Abstract:
The present invention relates to a distortion reduction system and method for reducing an acoustic distortion in an loudspeaker. The invention involves: a) generating a first sensor signal based on longitudinal displacement of the voice coil from the initial rest position; b) generating a second sensor signal based on longitudinal acceleration of the voice coil; c) processing and combining the first sensor signal and the second sensor signal to generate a feedback control signal; and d) adjusting an audio drive signal supplied to the voice coil to generate the acoustic waveform wherein the audio drive signal is adjusted based on the first feedback control signal.

Description:
FIELD OF THE INVENTION  
         [0001]    The present invention relates to a feedback system for distortion reduction in loudspeakers. More particularly, it relates to a method and apparatus for sensing and controlling the cone movement of a speaker by sensing acceleration and position.  
         BACKGROUND OF THE INVENTION  
         [0002]    The construction and operation of electro-dynamic loudspeakers are well known. The physical limitations in their construction are one cause of non-linear distortion, which is sensible in the generated sound reproduction. Distortion is particularly high at low frequencies, in relatively small sealed box constructions where cone displacement or excursions are at their maximum limit.  
           [0003]    In the past there have been numerous approaches taken in order to reduce speaker distortion. None of these approaches addresses the problem of cone offset.  
           [0004]    Accordingly, there is a need for a system simultaneously capable of providing increased distortion reduction and reducing non-linearity related distortions that result from large speaker cone displacements.  
         SUMMARY OF THE INVENTION  
         [0005]    An object of an aspect of the present invention is to provide an improved distortion reduction system for reducing an acoustic distortion in a waveform generated by a voice coil of an audio speaker.  
           [0006]    In accordance with this aspect of the present invention, there is provided a distortion reduction system for reducing a distortion in an acoustic waveform generated by a voice coil of an audio speaker, wherein an audio drive signal is supplied to the voice coil and the voice coil is longitudinally movable from an initial rest position to generate the acoustic waveform. The distortion reduction system comprises: a) a position sensor for generating a first sensor signal based on longitudinal displacement of the voice coil from the initial rest position; b) an acceleration sensor for generating a second sensor signal based on longitudinal acceleration of the voice coil; c) a feedback circuit for processing and combining the first sensor signal and the second sensor signal to generate a feedback control signal; and, d) a first audio drive signal adjustment means for receiving a first input audio signal and transmitting a first output signal derived from the first input audio signal and the feedback control signal, the audio drive signal being derived from the first output signal.  
           [0007]    An object of a second aspect of the present invention is to provide a method for reducing a distortion in an acoustic waveform generated by a voice coil of an audio speaker.  
           [0008]    In accordance with this second aspect of the present invention, there is provided a method of reducing an acoustic distortion in the waveform generated by a voice coil of an electro-dynamic loudspeaker. The method comprises: a) generating a first sensor signal based on longitudinal displacement of the voice coil from the initial rest position; b) generating a second sensor signal based on longitudinal acceleration of the voice coil; c) processing and combining the first sensor signal and the second sensor signal to generate a feedback control signal; and d) adjusting an audio drive signal supplied to the voice coil to generate the acoustic waveform wherein the audio drive signal is adjusted based on the first feedback control signal. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0009]    For a better understanding of the present invention and to show more clearly how it may be carried into effect, reference will now be made, by way of example, to the accompanying drawings, which show preferred embodiments of the present invention, and in which:  
         [0010]    [0010]FIG. 1 illustrates a schematic diagram of a loudspeaker with a motional feedback system for reducing non-linear distortion in an audio loudspeaker;  
         [0011]    [0011]FIG. 2 is a schematic diagram of the motional feedback system shown in FIG. 1, wherein a positional sensor and acceleration sensor feedback network is illustrated in accordance with the present invention;  
         [0012]    [0012]FIG. 3 is a circuit diagram of the positional sensor feedback network shown in FIG. 2;  
         [0013]    [0013]FIG. 4 illustrates a perspective side view of a first embodiment of a position sensor in accordance with the present invention;  
         [0014]    [0014]FIG. 5 illustrates a perspective side view of an alternative embodiment of the position sensor shown in FIG. 4;  
         [0015]    [0015]FIG. 6 illustrates a schematic diagram of an electrical sensor circuit used in collaboration with the position sensor shown in FIG. 5; and  
         [0016]    [0016]FIG. 7 illustrates a cross section view of the mechanical construction of the speaker device and the relative position of the acceleration sensor and position sensor. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0017]    [0017]FIG. 1 illustrates a motional feedback system  10  in accordance with the present invention, wherein a plurality of sensor devices are used in collaboration with a feedback control circuit. The feedback control circuit senses and controls the longitudinal motion or movement of a voice coil  22  of a loudspeaker  12 . Distortions which undesirably influence the longitudinal motion of the loudspeaker  12  in a manner which causes it to not to correspond an input audio signal  14  will be sensed. Once sensed, the distortion is accordingly compensated by a first feedback control signal  16 .  
