Patent Publication Number: US-10327068-B2

Title: Compression driver with side-firing compression chamber

Description:
TECHNICAL FIELD 
     Embodiments relate to a compression driver with a side-firing compression chamber, such as for use in a horn driver. 
     BACKGROUND 
     There are two major types of compression drivers, the first utilizing a dome diaphragm, and the other using an annular flexural diaphragm. The majority of modern annular diaphragms are made of polymer films. The advantage of annular diaphragms is the smaller radial dimensions of the moving part of the diaphragm compared to the dome diaphragms having the same diameter of the moving voice coil. The small radial clamping dimension of the annular diaphragm shifts the mechanical breakup resonances of the diaphragm to higher frequencies where they can be better mechanically damped, since the damping is more efficient at high frequencies in polymer films. Better damping is indicative of the smoother frequency response and lower nonlinear distortion generated by diaphragms&#39; breakups at high frequency. 
     In a compression driver, the diaphragm is loaded by a compression chamber, which is a thin layer of air separating the diaphragm from a phasing plug. The phasing plug receives an acoustical signal produced by the vibrating diaphragm and directs it to the exit of the compression driver. One of the primary features of a conventional compression driver is the difference between the larger effective area of the diaphragm and the smaller area of the compression chamber exit. The smaller area of the compression chamber exit increases its input impedance that loads the diaphragm. In theory, a compression driver reaches maximum efficiency when the mechanical output impedance of the vibrating diaphragm equals the loading impedance of the acoustical load. This assumption is approximate because, in reality, both impedances are different, complex, frequency-dependent functions. 
     A typical compression chamber has a single or multiple narrow exits expanding to the exit of the compression driver. Two types of linear distortion may occur in the compression chamber. One type is the attenuation of the high frequency sound pressure signal caused by the compliance of air trapped in the compression chamber. The volume of entrapped air is characterized by an acoustical compliance which is proportional to the volume of compression chamber. Acoustical compliance acts as a low-pass filter of the first order and it mitigates the high frequency signal. The second type of distortion is the irregularity of the high frequency sound pressure level (SPL) frequency response caused by air resonances in the compression chamber. The latter typically interact with high frequency mechanical resonances of the vibrating diaphragm. 
     SUMMARY 
     In one embodiment, a compression driver includes a magnet assembly and a waveguide mounted to the magnet assembly, the waveguide having a first side, an opposed second side, and a central aperture forming an exit of the compression driver. An annular diaphragm is disposed above the magnet assembly and adjacent the second side of the waveguide, the diaphragm having an external flat portion generally coplanar with an internal flat portion. A compression chamber is defined between the diaphragm and the second side of the waveguide, the second side of the waveguide having a final segment that tapers toward the central aperture, wherein part of the diaphragm is loaded by the compression chamber and part of the diaphragm radiates directly to the exit of the compression driver. 
     In another embodiment, a compression driver includes a magnet assembly including a back plate having a centrally disposed pole piece, and a hub portion mounted to the pole piece. A waveguide is mounted to the magnet assembly, the waveguide having a first side and an opposed second side, the waveguide having a central aperture generally aligned with the hub portion and forming an exit of the compression driver. An annular diaphragm is disposed above the magnet assembly and adjacent the second side of the waveguide, the diaphragm having a V-shaped section between an external flat portion and an internal flat portion. A compression chamber is defined between the diaphragm and the second side of the waveguide, the second side of the waveguide having an initial segment which is generally parallel to the external flat portion of the diaphragm and a final segment that tapers toward the central aperture, such that part of the diaphragm is loaded by the compression chamber and part of the diaphragm radiates directly to the exit of the compression driver. 
