to the “line” of the line array; for example, in  FIG. 1  the off-axis positions are up and down, rather than left and right of the line array. These effects result, in large measure, from the listener being at slightly different distances from each of the respective transducers, and sound from the closer transducers arriving sooner than sound from the farther transducers. The farther off-axis the listener moves, the greater the differences between the listener and each of the transducers. At various off-axis positions, some frequencies will be subject to constructive interference while other frequencies will be subject to destructive interference. At other off-axis positions, different sets of frequencies will be subject to constructive or destructive interference. In general, because high frequencies have shorter wavelengths than low frequencies, these off-axis effects are more pronounced in the higher frequencies and begin to significantly occur when the frequency is sufficiently high such that its wavelength is only twice as long as the spacing between adjacent transducers in the array. At this frequency, the output of two adjacent transducers will completely cancel each other out at an angle of 90 degrees off-axis, because the output of one will be exactly 180 degrees out of phase with the output of the other.  
         [0007]      FIG. 2  is a graph that illustrates the performance of one example of a line array, with five transducers on 4 cm center-to-center spacing. The horizontal (X) axis is frequency, and the vertical (Y) axis is sound pressure. Sixteen response curves are plotted; the on-axis curve is shown as a solid line, and the dotted lines represent fifteen response curves measured at 2 degree increments off-axis. The line array exhibits very good performance, with 98 dB sound pressure and minimal interference effects below about 1 kHz. Above about 1 kHz, however, the line array begins to exhibit significant comb filter interference patterns.  
         [0008]     U.S. Pat. No. 4,399,328 to Franssen teaches the known but little-used Bessell array of speakers, which was designed to address exactly this problem. Its principles will be explained with reference to  FIGS. 2-4 .  
         [0009]      FIG. 3  illustrates a Bessel array  20  of transducers  12  coupled to an enclosure  14  and driven by an amplifier  16 . Rather than simply being provided directly to each transducer, as in a line array, the audio signal from the amplifier is altered to be suitable for the Bessel array by a circuit  22 . The amplifier may be a pre-amplifier, and the final power amplification may be performed between the Bessel circuit and the transducers through the use of multiple power amplifiers.  
         [0010]     The advantage offered by a Bessel array is control of constructive and destructive interference patterns in listening positions which are off-axis in the direction of the line array—vertically in the example of  FIG. 3 . A Bessel array reduces this effect by powering the various speaker drivers with differently conditioned signals, rather than by merely splitting the same signal equally five ways. In the common five-driver Bessel array, the first driver  12 - 1  receives a half-strength, in-phase signal (referred to as “+½”); the second driver  12 - 2  receives a full-strength, inverted-phase signal (referred to as “−1”); the third and fourth drivers  12 - 3  and  12 - 4  each receives a full-strength, in-phase signal (“+1”); and the fifth driver  12 - 5  receives a half-strength, in-phase signal (“+½”).  
         [0011]     One method of providing the “−1” signal is simply to reverse the connections at the + and − terminals of the second driver. One method of providing the “+½” signals is to connect the first and fifth drivers in series with each other, and that series combination in parallel with each of the other drivers, as taught by Franssen. In other embodiments, the Bessel circuit may be e.g. a digital logic device.  
         [0012]     In some embodiments, a single amplifier&#39;s output is used to drive all of the transducers in the Bessel array. In other embodiments, each transducer may be driven by its own, dedicated amplifier; in such embodiments, each amplifier&#39;s output may be adjusted such that its output corresponds to the required Bessel coefficient for that particular driver. In that case, the amplifier settings themselves function as the Bessel circuit.  
         [0013]     A Bessel array sacrifices maximum sound pressure and efficiency versus a line array configuration of the same drivers, to gain improved off-axis sound performance. In low frequencies, a five-driver Bessel array uses five speaker drivers to generate the same sound pressure level that would be generated by two speaker drivers in a conventional line array.  
         [0014]      FIG. 4  is a graph illustrating the frequency response of a conventional 5-driver Bessel array with 4 cm center-to-center spacing, in 2 degree increments from 30 degrees below to 30 degrees above center. Comparing  FIG. 4  to  FIG. 2 , it is readily seen that the Bessel array has significantly reduced off-axis interference patterns compared to the conventional line array. However, it is also readily seen that the Bessel array has significantly reduced sound pressure than the conventional line array using the same transducers, the same amplifier (although only being driven at ⅘ths relative output), and the same signal—the conventional line array offers roughly 98 dB on-axis, while the Bessel array offers only 90 dB, an 8 dB reduction in the sound pressure level.  