         [0018]    In accordance with the present invention, an acceleration sensor device  18  and a position sensor device  20  are used to convert the physical movement of the loudspeaker voice coil  22  (not shown in detail in FIG. 1) into respective first and second electrical sensor signals  24  and  26 . The electrical sensor signals  24 ,  26  output from acceleration sensor device  18  and position sensor device  20  are combined by a first feedback network  30 , which generates the first feedback control signal  16 . Audio input signal  14  may typically be received from an audio source such as an audio amplifier. An error amplifier  32  (which may, for example, be a differential amplifier) receives both the audio input signal  14  and the first feedback control signal  16  and generates a differential voltage signal  34 . If the loudspeaker  12  exhibits any motional distortion, the electrical signals  24 ,  26  from the sensors  18 ,  20  will contain a corresponding distortion component. The distortion components on signals  24 ,  26  is also present in the first feedback control signal  16 , which is then subtracted from the audio input signal  14  by means of error amplifier  32 . As a result, the differential voltage signal  34  includes the audio input signal  14  minus the sensed distortion component in first feedback control signal  16 . By subtracting this distortion component from the audio input signal  14  the distortion added by the motion of the speaker is reduced.  
         [0019]    The loudspeaker voice coil  22  position correlates with the audio input signal  14  and the audio current drive signal  36  output from power amplifier  44 . Power amplifier  44  uses current sensing resistor  46  to operate as a current amplifier for driving the voice coil. Therefore, in accordance with the present invention, a first feedback control circuit, indicated along the path B to B″ via B′, comprises the first feedback network  30 , the acceleration sensor device  18  and the position sensor device  20 . This first feedback control circuit, indicated along the path B to B″ via B′, senses and compensates for any such sensed distortion in the longitudinal motional displacement of the loudspeaker voice coil  22 . In this way, for large speaker cone displacements needed for good bass reproduction in small box constructions, distortion is reduced.  
         [0020]    A second feedback network  40  receives the first electrical sensor signal  26  from the position sensor device  20  and generates a second feedback control signal  42 . The second feedback control signal  42  compensates for the inherent non-linearity in the loudspeaker  12  motor (not shown), wherein the motor comprises a speaker magnet and voice coil. This non-linearity, which contributes substantially to loudspeaker distortion is known in the art of speaker design. As the voice coil experiences large excursions, its position is displaced relative to its region of maximum magnetic density (i.e. optimum operating region). Therefore, the voice coil and attached speaker cone generate less force for the same current flowing through voice coil windings. This non-linear behavior, which leads to distortion in the loudspeaker  12  acoustic output waveform  50 , becomes more apparent with large voice coil displacement. A second feedback circuit, indicated along the path from A to A″ via A′, and comprising the second feedback network  40  and position sensor device  20 , senses and compensates for this distortion. As illustrated in FIG. 1, the differential voltage signal  34  is received as an input to the second feedback network  40 . Although the differential voltage signal includes distortion compensation from the first feedback network  30 , it is further processed by the second feedback network  40  in order to compensate for motor non-linear distortion.  
