Abstract:
The present invention provides methods and apparatuses for an audio transducer. The audio transducer is excited by driving a paddle of a diaphragm. A plurality of node regions of a paddle is determined for the higher-order modal components, which correspond to resonance frequencies and have an order greater than one. An intersection region of at least two higher-order modal components is identified, in which an excitation point is located with the intersection region. The diaphragm of the audio transducer includes a frame, at least one hinge, and a paddle. The paddle connects to the frame by the at least one hinge and is excited by a signal source at an excitation point to produce an acoustic signal.

Description:
FIELD OF THE INVENTION 
       [0001]    The invention relates to a paddle of a diaphragm in an audio transducer. 
       BRIEF SUMMARY OF THE INVENTION 
       [0002]    With one aspect of the invention, a method supports an excitation of an audio transducer. The audio transducer is excited by driving a paddle of a diaphragm. A plurality of node regions for a paddle is determined for the higher-order modal components, which correspond to resonance frequencies and have an order greater than one. An intersection region of at least two higher-order modal components is identified. An excitation point is located with the intersection region, in which the paddle is subsequently excited at the excitation point by a mechanical source. 
         [0003]    With another aspect of the invention, node regions for the second-order modal component and the third-order modal component are determined when determining the higher-order modal components. Additional modal components may be determined. 
         [0004]    With another aspect of the invention, at least one of the node regions is altered such as by reinforcing a portion of the paddle. 
         [0005]    With another aspect of the invention, a diaphragm of an audio transducer includes a frame, at least one hinge, and a paddle. The paddle connects to the frame by the at least one hinge and is excited by a signal source at an excitation point to produce an acoustic signal. The excitation point is located within an intersection region of at least two higher-order modal components. 
         [0006]    With another aspect of the invention, the at least one hinge includes two hinges that are separated by a slot region. 
     
