Abstract:
A loudspeaker is provided for receiving an incoming electrical signal and transmitting an acoustical signal. The loudspeaker may include a power amplifier that has an input and an output, where the input receives the incoming electrical signal. The loudspeaker may also include two or more passive filters, such as low-pass, band-pass, and/or high-pass filters, which are coupled to the output of the power amplifier. The passive filters may also be coupled to one or more speaker drivers. The arrangement of passive filters and speaker drivers may have a single input that has a combined input impedance. The output of the amplifier may have an output impedance. The output impedance may be between about 25% and about 400% of the combined input impedance. The power amplifier may include a current-feedback amplifier that is configured to maintain the desired output impedance.

Description:
FIELD OF THE INVENTION  
       [0001]     This invention relates generally to a loudspeaker system, and more particularly to a loudspeaker system having an amplifier, post-amplifier passive filters, and multiple speaker drivers.  
       BACKGROUND OF THE INVENTION  
       [0002]     It may be difficult to produce a speaker driver that accurately reproduces the 20 Hz to 20 kHz frequency range (audible spectrum) of sound generally associated with human hearing. Therefore, speaker drivers have been produced that accurately reproduce a more limited range. These limited-range speaker drivers may be used in conjunction with one another to more accurately reproduce the full range of sound. For example, a full range loudspeaker system may include a low frequency speaker driver, a midrange frequency speaker driver, and a high frequency speaker driver.  
         [0003]     Loudspeaker systems having two or more limited-range speaker drivers are known as “multi-way” loudspeaker systems. For example, a loudspeaker system having a low-frequency speaker driver and a high-frequency speaker driver is known as a “two-way” loudspeaker system. A loudspeaker system additionally having a mid-frequency speaker driver is known as a “three-way” loudspeaker system, and so on.  
         [0004]     Because a limited-range speaker driver is designed to handle a particular range of frequencies, it may be desirable to filter frequencies outside of this particular range from the electrical signal driving the limited-range speaker driver. For example, a two-way loudspeaker system may include a low-pass filter and a high-pass filter. A three-way loudspeaker system may include a low-pass filter, a band-pass filter, and a high-pass filter. Multi-way loudspeaker systems having more than four different limited-range speaker drivers (four-way, five-way, etc.) may include multiple band-pass filters in addition to a low-pass filter and a high-pass filter.  
         [0005]     Frequencies that are dividing points in a frequency range are known as crossover frequencies. For example, a two-way system may have one crossover frequency, so that frequencies above the crossover frequency are reproduced by a high-frequency speaker driver and frequencies below the crossover frequency are reproduced by a low-frequency speaker driver. Likewise, in a three-way loudspeaker system, it may be desirable to select two crossover frequencies, so that signals below the first crossover frequency drive the low-range speaker driver, signals above the first crossover frequency but below the second crossover frequency are sent to the mid-range speaker driver, and signals above the second crossover frequency drive the high-range speaker driver. Low-pass, band-pass, and high-pass filters used to filter signals for a multi-way loudspeaker system in this manner are known as crossover filters.  
         [0006]     Crossover filters can be placed in a signal path between a signal source, such as a microphone, tape deck, compact disc player, or the like, and power amplifiers that provide power to a multi-way loudspeaker system. In such an arrangement, each power amplifier receives signals in a certain frequency range, and drives limited-range speaker drivers that operate in that frequency range. Alternatively, crossover filters can be placed in a signal path between a power amplifier and limited-range speaker drivers of a multi-way loudspeaker system. In the latter case, the crossover filters may be passive inductor-capacitor (LC) networks. The advantage of a post-amplifier crossover arrangement may be a reduced number of amplifiers in the sound system.  
         [0007]     In a multi-way loudspeaker system using a post-amplifier crossover arrangement, it may be desirable to design crossover filters that achieve a flat response throughout a frequency range. To achieve a flat frequency response in a post-amplifier crossover arrangement, a crossover filter may be designed based on an impedance of a limited-range speaker driver that will operate with the crossover filter. For example a passive LC second order low-pass filter has all of its inductor (L) and capacitor (C) values chosen based upon the driver&#39;s impedance, say  4  Ohms. If the driver&#39;s impedance were to double and the crossover were to remain correctly tuned, the inductors would need to double in value and the capacitors would need to halve in value.  
         [0008]     When a multi-way loudspeaker system using a post-amplifier passive crossover arrangement is operated at high levels for a period of time, the tonal quality of the loudspeaker system may become altered. It has been discovered that this alteration in response is due to changes in the impedances of speaker drivers in a multi-way loudspeaker system as the coils in the speaker drivers become hot. These changes in impedances may cause “bumps” in the frequency response of the multi-way loudspeaker systems, because the crossover filters are usually designed to operate with the “cold” impedances of the speaker drivers and may not be able to adjust inductance (L) and capacitance (C) values to compensate for the higher driver impedances. It would be desirable to provide a sound system that compensates for changes in speaker drivers&#39; impedances in a multi-way loudspeaker system using a post-amplifier crossover arrangement.  
       SUMMARY  
       [0009]     A loudspeaker is provided for receiving an incoming electrical signal and transmitting an acoustical signal. The loudspeaker may include a power amplifier that receives the incoming electrical signal and provides a power signal to two or more passive filters, such as low-pass, band-pass, or high-pass filters, which are coupled to the output of the power amplifier. The passive filters may be coupled to one or more speaker drivers so that the arrangement of passive filters and speaker drivers has a single input with a single combined input impedance. The amplifier may have an output impedance between about 25% and about 400% of the combined input impedance of the arrangement of passive filters and speaker drivers. The power amplifier may include a current-feedback amplifier that is configured to maintain the desired impedance at the output.  
         [0010]     Alternatively, the power amplifier may include a voltage-source amplifier and a “ballast” resistor in series with the output of the voltage-source amplifier. In this arrangement, the resistance of the ballast resistor may be between about 25% and about 400% of the combined input impedance of the arrangement of passive filters and speaker drivers.  
         [0011]     When the power amplifier has an output impedance that is between a quarter and four times the impedance of the combined input impedance of the arrangement of passive filters and speaker drivers, impedance changes in the one or more speaker drivers may not affect the loudspeaker&#39;s frequency response as significantly as when the power amplifier has either an output impedance near zero (voltage source) or near infinity (current source).  
         [0012]     Other systems, methods, features and advantages of the invention will be, or will become, apparent to one with skill in the art upon examination of the following figures and detailed description. It is intended that all such additional systems, methods, features and advantages be included within this description, be within the scope of the invention, and be protected by the following claims. 
     