         [0015]     Furthermore, it is also seen that the conventional Bessel array performs the same interference pattern reduction, and loss of sound pressure, across the entire frequency range, whereas the interference pattern is really only a problem in the higher frequencies. At lower frequencies, the wavelengths are sufficiently long to swamp the distance difference between the off-axis listener and the respective speaker drivers.  
         [0016]     What is desirable, then, is a Bessel array which performs its interference pattern reduction function more in higher frequencies than in lower frequencies and which has less overall reduction in sound pressure and efficiency than a conventional Bessel array. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0017]      FIG. 1  shows a line array according to the prior art.  
         [0018]      FIG. 2  is a graph showing the frequency response of the 5-driver line array of  FIG. 1 .  
         [0019]      FIG. 3  shows a Bessel array according to the prior art.  
         [0020]      FIG. 4  is a graph showing the frequency response of the conventional 5-driver Bessel array of  FIG. 3 .  
         [0021]      FIG. 5  shows an improved Bessel array according to one embodiment of this invention.  
         [0022]      FIGS. 6A and 6B  are graphs showing the frequency response of the improved Bessel array of  FIG. 5 .  
         [0023]      FIG. 7  shows a Bessel square array according to the prior art.  
         [0024]      FIG. 8  shows an improved Bessel square array according to another embodiment of this invention.  
         [0025]      FIG. 9  shows another embodiment of an improved Bessel square array with the frequency-dependent Bessel coefficient feature applied in both row and column circuitry.  
         [0026]      FIG. 10  shows yet another embodiment of an improved Bessel square array.  
         [0027]      FIG. 11  shows another embodiment of a Bessel array with an additional improvement in that both the inverted Bessel coefficient and the half-amplitude Bessel coefficients are provided in a frequency dependent manner. 
     
    
     DETAILED DESCRIPTION  
       [0028]     The invention will be understood more fully from the detailed description given below and from the accompanying drawings of embodiments of the invention which, however, should not be taken to limit the invention to the specific embodiments described, but are for explanation and understanding only.  
         [0029]      FIG. 5  illustrates one embodiment of an improved Bessel array  30  according to this invention. The Bessel array may use a conventionally configured array of speaker drivers  12 - 1  to  12 - 5  mounted in an enclosure  14  and powered by a conventional source such as an amplifier  16 .  
         [0030]     The improvement lies in the Bessel circuit  32  which conditions the amplifier output to apply the required Bessel coefficients to the signals supplied to each of the respective drivers. In the five-driver Bessel array shown, the first driver  12 - 1  and fifth driver  12 - 5  each receives an in-phase, half-strength (“+½”) signal whose strength is reduced by a conventional voltage divider  24  or other suitable means (such as being coupled in series); the second driver  12 - 2  receives its signal (“+/−1”) from an inverting all-pass filter  34  or other such circuit which performs the desired function; and the third driver  12 - 3  and fourth driver  12 - 4  each receives a simple pass-through of the amplifier signal (“+1”).  
         [0031]     The inverting all-pass filter inverts the phase of high-frequency signals, but does not invert the phase of low-frequency signals; thus, the signal is identified as “+/−1” suggesting that it is “+1” in lower frequencies and “−1” in higher frequencies. The designer can select the phase-inverting cross-over point to be at any frequency, based on driver spacing and desired off-axis response control.  
         [0032]     Thus, the improved Bessel array is a “single-sided” Bessel array, in that it behaves like a Bessel array on one side (the high-frequency side) of its frequency range, but more like a conventional line array on the other side (the low-frequency side). It may also be thought of as being single-sided in that, in some embodiments, it will exhibit better performance in one off-axis direction than in the other.  
         [0033]      FIGS. 6A and 6B  are graphs illustrating the off-axis performance of the improved Bessel array of  FIG. 5 , which has 5 drivers on 4 cm center-to-center spacing.  FIGS. 6A and 6B  show the performance from center to 30 degrees above and below center, respectively, in 5 degree increments.  
         [0034]     Comparing  FIGS. 6, 4 , and  2 , it is seen that in the lower frequencies, the sound pressure level of the improved Bessel array of this invention is significantly better than that of the conventional Bessel array, and in the higher frequencies, the interference exhibited by the improved Bessel array of this invention is significantly better than that of a conventional line array and nearly as good as the conventional Bessel array. The improved Bessel array is somewhat asymmetrical, as seen by comparing  FIG. 6A  to  FIG. 6B , in that it has a different amount of off-axis interference control in one off-axis direction than in the other.  