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0007]      FIG. 1  shows a diaphragm of an audio transducer that is excited at an excitation point in accordance with an embodiment of the invention; 
           [0008]      FIG. 2  shows an audio transducer in accordance with an embodiment of the invention; 
           [0009]      FIG. 3A  a paddle of a diaphragm that is excited at a fundamental mode in accordance with an embodiment of the invention; 
           [0010]      FIG. 3B  a paddle of a diaphragm that is excited at a second-order mode in accordance with an embodiment of the invention; 
           [0011]      FIG. 3C  a paddle of a diaphragm that is excited at a third-order mode in accordance with an embodiment of the invention; 
           [0012]      FIG. 3D  a paddle of a diaphragm that is excited at a fourth-order mode in accordance with an embodiment of the invention; 
           [0013]      FIG. 4  depicts different node regions of a paddle, where each node region is associated with one of a plurality of modal components in accordance with an embodiment of the invention; 
           [0014]      FIG. 5  shows a measured earphone response in accordance with an embodiment of the invention; 
           [0015]      FIG. 6  shows a modeling of a paddle in accordance with an embodiment of the invention; 
           [0016]      FIG. 7  shows a measured paddle velocity for a prototype in accordance with an embodiment of the invention; and 
           [0017]      FIG. 8  shows a measured paddle velocity for a prototype in accordance with an embodiment of the invention. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0018]      FIG. 1  shows diaphragm  100  of an audio transducer that is excited at an excitation point in accordance with an embodiment of the invention. Diaphragm  100  includes paddle  101  that is connected to frame  103  through hinges  105  and  107 . Hinges  105  and  107  are separated by slot region  111 . Paddle  101  is separated from frame  103  by gap region  109 . In an embodiment of the invention, slot region  111  and gap region  109  are covered by a thin film of Mylar®. The film of Mylar seals the back from the front of paddle  101 . Otherwise, a positive pressure created on one side may be cancelled by a negative pressure on the other side of paddle  101 . Also, the film of Mylar may provide additional stiffness for paddle  101 . 
         [0019]    In an embodiment of the invention, paddle  101  is constructed of Aluminum 1100-H19 with a length L=6.76 mm, width of 3.86 mm, and a thickness of 0.002 inches. (As shown in  FIG. 1 , the length of paddle  101  does not include hinge sections  105  and  107 . However if one includes hinge sections  105  and  107 , one would add 0.254 mm to the length.) 
         [0020]    Functionally, the purpose of paddle  101  is to displace air (or fluid) in order to generate an acoustic signal. Paddle  101  is a continuous structure with isotropic material properties, and thus does not typically behave as a lumped system. If one were designing an earphone with multiple drivers, each expected to reproduce a narrow band of frequencies, one may be able to optimize the system based upon the lumped equivalents of the drivers. However, with a single broadband driver, one must compromise the lumped (low frequency) characteristics to obtain a degree of high frequency control. This approach amounts to understanding the mechanical behavior of the dynamic driver components. 
         [0021]    By properly locating excitation point  113  to drive paddle  101 , one can improve the high frequency response of an audio transducer. For linear, dynamic excursions, the displacement of paddle  101  can be represented mathematically as the weighted summation of modal components, where the weighting constants (modal participation factors) are functions of frequency and loading and the modes are functions of the material properties, geometry, and boundary conditions. Each modal component has an associated resonance frequency and may or may not contribute to the net displacement (determined by an integration of the mode over the paddle surface). The fundamental mode contributes the largest net displacement to the cantilevered paddle response. Therefore, it is desirable to extend the influence of the fundamental modal component throughout the entire frequency range. Unfortunately, a given cantilevered paddle may have many modal components below 20 kHz. Although the displacement is a superposition of all modal components, when a structure is excited at a single modal resonance frequency the resulting displacement will be composed of only that mode (the weighting constants for the remaining modes are all zero). This observation implies that at each of the modal resonance frequencies below 20 kHz the paddle displacement consists of a single modal contribution and therefore will not have a contribution from the fundamental mode except at the fundamental resonance frequency. However, this is only true when excitation does not occur at a node region (a position on the structure that does not undergo a modal displacement at the corresponding resonance frequency). 
         [0022]    As will be discussed, when the paddle  101  is excited at excitation point  113 , where all higher-order modal components have an associated node region (which may be idealized as a node line) that passes through excitation point  113 , the higher-order modal components will not contribute to the resulting paddle displacement. (A higher-order modal component has an order greater than one. The fundamental modal component has an order of one.) The contribution of higher-order modal components is typically undesirable because the resulting displacement partially cancels the displacement attributed to the fundamental modal component. One can significantly reduce the influence of higher-order modal components by carefully choosing the location of excitation point  113 . Moreover, applying excitation to any position on the paddle, besides the hinge node, will excite the fundamental modal component. Vibrating in its fundamental mode, the entire paddle moves in phase. 
         [0023]    In the exemplary embodiment shown in  FIG. 1 , the two lowest even-order modes (two and four) share a node region that runs through the middle of paddle  101  from hinges  105  and  107  to the tip of the free end. The second and fourth-order modal components have equal portions that vibrate out of phase and therefore integrate to zero and do not contribute to the net displacement. Excitation of these modal components, however, could potentially cause a sharp drop in response at the two resonance frequencies. 
         [0024]    The remaining odd-order (third) modal components below 20 kHz results in the free end of the paddle vibrating out of phase and will integrate to a smaller net displacement compared to the fundamental mode. In the exemplary embodiment, the location of the second node line (the first node line is at the hinge end) of the third mode is a distance approximately 0.66×L from the hinge, where L is the paddle length. Since this point along the center line is defined by the mode shape, the location of excitation point  113  is a function of the material properties, geometry, and boundary conditions. Applying the point force to the cantilevered paddle  301  at a point along the center line having a distance 0.66L from the hinge, excites the fundamental mode, but does not excite the remaining three modes below 20 kHz. This extends the influence of the fundamental mode well above the frequency one would obtain when the point force is applied at the paddle free end (i.e., at a distance L from the hinges). Therefore, the diaphragm  300  is controlled across a wider bandwidth before the influence of higher-order modal components becomes significant. 
         [0025]    Isolation of the fundamental vibration mode through reduction of the three remaining modal contributions below 20 kHz. Isolation is achieved by placement of the point force excitation at the intersection of the node lines of the three undesirable mode shapes. The specific location will be dependent upon geometry and material properties, but can be determined for various configurations using this technique. Computer simulation (finite element analysis) can be used to determine the location of the node lines and thus to predict the optimum excitation point. 
         [0026]    The paddle displacement (as modeled in two dimensions) may be expressed as: 
         [0000]    
       
         
           
             
               
                 
                   
                     η 
                      
                     
                       ( 
                       
                         ɛ 
                         , 
                         ζ 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         j 
                         = 
                         1 
                       
                       ∞ 
                     
                      
                     
                       
                         α 
                         j 
                       
                        
                       
                         
                           Ψ 
                           j 
                         
                          
                         
                           ( 
                           
                             ɛ 
                             , 
                             ζ 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     EQ 
                     . 
                     