    
     BRIEF DESCRIPTION OF THE FIGURES  
       [0013]     The invention can be better understood with reference to the following figures. The components in the figures are not necessarily to scale; emphasis is instead being placed upon illustrating the principles of the invention. Moreover, in the figures, like reference numerals designate corresponding parts throughout the different views.  
         [0014]      FIG. 1  is a loudspeaker system.  
         [0015]      FIG. 2  is a schematic for a first example passive filter for the loudspeaker system of  FIG. 1 .  
         [0016]      FIG. 3  is a schematic for a second example passive filter for the loudspeaker system of  FIG. 1 .  
         [0017]      FIG. 4  is a schematic for an example current-feedback amplifier for the loudspeaker system of  FIG. 1 .  
         [0018]      FIG. 5  is a graph of combined hot and cold input impedances versus frequency for the example loudspeaker system of  FIG. 1 .  
         [0019]      FIG. 6  is a frequency response graph for speaker drivers of the example loudspeaker system of  FIG. 1  using an example “voltage source” amplifier.  
         [0020]      FIG. 7  is a combined frequency response graph for speaker drivers of the example loudspeaker system of  FIG. 1  using an example “voltage source” amplifier.  
         [0021]      FIG. 8  is a “frequency response change” graph for speaker drivers of the example loudspeaker system of  FIG. 1  using an example “voltage source” amplifier.  
         [0022]      FIG. 9  is a frequency response graph for the speaker drivers of the example loudspeaker system of  FIG. 1  using the example current-feedback amplifier of  FIG. 4 .  
         [0023]      FIG. 10  is a combined frequency response graph for speaker drivers of the example loudspeaker system of  FIG. 1  using the example current-feedback amplifier of  FIG. 4 . 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0024]      FIG. 1  is a loudspeaker system  100 . The loudspeaker system  100  may include a power amplifier  102 , a first filter  104 , a second filter  108 , a first speaker driver  106  and a second speaker driver  110 . The loudspeaker system  100  may also include an enclosure  112  for housing the power amplifier  102 , the filters  104  and  108 , and the speaker drivers  106  and  110 . The first and second filters  104  and  108 , and the first and second speaker drivers  106  and  110  collectively comprise a driver circuit  114 . The driver circuit  114  has an input impedance.  
         [0025]     The speaker drivers  106  and  110  may each be either a wide-range speaker driver or a limited-range speaker driver, and may cover complimentary parts of the audible spectrum. The speaker drivers  106  and  110  may have coils (not shown) with respective impedances of Z A  and Z B  that may vary with, for example, coil frequency or temperature. The filters  104  and  108  may each be a high-pass, band-pass, or low-pass filter, and may be passive inductor-capacitor filters.  
         [0026]     For example, the first filter  104  may include a fourth-order Butterworth low-pass filter, as shown in  FIG. 2 . The second filter  108  may include a fourth-order Butterworth high-pass filter, as shown in  FIG. 3 . The first and second filters  104  and  108  may also include other types of filters, such as a Chebyshev filters, elliptic filters, or the like, and may also be of other orders. Details for example filters  104  and  108  shown in  FIGS. 2 and 3  are described in greater detail below. The power amplifier  102  may include a current-feedback amplifier with an output impedance, as shown in  FIG. 4  and described below.  
         [0027]     As shown in  FIG. 2 , an example of the first filter  104  may be a fourth-order Butterworth low-pass filter. A Butterworth filter is an all-pole filter having a maximally flat frequency response in a pass-band. Butterworth filters can be derived in various orders where an order is equal to the number of poles of attenuation at infinity for a low-pass filter or the number of poles of attenuation at zero for a high-pass filter. The first filter  104  could also be another type of filter and/or a filter of another order.  
         [0028]     The first filter  104  may include an input  202  and an output  204 . The input  202  may have an input impedance (as seen from the power amplifier  102  ( FIG. 1 )) that is about equal to the impedance of the first filter  104  and the first speaker driver  106  ( FIG. 1 ), which is coupled to the output  204 . The first filter  104  may receive an input signal from the power amplifier  102  at the input  202  and produce a filtered output signal at the output  204 . The illustrated first filter  104  may include a first inductor  206 , a second inductor  208 , a first capacitor  210  and a second capacitor  212 . A desired cutoff frequency ƒ c  in Hertz (the “−3 dB point”) for the first filter  104  has a value in radians of ω c  where: 
 