     In another embodiment, a compression driver includes a magnet assembly including a back plate having a centrally disposed pole piece, and a hub portion mounted to the pole piece. A waveguide is mounted to the magnet assembly, the waveguide having a first side and an opposed second side, the waveguide having a central aperture generally aligned with the hub portion and forming an exit of the compression driver. An annular diaphragm is disposed above the magnet assembly and adjacent the second side of the waveguide, the diaphragm having a V-shaped section between an external flat portion and an internal flat portion, the hub portion extending generally parallel to and over at least a portion of the internal flat portion of the diaphragm. A compression chamber is defined between the diaphragm and the hub portion and between the diaphragm and the second side of the waveguide, the second side of the waveguide having a final segment that tapers toward the central aperture, such that part of the diaphragm is loaded by the compression chamber and part of the diaphragm radiates directly to the exit of the compression driver. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  is a perspective view, partially cut away, of a compression driver having an open diaphragm configuration of the compression chamber according to an embodiment; 
         FIG. 1B  illustrates an air model of the configuration of  FIG. 1A ; 
         FIG. 1C  is a graph of the far-field relative SPL frequency response of the compression driver configuration of  FIG. 1A ; 
         FIG. 2A  is a perspective view, partially cut away, of a compression driver having a small side-firing compression chamber above the external flat surface of the diaphragm according to an embodiment; 
         FIG. 2B  illustrates an air model of the configuration of  FIG. 2A ; 
         FIG. 2C  is a graph of the relative SPL frequency response of the compression driver configuration of  FIG. 2A ; 
         FIG. 3A  is a perspective view, partially cut away, of a compression driver having an increased compression chamber with a side-firing configuration that starts “wrapping” of the profile of the diaphragm according to an embodiment; 
         FIG. 3B  illustrates an air model of the configuration of  FIG. 3B ; 
         FIG. 3C  is a graph of the relative SPL frequency response of the compression driver configuration of  FIG. 3A ; 
         FIG. 4A  is a perspective view, partially cut away, of a compression driver with a further increased compression chamber according to an embodiment; 
         FIG. 4B  illustrates an air model of the configuration of  FIG. 4A ; 
         FIG. 4C  is a graph of the relative SPL frequency response of the compression driver configuration of  FIG. 4A ; 
         FIG. 5A  is a perspective view, partially cut away, of a compression driver with a side-firing compression chamber that extends to the tip of the V-shape profile of the diaphragm according to an embodiment; 
         FIG. 5B  illustrates an air model of the configuration of  FIG. 5A ; 
         FIG. 5C  is a graph of the relative SPL response of the compression driver configuration of  FIG. 5A ; 
         FIG. 6A  is a perspective view, partially cut away, of a compression driver with a side-firing compression chamber that extends to the inner diameter edge of the V-shaped profile of the diaphragm according to an embodiment; 
         FIG. 6B  illustrates an air model of the configuration of  FIG. 6A ; 
         FIG. 6C  is a graph of the relative SPL response of the compression driver configuration of  FIG. 6A ; 
         FIG. 7A  is a perspective view, partially cut away, of a compression driver with a side-firing compression chamber that extends over the internal flat part of the diaphragm towards the center of the driver according to an embodiment; 
         FIG. 7B  illustrates an air model of the configuration of  FIG. 7A ; 
         FIG. 7C  is a graph of the relative SPL response of the compression driver configuration of  FIG. 7A ; 
         FIG. 8A  is a perspective view, partially cut away, of a compression driver with a side-firing compression chamber located above the internal flat side of the diaphragm according to an embodiment; 
         FIG. 8B  illustrates an air model of the configuration of  FIG. 8A ; 
         FIG. 8C  is a graph of the relative SPL frequency response of the compression driver configuration of  FIG. 8A ; 
         FIG. 9A  is a perspective view, partially cut away, of a compression driver with side-firing compression chambers positioned over the external and internal flat segments of the diaphragm according to an embodiment; 
         FIG. 9B  illustrates an air model of the configuration of  FIG. 9A ; 
         FIG. 9C  is a graph of the relative SPL frequency response of the compression driver configuration of  FIG. 9A ; 
         FIG. 10A  is a perspective view, partially cut away, of a compression driver with an annular ring slot exit from the compression chamber according to an embodiment; 
         FIG. 10B  illustrates an air model of the configuration of  FIG. 10A ; and 
         FIG. 10C  is a graph of the relative SPL frequency response of the compression driver configuration of  FIG. 10A . 
     