         [0035]      FIG. 7  illustrates a Bessel square array  40  according to the prior art, including an array of speaker drivers coupled to an enclosure  42 . The Bessel square array is a “Bessel of Bessels”. The speaker drivers are arranged in a two-dimensional array, typically but not necessarily having equal numbers of rows and columns. The speaker drivers within each given column are driven in Bessel array fashion, and the columns themselves are driven in Bessel array fashion.  
         [0036]     The amplifier output is provided to a main Bessel circuit  22 - 0 . Each output of the main Bessel circuit is provided as an input to a respective secondary or column Bessel circuit  22 - 1  through  22 - 5 . Each of the secondary Bessel circuits drives a corresponding Bessel array of drivers arranged in a column. The first column Bessel circuit  22 - 1  drives a first Bessel array of drivers  44 , the second column Bessel circuit  22 - 2  drives a second Bessel array of drivers  46 , and so forth. Each secondary Bessel circuit applies the Bessel function to whatever input signal it receives from its respective output of the main Bessel circuit. Thus, the signal provided to any given speaker driver is the product of its main and column Bessel signal values.  
         [0037]     The five drivers  44  in the first column are driven in Bessel array fashion, with the first driver  44 - 1  and the fifth driver  44 - 5  each receives a quarter-strength, in-phase signal “+¼”; the second driver  44 - 2  receives a half-strength, opposite-phase signal “−½”; and the third driver  44 - 3  and the fourth driver  44 - 4  each receives a half-strength, in-phase signal “+½”. The five drivers  52  in the fifth column are driven the same as those in the first column.  
         [0038]     The five drivers  46  in the second column are driven collectively by the “−1” of the main Bessel, which is fed through the second column Bessel circuit  22 - 2 . The first driver  46 - 1  and the fifth driver  46 - 5  each receives a half-strength, opposite-phase signal “−½”; the second driver  46 - 2  receives a full-strength, in-phase signal “+1” (a double negative); and the third driver  46 - 3  and the fourth driver  46 - 4  each receives a full-strength, opposite-phase signal “−1”.  
         [0039]     The third column Bessel circuit  22 - 3  receives a “+1” signal from the main Bessel circuit. The first driver  48 - 1  and the fifth driver  48 - 5  each receives a half-strength, in-phase signal “+½”; the second driver  48 - 2  receives a full-strength, opposite-phase signal “−1”; and the third driver  48 - 3  and the fourth driver  48 - 4  each receives a full-strength, in-phase signal “+1”. The five drivers  50  in the fourth column are driven the same as those in the third column.  
         [0040]      FIG. 8  illustrates the improved Bessel square array  60  according to one embodiment of this invention. In the embodiment shown, the inverting all-pass filter improvement is applied to only the primary Bessel circuit, with the five column Bessel circuits being conventional Bessel circuits which simply invert the phase of their input signals to generate their second drivers&#39; respective signals  
         [0041]     The first, third, fourth, and fifth columns&#39; drivers receive the same signals as in the conventional Bessel square array of  FIG. 7 . The improvement lies in the signals applied to the second column—the position which, in a conventional Bessel array receives the “−1” signal but which, in this invention such as shown in  FIG. 5 , receives the “+/−1” signal.  
         [0042]     The operation of the second column is slightly more complex than in the conventional Bessel square array, because according to this invention it receives a single-sided all-pass filter phase shifted signal “+/−1” from the second output of the primary Bessel circuit.  
         [0043]     In the low frequencies, the primary Bessel circuit is outputting a “+1” signal at its second output, and the second column Bessel circuit  22 - 2  provides a “+½” signal (main “+1” times column “+½”) to the first driver  46 - 1  and to the fifth driver  46 - 5 ; a “−1” (main “+1” times column “−1”) signal to the second driver  46 - 2 ; and a “+1” (main “+1” times column “+1”) signal to each of the third driver  46 - 3  and the fourth driver  46 - 4 .  
         [0044]     In the high frequencies, the primary Bessel circuit is outputting a “−1” signal at its second output, and the second column Bessel circuit  22 - 2  provides a “−½” signal (main “−1” times column “+½”) to the first driver  46 - 1  and to the fifth driver  46 - 5 ; a “+1” (main “−1” times column “−1”) signal to the second driver  46 - 2 ; and a “−1” (main “−1” times column “+1”) signal to each of the third driver  46 - 3  and the fourth driver  46 - 4 .  
         [0045]      FIG. 9  illustrates another embodiment of an improved Bessel square array  70  in which the improved Bessel circuit is used in both the main (row) Bessel and the column Bessel functions. The output from the amplifier(s) is fed into an improved main Bessel circuit  32 - 0 . The outputs of the main Bessel circuit are fed into respective improved column Bessel circuits  32 - 1  through  32 - 5 .  
