Abstract:
A surround for a diaphragm includes at least one rib section oriented to be extended during excursions of the diaphragm. The surround includes at least one membrane section supported by one or more rib sections contributing to a compliance characteristic different from the contribution of the one or more rib sections.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
       [0001]    This application is a continuation-in-part of application Ser. No. 11/756,119, filed on May 31, 2007, entitled diaphragm surround. 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    This invention relates to diaphragm surrounding. 
         [0003]    In traditional passive radiators and acoustic drivers, the surround that supports the diaphragm has a partially circular or elliptical cross-section and is made of a high durometer material to provide an approximately linear force-deflection response. Geometric non linearities at high axial excursions in some surrounds can cause dynamic instabilities, parametric excitation of sub-harmonic rocking modes, and buckling that affects the acoustic performance. 
       BRIEF SUMMARY OF THE INVENTION 
       [0004]    According to the invention a surround for a diaphragm includes at least one rib section oriented to be extended during excursions of the diaphragm. There is at least one membrane section supported by the one or more rib sections with the one or more rib sections contributing to a compliance characteristic of the surround differently from the one or more membrane sections. At least one membrane section may be thinner along the direction perpendicular to the surface of the diaphragm than a rib section. The compliance characteristic may have an axial stiffness and/or a rocking stiffness. A membrane section may have concave and/or convex shapes. A rib section may have an I-bean configuration in a cross-sectional view taken along a radial direction. A rib section may have a radial dimension that is larger than a circumferential dimension. The rib section may function as a cap that seals a concave membrane section on one side and a convex membrane section on the other. There may be four membrane sections. The membrane sections may comprise two concave and two convex membrane sections. The membrane sections may have a half-row structure. The diaphragm may have an outer flange extending radially and/or an inner flange that extends radially. The outer flange may extend in a direction that is perpendicular to the surface of the diaphragm and/or the inner flange. The outer periphery of the diaphragm may be shaped to match the inner flange and the inner periphery of the attachment frame maybe shaped to match the outer flange. The diaphragm, the apparatus and the attachment frame may be assembled by gluing or chemically bonding without a separate adhesive through insert molding, the inner flange onto the edge of the diaphragm and the outer flange onto the attachment frame. The rib sections may contribute more to an axial stiffness than do the membrane sections. The concave and convex membrane sections may be arranged in a cyclic symmetric manner to increase the rocking stiffness of the apparatus. 
         [0005]    Numerous other features, objects and advantages will become apparent from the following detailed description when read in connection with the accompanying drawing in which: 
     
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING 
         [0006]      FIG. 1  is a perspective view of a passive radiator; 
           [0007]      FIGS. 2 ,  4 ,  6 ,  8 ,  10 ,  12 ,  14 ,  16 , and  18  are perspective views of surrounds; 
           [0008]      FIGS. 3 ,  5 ,  7 ,  9 ,  11 ,  13 ,  15 ,  17 ,  19 , and  20  are a perspective views of portions of surrounds; 
           [0009]      FIG. 21A  is a perspective view of a speaker; 
           [0010]      FIG. 21B  shows a schematic cross-section of a vibrating diaphragm; 
           [0011]      FIG. 21C  shows a schematic cross-section of a rocking diaphragm; 
           [0012]      FIGS. 22A ,  24 A,  25 A,  26 A, and  27 A are top views of a diaphragm and surround assemblies; 
           [0013]      FIGS. 22B and 22C ;  24 B and  24 C;  25 B and  25 C;  26 B and  26 C; and  27 B and  27 C are side sectional and front sectional views of diaphragm and surround assemblies; 
           [0014]      FIG. 23A  is a perspective view of a diaphragm; 
           [0015]      FIG. 23B  is a perspective view of a surround; 
           [0016]      FIGS. 23C and 24D  are perspective views of a diaphragm and surround assemblies; 
           [0017]      FIG. 27D  is an enlarged side cross-sectional view of the diaphragm and surround assembly of  FIG. 27C ; 
           [0018]      FIGS. 28 ,  29 , and  30  show curves of restoring axial force as a function of excursion; and  FIGS. 31A ,  31 B and  31 C show plan, front sectional and end sectional views, respectively, of a surround of racetrack shape, 
       
    
    