    
    
     DETAILED DESCRIPTION 
     As required, detailed embodiments of the present invention are disclosed herein; however, it is to be understood that the disclosed embodiments are merely exemplary of the invention that may be embodied in various and alternative forms. The figures are not necessarily to scale; some features may be exaggerated or minimized to show details of particular components. Therefore, specific structural and functional details disclosed herein are not to be interpreted as limiting, but merely as a representative basis for teaching one skilled in the art to variously employ the present invention. 
     Embodiments of the compression driver disclosed herein include a side-firing compression chamber, where the compression chamber exit may be positioned by the internal diameter of the chamber. Therefore, part of the diaphragm is loaded by the “side-firing” compression chamber and part of the diaphragm radiates directly to the exit of the driver. The overall signal is a superposition of the compression chamber part and the direct-radiating part. This significantly simplifies the configuration of the compression driver and radial resonances are not excited in the audio frequency range. In addition, the simplicity in configuration provides lower production cost. 
     The acoustical behavior of a “side-firing” compression chamber open on its internal diameter is different from that of an annular compression chamber with hard walls on its internal and external diameters. Specifically, the side-firing compression chamber does not have a hard wall on its internal diameter, and it is loaded by the corresponding acoustical impedance of the waveguide and horn connected to it. Embodiments disclosed herein do not exhibit resonance behavior due to the different acoustical nature of the chamber and different boundary conditions. The compression driver maximizes the high-frequency SPL output as well as smoothness and simple equalizability of the SPL frequency response. 
     With reference first to  FIGS. 1A and 1B , an embodiment of a compression driver  10  is illustrated, where the compression driver  10  can be used in a horn driver with an attached horn (not shown). The compression driver  10  is generally disposed about a central axis  12 . The compression driver  10  may include a magnet assembly  14  which may comprise an annular permanent magnet  16  disposed between an annular top plate  18  and a back plate  20  that includes a centrally disposed cylindrical or annular pole piece  22 . The magnet assembly  14  provides a permanent magnetic field in the gap  24  between the pole piece  22  and an inside surface of the annular top plate  18  for electrodynamic coupling with a voice coil  26 . The voice coil  26  is disposed in the magnetic gap  24  and produces the movement of the flexible portion of a diaphragm  28 . 
     In the embodiments depicted herein, the diaphragm  28  is configured as an annular ring that is disposed coaxially with the central axis  12  above the magnet assembly  14 . The diaphragm  28  may include a profiled section  30  such as a V-shaped section between an external generally flat portion  32  and an internal generally flat portion  34 , wherein the external flat portion  32  and the internal flat portion  34  may be generally coplanar. In other implementations, the diaphragm  28  may have other suitable configurations. 
     With continuing reference to  FIGS. 1A and 1B , the compression driver  10  also includes a hub portion  36  which is coaxially disposed about the central axis  12 . The hub portion  36  may also be referred to as a bullet. The hub portion  36  has a first end  38  disposed proximate to the pole piece  22  and a second end  40  disposed at a distance from the pole piece  22  along the central axis  12 . An outer surface  42  of the hub portion  36  may taper in the direction along the central axis  12  from the first end  38  to the second end  40 , such that the radius of the cross-section of the hub portion  36  relative to the central axis  12  decreases in this direction. 
     The hub portion  36  may include a downwardly depending mounting member  44  which may have any configuration suitable for coupling the hub portion  36  to the rear section of the compression driver  10 . In one embodiment, the mounting member  44  is provided in the form of a cylinder that is arranged to be press fit into a central bore  46  formed in the pole piece  22 . 
     In the compression driver  10  disclosed herein, the typical front adapter and phasing plug are reduced to a single-piece, shallow waveguide  48  that provides compression, but only to a part of the diaphragm  28 . The waveguide  48  is attached to the top plate  18 , wherein a central aperture  50  of the waveguide  48  serves as a small diameter exit of the compression driver  10 . The aperture  50  may be circular as shown, or alternatively may have another shape, such as elliptical or rectangular. As assembled, the central aperture  50  of the waveguide  48  is generally aligned with the hub portion  36 . In one embodiment, the central aperture  50  is configured to substantially match the size and shape configuration of the horn inlet (not shown). 
