Abstract:
An impedance matched resonant circuit uses inductors coupling an audio source and a speaker array in order to reduce feedback reflection induced by an audio signal traveling from the audio source to the array of speakers. An RC circuit could also be coupled to the positive and negative terminals of the speaker array to reduce the slope differential of the audio signal at certain frequencies. The circuit can be packaged together in a single module with switches to activate and deactivate portions of the circuit to alter the effectiveness of the circuit depending upon need.

Description:
[0001]    This application is a continuation-in-part of U.S. application Ser. No. 14/279,111, filed May 14, 2014, which claims the benefit of U.S. Provisional Application No. 61/823,737, filed May 15, 2013. This and all other referenced extrinsic materials are incorporated herein by reference in their entirety. Where a definition or use of a term in a reference that is incorporated by reference is inconsistent or contrary to the definition of that term provided herein, the definition of that term provided herein is deemed to be controlling. 
     
    
     FIELD OF THE INVENTION 
       [0002]    The field of the invention is circuits to achieve substantially reflectionless impedance matching for use with a speaker system. 
       BACKGROUND 
       [0003]    The background description includes information that may be useful in understanding the present invention. It is not an admission that any of the information provided herein is prior art or relevant to the presently claimed invention, or that any publication specifically or implicitly referenced is prior art. 
         [0004]    All publications herein are incorporated by reference to the same extent as if each individual publication or patent application were specifically and individually indicated to be incorporated by reference. Where a definition or use of a term in an incorporated reference is inconsistent or contrary to the definition of that term provided herein, the definition of that term provided herein applies and the definition of that term in the reference does not apply. 
         [0005]    Efforts have been made in the past to match the impedance of an incoming signal to an output load. For example, U.S. Pat. No. 8,254,601 to Feldstein, issued Aug. 28, 2012, entitled “Impedance Matching Speaker Wire System” teaches a compensation circuit connected in series with a speaker system and an incoming signal. More specifically, Feldstein describes a coaxial line having a predetermined characteristic impedance wherein the circuit is configured with circuit components that allow for adjustment of the impedance of the output circuit. Moreover, in Feldstein, the range of frequencies the tuning circuit can process is limited due to its predetermined characteristic impedance resulting in inefficient filtering of some frequencies. As a consequence of the solution presented in Feldstein, the fidelity and level of definition in the music is significantly impaired. 
         [0006]    Additional efforts have been made through the use of capacitors. U.S. Patent Publ. 2007/0189554 to Innis, published Aug. 16, 2007, entitled “Audio speaker including impedance matching circuit” teaches impedance matching through integrated circuitry. By configuring the capacitors in parallel, a user can engage a switch to selectively shunt electrical current around the capacitors. The result is altering of effective speaker impedance. By quantifying the value of the speakers, the matching circuit in Innis is limited to only matching certain predefined input values. Consequently, the efficiency of the matching circuit is generally not optimal. 
         [0007]    Other efforts have been made to achieve reflectionless impedance matching. U.S. Pat. No. 1,832,452 to Feldtkeller et al. teaches a telephone interconnecting circuit that, by propor-tioning resistances to a transmission line, allows for termination that is practically free from reflection and attenuation from a transmitter to loud speakers. This solution, however, fails to take into account that audio signals—unlike transmission line signals—can contain many different frequencies, and thus using a resistor (a static component) to match impedance is suboptimal over a range of frequencies. 
         [0008]    U.S. Pat. No. 7,747,228 to Kasha et al. similarly shows efforts made to reduce signal reflection via impedance matching. Kasha et al. teaches the use of an impedance matching component placed between an amplifier output and an antenna. The result is that signal reflections are either reduced or eliminated. This reference, however, does not provide any detail as to what type of component might be used to achieve the goal of reflectionless impedance matching. 
         [0009]    U.S. Patent Application No. 2009/0175378 to Staszewski et al. teaches a system capable of matching impedances over a wide range of radio frequencies or other high frequency ranges. To accomplish this, it digitally transforms a first load impedance into a second load impedance. However, this reference fails to teach impedance matching using passive components. 
         [0010]    U.S. Application No. 2013/0325149 to Manssen et al. teaches a circuit that can tune impedance to match a frequency coming into an antenna. However, this reference requires active controlling to create matched impedance and thus fails to appreciate that impedance matching can be achieved using passive components. 
         [0011]    U.S. Pat. No. 8,190,109 to Ali et al. describes a system of active impedance matching. It measures the amount of reflected energy and then, using that value, varies the impedance of a component in the system before making another measurement and making another adjustment. In other words, Ali et al. teaches a closed-loop control system for impedance matching. In this way, it can converge on a solution resulting in substantially reflectionless matching. This system, as with Manssen et al., fails to appreciate that substantially reflectionless impedance matching can be achieved without the use of a feedback loop. 
         [0012]    U.S. Pat. No. 8,472,907 to Yamagajo et al. teaches an antenna system that includes one or more impedance matching elements. However, devices of this reference fail to teach impedance matching over a range of frequencies. 
         [0013]    Other related references are similarly deficient. See U.S. Patent Application No. 2010/0081379, U.S. Patent Application No. 2011/0159832A1, U.S. Pat. No. 4,006,315, U.S. Patent Application No. 2007/0201707. 
         [0014]    Thus, there is still a need to further improve the power efficiency of a speaker circuit by providing substantially reflectionless impedance matching using passive circuit components that allow for impedance matching over a wide range of frequencies. 
       SUMMARY OF THE INVENTION 
       [0015]    As used herein, an “array of speakers” has a positive terminal, a negative terminal, and has one or more speakers coupled in parallel and/or serially with those terminals. In one aspect of the inventive subject matter, a circuit is configured to reduce quantization noise present in a signal that has been reconstructed from a digitally encoded audio signal. Preferred embodiments of the circuit include two sets of circuit components, but even more preferred embodiments of the circuit include three sets of circuit components. Each set of circuit components provides improved impedance matching within the overall circuit, where the overall circuit also includes the audio signal source and the array of speakers. 