     DETAILED DESCRIPTION  
       [0019]    An active or passive acoustic source (e.g., a driver or a passive radiator) typically includes a diaphragm that reciprocates back and forth to produce acoustic waves. This diaphragm (which may be, e.g. a plate, cone, cup or dome) is usually attached to and supported by a non-moving structure through a resilient surround. 
         [0020]    An example of a diaphragm and surround assembly  20  that achieves good performance ( FIG. 1 ) includes a surround  26  that connects a diaphragm  22  to an outer attachment ring  36 . In this example, the diaphragm  22  has a top surface  21  that is flat and made of a stiff material such as plastic (e.g., polycarbonate or Acrylonitrile Butadiene Styrene) or metal (e.g., steel or aluminum). In some examples, the top surface  21  of the diaphragm  22  may be convex or concave to make the diaphragm stiffer. 
         [0021]    The diaphragm  22  is may be driven at its center  31  to produce acoustic waves by a source such as an electromagnetically driven acoustic driver (not shown). The acoustic waves are produced when the diaphragm vibrates back and forth in an intended direction  33  of travel that is substantially perpendicular to a plane  35  in which the diaphragm lies. This vibration causes additional acoustic waves to be created and propagated. A group of holes  24  in diaphragm  22  is used to secure a mass (not shown) which may be added to the diaphragm to tune to a desired resonant frequency of vibration. 
         [0022]    In a particular example, the diaphragm  22  has a diameter of about 132 mm. The surround may be made of a solid or foam elastomer, and in this example is a thermoset soft silicone elastomer such as Mold Max 27T sold by Smooth-On. Inc., 2000 Saint John Street, Easton, Pa. 18042. Mold Max 27T is a tin-cured silicone rubber compound. Further details on Mold Max 27T can be found at www.smooth-on.com. The thermoset elastomer used to make surround  26  preferably has (i) a Shore A durometer of between about 5 to about 70, for example, about 27; (ii) a 100% elongation static modulus of between about 0.05 MPa to about 10 MPa, and for example, about 0.6 MPa; (iii) an elongation at break above about 100%, for example, about 400%; and (iv) a static stiffness of between about 0.05 newtons/mm to about 50 newtons/mm when the diaphragm is at its neutral travel position, for example, about 3 newtons/mm. However, these properties may have different values depending on the diaphragm diameter, passive radiator system tuning frequency, and air volume in the speaker box. 
         [0023]    Generally, as the size of the surround gets smaller, a lower durometer material can be used. The use of a soft durometer material gives better design control for low in vacuo resonant frequencies of the diaphragm to keep this resonant frequency away from the tuned frequency occurring when the moving mass of the diaphragm and surround assembly resonate against the spring stiffness of the air in the speaker box and the surround stiffness. 
         [0024]    An attachment ring  28  is secured to and supports surround  26  along an outer annular periphery  27  of the surround. The attachment ring  28  in this example is made of the same material used for diaphragm  22 . The attachment ring  28  and the diaphragm  22  can be made of different materials. Ring  28  includes a series of large holes  30  along its circumference that are used with fasteners (not shown) to attach the passive radiator to another structure (discussed below).The arrangement of the attachment ring  28 , the surround  26 , and the diaphragm  22  provides an appropriate linear force-deflection response of the diaphragm, which can result in low harmonic distortions and good dynamic performance. 
         [0025]    Turning now to  FIGS. 2 and 3 , in some examples, the surround  26  includes generally flat (planar) membrane sections  40  which have a thickness T 1  of between about 0.1 mm to about 5 mm ( FIG. 3 ). In this case, thickness T 1  is measured in a direction normal to opposing top and bottom surfaces  40   a  and  40   b  of membrane section  40 . In this particular example, each membrane section is about 1 mm thick. 
         [0026]    Each membrane section  40  is supported by a support section  42 . In this example, the support section includes a pair of straight radial ribs  44 ,  46  (rib sections) as well as a circumferential rib  48 , which all support membrane section  40 . All three of these ribs have a thickness T 2  of between about 0.2 mm to about 25 mm. The ribs  44 ,  46  and  48  each have a surface  47  (a top surface) that is flat and perpendicular to an intended direction of travel  802  of the diaphragm  22 . A bottom surface  43  of ribs  44 ,  46  and  48  is also flat. Thickness T 2  is measured in a direction normal to opposing top and bottom surfaces  47  and  43  of ribs  44 ,  46  and  48 . An envelope that closely encompasses the surround  26  will include a substantially flat surface that is normal to an intended direction of travel of the diaphragm and coplanar with surface  47 . In this example, the thickness T 2  is about 8.5 mm, substantially thicker than the membrane sections. The ribs of the support section symmetrically extend above and below the membrane section. The membrane and ribs are made of the same material. 