         [0046]     The advantage gained over the embodiment of  FIG. 8  lies in the second row of transducers. In the low frequencies, each of those five drivers  44 - 2 ,  46 - 2 ,  48 - 2 ,  50 - 2 , and  52 - 2  receives an in-phase “+” signal, whereas in  FIG. 8  each received an opposite phase “−” signal in the low frequencies. In the  FIG. 8  configuration, the second row transducers contribute to low frequency sound pressure, rather than diminishing it. The disadvantage is that there are now six instances of the inverting all-pass filter circuitry—one in the main Bessel circuit, and five in the respective column Bessel circuits.  
         [0047]      FIG. 10  illustrates another embodiment of a Bessel square array  80  which retains the low frequency performance advantage of  FIG. 9 , but which requires only a single inverting all-pass filter circuit. The amplifier output is provided to an improved main Bessel circuit  84 . The five Bessel coefficient outputs of the main Bessel circuit are fed into five respective column partial Bessel circuits  82 - 1  through  82 - 5 . These are partial Bessel circuits in that they lack the inverting (second) Bessel output. A sixth partial Bessel circuit  82 - 6  is driven, in parallel with the second column partial Bessel circuit  82 - 2 , with the frequency-dependent inverting output of the main Bessel circuit. This sixth partial Bessel circuit drives transducers  44 - 2 ,  48 - 2 ,  50 - 2 , and  52 - 2  as indicated. The transducer  44 - 2  which lies at the missing inverting output of both the second column partial Bessel circuit  82 - 2  and the sixth partial Bessel circuit  82 - 6  is driven with a “+1” signal, which may be supplied by any handy source such as any other “+1” output or by its own amplifier or what have you.  
         [0048]      FIG. 11  illustrates the frequency-dependent improvement applied not only to the inverting (second) Bessel signal but also to the half-strength (first and fifth) Bessel signals, as well. The improved Bessel system  90  includes an improved Bessel circuit  92 , which includes the inverting all-pass filter  34  providing its second output and the straight pass-through paths providing its third and fourth outputs. In place of a conventional voltage divider (or series connection) at its first and fifth outputs, it includes a frequency-dependent voltage divider  94  providing its first and fifth outputs.  
         [0049]     In low frequencies, the frequency-dependent voltage divider does not perform any significant voltage division, and the first and fifth transducers receive full-strength, in-phase “+1” signals; the inverting all-pass filter does not perform phase inversion, and the second transducer receives a full-strength, in-phase “+1” signal; and, as always, the third and fourth transducers receive full-strength, in-phase “+1” signals. Thus, in low frequencies, the improved Bessel array performs substantially like a conventional line array, offering maximum sound pressure and efficiency.  
         [0050]     In high frequencies, the frequency-dependent voltage divider performs voltage division, such that the first and fifth transducers receive half-strength, in-phase “+½” signals; the inverting all-pass filter provides a full-strength, opposite-phase “−1” signal to the second transducer; and the third and fourth transducers continue to receive full-strength, in-phase “+1” signals. Thus, in high frequencies, the improved Bessel array performs substantially like a conventional Bessel array, reducing interference patterns in off-axis listening positions.  
         [0051]     This frequency-dependent voltage divider improvement can, of course, be applied to a Bessel square array, as well.  
       CONCLUSION  
       [0052]     The skilled reader will appreciate that the drawings are for illustrative purposes only, and are not scale models of optimized transducer systems.  
         [0053]     While the invention has been described with reference to embodiments in which it is configured as an audio speaker, in other embodiments it may be configured as a microphone, or other such apparatus which may be characterized as an electromagnetic transducer.  
         [0054]     The term “square” should not be interpreted to limit the invention to e.g. 5×5 Bessel arrays, but should be interpreted to also cover e.g. 5×7 or 9×7 Bessel arrays or what have you.  
         [0055]     Transducers need not be coupled to a common enclosure in order to function as a Bessel array. Indeed, low frequency performance will in many cases be improved if various ones of the transducers occupy separate enclosure volume(s) than other transducers. For example, it may generally not be ideal to have two “+1” transducers sharing an enclosure volume with a “−1” transducer, nor even with a “+½” transducer.  
         [0056]     When one component is said to be “adjacent” another component, it should not be interpreted to mean that there is absolutely nothing between the two components, only that they are in the order indicated. The various features illustrated in the figures may be combined in many ways, and should not be interpreted as though limited to the specific embodiments in which they were explained and shown. Those skilled in the art having the benefit of this disclosure will appreciate that many other variations from the foregoing description and drawings may be made within the scope of the present invention. Indeed, the invention is not limited to the details described above. Rather, it is the following claims including any amendments thereto that define the scope of the invention.