         [0016]    To accomplish this, the circuit includes at least three inductors and a capacitor. These components are organized two sets of components, where both sets are in series with each other and also with an audio signal source and an array of speakers. One set of components includes at least two inductors and a capacitor, and is coupled to both the positive terminal of the audio signal source and the positive terminal of the array of speakers. Another set of components includes at least one inductor and is coupled to both the negative terminal of the array of speakers and the negative terminal of the audio signal source. In some embodiments, this set of components can also include two inductors and a capacitor arranged in the same way. The first and second circuitry are coupled to the terminals as described above either directly or indirectly (e.g., wired or wirelessly, or having some other components between the described circuitry and the audio signal source and/or the array of speakers). 
         [0017]    In the circuitry components coupled to the positive terminals, an inductor is in series with a capacitor and both are in parallel with another inductor, such that a signal traveling from an audio signal source would encounter the inductors before encountering the capacitor. With this configuration the inductors work to prevent very high frequency signals from passing to the speakers (e.g., frequencies above 20 kHz, or more preferably 25 kHz). However, some amount of very high frequency signal will nevertheless make it past the first and second inductors. Since an inductor and the capacitor are in parallel with the other inductor, the signal will be split. On the branch with the inductor and the capacitor, the signal will pass the inductor before encountering the capacitor. On the other side, the signal will pass through the second inductor to the array of speakers. 
         [0018]    When high frequency portions of an audio signal move past the inductor on the branch of the circuit with the capacitor, the capacitor collects charge. As the same signal travels to the array of speakers along the branch of the circuit without the capacitor, the capacitor discharges into the signal. Charge from the capacitor is “injected” back into the audio signal slightly out of phase (i.e., lagging behind the signal). In this way, the capacitor helps to rebuild portions of the signal that are missing information resulting from the reconstruction of the signal from a digitally encoded audio file. 
         [0019]    In preferred embodiments, at least one of the first, second, and third inductors used with the circuit includes a paramagnetic material within the core. In other embodiments, the inductors include at least a ferromagnetic material, while in still further embodiments the inductors include some combination of one or more paramagnetic materials or one or more ferromagnetic materials. 
         [0020]    In another aspect of the inventive subject matter, the impedance matching qualities of the speaker are improved by the addition of a resistor and a capacitor (or their Thevenin equivalent components). In preferred embodiments, a resistor and a capacitor are in series with each other and positioned such that they are in parallel with the array of speakers. The resistor and the capacitor act as a high-pass filter (e.g., as frequency approaches infinity, the impedance of the capacitor approaches zero). Resistance and capacitance can be selected such that frequencies above a certain range are allowed to pass through the resistor and capacitor. The end result is that undesirable high frequency signals do not pass through the array of speakers, in effect improving sound quality by allowing the array of speakers to avoid reproduction of sounds that result from digital encoding and decoding. 
         [0021]    In a preferred embodiment, the circuit described above additionally includes switches to allow for phase shifting. The switches are configured to allow an audio signal to circumvent the inductors and capacitors (i.e., switches are in parallel with these components). Additionally a switch is preferably in series with the resistor and capacitor such that, when the switch is open, no signal can pass through the resistor or capacitor. 
         [0022]    These switches can be operated either manually or electronically. When operated electronically, a computer system can be implemented to effect precise phase shifting as needed to maximize sound production efficiency in the array of speakers. In preferred embodiments, the switches are operated individually or in tandem by a computer controlled system. 
         [0023]    In another aspect of the inventive subject matter, both the circuitry connected to the positive terminals of the audio signal source and the array of speakers and the circuitry coupled to the negative terminals of the same include at least two inductors and a capacitor. This configuration provides the benefit of a capacitor to both the positive and negative terminals of the array of speakers. Because audio signals fluctuate about 0 volts, it is advantageous to smooth the signal travelling to both the positive and negative terminals of the array of speakers. 
         [0024]    Preferred embodiments also include a resistor and capacitor that are in series with one another and in parallel with the array of speakers. The resistor and capacitor, as with the embodiment described above, provide filtering to allow signals above a particular frequency to pass (e.g., above 20 kHz or more preferably above 25 kHz). Because the resistor and capacitor are in parallel with the array of speakers, when signal passes through the resistor and capacitor, it does not pass through the array of speakers, thereby preventing frequencies above its cutoff range from reaching the array of speakers. 
         [0025]    In addition, the resistor and capacitor can be tuned to provide improved impedance matching. Either the resistor or the capacitor, or both, can be varied either manually or electronically. Varying the resistance and/or capacitance of the resistor and/or capacitor can provide improved impedance matching by changing the effective impedance of an array of speakers (i.e., because the resistor and capacitor are in parallel with the array of speakers, the effective impedance of the speakers is decreased by some factor depending on the resistance and capacitance of the resistor and capacitor). 
         [0026]    To maintain impedance matching and a desirable balance between the circuitry coupled to the positive terminals of an audio signal source and an array of speakers and the circuitry coupled to the negative terminals of an audio signal source and an array of speakers, the Thevenin equivalent impedances of those circuitries should be approximately equivalent. It is contemplated that the circuitries&#39; resultant impedances should be within 15% of one another. 
         [0027]    In preferred embodiments, switches can again be implemented to effect phase shifting. The switches must be positioned such that, when in the closed position, an audio signal circumvents the inductors and capacitors coupled to the positive and negative terminals of the array of speakers and the audio signal source, and such that signal cannot pass through the resistor and capacitor. The switches can be operated either manually or automatically, but preferably the switches are operated electronically such that a computer system can be implemented to open and close the switches very quickly. 
         [0028]    In preferred embodiments, the inductors include a gap portion and a core portion. The gap portion can be comprised of air or some other material, but in preferred embodiments the gap portion includes at least one of a ferromagnetic and a diamagnetic material. By including different materials in the gap and the core, the inductors can be designed to exhibit various, desired properties (e.g., different permeability and frequency response characteristics). 