         [0021]    The motional feedback system  10  illustrated in FIG. 1 is a distortion reduction system comprising the first and second feedback control circuit, wherein the first feedback control circuit utilizes two sensors  18 ,  20  (acceleration and position). Within any feedback control system, the bandwidth over which stable feedback is provided is of paramount importance. This, in effect, dictates the stability of the feedback circuit. The combination of the position sensor device  20  and the acceleration sensor device  18  enables the first feedback control circuit, indicated along the path B-B′-B″, to provide distortion corrective control over a selected frequency range (which will typically be selected to correspond to the frequency range of the loudspeaker) without the need for complex phase/gain compensation circuitry. The position sensor device  20  has a low pass filter characteristic ranging from DC to a cut off frequency a little over the loudspeaker resonance frequency. Hence, it has a flat gain response over this frequency range. The position sensor device  20  is not forced to operate above its cut off frequency, as the acceleration sensor takes over at frequencies above the loudspeaker resonance frequency. The acceleration sensor device has a high pass filter response up to frequencies above the speaker breakup mode frequencies. Therefore, the combination of high pass and low pass filter response in the first feedback control loop, indicated along the path B-B′-B″, provides a flat characteristic response (constant phase and gain) over the entire operating range of the loudspeaker  12 . Consequently, the feedback control circuit does not require compensation circuitry that will introduce additional noise to the loudspeaker  12 .  
         [0022]    The bandwidth of a single sensor used within a control feedback loop is limited and requires a compensating network that extends its bandwidth. However, the compensating network cannot recover certain components from the feedback signal. For example, information about cone position does not exist at the output of an accelerometer or velocity sensor device. Also, the compensation network will contribute additional noise to the feedback signal and hence to the audio drive signal applied to the voice coil.  
         [0023]    In order to generate a feedback loop with a constant gain/phase relationship over the entire operating range of the loudspeaker and to avoid the associated problems with compensation networks, the first electrical sensor signal  24  and the second electrical sensor signal  26  are combined by the first feedback network  30 . Feedback network  30  combines these signals  24 ,  26  in order to generate a feedback transfer function of unity, where the gain and phase of the signals between the input and output of the network  30  are constant over the entire operating frequency range of the loudspeaker  12 . The design of the feedback network  30  is supported with the aid of the following mathematical analysis.  
         [0024]    The cone acceleration A(s) or generated sound pressure for a speaker in a sealed box is given by equation (1)  
               A        (   s   )       =           (     s   /   Ω     )     2       1   +       (     s   /   Ω     )     /   Q     +       (     s   /   Ω     )     2         *   a             (   1   )                               
 
         [0025]    where s is a Laplace variable, Ω is the angular resonance frequency in the speaker box, Q is the Q factor and a is a constant.  
         [0026]    Similarly, cone displacement can be represented by equation (2)  
               X        (   s   )       =       1     1   +       (     s   /   Ω     )     /   Q     +       (     s   /   Ω     )     2         *   d             (   2   )                               
 
         [0027]    where s is a Laplace variable, Ω is the angular resonance frequency in the box, Q is the Q factor and d is a constant.  
         [0028]    From equations (1) and (2) it can be determined that cone acceleration has a second order high-pass filter response whilst cone displacement has a second order low-pass filter response.  
         [0029]    Equations (3) and (4) represent a first order high-pass and low-pass filter response, respectively.  
               HP        (   s   )       =       s   /   Ω       1   +     (     s   /   Ω     )                 (   3   )                 LP        (   s   )       =     1     1   +     (     s   /   Ω     )                 (   4   )                               
 
         [0030]    Where s is a Laplace variable, Ω is the angular resonance frequency in the speaker box and Q is the Q factor.  
         [0031]    The characteristic response of the acceleration and position sensors given by equations (1) and (2) can be combined with the characteristic response of a first order high-pass and low-pass filter, given by equations (3) and (4). By combining these equations, the desired flat response in the first feedback loop is realized (indicated along path B-B′-B″ of FIG. 1). This response is generated by combining equation (1), (2), (3) and (4) using the following relationship:  
               T        (   s   )       =         X        (   s   )       d     +       A        (   s   )       a     +       HP        (   s   )       *       X        (   s   )         d   ·   Q         +       LP        (   s   )       *       A        (   s   )         a   ·   Q                   (   5   )                               
 
         [0032]    Substituting equations (1)-(4) into equation (5) leads to equation (6): 
           T ( s )=1  (6) 
         [0033]    Consequently, by combining the characteristic response of the high-pass filter, low-pass filter, position sensor device and acceleration sensor device according to equation (5), the desired transfer function necessary for having a stable feedback control loop over the full bandwidth of the loudspeaker is generated.  