     The small exit diameter of the compression driver  10  provides excellent control of the directivity at high frequencies up to 20 kHz. In one embodiment, the diameter of the central aperture  50  of the waveguide  48  is about 0.6 in., which may be smaller than the diameter of the diaphragm  28  (1.4 in.) and even smaller than the diameter of the voice coil  26  (1.0 in.). In the embodiments depicted, the height of the hub portion  36  does not extend above a height of the waveguide  48 . 
     The waveguide  48  includes a generally planar first side  52 , facing the horn (not shown), and an opposing second side  54  generally facing the diaphragm  28 . A compression chamber  56  is defined in a space between the diaphragm  28  and the second side  54  of the waveguide  48  (see  FIGS. 2-10 ). The actuation of the diaphragm  28  generates high sound-pressure acoustical signals within the compression chamber  56 , and the signals travel towards the center of the compression driver  10 , immediately adjacent to the central aperture  50  of the waveguide  48 . From the aperture  50 , the sound waves enter and radiate through the attached horn (not shown) and propagate into the ambient environment. 
       FIGS. 1-10  show different configurations of the compression driver  10  beginning from an open diaphragm  28  that radiates towards the central aperture  50  or exit of the compression driver  10  without a compression chamber ( FIG. 1 ), to the classical design having a single narrow annular slot positioned at the radius of the first mode&#39;s null ( FIG. 10 ). All ten figures show a cut away view of the compression driver  10 , an “air” model (i.e. the acoustical part from the diaphragm  28  to the driver exit  50 ), and the relative SPL frequency response obtained by acoustical numerical modeling. The BEA-based numerical acoustic simulation shown included a horn model, where the horn is characterized by an extremely smooth acoustical input impedance and transfer function on and off axis, and where the length of the horn is 178 mm and the mouth diameter is 280 mm. The modeling was carried out for a constant acceleration of a diaphragm considered to be an infinitely hard annular shell (no breakup modes), having the shape of the real diaphragm and oscillating pistonically. The real annular flexural diaphragm is clamped by its internal and external radii and, strictly speaking, it does not move pistonically even at low frequencies. 
       FIG. 1A  depicts an embodiment of a compression driver  10  with an open diaphragm  28  radiating directly towards the exit  50  of the driver  10 . In this configuration, the second side  54  of the waveguide  48  does not follow a contour of the external flat portion  32  of the diaphragm  28 , and instead the second side  54  tapers from an outer edge  58  of the external flat portion  32  toward the driver exit  50 . For example, an angle of the second side  54  may be similar to an angle of the outer surface  42  of the hub portion  36 .  FIG. 1B  illustrates an air model of this configuration, where the bold line is the profile of the diaphragm  28 .  FIG. 1C  is a graph of the far-field relative SPL frequency response of the compression driver  10  of  FIG. 1A . As shown in  FIG. 1C , the SPL response rolls down gradually from 1 kHz to 20 kHz. The overall decrease of the response between 3 kHz (end of the flat part of the response) to 20 kHz is 20 dB SPL. The response is smooth in general but it has comparatively low high-frequency output from 10 kHz to 20 kHz. 
       FIG. 2A  shows an embodiment of the compression driver  10  with a small side-firing compression chamber  56  positioned above the external flat portion  32  of the diaphragm  28 . In this embodiment, the second side  54  of the waveguide  48  has an initial segment  60  which is generally parallel to the external flat portion  32  of the diaphragm  28 , and may extend over at least a portion of the V-shaped section  30  of the diaphragm. The second side  54  of the waveguide  48  further includes a final segment  62  that tapers toward the driver exit  50 . For example, an angle of the second side  54  may be similar to an angle of the outer surface  42  of the hub portion  36 .  FIG. 2B  illustrates an air model of this configuration, and  FIG. 2C  is a graph of the relative SPL frequency response of the compression driver  10  of  FIG. 2A . As shown in  FIG. 2C , the SPL frequency response also gradually and smoothly rolls down from 3 kHz to 20 kHz, but its SPL output is 5 dB higher compared to the embodiment of  FIG. 1A . The overall output is a superposition of the SPL generated by the side-firing compression chamber  56  and the part of the diaphragm  28  radiating without compression. 