         [0029]    The inductors coupled to the positive and/or negative terminals are preferably made at least in part with one or more magnetically responsive materials including, for example, paramagnetic materials, diamagnetic materials, and/or ferromagnetic materials. Generally the magnetically responsive material(s) would comprise the core and/or gap of the inductor(s). The core and/or gap can be formed into a cylinder or bar with wire wrapped around it, or in any other suitable arrangement. Another possible configuration includes, for example, a toroid with the coil of wire threaded through the central hole. In some embodiments, the inductor comprises a combination of materials, such as two ferromagnetic, diamagnetic, and/or paramagnetic bars separated by a ferromagnetic, diamagnetic, and/or paramagnetic material in the gap portion between the bars or a ferromagnetic, diamagnetic, and/or paramagnetic toroid having a ferromagnetic, diamagnetic, and/or paramagnetic gap. 
         [0030]    The inductance of each inductor determines a frequency beyond which amplitude drop-off occurs for signals passing through each inductor. Taking advantage of this effect, inductors can be selected and/or designed to create signal drop-off at a desired frequency. In embodiments where a user might prefer a drop off in signal levels beyond a first frequency at one time, and a drop off in signal levels beyond a second frequency at a second time, a plurality of inductors could be provided having switches that activate preferred inductors and deactivate non-preferred inductors. Alternatively, a variable inductor could be provided that is configured to vary inductance of the inductor coupled to the positive terminal and/or the negative terminal, allowing a user to tune the circuit to produce a preferred sound quality. Switches could be provided that bypass the inductor altogether in embodiments where a user might not want the input signal to be altered by an inductor at all. A single control station could, for example, set the inductance in a first circuit to be 100 μH during the first 30 seconds of a song, raise the inductance to be 500 μH for the next 30 seconds, and then lower the inductance to 300 μH for the rest of the song. In this manner, a user could configure an audio enhancement kit to have a plurality of signal drop-off levels throughout a song from a single control station, where that song has a range of frequencies. 
         [0031]    In embodiments where there is an inductor coupled to the negative terminal of the array of speakers, the inductor is configured to provide improved impedance matching. By matching the impedance between the negative terminal of the array of speakers and the negative terminal of the audio signal source, the array of speakers is able to perform better, because the driver of any speaker in the array of speakers would be able to more freely resonate. This effect is brought about by the inductor&#39;s tendency to absorb current generated by the electromagnetic effect of the permanent magnet of a speaker moving relative to a voice coil. Thus, coupling inductors to both the positive and negative terminals of the array of speakers provides the benefit of compensating for electromagnetic effects on both the positive and negative sides of the array of speakers. In preferred embodiments, it is advantageous for the circuitry coupled to the negative terminal of the array of speakers to have an impedance that is substantially similar to the impedance of the circuitry coupled to the positive terminal of the array of speakers. 
         [0032]    In preferred embodiments, the different components of the circuit are variable, either mechanically or electrically. For example, the capacitors of some embodiments are varied mechanically to adjust their capacitances. Such adjustments can change the resultant Thevenin equivalent impedance of the various circuitries, allowing a user to physically adjust the capacitances to, in effect, tune the circuit&#39;s response to an audio signal. In other embodiments, the capacitance of the capacitor can be adjusted electronically (e.g., via an electrical signal from a computer or other signal generating component). In still other embodiments, at least one of the first, second, and third inductors can be variable (e.g., mechanically, electronically, or otherwise). 
         [0033]    It should be apparent to those skilled in the art that many modifications besides those already described are possible without departing from the inventive concepts herein. The inventive subject matter, therefore, is not to be restricted except in the spirit of the appended claims. Moreover, in interpreting both the specification and the claims, all terms should be interpreted in the broadest possible manner consistent with the context. In particular, the terms “comprises” and “comprising” should be interpreted as referring to elements, components, or steps in a non-exclusive manner, indicating that the referenced elements, components, or steps may be present, or utilized, or combined with other elements, components, or steps that are not expressly referenced. Where the specification claims refers to at least one of something selected from the group consisting of A, B, C . . . and N, the text should be interpreted as requiring only one element from the group, not A plus N, or B plus N, etc. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWING 
         [0034]      FIG. 1  shows a circuit for improving efficiency of an array of speakers that includes an inductor and a capacitor. 
           [0035]      FIG. 2  shows a circuit for improving efficiency of an array of speakers that includes two inductors. 
           [0036]      FIG. 3  shows a circuit for improving efficiency of an array of speakers that includes two inductors, a resistor, and a capacitor. 
           [0037]      FIG. 4  shows a circuit for improving efficiency of an array of speakers that includes two inductors, a resistor, a capacitor, and three switches. 
           [0038]      FIG. 5  is an abstract depiction of a box that can contain a circuit for improving the efficiency of an array of speakers. 
           [0039]      FIGS. 6   a  and  6   b  illustrate possible configurations for a specialized inductor that can be used in the circuit. 
           [0040]      FIGS. 7   a  and  7   b  shows both theoretical and actual gain characteristics of an embodiment of the circuit using the specialized inductor of  FIG. 6 . 
           [0041]      FIG. 8  shows a depiction of an original analog signal, a quantized version, and a reconstructed version of that signal created using the circuit. 
           [0042]      FIG. 9  shows a circuit for improving efficiency of an array of speakers and reducing quantization noise present in an audio signal. 
           [0043]      FIG. 10  shows a circuit as in  FIG. 9  that also includes a resistor and capacitor to further improve impedance matching. 
           [0044]      FIG. 11  shows a circuit as in  FIG. 10  that also includes switches to allow for phase shifting of an audio signal. 
           [0045]      FIG. 12  shows a circuit as in  FIG. 9  that has symmetric components between the positive and negative terminals of an array of speakers and an audio signal source. 
           [0046]      FIG. 13  shows a circuit of  FIG. 12  that also has a resistor and capacitor to further improve impedance matching. 
           [0047]      FIG. 14  shows a circuit as in  FIG. 13  that also includes switching as in  FIG. 11  to allow for phase shifting of an audio signal. 
       