         [0027]    The passive radiator  20  can be made by forming the diaphragm  22  and the attachment ring  28  in separate injection molding operations. The diaphragm  22  and attachment ring  28  are then placed in an insert mold and a thermoplastic or thermoset elastomer is injected into the mold. The elastomer is allowed to cure, thus forming surround  26 . The thermoset elastomer covers the surfaces along the outer periphery of the diaphragm  22  and along the inner periphery of the attachment ring  28  which are adjacent the surround  26 . This assists in securing (joining) the surround  26  to the diaphragm  22  and the attachment ring  28 . The elastomer also preferably covers at least part of surfaces  32  and  36  (on both sides of the passive radiator  20 , thereby helping to secure surround  26  to the diaphragm  22  and attachment ring  28 . A series of holes  34  and  38  provide paths for molten elastomer to be injected to form the surround  26 . 
         [0028]    In operation, as the diaphragm  2  starts moving away from a home position (shown in  FIG. 1 ), the rib sections  44 ,  46  and  58  start to elastically elongate along their length (in a radial direction in this example). The rib sections  44 ,  46  and  58  will continue to elastically elongate as the diaphragm  22  moves in an intended direction (i.e. perpendicular to a plane in which the passive radiator lies) further away from the home position. The radial ribs return to their original length when the diaphragm  22  returns to its home position. A restoring force which returns the diaphragm to the home position is attributable more to deformation of the radial rib sections  44  and  46  than to deformation of the membrane section  40 . The combined volume of all the radial ribs and circumferential rib  48  for the whole surround is about 27.5 cm 3 . The combined volume of all the membrane sections for the whole surround is about 5.4 cm 3 . This yields a volume ratio for this example of ribs to membrane sections of about 5.1. Generally speaking, as the surround gets smaller in the radial and/or axial directions this ratio gets smaller. In some examples, this ratio is at least about 0.3. 
         [0029]    The circumferential rib  48  extends circumferentially. Each radial rib extends away from the diaphragm along the rib&#39;s entire length in a generally radial direction (a direction perpendicular to an intended direction of travel of the diaphragm  22  and also perpendicular to the circumferential rib). Although the ribs  44 ,  46  are shown extending away at a 90° angle to the diaphragm  22 . ribs  44 ,  46  can be arranged to extend at an angle less than 90° (e.g., at an angle of 60° which would result in triangular or trapezoidal membrane sections. Radial ribs  44 ,  46  are in an outer group of radial ribs. Membrane section  40  has a pair of edges  51  (only one edge is visible in  FIG. 3 ) which extend in a radial direction and which are supported along their entire length by ribs  44  and  46 . The interface between membrane section  40  and another element (e.g. rib  46 ) can be filleted. Membrane section  40  and support section  42  are connected to each other with no gap, so no air can leak past the interface between the membrane section and support section. 
         [0030]    There are a large number of membrane sections and support sections in surround  26  arranged in two rings  52 ,  54  ( FIG. 2 ). A radial rib  58  belongs to an inner group of radial ribs. The inner group of radial ribs (including rib  58 ) is offset radially from the outer group of radial ribs (which includes ribs  44 ,  46 ). The outer group of ribs is further from center  24  than the inner group of ribs. The inner group of radial ribs is also offset circumferentially from the outer group of radial ribs. The outer group of ribs is shifted in a circumferential direction from the inner group of ribs so that each inner rib is equidistant from its two closest outer ribs and vice versa in this example. The inner group of radial ribs are joined to the outer group of radial ribs by circumferential rib  48 . The inner group of radial ribs (including rib  58 ) are joined to each other and connected to the diaphragm  22  by elastomer  56 . The outer group of radial ribs (including ribs  44 ,  46 ) are joined to each other and connected to the attachment ring  28  by elastomer  50 . 
         [0031]    Referring now to  FIGS. 4 and 5 , in some examples, membrane sections  60 ,  62   are curved. The membrane sections alternate in a circumferential direction between concave (membrane  60 ) and convex (membrane  62 ). The membrane sections in the outer ring are also curved. 
         [0032]    Turning to  FIGS. 6 and 7 , in some examples, each radial rib in the inner group (including rib  58 ) is aligned circumferentially with a respective radial rib in the outer group (including a rib  64 ). 