         [0034]    [0034]FIG. 2 provides a more detailed illustration of the motional feedback system shown in FIG. 1. The input audio signal  14  is applied to a summing amplifier  52 , where the summing amplifier  52  includes resistors  54 ,  56 ,  58  and capacitor  60 . Capacitor  60 , connected in parallel to resistor  56 , provides low-pass filtering, where the cut off frequency is selected to be below the loudspeaker breakup mode frequencies. Appropriate selection of capacitor  60  and resistor  56  satisfies this criteria and avoids any instability caused by these breakup mode frequencies. The second input to the summing amplifier is received from the first feedback control signal  16 . This feedback signal  16  is 180 degrees inverted with respect to the audio input  14 . Therefore, the summing amplifier  52  operates in the same manner as error amplifier  32  (FIG. 1).  
         [0035]    The generated differential voltage signal  34  is received by the second feedback network  40 , wherein the differential voltage signal  34  which is input to the network  40  at U. As previously mentioned, network  40  provides distortion compensation for inherent motor distortion which occurs as a result of large voice coil (and speaker cone) motional displacement (or excursions). The force generated by the voice coil is given by equation (7): 
           F=Bl ( X )· I (7) 
         [0036]    where Bl(X) is the product of magnetic flux (B) generated by the magnet and length of wire (I) in the voice coil, as a function of the voice coil position X. The voice coil position X is the position of the voice coil relative to its rest position, where X=0. Also, I in equation (7) is the current flowing through the voice coil. Ideally, a speaker should have a constant Bl(X). Satisfying this condition requires a large magnet assembly, which is typically quite expensive. As a result of the use of less than ideal magnet assemblies in practice, Bl(X) may drop to approximately 50% of its value at the cone rest position. Therefore, Bl variations are a source of significant distortion which can be attributed to the motor of a speaker device. According to equation (7), force F is proportional to voice coil current and not the voltage present at the speaker input. Using a power amplifier  44  in current mode therefore simplifies the circuitry for compensating the Bl(X) changes.  
         [0037]    In practice, the Bl(X) function can be approximated by equation (8): 
           Bl ( X )= Bl (0)·(1 = 31  k·X   2 )  (8) 
         [0038]    where Bl(0) is the B product when the voice coil is in the rest position and k is a constant. From equation (8) it can be deduced that as the voice coil departs from its rest position (i.e. X&gt;0), the Bl(X) product decreases. Based on equation (8), it is possible to provide a feedback network that compensates for the reduction in Bl(X) due to the (1−kX 2 ) factor. Therefore, the feedback network must have a transfer function of 1(1−kX 2 ) in order to cancel the effect of the (1−kX 2 ) factor. For this reason, in accordance with the present invention, the second feedback network  40  has a characteristic response of:  
             Z   =     U     1   -     k   ·     X   2                   (   9   )                               
 
         [0039]    where U is the input to the second feedback network  40 , X is the voice coil position and Z is the output from the second feedback network  40 .  
         [0040]    The second feedback network  40  has two main process stages. The first process stage  62  processes the first electrical sensor signal indicative of the voice coil position X by squaring (X 2 ) and inverting (−X 2 ) it. It will also be appreciated that the amplitude of the first electrical sensor signal  19  is increased by amplifier  66  prior to being received by the first process stage  62 . The second process stage  64  further processes the output Y=(−X 2 ) from the first process stage  62  by combining it with the input differential voltage signal U  34  according to equation (9). The output Z from the second process stage  64  generates the second feedback control signal  42  which reduces the non-linear distortion caused by the motor. This signal  42  is a distortion compensated electrical audio signal, which is received and amplified by power amplifier  44 . That is, the signal  42  is distorted or modified in a way that compensates for subsequent distortion, such that the modification and subsequent distortion cancel out. Using the current sensing resistor  46 , power amplifier  44  generates the audio current drive signal  36  which drives the voice coil of the loudspeaker  12 . Hence, the second feedback loop, indicated along path A-A′-A″, provides non-linear motor distortion compensation for the loudspeaker  12 . Therefore, the second feedback control loop and second feedback network  40  servo the speaker voice coil so it predominantly moves or undergoes excursions in an optimum operating region centered about its rest position. By making sure that the voice coil movement region is centered about the rest position (X≈0), the effect of reduced voice coil force as a function of voice coil position X in relation to the rest position is greatly reduced.  