ω c =2*π* f   c    (1) 
 
 The inductor  206  may have an inductance of L 1 , the second inductor  208  may have an inductance of L 2 , the first capacitor  210  may have a capacitance of C 1 , and the second capacitor  212  may have a capacitance of C 2 . Where the first filter  104  is designed to have a zero Ohm input characteristic termination impedance at input  202 , and an output characteristic termination impedance of R F1  at output  204 , values for L 1 , L 2 , C 1  and C 2  may be determined as follows: 
 
 L   1 =(1.531* R   F1 )/ω c    (2) 
 
 C   1 =1.577/( R   F1 *ω c )   (3) 
 
 L   2 =(1.082* R   F1 )/ω c    (4) 
 
 C   2 =0.383/( R   F1 *ω c )   (5) 
 
 The equations (2)-(5) are equations for calculating component values for a fourth-order Butterworth filter. In other example filters, the components and equations for calculating the component values may be different. The first filter  104  may provide a filtered output signal to the speaker driver  106 . The speaker driver  106  may have a “cold” impedance Z A  of R F1 , so that in this example the impedance of the first filter  104  is chosen to match the cold impedance of the first speaker driver  106 . 
 
         [0029]     Turning to  FIG. 3 , an example of the second filter  108  may be a fourth-order Butterworth high-pass filter. The second filter  108  may include a first capacitor  306 , a second capacitor  308 , a first inductor  310 , and a second inductor  312 . The first capacitor  306  may have a capacitance of C 1  and the second capacitor  308  may have a capacitance of C 2 . The first inductor  310  may have an inductance of L 1  and the second inductor  312  may have an inductance of L 2 . For a desired cutoff frequency ƒ c  in Hertz, a frequency value in radians of ω c  may be calculated according to equation (1). 
        Where the second filter  108  is designed to have a zero Ohm input characteristic termination impedance at input  302 , and an output characteristic termination impedance of R F2  at output  304 , values for C 1 , C 2 , L 1  and L 2  may be determined as follows: 
 
 C   1 =0.653/( R   F2 *ω c )   (6) 
 
 L   1 =0.634 *R   F2 /ω c    (7) 
 
 C   2 =0.924/( R   F2 *ω c )   (8) 
 
 L   2 =2.613 *R   F2 /ω c    (9) 
 
 The equations (6)-(9) are equations for calculating component values for a fourth-order high-pass Butterworth filter. The second filter  108  may provide a filtered output signal to the second speaker driver  110 . The second speaker driver  110  may have a cold impedance Z B  of R F2 , so that in this example the impedance of the second filter  108  is chosen to match the cold impedance of the second speaker driver  110 . 
       