    
    
     DETAILED DESCRIPTION 
       [0048]    Various objects, features, aspects and advantages of the inventive subject matter will become more apparent from the following detailed description of preferred embodiments, along with the accompanying drawing figures in which like numerals represent like components. 
         [0049]    The following discussion provides many example embodiments of the inventive subject matter. Although each embodiment represents a single combination of inventive elements, the inventive subject matter is considered to include all possible combinations of the disclosed elements. Thus if one embodiment comprises elements A, B, and C, and a second embodiment comprises elements B and D, then the inventive subject matter is also considered to include other remaining combinations of A, B, C, or D, even if not explicitly disclosed. 
         [0050]    In some embodiments, the numbers expressing quantities of ingredients, properties such as concentration, reaction conditions, and so forth, used to describe and claim certain embodiments of the invention are to be understood as being modified in some instances by the term “about.” Accordingly, in some embodiments, the numerical parameters set forth in the written description and attached claims are approximations that can vary depending upon the desired properties sought to be obtained by a particular embodiment. In some embodiments, the numerical parameters should be construed in light of the number of reported significant digits and by applying ordinary rounding techniques. Notwithstanding that the numerical ranges and parameters setting forth the broad scope of some embodiments of the invention are approximations, the numerical values set forth in the specific examples are reported as precisely as practicable. The numerical values presented in some embodiments of the invention may contain certain errors necessarily resulting from the standard deviation found in their respective testing measurements. 
         [0051]    As used in the description herein and throughout the claims that follow, the meaning of “a,” “an,” and “the” includes plural reference unless the context clearly dictates otherwise. Also, as used in the description herein, the meaning of “in” includes “in” and “on” unless the context clearly dictates otherwise. 
         [0052]    The recitation of ranges of values herein is merely intended to serve as a shorthand method of referring individually to each separate value falling within the range. Unless otherwise indicated herein, each individual value is incorporated into the specification as if it were individually recited herein. All methods described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The use of any and all examples, or exemplary language (e.g. “such as”) provided with respect to certain embodiments herein is intended merely to better illuminate the invention and does not pose a limitation on the scope of the invention otherwise claimed. No language in the specification should be construed as indicating any non-claimed element essential to the practice of the invention. 
         [0053]    Groupings of alternative elements or embodiments of the invention disclosed herein are not to be construed as limitations. Each group member can be referred to and claimed individually or in any combination with other members of the group or other elements found herein. One or more members of a group can be included in, or deleted from, a group for reasons of convenience and/or patentability. When any such inclusion or deletion occurs, the specification is herein deemed to contain the group as modified thus fulfilling the written description of all Markush groups used in the appended claims. 
         [0054]    As used herein, and unless the context dictates otherwise, the term “coupled to” is intended to include both direct coupling (in which two elements that are coupled to each other contact each other) and indirect coupling (in which at least one additional element is located between the two elements). Therefore, the terms “coupled to” and “coupled with” are used synonymously. 
         [0055]    As used herein, a “capacitor” can be either a single component having a capacitance, or any combination of commonly used circuit components that have the same Thevenin equivalent capacitance. As used herein, an “inductor” can be either a single component having an inductance, or any combination of commonly used circuit components that have the same Thevenin equivalent inductance. 
         [0056]    The inventive subject matter described herein is directed to a circuit that minimizes signal reflection by substantially matching the impedances of an audio signal source (e.g., a music player, an amplifier, etc.) and an array of speakers. As defined herein the term “array of speakers” means one or more speakers that are coupled with each other in series and/or in parallel. In addition, some embodiments of the circuit modify an audio signal to reduce quantization errors. 
         [0057]    When a power source, such as an audio amplifier, feeds an array of speakers, the power transferred between the two is limited by the extent to which the impedances of the two are matched. Two types of impedance matching exist in electrical circuits. The first is maximum power transfer matching and the second is electrical matching. Both are described in detail below. 
         [0058]    To obtain maximum power transfer from a source to a load, the load impedance must be matched to the source impedance. For a resistive circuit, this match is achieved by ensuring the source and load resistances are equal. For a complex circuit that includes a time dependent signals, such a match is achieved when the load impedance is the complex conjugate of the source impedance. 
         [0059]    Maximum power transfer matching is advantageous when the goal is to get as much power as possible out of a source and neither the source nor the feed impedances can be changed. However, a system designed for maximum power transfer is not always the most efficient system and, in fact, efficiency of such a system is half that of a system matched for reflectionless signal transmission. 
         [0060]    When an electrical signal encounters a resistance (or an impedance), a portion of that signal can be reflected back toward the source. In reflectionless matching, source and load impedances are matched such that substantially no part of an electrical signal is reflected back to the source. In the case of a circuit dealing with a non-time dependent signal, reflectionless matching is achieved by the extent to which the real component of the source and load impedances are equal. For complex circuits that handle AC signals, reflectionless matching is achieved when both the real and imaginary parts of the source and load impedances are equal. Note that reflectionless matching and maximum power transfer matching have the same result for non-time dependent signals since a signal that is not time dependent will have no complex component. 
         [0061]    Signal reflection is undesirable in many applications, including for example, sound reproduction. Signal reflection can cause issues including amplification of some frequencies, cancellation of other frequencies, and it can affect dynamic ranges and cause distortion. 
         [0062]    Impedance matching in the case of a DC circuit (i.e., a circuit without a complex source) can be achieved by matching a source resistance with a load resistance. As used herein, a “source resistance” is a Thevenin equivalent resistance of a signal source while a “load resistance” is a Thevenin equivalent resistance of a load. Matching these resistances results in maximum power dissipated across the load resistance. This can be explained using Ohm&#39;s law and the equation describing electronic power. Ohm&#39;s law is, 
         [0000]    
       
      
       V=IR  
      
     
         [0000]    and electronic power is described as, 
         [0000]    
       
      
       P=IV  
      
     
         [0000]    where V is voltage, I is current, R is resistance, and P is power. 
         [0063]    For example, given a source having a constant resistance of 50Ω and constant voltage of 100 V, Table 1 shows how power dissipated by the load is affected when the load resistance (R Load ) is varied from 45 to 55Ω. Notably, power dissipation in the load is maximized when the source resistance is equal to the load resistance. 
         [0000]    
       
         
               
               
               
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 V Load   
                 I 
                 R Load   
                 P Load   
               
               
                   
                   
               
             
             
               
                   
                 47.4 
                 1.05 
                 45 
                 49.861 
               
               
                   
                 47.9 
                 1.04 
                 46 
                 49.913 
               
               
                   
                 48.5 
                 1.03 
                 47 
                 49.952 
               
               
                   
                 49.0 
                 1.02 
                 48 
                 49.979 
               
               
                   
                 49.5 
                 1.01 
                 49 
                 49.995 
               
               
                   
                 50.0 
                 1.00 
                 50 
                 50.000 
               
               
                   
                 50.5 
                 0.99 
                 51 
                 49.995 
               
               
                   
                 51.0 
                 0.98 
                 52 
                 49.981 
               
               
                   
                 51.5 
                 0.97 
                 53 
                 49.958 
               
               
                   
                 51.9 
                 0.96 
                 54 
                 49.926 
               
               
                   
                 52.4 
                 0.95 
                 55 
                 49.887 
               
               
                   
                   
               
             
          
         
       
     
         [0064]    This is also true for AC signal sources (e.g., an audio signal source). In AC circuits, there are two types of impedance matching: reflectionless matching and maximum power transfer matching. The circuit of the inventive subject matter represents an effort to achieve reflectionless impedance matching between an audio signal source and an array of speakers. For purposes of explanation of the concept, the audio signal source is referred to as having a source impedance and the array of speakers is referred to as having a load impedance. It should be recognized that perfectly reflectionless matching may be unattainable for audio signal sources and speaker arrays that have different impedances, but the inventive subject matter is drawn toward a novel new system of minimizing, or at least substantially reducing, signal reflection. 
         [0065]    Impedance is different from resistance in that impedance takes into account reactance as well as resistance. In a broad sense, impedance is a measure of opposition that a circuit presents to a current when a voltage is applied. More specifically, impedance has a resistance value and a reactance value. It is expressed as, 
         [0000]    
       
      
       Z=R+jX  
      
     
         [0000]    where Z is impedance, R is resistance, X is reactance, and j is the imaginary unit. Simply put, impedance can be any combination of resistors, capacitors, and inductors, where the real component of impedance is resistance and the imaginary component is reactance (e.g., capacitor and/or inductor reactance). Finally, impedance can similarly be applied to Ohm&#39;s law as, 
         [0000]    
       
      
       V=IZ  
      
     
         [0000]    thus extending Ohm&#39;s law to AC circuits. 
         [0066]    Because of the similarities between DC circuits and AC circuits, impedance matching can be accomplished in AC circuits in a manner similar to resistance matching in DC circuits. As mentioned above, there are two types of impedance matching that can be accomplished in AC circuits. This results from the fact that impedance in AC circuits has a complex reactance component as well as a resistive component. The first type of impedance matching results in maximum power transfer and is achieved by matching a source impedance with the complex conjugate of a load impedance. This is expressed as, 
         [0000]        Z   S   =Z   L * 
         [0000]    where Z S  is a source impedance and Z L  is a load impedance, the asterisk represents the complex conjugate of the variable Z L *. 
         [0067]    The second type of impedance matching results in minimized signal reflection from the load, Z L . To minimize signal reflection source impedance and load impedance must be equal. This is expressed as, 
         [0000]    
       