         [0041]    As previously discussed, by combining the characteristic response of a first order high-pass filter, first order low-pass filter, position sensor  20  and acceleration sensor  18  according to equation (5), the desired transfer function necessary for having a stable feedback control loop over the full bandwidth of the loudspeaker  12  is realized. As shown in FIG. 2, this is achieved by adding the first feedback network  30  into the first feedback loop, indicated along path B-B′-B″. Both the first and second electrical sensor signals output from the position sensor  18  and acceleration sensor  20  are amplified by amplifier  66  and  68  respectively. The amplified first electrical sensor signal (acceleration sensor  18  output)  24  is filtered by a first order low pass filter comprising resistor  68  and capacitor  70  prior to being received by input  76  of a summing amplifier circuit. The summing amplifier circuit comprises summing amplifier  74 , input resistors  84 ,  86  and  88 , and feedback resistor  90 . Similarly, the amplified second electrical sensor signal (position sensor  20  output)  26  is filtered by a first order high pass filter comprising capacitor  70  and resistor  68  prior to also being received by input  76  of the summing amplifier circuit. The values of capacitor  70  and resistor  68  must satisfy equation (10):  
               Resistor                   68   ·   Capacitor                   70     =     1   Ω             (   10   )                               
 
         [0042]    where Ω is the angular resonance frequency of the speaker box (2πf r ).  
         [0043]    The amplified first electrical sensor signal  24  (acceleration sensor  18  output) is directly received (i.e. not filtered) by input  78  of the summing amplifier circuit. Also, the amplified second electrical sensor signal (acceleration sensor  18  output)  26  is directly received (i.e. not filtered) by input  80  of the summing amplifier circuit. The output of this summing amplifier circuit  16  generates an amplified sum of the electrical signals present at inputs  76 ,  78  and  80 .  
         [0044]    It will be appreciated that the electrical signals present at each of these inputs  76 ,  78 ,  80  represents each term in equation (5), where the term:  
           HP        (   s   )       *       X        (   s   )         d   ·   Q         +       LP        (   s   )       *       A        (   s   )         a        ·   Q                                 
 
         [0045]    is realized by combining the low-pass filtered first electrical sensor signal (acceleration sensor output  18 ) and the high-pass filtered second electrical sensor signal (position sensor output  20 ) at input  76  of the summing amplifier circuit. Similarly, terms:  
           X        (   s   )       d                   and                     A        (   s   )       a                           
 
         [0046]    represent the amplified first electrical sensor signal (acceleration sensor  18  output)  24  and the amplified second electrical sensor signal (position sensor  20  output)  26  received by inputs  78  and  80 . Consequently, the first feedback control signal  16  output from the summing amplifier circuit is the amplified sum of all the terms presented in equation (5). This shows that the network  30  generates an output  16  which has the same transfer characteristics as equation (5), where T(s)=1. Hence, first feedback control signal  16  has a flat amplitude and phase response, which enables a high feedback loop gain. It will be appreciated that resistor  86  must be Q times larger than the value of resistor  88  and  84 . This condition must hold in order for T(s) to be unity and therefore be frequency independent. The reason for this scaling factor is that a combined signal is received by resistor  86 , and therefore, in order to compensate for receiving this combined signal, resistor  86  is chosen to be Q times larger than resistor  88  and  84 .  
         [0047]    The high feedback loop gain in turn increases the sensitivity of the feedback system, which increases its motion-dependent distortion reduction capability. Therefore, in accordance with the present invention, a motional feedback system in proposed, which is capable of providing enhanced distortion reduction over the entire operating frequency range of the loudspeaker. Consequently, the motional feedback system is a feedback circuit, which includes a first and second feedback circuit. The first feedback circuit reduces motion dependent distortions due to physical speaker construction limitations, whilst the second feedback system reduces motion dependent distortion introduced by the loudspeaker motor.  
         [0048]    [0048]FIG. 3 illustrates a schematic diagram for the electrical circuit of the second feedback network  40 . The first process stage  62  is an analogue multiplier circuit, which includes resistor components  94 ,  96 ,  98 ,  100 ,  102 ,  104 ,  106 ,  108  and transconductance amplifier (which may be an LM13700 transconductance amplifier or another transconductance amplifier)  110 . The amplified second electrical sensor signal  26  is received by the analogue multiplier circuit, and generates an output signal Y, indicated at  114 . The generated output signal Y is proportional to the square of the received signal, indicated at  26 , where 
         
       Y=−kX 
       2 
     
         [0049]    In this equation, k is a constant and X is a position control signal received from the output of a position sensor circuit (see FIG. 6). The position sensor circuit includes position sensor  20  and an electrical sensor circuit  140  (FIG. 6), wherein the sensor circuit  140  processes the output from the position sensor  20  and generates the position control signal  19 . It will be appreciated that the position control signal  26  of FIG. 6 is the same as the second electrical sensor signal  26  of FIGS. 1 and 2.  