 
         [0031]     As mentioned above, the loudspeaker system  100  may exhibit a degradation in tonal quality if the coils of the speaker drivers  106  and  110  become hot, and the impedances of the coils change. In laboratory experiments, impedances of speaker drivers were observed to increase by as much as 100%. For example, a speaker driver having a cold impedance of 4 Ohms may have an impedance of 8 Ohms when the coil is hot. Such heating may occur, for example, in professional sound reinforcement applications, where power amplifiers frequently produce more than a kilowatt of continuous power. The effect of speaker driver impedance changes on frequency response is described in detail below.  
         [0032]      FIG. 5  is an input impedance versus frequency graph for the example driver circuit  114  shown in  FIGS. 1-3 . The graph of  FIG. 5  compares hot and cold input impedances for the driver circuit  114 . For the driver circuit  114 , the first filter  104  is a fourth-order Butterworth low-pass filter having a cutoff frequency ƒ c  of 1,000 Hz, and the second filter  108  is a fourth-order Butterworth high-pass filter, also having a cutoff frequency ƒ c  of 1,000 Hz. The filters  104  and  108  are each designed to have a zero Ohm input characteristic termination impedance and an output characteristic termination impedance of 4 Ohms.  
         [0033]     In this example, the cold and hot impedances of each speaker driver  106  and  110  are 4 Ohms and 8 Ohms, respectively. For cases where the speaker drivers  106  and  110  are heated to a lesser degree, the impedance increase may be less. The solutions disclosed for correcting tonal quality problems caused by impedance increases work equally well over a wide range of impedance increases, and the use of a 4 Ohm increase in this example should not be considered a limitation. As can be seen in  FIG. 5 , when the speaker drivers  106  and  110  are hot, the input impedance of the driver circuit  114  varies from a high of 8 Ohms at the cutoff frequency ƒ c  to a low of 2 Ohms on either side of the cutoff frequency ƒ c .  
         [0034]     Many commercially available power amplifiers are “voltage source” amplifiers that have an output impedance that is near zero Ohms. A voltage source power amplifier  102  may have an output impedance of, for example, 5 milli-Ohms.  FIG. 6  is a current excitation frequency response graph for the speaker drivers  106  and  110  where a voltage source amplifier is connected to the driver circuit  114 .  FIG. 6  compares the frequency responses when the speaker drivers  106  and  110  are cold to the frequency responses when the speaker drivers  106  and  110  are hot.  
         [0035]     Plot lines  602  and  604  show the magnitudes of currents that flow through the first speaker driver  106  and plot lines  606  and  608  show the magnitudes of currents that flow through the second speaker driver  110 . The intrinsic forcing function of a speaker driver is directly related to currents (Lorentz force) flowing through the speaker driver&#39;s coil, not voltages across the coil. For example, when the coil&#39;s impedance increases, but voltage driving the coil does not, there will be an attendant gain compression as a consequence of a reduction in the voice coil&#39;s current. Therefore, the gains of interest for determining how the loudspeaker system  100  “sounds” are current gains for the coils of the speaker drivers  106  and  110 .  
         [0036]     As can be seen in  FIG. 6 , when the coils of the speaker drivers  106  and  110  are cold, the frequency response is a maximally-flat response, where the cutoff frequency ƒ c  (−3 dB point) for each of the filters  104  and  110  is 1,000 Hz. When the coils of the speaker drivers  106  and  110  are hot, however, the frequency response for each of the filters  104  and  110  has an undesirable “bump” of almost 6 dB near the cutoff frequency. Additionally, the first example filter  104  has a cutoff frequency ƒ c  that is significantly below the desired cutoff frequency of 1,000 Hz, while the second example filter  108  has a cutoff frequency ƒ c  that is significantly above the desired cutoff frequency of 1,000 Hz. As the coils of speaker drivers  106  and  110  heat and cool, resulting in impedance variations, the frequency response for the loudspeaker system  100  will correspondingly vary between the hot and cold plots shown in  FIG. 6 , causing dynamic changes in tonal quality.  