      
       Z 
       S 
       =Z 
       L  
      
     
         [0000]    where Z S  is a source impedance and Z L  is a load impedance. 
         [0068]    In the inventive subject matter, the goal is to minimize signal reflection between a load (e.g., an array of speakers) and a source (e.g., an audio signal source). In the case of an audio signal source and an array of speakers, both source and load impedances are functions of frequency. Frequency dependence of reactance makes impedance matching difficult when frequency constantly varies as with an audio signal (e.g., music and/or audio books). The impedance of a source and a load may not vary by the same amount across all frequencies resulting in a mismatch leading to signal reflection. 
         [0069]    Embodiments of the inventive subject matter solve this problem by providing a circuit comprising at least one inductor between the signal source and the load. When an inductor having an appropriate inductance is placed between an audio signal source and an array of speakers, it will naturally provide some degree of impedance matching. An inductor can be placed in different locations of the circuit (e.g., on the positive side that couples the positive terminal of an audio signal source to the positive terminal of an array of speakers and/or on the negative side that couples the negative terminal of an array of speakers to the negative terminal of an audio signal source) to provide optimal impedance matching for different speaker set ups and/or different ranges of audio signals. 
         [0070]    The circuit additionally reduces quantization error instantiated during analog-to-digital conversion of an audio signal into a digital format. Quantization distortion is also known as quantization error, and it represents a difference between an actual analog value and a corresponding quantized digital value. Such errors are caused by rounding or truncation of an audio signal when it is encoded into a digital format. 
         [0071]    Quantization errors are often manifested during signal reconstruction from a digital format: the signal is rebuilt into as many segments as were originally sampled, resulting in digital “jumps” in signal amplitude along sloped portions. Since these jumps represent sharp rises or falls in a signal, the frequency associated with a jump is typically very high (e.g., greater than 20 kHz). 
         [0072]    Circuits of the inventive subject matter accomplish this by virtue of the reactance of inductors. Inductor reactance is expressed as, 
         [0000]    
       
      
       X 
       L 
       =ωL  
      
     
         [0000]    where ω is frequency in radians and L is inductance. Therefore, as ω approaches infinity, the reactance of the inductor similarly approaches infinity. Based on the inductance of the particular inductor used in some embodiments of the circuit, reactance can approach infinity at different rates. Thus, very high frequency signals will be excluded by the inductors to some degree. 
         [0073]    A simple analogy to mechanical systems provides an excellent example for easy understanding. Inductors can be viewed as operating as a mass does in a mechanical system. So for example, in a rotational system, flywheels are used to prevent sudden changes in rotational velocity. The same is true of inductors in an electrical system—inductors can be viewed as acting as flywheels to prevent sudden changes in current. Depending on the mass of the flywheel (i.e., inductance), sensitivity to change can be tuned to a desired level. 
         [0074]    The result of passing an audio signal through the circuit is that quantization errors in the audio signal will be reduced according to the selected inductance for each inductor in the circuit (e.g., 10 μH, 15 μH, 20 μH, 25 μH, 30 μH, 45 μH, 50 μH, 10-15 μH, 15-20 μH, 20-25 μH, 25-30 μH, 30-35, μH, 35-40 μH, 40-45 μH, 45-50 μH, 50-100 μH, 100-200 μH, 500 μH, 1-10 mH, 10-50 mH, 50-100 mH, 100-250 mH, 250-400 mH 400-500 mH). Ultimately, the circuit is configured to not only match the impedances of an audio signal source and an array of speakers, it is also configured to modify an audio signal so that the signal better imitates the original analog waveform. 
         [0075]      FIG. 1  depicts an example circuit  100  disposed to couple an audio source (not shown) and an array of speakers  114  and reduces signal reflection by improving impedance matching. The circuit  100  comprises an inductor  110 , a resistor  112 , and a capacitor  116 . The circuit  100  has four terminals  102 ,  104 ,  106 , and  108 , coupled to a positive terminal of an audio signal source, a negative terminal of an audio signal source, a positive terminal of an array of speakers, and a negative terminal of an array of speakers, respectively. The audio signal source coupled to terminal  102 , generates an audio signal that can fluctuate in frequency (e.g., primarily frequencies between 20 Hz and 20 kHz for sounds detectible by most humans, but could also include frequencies between 20 kHz-100 kHz and/or 100 kHz-200 kHz caused by noise in the signal). The audio signal generated by the audio signal source enters the circuit  100  via terminal  102 , passes to the array of speakers  114  via terminal  106 , passes to the circuit  100  from the array of speakers  114  via terminal  108 , and finally passes back to the audio signal source (or to some other component, like ground) via terminal  104 . In this particular configuration, the inductor  110  is located on the positive side of the circuit  100  that connects directly to the positive terminals  102  and  106 . As used herein with respect to circuits, the term “directly” means there is no intervening electrical component. 
         [0076]    The inductor  110  is generally configured to match the impedances of the audio signal source and the array of speakers  114 . In this embodiment, the audio signal source and the array of speakers  114  can each have different Thevenin equivalent impedances, and the circuit  100  provides a balancing effect between the two to create an impedance match. As mentioned above, the frequency of an audio signal can fluctuate, which affects the impedances of both the audio signal source and the array of speakers  114 . As such, the circuit  100  substantially compensates for changes in frequency to maintain impedance matching between the audio signal source and the array of speakers. For example, if the audio signal source has an impedance of 6 Ohms at some frequency, and the array of speakers  114  has an impedance of 8 Ohms at that frequency, then the circuit will provide approximately 2 Ohms of impedance at that frequency. The result is that the audio signal source impedance combined with the inductor impedance is approximately 8 Ohms, which matches the impedance of the array of speakers  114 . 
         [0077]    Similarly, if the audio signal source has a Thevenin equivalent impedance of 8 Ohms at some frequency and the array of speakers  114  has a Thevenin equivalent impedance of 6 Ohms at that frequency, the circuit will again provide 2 Ohms of impedance at that frequency. This helps to balance the two because when looking from the audio signal source toward the array of speakers, the equivalent impedance of the audio signal source with the circuit  100  is 8 Ohms, thus eliminating, or substantially reducing, reflection of the audio signal from the array of speakers back towards terminal  102 . 
         [0078]    Since the frequency of the audio signal tends to vary over time, the impedance selected for inductor  110  is generally determined about an average frequency over the span of a selection of music, or a preferred frequency, such as a sustained note. Where inductor  110  is a variable inductor, a control unit (not shown) could be included that allows a user to select the inductance of inductor  110 . In some embodiments where the inductance of the audio source and the array of speakers  114  is known, a control unit (not shown) of inductor  110  could allow a user to select a frequency, and inductor  110  will adjust to that frequency. For example, the control unit could be configured to impedance match the best at 1 kHz, at 5 kHz, and at 10 kHz, where a user simply selects the preferred frequency of the circuit. Where inductor  110  is a variable inductor, a user could vary the inductance of inductor  110  until the circuit matches the impedance of the input audio source and speaker array  114  about the preferred frequency, or preferred frequencies where the user wishes to have one preferred frequency for one song, and another preferred frequency for a second song. 
         [0079]    The circuit  100  also includes a resistor  112  and a capacitor  116  that are in series with each other while in parallel with the array of speakers  114 . The resistor  112  and capacitor  116  act as a high-pass filter preventing high frequency signals above a certain frequency from reaching the array of speakers  114 . This is caused by the nature of the impedance of a capacitor, described as, 
         [0000]    
       