         [0033]    Referring to  FIG. 7 , support section  42 , including the radial and circumferential ribs, is symmetric about an imaginary plane  66  (this is also true for at least some of the other examples described here). Portion  68   a  lies below plane  66  and portion  68   b  lies above the plane. Diaphragm  22  ( FIG. 1 ) preferably lies in the plane  66 . Additionally, for any of the examples with flat membrane sections (e.g.  FIGS. 2 ,  3 ,  6  and  7 ) imaginary plane  66  bisects the membrane section. Assuming that the imaginary plane  66  aligns with the point of attachment of the surround to the diaphragm and the attachment ring, the symmetry yields similar responses for the both positive and negative travels of the diaphragm from its neutral rest position. 
         [0034]    Referring to  FIGS. 8 and 9 , membrane sections  70 ,  72  are curved instead of being flat. The membrane sections alternate in a circumferential direction from being concave shaped (membrane  70 ) to convex shaped (membrane  72 ). The membrane sections also alternate in a radial direction from being concave shaped (membrane  70 ) to convex shaped (membrane  74 ). 
         [0035]    Referring now to  FIGS. 10 and 11 , (a) radial ribs  44 ,  46  and  58  can be replaced by shortened (in the radial direction) radial ribs  78 ,  80 ,  76  and (b) circumferential rib  48  can be replaced by a zigzagging rib  82  having a multiplicity of short rib sections  82   a,    82   b.  Each membrane section is then pentagonal. 
         [0036]    With reference to  FIGS. 12 and 13 , a further example of a surround is shown that is similar to the example shown in  FIGS. 10 and 11  except that membrane sections  84 ,  86  are curved instead of being flat. The membrane sections alternate in a circumferential direction from being concave shaped (membrane  84 ) to convex shaped (membrane  86 ). 
         [0037]    Referring now to  FIGS. 14 and 15 , another example is shown that is similar to the example shown in  FIGS. 2 and 3  except that circumferential rib  48 , the radial ribs in outer annular ring  52 , and the membrane sections in outer annular ring  52  have been eliminated. This arrangement might be used for supporting a smaller diaphragm whereas the previous examples might be used to support a larger diaphragm. 
         [0038]    With reference to  FIGS. 16 and 17 , a further example of a surround is shown that is similar to the example shown in  FIGS. 14 and 15  except that membrane sections  88 ,  90  are curved instead of flat. The membrane sections alternate in a circumferential direction from being concave shaped (membrane  88 ) to convex shaped (membrane  90 ). 
         [0039]    Turning to  FIGS. 18 and 19 , a surround  110  includes six radial ribs  112  and a membrane  114 . The ribs  112  sit on top of the membrane  114 . A diaphragm (not shown) is located between a first lip  116  of the ribs  112  and a first lip  118  of the membrane  114 . An attachment ring is located between a second lip of the ribs  120  and a second lip  122  of the membrane  114 . The surround  110  is insert molded to a preformed diaphragm and attachment ring. 
         [0040]      FIG. 20  provides another example of a surround. A pair of radial ribs  91  support a membrane section  93 . In this example there is no clear line of demarcation between where the ribs end and where the membrane section begins. A portion  95  of the surround is secured to either a circumferential rib or to an attachment ring (not shown). A portion of the surround opposite the portion  95  is secured to a diaphragm (not shown). 
         [0041]    In general, the ribs of the support section provide a linear force-deflection response and the thin membrane provides a non-linear force deflection response. The total stiffness is a combination of the ribbed and the membrane responses so it is desirable to minimize the contribution of the membrane. One example provides a linear performance of the system over a 22 mm peak-to-peak travel of the diaphragm. In one example using a soft silicone rubber the rubber goes through an elongation or strain of about 30%. 
         [0042]    As shown in  FIG. 21A , a speaker  92  has an acoustic driver  102  and a passive radiator  20  mounted on two sides  94 ,  104  of a closed housing  105  of the speaker  92 . The sides  94  and  104  are perpendicular to one another. The acoustic driver  102  has a diaphragm  106  that vibrates when driven by electrical signals. The vibration of the diaphragm  106  propagates through air inside the speaker  92  and causes the diaphragm  22  of the passive radiator  20  to vibrate. Surrounding the diaphragm  22  is the passive radiator surround  21 . The physical and geometrical characteristics of the surround  21  affect the characteristics of the vibrating movement of the diaphragm  22 . The surround  21 , being made of elastic materials, pulls the diaphragm back when the diaphragm moves away from a neutral position, by generating a restoring force. A surround made of more rigid material will tend to generate a larger restoring force, and to induce faster but smaller movements in the diaphragm attached to it. A surround made of softer material will tend to generate a smaller restoring force, and to induce slower but larger movements in the diaphragm. 