         [0050]    The output signal Y  114  from the first process stage  62  is received by the second process stage  64 . The second process stage  64  is a voltage controlled amplifier (VCA) circuit which includes resistor components  118 ,  120 ,  122 , and  124 , capacitor component  126 , operational amplifier  128  and transconductance amplifier  130 . Output signal Y  114  is received by the bias input of transconductance amplifier  130 , whilst the differential voltage signal U  34  is input to resistor  124 . The resulting output signal Z  42  from the second process stage  64  is given by equation (11).  
             Z   =     U     1   -     k   ·     X   2                   (   11   )                               
 
         [0051]    Where X is the position control signal  26 , k is a constant and U is the differential voltage signal  34 . For example, if the voice coil is operating about its ‘optimum operating point’ (centered about the rest position), the position control signal X will be approximately 0 V and no signal compensation is provided at the output Z of the second feedback circuit  40 . The polarity of the position control signal X  34  depends on the direction in which the voice coil has departed from the ‘optimum operating point’.  
         [0052]    Consequently, the output from the second process stage  64 , which is the output from the second feedback network  40 , compensates for non-linear distortion in the motor. Although term 1−kX 2  does not model the speaker motor perfectly, in practice, the second feedback control loop (path A-A′-A″ shown in FIGS. 1 and 2) and second feedback network  40  reduce distortion substantially. The remaining distortion elements are further reduced by the first feedback control loop (path B-B′-B″ shown in FIGS. 1 and 2) and first feedback network  30 .  
         [0053]    The design steps involved in realizing the functionality of the analogue multiplier  62  and VCA circuit  64  can typically be determined by referring to the transconductance amplifier data sheet.  
         [0054]    [0054]FIG. 4 illustrates the position sensor device  20 , which includes a first and second inductance coil  132 A,  132 B and an approximately triangular shaped conductive core  134 . Optionally, all of these components  132 A,  132 B,  134  are manufactured on printed circuit boards (PCB). Furthermore, the coils may be printed on both sides of the PCB boards and electrically connected in series in order to maximize their total inductance. The conductive region  135  of the conductive core  134  is longitudinally displaced within a finite gap region, defined by  138 . As the conductive core  134  moves in the direction indicated by Arrow X, a larger amount of copper is immersed in the magnetic field generated by the coils  132 A,  132 B. This in turn decreases the inductance of the coils  132 A,  132 B. Conversely, as the conductive core  134  moves in a direction indicated by Arrow Y, a smaller amount of copper is immersed in the magnetic field generated by the coils  132 A,  132 B, which in turn increases the inductance of the coils  132 A,  132 B. The conductive core  134  is geometrically compensated in order to ensure that its longitudinal displacement (X or Y Arrow direction) in the center of the finite gap region  138  generates a linear change in the output voltage of the position sensor circuit. Hence, a linear position control signal (position sensor output  19  shown in FIG. 6) is generated as a result of this inductance change. As illustrated in FIG. 4, the shape of the conducting region  135  is not precisely triangular. It is shaped to linearize the relationship between the output voltage of the position sensor and the displacement of the core  134 . Conducting region  135  has a curved shape. As illustrated in FIG. 4, in use, the first and second inductance coils  132 A,  132 B are stationary, whilst the conductive core  134  is attached to the bobbin of the voice coil  133 . Therefore, as the voice coil longitudinally moves, the conductive core  134  is longitudinally displaced within the finite gap region  138  between the coils  132 A,  132 B. Hence, the inductance of the coils  132 A,  132 B varies in unison with voice coil movement. Although the coils  132 A,  132 B are stationary and the conductive core  134  moves, in an alternative embodiment, it will be appreciated that the coils  132 A,  132 B may be connected to the voice coil, whilst the conductive core  134  remains stationary. However, it is found that by connecting the core  134  to the voice coil, a rigid connection which generates satisfactory position sensing is provided.  
         [0055]    [0055]FIG. 5 shows an alternative embodiment of the position sensor  20 , wherein the conductive core  136  is comprised solely of a conductive region. The operation of this sensor is essentially the same as that of the sensor described and illustrated in FIG. 4.  