       FIG. 3A  is a perspective view, partially cut away, of an embodiment of the compression driver  10  with an increased compression chamber  56  that follows a contour of at least a portion of the V-shaped section  30  of the diaphragm  28 . In this embodiment, the second side  54  of the waveguide  48  has an initial segment  60  which is generally parallel to the external flat portion  32  of the diaphragm  28 , an intermediate segment  64  that generally follows the contour of at least a portion of the V-shaped section  30  of the diaphragm  28 , and a final segment  62  that tapers toward the driver exit  50 , for example, at an angle which may be similar to an angle of the outer surface  42  of the hub portion  36 .  FIG. 3B  illustrates an air model of this configuration, and  FIG. 3C  is a graph of the relative SPL frequency response of the compression driver  10  of  FIG. 3A . 
       FIG. 4A  is a perspective view, partially cut away, of an embodiment of the compression driver  10  with a compression chamber  56  which follows a contour of a larger portion the V-shaped section  30  of the diaphragm  28  as compared to  FIG. 3A . In this embodiment, the second side  54  of the waveguide  48  again has an initial segment  60  which is generally parallel to the external flat portion  32  of the diaphragm  28 , an intermediate segment  64  that generally follows the contour of at least a portion of the V-shaped section  30  of the diaphragm  28 , and a final segment  62  that tapers toward the driver exit  50 , for example, at an angle which may be similar to an angle of the outer surface  42  of the hub portion  36 .  FIG. 4B  illustrates an air model of this configuration, and  FIG. 4C  is a graph of the relative SPL frequency response of the compression driver  10  of  FIG. 4A . 
       FIG. 5A  depicts an embodiment of the compression driver  10  with a side-firing compression chamber  56  that extends to a tip  66  of the V-shaped section  30  of the diaphragm  28 . In this embodiment, the second side  54  of the waveguide  48  has an initial segment  60  which is generally parallel to the external flat portion  32  of the diaphragm  28 , an intermediate segment  64  that generally follows the contour of the V-shaped section  30  of the diaphragm  28  to its tip  66 , and a final segment  62  that tapers toward the driver exit  50 , for example, at an angle which may be similar to an angle of the outer surface  42  of the hub portion  36 .  FIG. 5B  illustrates an air model of this configuration, and  FIG. 5C  is a graph of the relative SPL response of the compression driver  10  of  FIG. 5A . As shown in  FIG. 5C , the frequency response starts rolling off above 13 kHz. 
       FIG. 6A  is a perspective view, partially cut away, of an embodiment of the compression driver  10  with a side-firing compression chamber  56  that extends along substantially the entire V-shaped section  30  of the diaphragm  28 , terminating at an inner edge  68  of the internal flat portion  34  of the diaphragm  28 . In this embodiment, the second side  54  of the waveguide  48  has an initial segment  60  which is generally parallel to the external flat portion  32  of the diaphragm  28 , an intermediate segment  64  that generally follows the contour of the V-shaped section  30  of the diaphragm  28  to the inner edge  68  of the internal flat portion  34  of the diaphragm  28 , and a final segment  62  that tapers toward the driver exit  50 .  FIG. 6B  illustrates an air model of this configuration, and  FIG. 6C  is a graph of the relative SPL response of the compression driver configuration of  FIG. 6A . As shown in  FIG. 6C , the high frequency roll-off continues increasing. 
     Further extension of the side-firing compression chamber  56  towards the center of the driver  10  results in the onset of the first radial mode in the compression chamber  56 .  FIG. 7A  depicts an embodiment of a compression driver  10  with a side-firing compression chamber  56  which further extends towards the center of the driver  10 , over the internal flat portion  34  of the diaphragm  28 . In this embodiment, the second side  54  of the waveguide  48  has an initial segment  60  which is generally parallel to the external flat portion  32  of the diaphragm  28 , an intermediate segment  64  that generally follows the contour of the V-shaped section  30  of the diaphragm  28 , and a final segment  62  that is generally parallel to and extends over at least a portion of the internal flat portion  34  of the diaphragm.  FIG. 7B  illustrates an air model of this configuration, and  FIG. 7C  is a graph of the relative SPL response of the compression driver  10  of  FIG. 7A . This configuration and its acoustical behavior are similar to a compression chamber that has hard-wall boundary conditions on both internal and external radii of the chamber and with an exit that is positioned incorrectly and does not block the first radial mode (A. Voishvillo, “Compression Drivers&#39; Phasing Plugs—Theory and Practice”, presented at the 141 th  AES Convention, 2016, Los Angeles, preprint 9618). 