         [0037]      FIG. 7  is a frequency response graph where a voltage source amplifier is used with the driver circuit  114 . Essentially,  FIG. 7  includes one “hot plot”  704  that is equal to the vector sum of the two “hot plots”  604  and  608  from  FIG. 6 , and one “cold plot”  702  that is equal to the vector sum of the two “cold plots”  602  and  606  from  FIG. 6 . As used herein, the terms “hot plot” and “hot frequency response” refer to a plot of a frequency response of the loudspeaker system  100  as a whole and/or plots of frequency responses of the speaker drivers  106  and  110 , when the coils of the speaker drivers  106  and  110  are each hot and each have an impedance of 8 Ohms. Likewise, the terms “cold plot” and “cold frequency response” refer to a plot of a frequency response of the loudspeaker system  100  as a whole and/or plots of frequency responses of the speaker drivers  106  and  110 , when the coils of the speaker drivers  106  and  110  are each cold and each have an impedance of 4 Ohms.  
         [0038]      FIG. 7  shows more clearly the severity of the distortion from the cold frequency response when the coils of the speaker drivers  106  and  110  become hot. As can be seen in  FIG. 7 , the cold plot  702  has about a 3 dB “bump” at the cutoff frequency of 1,000 Hz, which is a natural feature for a fourth order filter that results from phasing the filters  104  and  110  to produce in-phase signals at the cutoff frequency. The hot plot, however, has about a 3 dB dip at the cutoff frequency, which is further complicated by the “bumps” on either side of the cutoff frequency.  
         [0039]     The loudspeaker system  100  lessens frequency response variations, such as those shown in  FIGS. 6 &amp; 7 , which result from temperature changes in the coils of the speaker drivers  106  and  110 . The desired result is a hot frequency response that is relatively flat compared to a cold frequency response. To better illustrate the problem of frequency response fluctuation,  FIG. 8  shows a plot of a “frequency response change” plot  802  that is equal to the hot frequency response plot  704  from  FIG. 7  divided by the cold frequency response plot  702  from  FIG. 7 . Ideally, the frequency response change plot  802  would be a horizontal line at all frequencies, indicating that the hot response  704  is flat with respect to the cold response  702 . As shown in  FIG. 8 , the relative frequency response plot  802 , where a voltage source amplifier is used with the driver circuit  114 , is not ideal.  
         [0040]     The frequency response variations shown in  FIG. 8  that result from temperature changes in the coils of the speaker drivers  106  and  110  may be lessened by using the current-feedback power amplifier  102 , an example of which is shown in  FIG. 4  and described below, instead of a voltage source power amplifier. In particular, the output impedance Z o (s) of the amplifier  102  may be designed to be about equal to the input impedance of the driver circuit  114 . Alternatively, the output impedance Z o (s) of the amplifier  102  may be designed to be more or less than the input impedance of the driver circuit  114 , but significantly more than zero and significantly less than infinite.  
         [0041]     Alternatively, the frequency response variations may be lessened by using a voltage-source amplifier and a “ballast” resistor having an impedance about equal to the input impedance of the driver circuit  114 , where the ballast resistor is coupled in series with the output of the voltage-source amplifier. Such a ballast resistor, however, may dissipate approximately half of the output power of the amplifier. The current-feedback power amplifier  102 , on the other hand, may provide the desired output impedance with almost no power loss.  
         [0042]     As shown in  FIG. 4 , an example current-feedback power amplifier  102  may have an input  402  and an output  404 . The output  404  may have an output impedance. The power amplifier  102  may operate in the frequency (s) domain as follows. The power amplifier  102  may receive an input electrical signal V i (s) at input  402  and generate an output electrical signal V o (s) at output  404 . The power amplifier  102  may include an amplifier  406  having a gain (G), and a current monitor  408 . The current monitor  408  may include a current sensing resistor  410  of value R s  and a difference amplifier  412  having a gain constant K A . The result is a voltage signal V 1 (s) generated by the current monitor  408  which stated as an equation is: 
 