                         
                     
                      
                     1 
                   
                   ) 
                 
               
             
           
         
       
     
         [0000]    where η is the paddle displacement at location (β,ζ), α j  is a modal weighing factor that is a function of frequency and loading, and Ψ j (ε,ζ) is the modal displacement for the j th  order modal component. The modal displacement is a function of the boundary conditions and defines what is typically called the mode shape. The paddle displacement η at a particular point (ε,ζ) is the summation of the modal displacements at point (ε,ζ) multiplied by the weighing factors, which may be real or complex. In ideal (no loss) materials, exciting the structure at f=f j  (corresponding to the j th  resonance frequency) will excite only the j th  order modal component (i.e., η=α j Ψ j ), provided that the excitation point is not located on a node region. (A node region, which may be referred as a node line, identifies a region having essentially zero displacement for the corresponding modal component.) 
         [0027]    In real materials, internal losses (structural damping) introduces modal damping resulting in a response that is a summation of the modal components Ψ 1  and Ψ j  (η=α 1 Ψ 1 +α j Ψ j ), provided that the excitation point is not located within the node regions (e.g. as shown in  FIG. 4 ) of the modal components. If the displacement for a modal component integrates to zero over paddle  101 , the modal component does not contribute to the paddle response (no fluid or air displacement). 
         [0028]    With the exemplary embodiment, excitation point  113  is located approximately 4.43 mm (i.e., 0.66L) from hinges  105  and  107 . While theoretical calculations and simulated results provide an approximate location of excitation point  113 , experimental results from a prototype may suggest that the location be adjusted as a result of the prototype deviating from an ideal model. For example, theoretical results are dependent on the modeling of the paddle. 
         [0029]      FIG. 2  shows audio transducer  200  in accordance with an embodiment of the invention. Diaphragm  201  (corresponding to diaphragm  100  as shown in  FIG. 1 ) is driven (excited) by drive pin  203  at drive pin attachment point  205 . In turn, drive pin  203  is driven by reed  207  in conjunction with an armature structure (comprising magnet  209  and coil  211 ), which is excited by an electrical signal (typically in an audio frequency range) from electronic circuitry (not shown). In the embodiment, drive pin attachment point  205  is modeled as a single point on the surface of a paddle (corresponding to excitation point  113  as shown in  FIG. 1 ). 
         [0030]      FIGS. 3A-3D  show a displacement analysis of paddle  301  for diaphragm  300  with gap region  309  (corresponding to paddle  101  of diaphragm  100  with gap region  109  as shown in  FIG. 1 ). As previously discussed, with an exemplary embodiment paddle  301  has a length L=6.76 mm, a width W=3.86 mm. In simulations  351 ,  353 ,  355 , and  357  the displacements are determined from finite element analysis (FEA). With FEA a computer model of paddle  301  is constructed with selected points (often referred as nodes) arranged as a grid called a mesh. In the simulations, paddle  301  is modeled with the material properties of Titanium Grade 1, although alternative simulations may utilize the material properties of aluminum 1100-H19. 
         [0031]    With an embodiment of the invention paddle  301  is modeled with two ribs located along the length of paddle  301 . The ribs typically raise the resonance frequencies of paddle  301 . Raising the resonance frequencies is typically desirable because the effects of the higher-order modal components are reduced. However, adding ribs also increases the stiffness of paddle  301  and consequently tends to reduce the acoustic response of paddle  301 . Note that the modal structures shown in  FIGS. 3A-3D  are independent of the excitation point. 
         [0032]      FIG. 3A  shows simulation  351 , in which paddle  301  is excited at a fundamental mode (corresponding to j=1 in EQ. 1) in accordance with an embodiment of the invention. The corresponding resonance frequency (f 1 ) approximately equals 786 Hz. As shown in  FIG. 3A , the amount of displacement of paddle is shown with different shades where the darker the region, the less the displacement. (Within a black region, the displacement is approximately zero. Thus, the black regions are node regions.) Correspondingly, node region  391  (fundamental modal component) corresponds to an approximately zero displacement. 
         [0033]      FIG. 3B  shows simulation  353 , in which paddle  301  is excited at a second-order mode (corresponding to j=2 in EQ. 1) in accordance with an embodiment of the invention. The corresponding resonance frequency (f 2 ) approximately equals 3690 Hz. Node region  393  (second-order modal component) has an approximately zero displacement. 