         
           
             
               X 
               C 
             
             = 
             
               1 
               
                 ω 
                  
                 
                     
                 
                  
                 C 
               
             
           
         
       
     
         [0000]    where X C  is the impedance of a capacitor, ω is the frequency of the signal, and C is capacitance. As frequency approaches infinity, the impedance of a capacitor approaches 0. The effect of this is that a signal having a very high frequency will tend to pass through resistor  112  and capacitor  116  instead of through the array of speakers  114 , since current tends to travel through the path of least resistance (or impedance). By placing a resistor  112  and a capacitor  116  in series with each other, a “drop-off” in signal occurs above some frequency. Changing the resistance and capacitance will change both the slope of the ramp portion of the drop-off and the frequency above which the drop-off occurs. 
         [0080]    Resistance in embodiments of the circuit  100  can be varied in a number of different ways. In one way, a resistor can be incorporated into the circuit  100  such that it is simply plugged in, and when a different resistance is desired, a different resistor can be plugged in. Another way to vary resistance is to incorporate a potentiometer into the circuit. Potentiometers are typically manually operated, although electronically operated variable resistors are also contemplated. Capacitor control can be achieved similarly. For example: capacitors having difference capacitances can be plugged into the circuit depending on the desired traits of the circuit; variation in capacitance can be achieved mechanically via manual manipulation (e.g., operating a screw); or capacitance can be modified electronically using, for example, a computer or a microcontroller. Similar to the exemplary control unit above, another control unit could be included that allows a user to select the resistance of resistor  112  and capacitance of capacitor  116 , or the drop-off frequency itself. 
         [0081]      FIG. 2  depicts another exemplary circuit  200  for matching impedance between an audio source and an array of speakers  214 . Instead of having just one inductor as shown in the circuit  100  of  FIG. 1 , the circuit  200  includes two inductors  210  and  212 . As shown, the two inductors  210  and  212  are located on different sides of the circuit  200 . Specifically, a first inductor  210  is located on the positive side of the circuit  200  and is coupled to the positive terminal of the audio signal source and the positive terminal of the array of speakers. A second inductor  212  is located on the negative side of the circuit  200  and is coupled to negative terminal of the audio signal source and the negative terminal of the array of speakers.  FIG. 2  also shows that the resistor and capacitor of  FIG. 1  can be optional to the circuit. 
         [0082]    Providing a second inductor  212  on the other side of the circuit  200  (i.e., between the negative terminal of the array of speakers  206  and the negative terminal of the audio signal source  204 ) further helps to match impedance. An audio signal is typically an AC sinusoidal signal and thus fluctuates about a 0 value (i.e., 0 volts). Thus, the audio signal drives current in both directions through the circuit  200 , which causes the diaphragm(s) of the speaker(s) in the array of speakers to be actively pulled in different directions by the voice coil(s) to create sound waves. Because current travels in both directions through the circuit and the array of speakers, it can be advantageous for the circuit to be symmetrical. This symmetry results in the ability of the circuit to compensate for the electromagnetic effects caused by movement of the permanent magnet in the speaker driver(s) relative to the voice coil of the driver(s). Having inductors on both sides allows the circuit  200  to absorb current created by such movement and allow the speaker diaphragm(s) in the array of speakers  214  to more freely resonate without experiencing as much mechanical reluctance caused by the electromagnetic effect of the permanent magnet(s) moving relative to the voice coil(s). 
         [0083]      FIG. 3  is a circuit diagram of an embodiment of the circuit  300  having two inductors  310  and  312 , a resistor  316 , and a capacitor  318 . As discussed in relation to  FIG. 1 , the resistor  316  and capacitor  318  act as a low-pass filter, and, as discussed above, the inductors  310 ,  312  help to achieve substantially reflectionless impedance matching between the audio signal source (e.g., an amplifier) and the array of speakers  314 . An audio signal enters the circuit through terminal  302 , passes through inductor  310 , and is affected by the filtering properties of the resistor  316  and the capacitor  318  before leaving the circuit via terminal  306 . Terminal  306  is coupled to the positive terminal of the array of speakers  314 , which the signal passes through before returning to the circuit via terminal  308 . From there, it passes back through terminal  304  to the audio signal source. 
         [0084]    The embodiment of  FIG. 3  brings together two key advantageous aspects (both described in more detail above): (1) the advantages of a circuit  300  having an inductor  310  between the positive terminals of the audio signal source and the array of speakers, as well as an inductor  312  between the negative terminals of the same, and (2) the advantages of having a resistor  316  and capacitor  318  across the positive and negative terminals of the array of speakers  314 . 
         [0085]    Having the resistor  316  and the capacitor  318  coupled to the positive and negative terminals allows the signal or a portion of the signal to pass back to the audio signal source without first travelling through the array of speakers  314 , as discussed above. In this embodiment, any signal, or portion of a signal, circumventing the array of speakers  314  will nevertheless encounter this inductor  312 . 
         [0086]    When signal passes through the resistor  316  and the capacitor  318 , and subsequently encounters inductor  312 , the signal that passed through the speakers is phase shifted relative to the signal that has passed through the resistor  316  and the capacitor  318 . Signal that has passed through the resistor and the capacitor encounters signal that has passed through the array of speakers and cancels out the phase shift brought on by the array of speakers, thus allowing the inductor  312  to operate more effectively and in sync with the other inductor  310 . One advantageous result of this, as discussed above, is that the speakers are able to more freely mechanically resonate since the inductors are able to absorb electromagnetically induced current. 
         [0087]      FIG. 4  is a circuit diagram of another embodiment of the circuit  400 . It is similar to the circuit of  FIG. 3 , except that it includes switches. The switches  420 ,  422 ,  424  can be closed to essentially take the corresponding circuit component out of the circuit. For example: if switch  420  is closed, then inductor  410  is shorted out of the circuit; if switch  422  is closed, then resistor  416  and capacitor  418  are removed from the circuit; and if switch  424  is closed, then inductor  412  is shorted out of the circuit. 