         [0043]    The passive radiator  20  augments the vibrating movement of the acoustic driver  102 . The acoustic waves together generated by the acoustic driver  102  and the passive radiator  20  as perceived by a listener define sound qualities of the speaker  92 . It is desirable that the diaphragm  22  of the passive radiator  20  replicate the vibrating movement of the diaphragm  106  of the acoustic driver without any distortion. Distortion occurs when a restoring force generated by the surround is non-linear or when the surround generates a rotating torque that rocks the diaphragm. 
         [0044]      FIG. 21B  illustrates the vibrating motion of the diaphragm  22 . As the diaphragm  22  moves away from a neutral position, plane  28 , along the axis  27 , restoring forces  24  generated by the surround  21  pull the diaphragm  22  back to its neutral position, plane  28 . 
         [0045]      FIG. 21C  illustrates the rocking motion of the diaphragm  22  about an axis  27 . The diaphragm  22  in  FIG. 21C  is rocking as the left side of the diaphragm  22  moves upward and the right side of the diaphragm  22  moves downward. The rocking motion is caused by a torque, which is defined as: 
         [0000]        {right arrow over (T)} =2 {right arrow over (F)}•{right arrow over (r)}   
         [0046]    In surrounds, it is desirable to attain a linear restoring force in the surround as the diaphragm moves away from its neutral position along the axis  27  and to minimize rotating torque in the surround to reduce rocking motion in the diaphragm. The tendency of a diaphragm to return to its neutral position after being displaced along the axis  27  is measured by its axial stiffness coefficient, which can be expressed as restoring force per unit excursion. The tendency of a diaphragm to return to its normal orientation after rocking is measured by its rocking stiffness coefficient, which can be expressed as restoring torque per unit angle displacement. Rocking stiffness, in turn, determines a rocking frequency of the diaphragm, the frequency at which the diaphragm rocks resonantly, an undesirable state in which the rocking movement of the passive radiator&#39;s diaphragm can be significant and the distortion of the diaphragm pronounced. For a particular diaphragm, the higher the rocking stiffness, the higher the rocking frequency. 
         [0047]      FIGS. 22A ,  22 B, and  22 C show an example of a surround assembly  2200  designed to provide more linear restoring forces and to reduce rocking motion of the diaphragm  2218  attached to the surround  2201 . The surround assembly  2200  includes a surround  2201 , a square attachment frame  2202 , and a diaphragm  2218 , which can be assembled using an adhesive rather than forming the three parts together in a molding process. 
         [0048]    The inner periphery  2220  of the attachment frame  2202  supports and is attached to the surround  2201  and the attachment frame holds the surround assembly  2200  on the speaker  92  using fasteners that pass through the four holes  2204 . The attachment frame can also be a ring, or another shape. 
         [0049]    A mass (not shown) of a selected size is mounted in a central hole  2216  in the diaphragm. Adjusting the mass of the object tunes the resonant frequency of the speaker  92  occurring when the moving mass of the diaphragm and surround assembly resonate against the spring stiffness of the air in the speaker box and the surround stiffness. 
         [0050]    The surround  2201  is segregated into six arc sections,  2206  and  2208 , by six ribs  2210 . The ribs  2210  each have a thickness  2212  of 0.058 inches. The six sections will be referred to as membranes in the rest of the application although the sections can be in any shapes and configurations. Membrane includes any shape or configuration, and there can be other numbers of sections including as few as two and as many as eight or more. Among the six membranes, three of them, sections  2208 , have a convex shape, and three of them, sections  2206 , have a concave shape. The convex and concave membranes alternate around the surround. 
         [0051]    Two cross-sectional views of the surround assembly  2200  are taken to further illustrate the shapes of the ribs  2210  and the membranes,  2206  and  2208 . The cross-sectional view FRONT-FRONT  2250  is depicted in  FIG. 22B  to show the cross-section of the diaphragm  2218  and the ribs  2210 . The cross-sectional view RIGHT-RIGHT  2280  is depicted in  FIG. 22C  to show the cross section of the diaphragm  2218 , the concave membranes  2206 , and the convex membranes  2208 . 
         [0052]    In referring to  FIG. 22B , the cross-sectional view  2250  shows two ribs  2210 . Each rib has an I-beam configuration. The two sides  2211 ,  2213  of each of the ribs  2210  curve inward. The attachment frame  2252  and the diaphragm  2218  bulge outward to match the inward curves of the two sides,  2212  and  2213 . The recessed parts of the rib  2210  allow the attachment frame  2252  and the diaphragm  2218  to fit snuggly into the rib  2210 . 