 V   1 ( s )= I   o ( s )* R   s   *K   A    (10) 
 
         [0043]     The power amplifier  102  may also include a summer  416  and a feedback circuit  414 . The feedback circuit  414  may have a transfer ratio of Z F (s) and generate a feedback signal V 2 (s). Therefore, the transfer ratio of Z F (s) of the feedback circuit  414  may be: 
 
 Z   F ( s )= V   2 ( s )/ V   1 ( s )   (11) 
 
         [0044]     The summer  416  may receive the input signal V i (s) and sum it with the feedback signal V 2 (s) from the feedback circuit  414 . Therefore, the output signal V o (s) may be represented as: 
 
 V   o ( s )=[ G*V   i ( s )]+[ G*I   o ( s )* R   s   *K   A   *Z   F ( s )]   (12) 
 
         [0045]     Because impedance is equal to voltage divided by current, the output  404  may have an output impedance of Z o (s) that can be expressed as: 
 
 Z   o ( s )= V   o ( s )/ I   o ( s )   (13) 
 
         [0046]     Solving equations (10) through (13) for V i (s)=0, Z o (s) may be also be expressed as: 
 
 Z   o ( s )= G*R   s   *K   A   *Z   F ( s )   (14) 
 
         [0047]     As shown by equation (14), the power amplifier  102  may be designed to have a desired output impedance Z o (s) by choosing a feedback circuit  414  having a transfer ratio of like form. The product G*R s *K A  may be approximately unity, in which case the output impedance Z o (s) is equal to the transfer ratio Z F (s).  
         [0048]      FIG. 9  is a frequency response graph for the speaker drivers  106  and  110  where the current-feedback amplifier  102  shown in  FIG. 4  drives the driver circuit  114  shown in  FIGS. 1-3 . In this example, the power amplifier  102  has an output impedance about equal to the cold input impedance of the driver circuit  114 . As shown in  FIG. 9 , in this example the hot frequency response plots  904  and  908  for the speaker drivers  106  and  110 , respectively, are flat with respect to the cold frequency response plots  902  and  906 .  
         [0049]     The relative flatness between the hot frequency response plots  904  and  908  and the cold frequency response plots  902  and  906  is more clearly shown in  FIG. 10 .  FIG. 10  includes a cold frequency response plot  1002  that is equal to the sum of the cold frequency response plots  902  and  906 , and a hot frequency response plot  1004  that is equal to the sum of the hot frequency response plots  904  and  908 . The hot frequency response plot  1004  for the loudspeaker system  100  is about 4.5 dB below the cold frequency response plot  1002  over the entire frequency range, including at the cutoff (crossover) frequency. Although not shown, a relative response plot that is equal to the hot frequency response plot  1004  divided by the cold frequency response plot  1002  (a relative frequency response similar to  FIG. 8 ) is indeed a flat line at −4.5 dB from 100 Hz to 10,000 Hz.  
         [0050]     As mentioned above, the output impedance Z o (s) of the power amplifier  102  may be designed to be more or less than the cold input impedance of the driver circuit  114 . Other values for the output impedances Z o (s), such as 2 Ohms and 8 Ohms, also provide flatter relative frequency responses than a voltage-source amplifier provides. Where 2 Ohms is used for the output impedance Z o (s) of the power amplifier  102 , however, the relative frequency response may be under compensated, resulting in a “valley” at the cutoff frequency with two adjacent “bumps” that are about 2 dB above the valley. This result, while not ideal, may still be significantly better than the relative frequency response shown in  FIG. 8  that has a “valley” at the cutoff frequency with two adjacent “bumps” that are about 6 dB above the valley.  
         [0051]     Where 8 Ohms is used for the output impedance Z o (s) of the power amplifier  102 , the relative frequency response may be over compensated, resulting in a “bump” at the cutoff frequency with two adjacent “valleys” that are about 2 dB below the bump. Again, this result may not be ideal, but may still be significantly better than the relative frequency response shown in  FIG. 8 .  
         [0052]     In conclusion, matching an output impedance of an amplifier to a cold input impedance of an arrangement of filters and speaker drivers that is coupled to the output of the amplifier compensates for frequency response changes that may result when the voice coils of the speaker drivers become heated. The loudspeaker system  100  is one such matched configuration that includes a current-feedback amplifier, two speaker drivers, and two fourth-order Butterworth filters. The loudspeaker system  100 , however, could also comprise other types of filters, and/or more filters and speaker drivers.  
         [0053]     For example, when using odd order filters, it may not be possible to obtain a completely flat relative frequency response by impedance matching alone. In such cases, it may be desirable to match the output impedance for the amplifier  102  to a “nominal working” input impedance of the driver circuit  114 , which is somewhere between a hot and a cold input impedance, so that the hot and cold frequency responses are above and below the nominal frequency response.  
         [0054]     While various embodiments of the invention have been described, it will be apparent to those of ordinary skill in the art that many more embodiments and implementations are possible that are within the scope of this invention. Accordingly, the invention is not to be restricted except in light of the attached claims and their equivalents.