       FIG. 8A  shows an embodiment of a compression driver  10  with a side-firing compression chamber  56  located above the internal flat portion  34  of the diaphragm  28  and with an open external part. In this embodiment, the compression chamber  56  may be created by the hub portion  36  extending generally parallel to and over at least a portion of the internal flat portion  34  of the diaphragm  28 . The second side  54  of the waveguide  48  does not follow a contour of the external flat portion  32  of the V-shaped section  30  of the diaphragm  28 , and instead tapers from the outer edge  58  of the external flat portion  32  toward the driver exit  50 .  FIG. 8B  illustrates an air model of this configuration, and  FIG. 8C  is a graph of the relative SPL frequency response of the compression driver  10  of  FIG. 8A . As shown in  FIG. 8C , the SPL frequency response has a slight bump at 3 kHz and then drops by 22 dB at 20 kHz. 
       FIG. 9A  is a perspective view, partially cut away, of an embodiment of a compression driver  10  with side-firing compression chambers  56  positioned over the external and internal flat portions  32 ,  34  of the diaphragm  28 . In this embodiment, one compression chamber  56  may be created by the hub portion  36  extending generally parallel to and over at least a portion of the internal flat portion  34  of the diaphragm  28 . Another compression chamber  56  may be created by the second side  54  of the waveguide  48  having an initial segment  60  extending generally parallel to and over at least a portion of the external flat portion  32  of the diaphragm  28 . The second side  54  of the waveguide  48  may further include an intermediate segment  64  that generally follows the contour of at least a portion of the V-shaped section  30  of the diaphragm  28 , and a final segment  62  that tapers toward the driver exit  50 , for example, at an angle which may be similar to an angle of the outer surface  42  of the hub portion  36 .  FIG. 9B  illustrates an air model of this configuration, and  FIG. 9C  is a graph of the relative SPL frequency response of the compression driver  10  of  FIG. 9A . As shown in  FIG. 9C , the high-frequency SPL frequency response is higher than that of the previous three configurations, but it is not smooth and has a 7 dB spike at 16.7 kHz followed by a steep drop. 
     The final embodiment shown in  FIG. 10A  is a compression driver  10  with an annular ring slot exit  70  from the compression chambers  56  to suppress the first radial mode. In this embodiment, one compression chamber  56  may be created by the hub portion  36  extending generally parallel to and over the internal flat portion  34  and at least a portion of the V-shaped section  30  of the diaphragm  28 . Another compression chamber  56  may be created by the second side  54  of the waveguide  48  having an initial segment  60  which is generally parallel to the external flat portion  32  of the diaphragm  28 , an intermediate segment  64  that generally follows the contour of at least a portion of the V-shaped section  30  of the diaphragm  28 , and a final segment  62  that tapers toward the driver exit  50 .  FIG. 10B  illustrates an air model of this configuration, and  FIG. 10C  is a graph of the relative SPL frequency response of the compression driver  10  of  FIG. 10A . As shown in  FIG. 10C , the SPL response is comparatively flat from 2 kHz to 8 kHz with a 2 dB bump at 7 kHz, a roll-off to 14 kHz, a sharp spike at 17 kHz, and an abrupt drop above 17 kHz. The first radial mode in the compression chamber  56  is blocked by the annular slot exit  70  positioned at the radius of the mode&#39;s null. The frequency of the first mode is 13.84 kHz, and the higher-order modes are above the audio frequency range (26.79 kHz, 39.89 kHz, etc.). 
     The acoustical analysis of traditional and side-firing annular compression chambers is described below. The acoustical field in an annular compression chamber modeled by a flat annular ring is characterized by radial resonance modes (A. Voishvillo, “Compression Drivers&#39; Phasing Plugs—Theory and Practice”, presented at the 141 th  AES Convention, 2016, Los Angeles, preprint 9618). In general, an acoustical field in the chamber results from the solution of the zero-order Bessel equation with Neumann boundary conditions (zero velocity at the internal and external radii). 
     