         [0053]    In referring to  FIG. 22C , the material that makes the membranes  2206  and  2208  has a thickness  2284  of 0.040 inches. The membranes  2206  and  2208  in  FIG. 22C  have a half-roll structure. But the membranes can be of any other curve or shape, for example, elliptic, angular, oval or rectangular. Extending from both sides of the membrane  2208  are two annular and alternating flange sections  2288 . The flange sections  2288  on the inside of the membrane  2208  are attached to the diaphragm  2218 . The flange sections  2288  on the outside of the membrane  2208  are attached to the attachment frame  2202 . The membranes  2208  have the same flange arrangement (not shown). 
         [0054]    The diameter  2214  of the surround assembly  2200  is 2.375 inches and the thickness  2252  of the surround assembly  2200  is 0.250 inches as indicated in the cross-sectional view  2250  in  FIG. 22C . 
         [0055]      FIGS. 23A and 23B  depict the diaphragm  2218  and the surround  2201  as individual parts and  FIG. 23C  depicts the diaphragm  2218  and the surround  2201  as being assembled into the surround assembly  2200 . In  FIG. 23A , the perspective view  2310  of the diaphragm  2218  shows that the edge of the diaphragm is shaped to match the flange arrangement on the convex and concave membrane sections of on the surround. The edge of the diaphragm  2218  includes a sunken section  2287 , a raised section  2286 , and a narrow protruding section  2254 . The narrow protruding section  2254  fits into the recessed parts of the ribs  2210 . The flanges of the concave membrane sections  2206  can be fitted onto the raised sections  2286  and the flanges of the convex membrane sections  2208  can be fitted onto the sunken sections  2287 . 
         [0056]    On the surround  2201 , each rib,  2210 , is situated between a concave membrane  2206  and a convex membrane  2208  and acts as a cap that seals the ends of the membranes. The upper section of each rib  2210  caps a convex membrane  2208  on one side and the lower section of each rib  2210  caps a concave membrane  2206  on the other side. Each rib  2210 , having an I-beam configuration, has a flat top and bottom that extend slightly over the membrane sections. 
         [0057]    Assembly of the diaphragm  2218  into the surround  2201  can be carried out by fitting the inner flanges of the membranes of the surround  2201  onto the receiving sections  2286  and  2287  of the diaphragm  2218 , and fitting the outer flanges of the membranes of the surround  2201  onto the rim of the attachment frame, and then fitting the protruding sections  2252  of the attachment frame and the protruding sections  2254  of the diaphragm into the recessed parts of the ribs  2210 . The parts can be glued together or chemically bonded by molding the surround with the diaphragm and attachment frame in place by using materials that will bond to each other with or without a primer applied to the inserted parts. 
         [0058]    Another example of a surround assembly  2400  is shown in  FIGS. 24A ,  24 B,  24 C, and  24 D. In  FIG. 24A , the surround assembly  2400  includes three parts, an attachment frame  2402 , a diaphragm  2418 , and a surround  2401 . Compared to the surround assembly  2200  in  FIG. 22A , the attachment frame  2402  is similar to the attachment frame  2202 , and the diaphragm  2418  to the diaphragm  2218 . But the surround  2401  is divided into eight arc sections,  2406  and  2408 , by eight ribs,  2410 , instead of six arc sections by six ribs as is the case for the surround  2201 . Other than the number of arc sections, the surround  2401  is similar to the surround  2201  in several aspects. 
         [0059]    For example, each rib  2410  caps a concave membrane  2206  and a convex membrane  2208  that are situated on either side of the rib and has a flat top and bottom that extend slightly over the membrane sections, as shown in  FIG. 24D . Also, as shown in the cross sectional view FRONT-FRONT  2420  in  FIG. 24B , the ribs  2410  have the same I-beam configuration as the ribs  2210  and the thickness  2424  of the diaphragm and the thickness  2426  of the surround assemble are the same as those of the surround assemble  2200 . The cross sectional view 22.5-22.5  2440  shown in  FIG. 24C  presents the cross section of two convex membrane sections  2408 , the diaphragm  2418 , and the attachment frame  2402 , that is similar to the cross section presented in  FIG. 22C . Each convex membrane  2408  has a thickness  2484  of 0.04 inches and the circular part of each convex membrane  2408  has a diameter  2488  of 0.195 inches. Each convex membrane  2408  also has two flange sections  2486  that can be used to fit into the diaphragm  2418  and the attachment frame  2402 . Each concave membrane  2406  (not shown in  FIG. 24C ) has the same geometrical dimensions as the convex membrane  2408 . 
         [0060]      FIG. 25  shows another example of a surround assembly  2500 . The surround  2501  in the surround assembly  2500  is divided into four arc sections,  2506  and  2508 , by four ribs,  2510 . Two of the arc sections,  2506 , are of convex shape and two of the arc sections,  2508 , are of concave shape. With respect to the geometric dimensions and shapes, the surround assembly  2500  is similar to the surround assemblies  2400  and  2200 . 