         [0088]    Operating switches  420 ,  422 , and  424  in a coordinated fashion can produce desirable results, such as phase shifting of an audio signal. The switches  420 ,  422 , and  424  can be mechanical relays, electronic switches such as, for example, transistors, or any other switches known in the art. Switches  420 ,  422 , and  424  can additionally be operated either mechanically or electronically. Mechanical operation involves mechanically changing the state of a switch, while electronic operation involves changing the state of a switch using electricity (e.g., a transistor). 
         [0089]    A phase shift in this context can refer to any change in phase of a signal, or in the phase difference between two or more signals. In the embodiment of  FIG. 4 , the desired phase shift involves shifting an audio signal in the time domain. In other words, the signal is delayed by some fraction of time, causing the wave form to lag in time behind where it might otherwise be. This effect is desirable for the same reason as described above with regard to canceling phase shifting. By providing an avenue to control phase shifting, the negative effects of phase shifting caused by the array of speakers  414  can be minimized. Thus, phase shifting can be used to advantageously to enable the speaker(s) of the array of speakers  414  to resonate more freely, which allows the array of speakers to perform better across a broader range of frequencies than it otherwise would without the circuit  400 . 
         [0090]      FIG. 5  shows an embodiment of the inventive subject matter as a black box  500 . The black box  500  can contain any embodiment of the circuits including those described above. The black box  500  has four terminals  502 ,  504 ,  516 , and  518  that are used to transmit an audio signal. Terminal  502  is coupled to the positive terminal of an audio signal source, and terminal  516  is coupled to a positive terminal of a speaker or array of speakers. Terminal  518  is coupled to a negative terminal of a speaker or array of speakers. Finally, terminal  504  is coupled to the negative terminal of an audio signal source. In alternative embodiments, terminal  502  and  504  could be incorporated into a single input port and terminal  516  and  518  could be incorporated into a single output port without departing from the scope of the current invention. 
         [0091]    In some embodiments, the positive terminal of an audio signal source transmits a signal to a speaker, while the negative terminal completes a circuit with the speaker and the audio signal source. In most home theater systems, for example, the audio signal source is an amplifier. Other examples of signal sources include CD players, digital music players (e.g., cell phones, tablets, iPod touches and similar devices, etc.). It is foreseeable that the device of some embodiments can be used with any music signal from any source, even if the source does not provide a digitally reconstructed signal (e.g., a vinyl record player). Any speaker associated with an embodiment of the system has a positive and negative terminal corresponding to the positive and negative terminals of the audio signal source. The black box  500  is a unit designed to sit between the audio signal source and the array of speakers, thus it has four terminals  502 ,  504 ,  516 , and  518 . 
         [0092]    The black box  500  can additionally have a number of inputs  506 ,  508 ,  510 ,  512 , and  514 . Inputs  506 ,  508 , and  510  provide for control of switches that can optionally be included in the circuit contained within the black box. First switch control  506  provides for control of a first switch, for example switch  420 , second switch control  508  provides for control of a second switch, for example switch  422 , and third switch control  510  provides for control of a third switch, for example switch  424 . Additional switches could be incorporated without departing from the scope of the current invention. Switching inputs are optional, however, and depend on the configuration of the circuit within the black box  500 . Inputs  512  and  514  provide for control of a resistor and capacitor, respectively. Resistor control  512  allows for variation of a resistor in a circuit contained with the black box  500 , while capacitor control  514  allows for variation of the capacitance of a capacitor. This feature is optional, and inclusion in the device depends on whether a variable resistor and/or capacitor has been used in the circuit. 
         [0093]    The switches could be manual switches controlled by moving a switch or a bar across an interface, or could be electronic switches that are controlled by a centralized control interface (not shown). In embodiments where the switches are manual switches, indicators are preferably placed near the switches to indicate how the properties of the circuit are changed. For example in one embodiment first switch control  506  could have an indicator showing that it controls inductor  1 , which could be turned ON for impedance matching or OFF to deactivate impedance matching, and/or could even have indicators that show that a first position sets inductor  1  to a first inductance of 25 μH, a second position that sets inductor  1  to a second inductance of 50 μH, and a third position that sets inductor  1  to a third inductance of 100 μH. Similar indicators could be provided to adjust the resistance and/or capacitance of an RC circuit, and/or another inductor included in black box  500 . Where the switches are electronic inputs, a separate user interface (not shown) would preferably have such indicators. 
         [0094]      FIGS. 6   a  and  6   b  show exemplary inductors  600   a ,  600   b  that can be used with any of the embodiments from  FIGS. 1-5  to produce better impedance matching over a range of frequencies. Inductors have three main components: (1) a coiled wire  602   a ,  602   b ; (2) a core  604   a ,  604   b ; and (3) a sometimes one or more gaps  606   a ,  606   b . When current passes through the coiled wire  602   a ,  602   b , a magnetic field is generated within the core  604   a ,  604   b  and gap  606   a ,  606   b . Depending on the material within the core  604   a ,  604   b  and the gap  606   a ,  606   b , the magnetic field can have different effects. 
         [0095]    Providing a component having an impedance between two other components having two different resulting impedances normally results in an impedance match only in the vicinity of a specific signal frequency. This results because impedance is a function of frequency, and thus as frequency changes, impedances change at different rates. Embodiments of the inventive subject matter solve this problem by using inductors whose impedances vary at a rate that is proportional to the rate of change of both the impedance of the audio signal source and the impedance of the array of speakers. In this way, the impedances remain matched across a wide range of signal frequencies. 
         [0096]    In essence, the ability of the inductor to vary at a desired rate makes matching across a range of frequencies possible. For example, if the audio signal source has an impedance of 2 Ohms at 100 Hz and the array of speakers has an impedance of 8 Ohms at 100 Hz, then the inductor will have approximately 6 Ohms impedance at 100 Hz to create an impedance match. If those same components have impedances of 6 Ohms and 24 Ohms at 10 kHz, respectively, then the inductor will ideally have an impedance of approximately 18 Ohms at 10 kHz to create an impedance match. 
         [0097]    Inductance can be described generally as, 
         [0000]    
       