       
         
           
             
               
                 
                   
                     
                       
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     where R 1  and R 2  are the internal and external radii of the compression chamber 
               k   =       ω   c     -     wave   ⁢           ⁢   number         ,         
c is the speed of sound.
 
     Since the equation (1) is the zero-order Bessel equation, its solutions exist in the following forms: 
     At k 0 =0 the solution exists in the form P 0 (r)=const 
     At k i ≠0 the solution exists in the form:
 
 P ( k   i   r )= AJ   0 ( k   i   r )+ BY   0 ( k   i   r ), i= 1,2,3  (3)
 
     where A and B are constants not depending on radius r, but depending on wave numbers k i , J 0 (k i r) is a Bessel function of the first kind, zeroth order, and Y 0 (k i r) is a Bessel function of the second kind, zeroth order. 
     Equation (4) for the search of the radial modes&#39; wave numbers k i  values and the corresponding frequencies of the modes in the chamber f i =k i c/2π are derived from the equation (1) and the boundary conditions (5).
 
 Y   1 ( k   i   R   1 ) J   1 ( k   i   R   2 )+ Y   1 ( k   i   R   2 ) J   1 ( k   i   R   1 )=0  (4)
 
 AJ   1 ( kr )=− BY   1 ( kr ) at  r=R   1  and  r=R   2   (5)
 
     i=1, 2, 3 . . . ∞ 
     The equation (4) is solved numerically. The roots of (4) are the wave numbers k i  corresponding to the i-order radial resonances in the annular compression chamber. 
     Distributions of the sound pressure across the chamber at the found frequencies of radial modes are obtained from a numerical solution of equation (6):
 
 F   i ( k   i )= C   i ( Y   1 ( k   i   R   2 ) J   0 ( k   i   r )− J   1 ( k   i   R   2 ) Y   0 ( k   i   r ))  (6)
 
     where C i  are constants not depending on r. 
     For the particular chamber shown in  FIG. 10B  the frequencies of the first three modes are: 
     f 1 =13.8 kHz 
     f 2 =26.8 kHz 
     f 3 =39.89 kHz 
     Frequency of the first mode is within the audio range whereas the frequencies of the second and third mode are above frequency range and do not present interest. By equating (6) to zero, and by solving the equation (6) numerically, radius R 0  corresponding to the zero value of the first mode is found. If the assumption of the diaphragm&#39;s pistonic movement is valid, then by positioning the exit slot at the radius R 0 , the first radial mode is blocked (but is still excited in the compression chamber!). Therefore, the first mode does not produce a severe notch on the SPL frequency response at the frequency 13.8 kHz— FIG. 10C . 
     Acoustical behavior of the system consisting of the side-firing annular compression chamber and part of the diaphragm radiating directly into the acoustical load differs from that of traditional annular compression chamber and an annular narrow slot exit. The direct-radiating part of the diaphragm is loaded by the acoustical path to the driver&#39;s exit (short “waveguide”) and by the output impedance of the side-firing compression chamber. The chamber is loaded by the acoustical path that connects chamber&#39;s exit to the exit of the driver. Since the acoustical output impedance of the chamber is significantly higher than the impedance of acoustical path to the exit of the driver, the influence of the chamber&#39;s output impedance on radiation of the open part of the diaphragm may be ignored. 
     The frequencies of the resonance modes in the chamber are found through solution of Helmholtz equation in cylindrical coordinates with the corresponding boundary conditions (sound pressure gradient equals to zero at r=R 1  and r=R 2 )—see (1) and (2). In case of the side-firing chamber, the situation is different. The boundary condition on the external radius R 2  corresponds to the condition 
                   ∂     P   ⁡     (   r   )           ∂   r       =   0     ,     r   =     R   2       ,         
whereas the boundary condition at the exit R 1  is found from the following expression (7):
 