         [0034]      FIG. 3C  shows simulation  355 , in which paddle  301  is excited at a third-order mode (corresponding to j=3) in accordance with an embodiment of the invention. The corresponding resonance frequency (f 3 ) approximately equals 11400 Hz. Node region  395  (third-order modal component) has an approximately zero displacement. 
         [0035]      FIG. 3D  shows simulation  357 , in which paddle  301  is excited at a fourth-order mode (corresponding to j=4) in accordance with an embodiment of the invention. The corresponding resonance frequency (f 4 ) approximately equals 16600 Hz. Node region  397  (fourth-order modal component) has an approximately zero displacement. 
         [0036]    While  FIGS. 3A-3D  show simulations for the first four modal components, modal components for orders greater than four (i.e., j&gt;4) may be determined using finite element analysis. However, typical audio applications typically consider only frequencies less than 20 KHz because of limitations of the human ear. 
         [0037]      FIG. 4  depicts different node regions of paddle  101 , where each node region is associated with one of a plurality of modal components in accordance with an embodiment of the invention. Note that  FIG. 4  only depicts the different node regions.  FIGS. 3A-D  shows the simulated node regions for an exemplary embodiment. Node regions  401 ,  403 ,  405 , and  407  correspond to node regions  391 ,  393 ,  395 , and  397 , respectively. Modal components having an order greater than one are termed higher-order modal components. 
         [0038]    The even-order modal components have node regions that are symmetric to center line  451  of paddle  101 . Since the excitation point  113  is typically located on center line  451 , the even-order modal components are not excited. (However, embodiments of the invention enable excitation point  113  to be asymmetrically located with center line  451  within region  453  as will be discussed.) A small amount of asymmetrical loading will excite the even-order modal components; although the nearly equal contributions of positive and negative displacement results in a net displacement that is small enough to be negligible to the over-all displacement response of paddle  101 . 
         [0039]    An intersection region  453  is determined by the intersection of the higher-order modal regions. As shown in  FIG. 4 , intersection region  453  corresponds to the intersection of node regions  403 ,  405 , and  407 . If excitation point  113  is located within intersection region  453 , the displacement that is attributed to the higher-order modal components is reduced and may be ignored in the displacement analysis of paddle  101 . Consequently, the excitation of paddle  101  is essentially determined by the fundamental excitation (as shown in  FIG. 3A ). In the exemplary embodiment, excitation point  113  is approximately located at 0.66L (where L is the length of paddle  101 ) from the hinges  105  and  107  along center line  451 . 
         [0040]    While paddle  101  may be analyzed using finite element analysis as described above, one may determine the location of excitation point  113  using other approaches. For example, neglecting the acoustical reactionary loading of paddle  101 , the paddle displacement may be approximated using the analysis as modeled in  FIG. 6  as will be discussed. Also, one may measure the displacement of paddle  101  for different modal components in order to determine the intersection region. Measuring the displacement to determine the placement of excitation point  113  is empirical and is typically time consuming. Moreover, one must repeat the measurements when paddle  101  is altered (e.g., changing the paddle shape or adding ribs.) 
         [0041]      FIG. 5  shows measured earphone response  500  in accordance with an embodiment of the invention. Frequency response  501  shows the response for paddle  301  where the excitation point is located approximately at the end of paddle  301  (i.e., x=0.90L), while frequency response  503  shows the response where the excitation point is located at approximately x=0.66L. Measured earphone response  500  suggests that the frequency response is extended when the excitation point is located within intersection region  453 . In particular, the contribution from the third-order modal component is substantially reduced in accordance with the above discussion. 
         [0042]      FIG. 6  shows a modeling of paddle  601  in accordance with an embodiment of the invention. With an embodiment of the invention, paddle  601  may be analyzed in order to determine the location of an excitation point to reduce higher-order modal components, e.g., the third order modal component. Paddle  601  is modeled as a cantilevered beam having a length L, a constant width b, and a constant thickness h. Paddle  601 , as modeled as a cantilevered beam, has a mode shape given by: 
         [0000]      Ψ j ( x )= C (λ j   x )−γ j   D (λ j   x )  (EQ. 2) 
         [0000]    The characteristic equation, which determines the natural frequencies of the cantilevered beam, is obtained by: 
         [0000]      cos  h (λ j   L )×cos(λ j   L )+1=0  (EQ. 3) 
         [0043]    The modal weighing factors are determined from: 
         [0000]    
       