         [0061]      FIG. 26  shows a surround  2601  that is of different geometric dimensions than the surround  2501 . The overall thickness  2640  of the surround assembly  2600  is 0.145 inches, thinner than the surround assembly  2500  which is 0.250 inches thick (See  FIGS. 25C and 26C ). The surround  2601  has four arc sections,  2606  and  2608 , segregated by four ribs,  2610 . The ribs  2610  of the surround  2601  are of different shape than the ribs  2510  of the surround  2501 . As shown in  FIG. 26B , the ribs  2610  have an oval shape, while the ribs  2501  have an I-beam configuration as shown in  FIG. 25B . 
         [0062]    The ribs  2610  have a height  2632  of 0.215 inches and a width  2631  of 0.260 inches as indicated in  FIG. 26B . The flange sections  2634  of the ribs  2610  have a thickness  2636  of 0.040 inches. The height of the ribs  2610  is slightly less than the height  2638  of the surround assembly which is 0.240 inches. 
         [0063]      FIGS. 27A ,  27 B,  27  C, and  27  D show yet another embodiment of a surround assembly  2700 . The surround assembly  2700  is similar to the surround assembly  2200  shown in  FIG. 22A  in that both the surrounds,  2201  and  2701 , are divided into six arc sections by six ribs and that both the surround assemblies,  2200  and  2700 , are of the same geometrical dimensions. The surround  2701  is also different from the surround  2201  in several other aspects. 
         [0064]    First, the ribs of these two surrounds,  2201  and  2701 , have different shapes. The ribs  2210  of the surround  2201  have an I-beam configuration.  FIG. 27B  shows that the ribs  2710  of the surrounds  2701  are a composition of two circular segments,  2722  and  2726 , and one rectangular section,  2724 , with the rectangular section  2724  in between the two circular segments,  2722  and  2726 . 
         [0065]    Second, the convex membranes  2706  and concave membranes  2708  do not have flange sections as the membranes  2206  and  2208  do. 
         [0066]    Third, instead of having flange sections extending from the membranes, the surround  2701  has an inner wall  2712  and an outer wall  2714 . Both the ribs  2710  and the membranes  2706  and  2708  are enclosed in between these two walls. Like the flange sections  2286  that can be used to connect the surround  2201  to the attachment frame  2202  and the diaphragm  2218 , these two walls can be used to fit the surround  2701  into the surround assembly  2700  with the inner wall  2712  glued or the surround insert molded to the outer periphery of the diaphragm  2718  and the outer wall  2714  to the inner periphery of the attachment frame  2712 . 
         [0067]      FIGS. 22-25  present five different embodiments of surround assembly that can be used in passive radiators as well as acoustic drivers. They are designed to achieve superior sound qualities. The number of arc sections, the number of ribs, the shape of the ribs, the shape of the membranes, and the geometric dimensions are selected and arranged for that purpose. 
         [0068]    A surround according to the invention provides good linear restoring axial forces and reduced rocking motion of the diaphragm. In referring to  FIG. 21B , the axial restoring forces  24  as provided by the surround  21  are linear when the restoring forces  24  are proportional to the excursion E as the diaphragm  22  travels along the axis  27  away from the neutral position, plane  28 . Both the membranes and the ribs contribute to the restoring forces  24 . 
         [0069]    In  FIGS. 28 ,  29 , and  30 , restoring forces are plotted as a function of excursion ΔE of the diaphragm for the surround assembly  2200 ,  2400 , and  2500 . As demonstrated in those figures, the restoring forces are linear when the excursion ΔE is small (ΔE&lt;0.05 inches in either direction). 
         [0070]      FIG. 28  shows the restoring forces for two models, RF2_pr — 061608 — 12 — 3D and RF2_pr — 061608 — 13 — 3D. The solid curve  2802  represents model RF2_pr — 061608 — 12 — 3D and the dotted curve  2804  represents model RF2_pr — 061608 — 13 — 3D. The two models differ in their geometric shapes and dimensions. In model RF2_pr — 061608 — 12 — 3D, the rib thickness ( 2712  in  FIG. 27A  is 0.050 inches and all other thicknesses ( 2284  in  FIG. 27D  are 0.010 inches. In model RF2_pr — 061608 — 13 — 3D, the rib thickness is 0.010 inches and all other thicknesses are 0.041 inches. 
         [0071]    Though different in their geometric shapes and dimensions, these two models have the same small signal axial stiffness coefficient. As defined above, axial stiffness coefficient can be expressed as restoring force per unit excursion. Small signal axial stiffness coefficient of a model is the axial stiffness coefficient in the small signal range. In  FIG. 28 , axial stiffness coefficient of a surround model is the slope of the curve that represents the model. When the signals are small, the two curves coincide with each other. Thus, the two models have the same small signal axial stiffness coefficient (SSAS) which can be calculated using the following expression: 
         [0000]    
       