     
       
         
           
             
               
                 
                   
                     
                       ∂ 
                       P 
                     
                     
                       ∂ 
                       r 
                     
                   
                   = 
                   
                     
                       - 
                       j 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     ω 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     ρ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       P 
                       
                         
                           Z 
                           l 
                         
                         ⁡ 
                         
                           ( 
                           
                             j 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             ω 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     A side-firing compression chamber with an exit along its internal radius R 1  does not have radial resonances at high frequencies if its acoustical loading can be approximated by a non-reactive acoustical impedance ρc/S t  (where ρ is air density and c is the speed of sound, and S t  is the area of the chamber&#39;s exit). A regular annular compression chamber has hard walls at external and internal radii that cause reflections of radially propagating sound waves and generate corresponding standing waves (resonances) that may adversely affect high-frequency SPL response. In a side-firing compression chamber, reflection from the exit may not occur, but acoustical signals excited at the different radial distances of the chamber come to the exit with different time delays and phases. If the radial dimension of the chamber is comparable with the wavelength of the radiated acoustical signal, a “combing effect” or “interference” may occur, and it would generate notches on the SPL frequency response. However, with an optimal radial dimension of the side-firing compression chamber, the adverse “interference” can be avoided. 
     The aforementioned effect presumes pistonic movement of the diaphragm. In reality, at high frequencies, the diaphragm may not vibrate as a piston, and its movement would be characterized by partial vibrations, i.e. mechanical resonances. A negative effect produced by the diaphragm&#39;s mechanical resonances is potential irregularity of the SPL response at high frequencies. Another negative aspect of the mechanical resonances is their interaction with acoustical resonances in the compression chamber that may cause inaccuracy of the driver performance&#39;s prediction based on the acoustical model and the assumption of the diaphragm&#39;s pistonic movement throughout the audio frequency range. A positive effect of the mechanical resonances is that the elevated level of the overall displacement, velocity, and acceleration at resonances produce higher SPL output. Such a diaphragm property is actually intentional and is a result of the mechanical structural FEA numerical optimization intended to increase the energy of the diaphragm vibration at the high frequency range. 
     In the above embodiments and analysis, in one example, dimensions of the compression chamber dimensions may be as follows: internal radius R 1  is 6.2 mm, external radius R 2  18 mm, radius of the V-shaped apex is 12.5 mm, depth of the diaphragm (distance from the apex to the flat part is 1.9 mm, internal flat part radii are 6.2 mm and 8.8 mm, external flat part radii are 15.6 mm and 18 mm, radius of the driver&#39;s acoustical exit is 7.6 mm. In addition, for the above analysis, the driver is loaded by a reference axisymmetric horn having 140 mm mouth radius and 190 mm length, and the acoustical FEA simulations correspond to 1 meter from the mouth of the horn. 
     The new topology is scalable for different diameters of the voice coil, and it provides significant simplification of the configuration of the compression driver and correspondingly lower production cost without sacrificing the driver&#39;s performance. The SPL frequency response is characterized by smoothness and easy equalizability, which implies the use of minimal components in a crossover network to match the driver&#39;s response with the response of its corresponding woofer. The compression driver can be used in cost-effective studio monitors, CBT arrays, karaoke systems, various other types of arrays, and in automotive audio systems. 
     While exemplary embodiments are described above, it is not intended that these embodiments describe all possible forms of the invention. Rather, the words used in the specification are words of description rather than limitation, and it is understood that various changes may be made without departing from the spirit and scope of the invention. Additionally, the features of various implementing embodiments may be combined to form further embodiments of the invention.