         [0056]    Referring to FIG. 4, the position sensor  20  is also positioned, such that no electrical cross talk occurs between the inductance coils  132 A,  132 B and the voice coil. This is achieved ensuring that the vector orientation of the magnetic field generated by the inductance coils  132 A,  132 B is orthogonal to the vector orientation of the magnetic field generated by the voice coil. In terms of the physical positioning of the inductance coils  132 A,  132 B and the voice coil, their respective axes must be orthogonal in order to eliminate electrical cross talk. This means that a concentric longitudinal axis  137 , which passes concentrically through the voice coil must be orthogonal to a first axis  139  which passes through the center of both inductance coils  132 A,  132 B.  
         [0057]    [0057]FIG. 6 illustrates the position sensor circuit comprising the position sensor device  20  and processing circuit  140 . The circuit  140  coverts the changes in the inductance of the position sensor  20  and generates the position control signal  19  wherein the voltage magnitude of the position control signal  19  is proportional to the displacement of the core  134 . Within the circuit of FIG. 6, an oscillator circuit  142  comprises a crystal (6 MHz, for example)  144 , capacitor component  146 , capacitor component  148 , resistor component  150 , resistor component  152 , XOR logic gate  154  and XOR logic gate  156 . This circuit  142  generates a 6 MHz squarewave signal at the output  158  of XOR gate  156 . The 6 MHz squarewave signal at the output  158  of XOR gate  156  is then applied to the clock input of D-Type flip-flop  160 , which divides the signal into a 3 MHz squarewave. The 3 MHz output  162  from D-Type flip-flop  160  is applied to the clock input of D-Type flip-flop  164 , which further divides the signal into a 1.5 MHz squarewave signal. D-Type flip-flop  164  has two complementary outputs  166 ,  170 , where the first output  166  generates a first 1.5 MHz squarewave, which is applied to the clock input of D-Type flip-flop  168 . The second output  170  generates a second 1.5 MHz squarewave, which is 180 degrees out of phase with the a first 1.5 MHz squarewave. This signal is applied to the clock input of D-Type flip-flop  172 . D-Type flip-flop  168  divides the first 1.5 MHz squarewave to a first 750 KHz squarewave signal, which is present at its output  174 . Similarly, D-Type flip-flop  172  divides the second 1.5 MHz squarewave to a second 750 KHz squarewave signal, which is present at its output  176 . The first and second 750 KHz squarewaves are 90 degrees out of phase as a result of being clocked by the anti-phase first and second 1.5 MHz squarewaves.  
         [0058]    The series connected coils  132 A,  132 B and capacitor  180  provide a parallel resonant circuit tuned to 750 KHz when the conductive core  132  is in its center position (i.e. voice coil is in the optimum operating region). The second 750 KHz squarewave at output  176  is filtered by capacitor  184  and resistor  182 , such that at point B at the terminal of resistor  182 , the second 750 KHz squarewave is converted to a 750 KHz sinusoidal signal of the same phase. Provided that the triangular conductive core  132  is in its center position, the phase of the 750 KHz sinusoidal signal does not change. The 750 KHz sinusoidal signal is then re-converted back to a 750 KHz squarewave by comparator circuit  186 , whereby if the phase has not been affected by the resonant circuit (i.e. core  132  is in its center position), the 750 KHz squarewave has the same phase as the signal output from D-Type flip-flop  172 . Therefore, it will still have a 90-degree phase shift relative to the first 750 KHz signal generated by the output  174  of D-Type flip-flop  168 : It will be appreciated however, that the comparator circuit  186  has first and second complementary outputs  188 ,  190  that are 180 degrees out of phase. Hence, the first output  190  will have the same 90-degree phase shift relative to the first 750 KHz signal generated by the output  174  of D-Type flip-flop  168 , and the second output  188  will have a 270-degree phase shift relative to this signal (output from  174 ).  
         [0059]    EXOR logic gate  192  and low pass filter network  194  form a first phase comparator circuit, whilst EXOR logic gate  196  and low pass filter network  198  form a second phase comparator circuit. The first 750 KHz signal generated by the output  174  of D-Type flip-flop  168  is applied to the first input  200 ,  202  of both the first and second phase comparator network, respectively. Also, the first output  190  and the second output  188  from comparator  186  are applied to the second input  206 ,  204  of the first and second phase comparator network, respectively.  