         
           
             
               
                 
                   
                     α 
                     j 
                   
                   = 
                   
                     
                       
                         ∫ 
                         0 
                         L 
                       
                        
                       
                         
                           q 
                            
                           
                             ( 
                             x 
                             ) 
                           
                         
                          
                         
                           
                             Ψ 
                             j 
                           
                            
                           
                             ( 
                             x 
                             ) 
                           
                         
                          
                         
                            
                           x 
                         
                       
                     
                     
                       
                         ( 
                         
                           
                             EI 
                              
                             
                                 
                             
                              
                             
                               λ 
                               j 
                               4 
                             
                           
                           - 
                           
                             ρ 
                              
                             
                                 
                             
                              
                             A 
                              
                             
                                 
                             
                              
                             
                               ω 
                               2 
                             
                           
                         
                         ) 
                       
                        
                       
                         
                           ∫ 
                           0 
                           L 
                         
                          
                         
                           
                             
                               Ψ 
                               j 
                               2 
                             
                              
                             
                               ( 
                               x 
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                     . 
                     
                         
                     
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                     4 
                   
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         [0000]    where q(x) is the force as a function of x, E is the Young&#39;s Modulus of the material, I is the area moment, ρ is the material density, and A is the cross sectional area. Note that α j  is a function of ω but is a constant because it is not a function of the position x. Because the cantilevered beam has a constant rectangular cross section of width b and thickness h, the area moment I is given by: 
         [0000]    
       
         
           
             
               
                 
                   I 
                   = 
                   
                     
                       bh 
                       3 
                     
                     12 
                   
                 
               
               
                 
                   ( 
                   
                     EQ 
                     . 
                     
                         
                     
                      
                     5 
                   
                   ) 
                 
               
             
           
         
       
     
         [0000]    Consequently, modal resonance frequency ω j  is given by: 
         [0000]    
       
         
           
             
               
                 
                   
                     ω 
                     j 
                   
                   = 
                   
                     
                       λ 
                       j 
                       2 
                     
                      
                     
                       
                         EI 
                         
                           ρ 
                            
                           
                               
                           
                            
                           A 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     EQ 
                     . 
                     
                         
                     
                      
                     6 
                   
                   ) 
                 
               
             
           
         
       
     
         [0044]    In order to locate an excitation point that reduces a higher-order modal component, one can vary x, where q(x) is a force applied at a single point x′ along the cantilevered beam, so that α j  is essentially zero in order to eliminate the contribution of the j th  modal component. If the excitation point is located at the center line of the paddle, the displacement contribution of the even-order modal components is essentially zero. In such a case, the third-order modal component has the largest effect of the higher-order modal components. Consequently, one varies the location of the excitation point along the length of the paddle in order to reduce α 3  (the modal weighing factor of the third-order modal component). 
         [0045]      FIG. 7  shows paddle velocity plot  701  for a first paddle prototype (not shown) measured at 7400 Hz in accordance with an embodiment of the invention. (The paddle velocity is measured in mm/sec as a function of the position along the paddle.) The x axis only shows the number of the measurement point. To convert to an actual distance I would need to get the scanning resolution (number of points per meter)). With the first paddle prototype, the excitation point is located near the end of the paddle (x=0.90L), where the hinge is located at point  112  on the x axis. One observes that a contribution from the third-order modal component with a lesser contribution from the fundamental (first) order modal component. The contribution from the third-order modal component increases with the excitation frequency until the excitation frequency equals the third resonance frequency f 3 , which approximately equals 11400 Hz. 
         [0046]      FIG. 8  shows paddle velocity plot  801  for a second paddle prototype (not shown) measured at 7400 Hz in accordance with an embodiment of the invention. The excitation point is located at approximately 0.66L from the hinge portion of the diaphragm. Compared with paddle velocity plot  701 , the displacement contribution from the third-order modal component is negligible while the movement of the paddle is dominated by the fundamental mode shape. The experimental results shown in  FIGS. 7 and 8  suggest that the placement of the excitation away from the paddle end, as discussed above, substantially reduces the contribution from the higher-order modal components and consequently improves the frequency response of an acoustic device. 
         [0047]    While the invention has been described with respect to specific examples including presently preferred modes of carrying out the invention, those skilled in the art will appreciate that there are numerous variations and permutations of the above described systems and techniques that fall within the spirit and scope of the invention as set forth in the appended claims.