         
           
             
               S 
                
               
                   
               
                
               S 
                
               
                   
               
                
               A 
                
               
                   
               
                
               S 
             
             = 
             
               
                 
                   Δ 
                    
                   
                       
                   
                    
                   F 
                 
                 
                   Δ 
                    
                   
                       
                   
                    
                   E 
                 
               
               = 
               
                 
                   
                     0.02 
                      
                     
                         
                     
                      
                     lbf 
                   
                   
                     0.1 
                      
                     
                         
                     
                      
                     in 
                   
                 
                 = 
                 
                   0.2 
                    
                   
                       
                   
                    
                   
                     lbf/in 
                   
                 
               
             
           
         
       
     
         [0072]    As shown in  FIG. 28 , the restoring forces for both models are linear when the excursion of the diaphragm is small, i.e., the driving signals are small. The restoring forces stay linear with only slight deviation when the signals increase but are still within the operating range  2806  (ΔE&lt;0.1 inches in either direction). Only outside the operating range  2806  does the deviation of the restoring force from linear become more significant. 
         [0073]    Contribution to the axial stiffness coefficient of a surround comes from both the ribs and the membranes as illustrated in  FIGS. 29 and 30 . In  FIG. 29 , two curves  2902  and  2904  are plotted. The solid curve  2902  represents the combined contribution to the axial stiffness coefficient from the ribs and the membranes. The curve  2902  corresponds to a real surround model, model RF2_pr — 061608 — 12 — 3D. On the other hand, the dotted curve  2904  represents the contribution to the axial stiffness coefficient from the ribs only and corresponds to a theoretical model in which the rib thickness is 0.050 inches and all other parts have a thickness of zero inch. The vertical difference between the curves  2902  and  2904  represents the contribution to the axial stiffness coefficient from the membranes only. In  FIG. 29 , throughout the entire range of the excursion, the curves  2902  and  2904  are close together, which means the contribution to the axial stiffness coefficient from the membranes remain small through out the entire range. In other words, in  FIG. 29 , the contribution to the axial stiffness coefficient from the ribs dominates both in the small and large signal ranges. 
         [0074]    In  FIG. 30 , again two curves,  3002  and  3004 , are plotted. The solid curve  3002  represents the contribution to the axial stiffness coefficient from the ribs and membranes, and is computed based on model RF2_pr — 061608 — 13 — 3D. The dotted curve  3004  represents the contribution to the axial stiffness coefficient from the ribs only and is computed based on a theoretical model in which the rib thickness is 0.010 inches and the thickness of all other parts is zero. 
         [0075]    In  FIG. 30 , throughout the entire range of the excursion, the curves  3002  and  3004  are farther apart than the two curves  2902  and  2904  in  FIG. 29 . As in  FIG. 29 , the vertical difference between the curves  3002  and  3004  represents the contribution to the axial stiffness coefficient from the membranes only. Different from  FIG. 29 , the vertical difference between the two curves  3002  and  3004  is larger than the contribution from the ribs as represented by the dotted curve, throughout the entire range of excursion. In other words, in  FIG. 30 , the contribution to the axial stiffness coefficient from the membranes dominate in both the small and large signal ranges. 
         [0076]    Rocking stiffness coefficient is defined above as restoring torque per unit angle displacement. Rocking stiffness coefficient is related to axial stiffness coefficient, but also depends on many other factors, such as relative volumes of the ribs and membranes. Since the volumes of the ribs and membranes effect their contributions to the axial stiffness coefficient, rocking stiffness coefficient depends on the ratio of the contributions of the ribs and membranes to the axial stiffness coefficient. 
         [0077]    For example,  FIG. 28  shows that in the small signal range (ΔE&lt;0.05 inches), model RF2_pr — 061608 — 12 — 3D and model RF2_pr — 061608 — 13 — 3D have the same axial stiffness coefficient but different rocking stiffness coefficient. Model RF2_pr — 061608 — 12 — 3D has a rocking stiffness coefficient of 0.097 in-lbf/rad and model RF2_pr — 061608 — 13 — 3D has a rocking stiffness coefficient of 0.105 in-lbf/rad. This is because the ratios of the contributions to the axial stiffness coefficient are different for these two models, as shown in  FIGS. 29 and 30 . A ratio of the contributions to the axial stiffness coefficient from the membranes and the ribs at a certain excursion can be computed by dividing the contribution from the ribs (the vertical value of the dotted line) by the contribution from the membranes (the vertical difference between the dotted line and the solid line). 
         [0078]    Furthermore, the rocking frequency of a surround is related to the rocking stiffness coefficient. The higher the rocking stiffness coefficient, the higher the rocking frequency. A good surround design preferably places the rocking frequency out of the band of the operating frequency or much higher than the frequency at which the surround has greatest axial excursion. The higher the rocking frequency, the less likely the rocking frequency will excite rocking modes. Because model RF2_pr — 061608 — 13 — 3D has a higher rocking stiffness coefficient than model RF2_pr — 061608 — 12 — 3D, the former has a higher rocking frequency. 
         [0079]    Pushing the rocking frequency downwards so that it falls below the lower limit of the band of the operating frequency is also feasible. 
         [0080]    Other examples are within the scope of the claims. 
         [0081]      FIGS. 31A ,  31 B and  31 C show plan, front sectional and end sectional views, respectively, of a surround of racetrack shape. For instance, while the examples described herein are generally circular in shape, surrounds can be square, rectangular, race-track, or other shapes. Additionally, there are many different ways of arranging the ribs and membranes of the surround in addition to the several that have been described herein. 
         [0082]    It is evident that those skilled in the art may now make numerous departures from and modifications of the specific apparatus and techniques described herein without departing from the inventive concepts. Consequently, the invention is to be construed as embracing each and every novel feature and novel combination of features present in or possessed by the apparatus and techniques described herein and limited only by the spirit and scope of the appended claims.