         [0060]    Under these conditions, where the triangular core  134  is in the rest position, and the signals from the comparator  186  output  190  and the D-Type flip-flop  168  output  174  have a 90 degree phase difference, the first phase comparator XOR gate  192  output  208  will generate a squarewave signal with a 50% duty cycle. Therefore, the corresponding averaging applied to this signal by the low pass filter  194  will generate a DC voltage of 0 V at output  210 . Similarly, when the signals from the comparator  186  complementary output  188  and the output  174  from D-Type flip-flop  168  have a 270-degree phase difference, the second phase comparator XOR gate  196  output  212  will also generate a squarewave signal with a 50% duty cycle. Accordingly, this signal is averaged through the low pass filter  198 , wherein the averaged signal at output  214  is a DC voltage of approximately 0 V. Both DC outputs  210 ,  214  from the phase comparators are received by a differential amplifier  218 , which generates a difference signal based on the DC outputs  210  and  214 . This corresponding difference signal is the position control signal  26  which is also referred to as the second electrical sensor signal in the descriptions of FIGS. 1 and 2. Therefore, the position control signal  26  is 0V and the second feedback compensation network  40  does not provide any distortion compensation.  
         [0061]    Under the conditions where the speaker voice coil movement is centered about a position offset from its center position (i.e. optimum operating region centered about rest position), the change in inductance of the position sensor  20  varies the resonance frequency of the parallel resonance circuit generated by the coils  132 A,  132 B and capacitor  180 . This in turn causes an additional phase shift in the 750 KHz sinusoidal signal, at point B, relative to the first 750 KHz squarewave signal, which is present at the output  174  of D-Type flip-flop  168 . The relative phase difference between these two signals will depart from 90-degrees (depending on direction of core  134  movement), which causes one output (e.g.  208 ) from one XOR gate (e.g.  192 ) to generate a squarewave signal with a duty cycle greater than 50%, whilst the other output (e.g.  212 ) from the other XOR gate (e.g.  196 ) generates a squarewave signal with a duty cycle less than 50%. DC averaging of the squarewave with a duty cycle greater than 50% will generate a positive DC voltage in proportion to the width of the pulses. Also, DC averaging of the squarewave with a duty cycle less than 50% will generate a lesser magnitude DC voltage in proportion to the width of the pulses. The DC voltages from the low pass filter  194 ,  198  outputs  210 ,  214  are received by the differential amplifier  218 , and a corresponding position control signal is generated  19 . The more the core  134  is displaced relative to its center position, the more the duty cycle of the squarewave signals is effected. Therefore, the magnitude difference between the DC voltages generated by averaging these squarewaves is increased. Hence, the position control signal  19  generated by the differential amplifier  218  increases. The generated position control signal is directly proportional to the voice coil  133  and hence the core  134  displacement (see FIG. 4). As illustrated in FIG. 2, this signal  19  is amplified, as indicated at  26 , then applied (input X) to the second feedback network (pre-distortion circuit) for providing distortion compensation (for motor non-linearity).  
         [0062]    [0062]FIG. 7 illustrates the mechanical construction of the speaker device  12  and the relative position of the acceleration sensor  18  and position sensor  20 . As illustrated in the FIG. 7, the acceleration sensor  18  and position sensor&#39;s triangular conductive core  134  are connected to the bottom region of the voice coil bobbin  136 . The first and second inductance coils  132  (only one coil shown) are connected to a fixed (stationary) position or physical location on the speaker either side of the triangular conductive core  134 . Consequently, as the voice coil moves, the triangular conductive core  134  moves within the inductance coils  132 . Therefore, the position sensor generates the electrical feedback control signal (or position control signal) necessary for distortion reduction. As shown in FIG. 7, the triangular conductive core  134  is connected to the bobbin  136  by means of bracket  135 . The acceleration sensor  18  also generates the electrical feedback control signal, which is linearly proportional to the movement of the voice coil  180  and bobbin  136 .  
         [0063]    The described embodiments of the present invention provide an electrical motional feedback system for reducing distortion in loudspeakers, in particular loudspeakers having small cabinet or box sizes and high speaker cone excursions. It should be understood that various modifications can be made to the preferred and alternative embodiments described and illustrated herein without departing from the spirit and scope of the invention.