         
           
             L 
             = 
             
               
                 μ 
                  
                 
                     
                 
                  
                 
                   N 
                   2 
                 
                  
                 A 
               
               l 
             
           
         
       
     
         [0000]    where μ is the permeability of the core, N is the number of times the wire has been wound around the core, A is the cross-sectional area of the core, l is the length of the core, and L is inductance. Thus, altering permeability of the core affects inductance and thus the response characteristics of an inductor. Core material can also affect the resonant characteristics of an inductor, because a core material has a characteristic frequency at which the inductor exhibits the highest inductance. As a result, one or more core materials can be selected such that the inductor&#39;s performance peaks at particular frequency or across a range of frequencies. 
         [0098]    The concept of selecting a core material to provide peak performance at a particular frequency can be expanded by creating an inductor using multiple materials having multiple characteristic frequencies. For example, a part of the core can be made from one material having a permeability and characteristic frequency, while the rest of the core can be made from another material having a different permeability and characteristic frequency. Such a combination results in the inductor having two different performance peaks at two different frequencies. For applications such as audio signals, the overall effect is that such inductors are able to perform better over a broader range of audio signal frequencies. For example, an inductor can one or more core materials (e.g., blended or having boundary layers) where the material or materials all have different material properties (e.g., different permeabilities). 
         [0099]    By carefully selecting core materials based on desired permeability and material properties, an inductor can be created that exhibits advantageous characteristics across a broader range of frequencies than a standard inductors having only a single core material. 
         [0100]    The same concept can be applied the gap portion of the inductor. It can be made up of one or more materials selected based on desired permeability and desired effects across a range of frequencies. 
         [0101]    The materials used in the core and gap can be some combination of paramagnetic, ferromagnetic, and/or diamagnetic materials. Some paramagnetic materials include (written in the form of, “material (approximate relative permeability)”): air (1.0000004), aluminum (1.00002), and palladium (1.0008). Some ferromagnetic materials include: 2-81 Permalloy powder (130), cobalt (250), nickel (600), ferroxcube 3 (1,500), mild steel (2,000), iron (5,000), silicon iron (7,000), 78 Permalloy (100,000), mumetal (100,000), purified iron (200,000), and superalloy (1,000,000). Some diamagnetic materials include: bismuth (0.99983), silver (0.99993), lead (0.99993), copper (0.999991), and water (0.999991). 
         [0102]    The inductor can be made in many configurations based on the frequency requirements. For example, the frequency range that the inductor is to be used with is an important factor to consider when determining the size of the gap portion of the inductor. The gap and/or can include, for example, Ti02-6 (e.g., 30-35%, 35-40%, 40-45%, 45-50%, 50-55%, 55-60%, 60-65%, 65-70%, 70-75%, 75-80%, 80-85%, 85-90%, or 90-98% by volume), aluminum (e.g., 5-10%, 10-15%, 15-20%, 20-25%, 25-30% by volume), Cobalt (e.g., 2-5%, 5-10%, 10-15%, 15-20%, 20-25%, 25-30% by volume), and sometimes tin binders (0.5-2%, 2-4%, 4-6%, 6-8%, 8-10%). The proportions for each material used in the core and/or gap are determined based on a frequency range to be used with the inductor. In addition to the specific materials listed above, it is contemplated that these ranges can similarly apply to any paramagnetic, diamagnetic, or ferromagnetic material that is used to create the inductor. 
         [0103]    Any combination of materials is contemplated to alter the properties of inductor  600   a  or inductor  600   b . For example,  604   a  could comprise a paramagnetic material comprising at least 60% by volume while gap  606   a  could comprise a ferromagnetic material comprising at least 30% by volume, or  604   b  could comprise a ferromagnetic material comprising at least 70% by volume while gap  606   b  could comprise a diamagnetic material comprising at least 25% by volume. A plurality of gaps (not shown) could be used to further vary the properties of the inductor, such as an inductor having a paramagnetic core, a first gap of ferromagnetic material, and a second gap of diamagnetic material. One, two, three, or more such gaps could be embedded in an inductor to alter its properties. In other embodiments, the core itself is partitioned into segments of different materials, such as a first segment of paramagnetic material, a second segment of diamagnetic material, a third segment of ferromagnetic material, and a fourth segment of paramagnetic material. 
         [0104]      FIGS. 7   a  and  7   b  show a number of graphs  700   a ,  700   b  depicting gain characteristics of systems using embodiments of the circuit with inductors from  FIG. 6 . Graph  700   a  shows simulated gain relative to 1 kHz both with and without an embodiment of the circuit activated to modify the signal. Data set  702   a  depicts a simulation of gain relative to 1 kHz without an embodiment of the circuit connected between the audio source and the speaker array, and data set  704   a  depicts a simulation of gain relative to 1 kHz with an embodiment of the circuit connected between to the audio source and the speaker array. The simulated results show that passing a signal through a system using an embodiment of the circuit should result in a drop in gain relative to a system that is not using an embodiment of the circuit beginning around 2 kHz. 
         [0105]    Graph  700   b  depicts actual measured results comparing the gain of a system that does not use an embodiment of the circuit compared to a system that does use an embodiment of the circuit. Data set  702   b  depicts a simulation of gain relative to 1 kHz without an embodiment of the circuit, and data set  704   b  depicts a simulation of gain relative to 1 kHz with an embodiment of the circuit connected. The gain fluctuates more in the real-world system than in the simulated system, due in large part to un-modeled nonlinear behaviors in many of the components of the system. However, the real-world results also show that passing a signal through a system using an embodiment of the circuit should result in a drop in gain relative to a system that is not using an embodiment of the circuit beginning around 2 kHz. 
         [0106]      FIG. 8  shows a depiction of an example audio signal in three different forms. The first graph  800  shows an original audio signal  801  before it has been converted into a digital format, the second graph  820  shows the audio signal  803  after it has been reconstructed after digitization, and the third graph  840  shows the signal  805  after it has passed through an embodiment of the inventive subject matter. The original audio signal  801  is first divided into different segments of time, which correspond to sample times  802 . At each sample time  802 , the amplitude of the signal is detected and stored for an entire time segment. For example, when the original audio signal  801  is sampled at time  804 , the amplitude of the signal at that time is extended for the duration of that time segment. Thus, segment  806  becomes segment  808  as seen in graph  820 . Finally, after passing through an embodiment of the circuit, signal segment  808  appears approximately as signal segment  810  in graph  840 , which more closely resembles the analog input than digital output  808 . 
         [0107]      FIG. 9  shows a circuit diagram  900  of a circuit that provides not only improved impedance matching between an audio signal source and an array of speakers  912 , but it also reduces quantization noise in an audio signal passing from an audio signal source to an array of speakers  912 . 
         [0108]    To improve impedance matching, inductors  904  and  906  combined with capacitor  908  are configured to have a resultant impedance that improves impedance matching between and audio signal source and an array of speakers  912 . Inductor  904  is placed in series with capacitor  908 , which are both in parallel with inductor  906 . These components make up circuitry that couples the positive terminal  902  of an audio signal source to the positive terminal of the array of speakers  910 . A third inductor  916  couples the negative terminal of the audio signal source  918  to the negative terminal of the array of speakers  914 . Desirable properties (e.g., one or more permeabilities and/or inductances) of the first  912 , second  914 , and third inductors  916  can be achieved by way of designing the inductors as described above in detail. By selecting gap and core materials having desirable material properties, inductor(s) can be produced having one or more desired permeabilities, which in turn causes the inductor(s) to resonate at one frequency or across a range of frequencies. 
         [0109]    As with previously described embodiments, impedance matching remains important. To achieve impedance matching, the components of the circuitries (e.g., the inductors  904 ,  906  and  916  and capacitor  908 ) can have a wide variety of inductances and capacitances. The required resultant impedances necessary for improved impedance matching are determined by the impedances of the audio signal source and array of speakers  912  that are coupled by the circuit  900 . Specifically, inductors  904  and  906  and capacitor  908  can be different from embodiment to embodiment so long as the resultant impedance of the three components is approximately the same as the impedance of inductor  916 . However, it is preferable for inductors  904  and  906  to have substantially similar inductances (e.g., to be within 10% of one another). 
         [0110]    To create a balanced, impedance matched circuit, the equivalent impedance of inductors  904  and  906  and capacitor  908  should be approximately equal to the impedance of inductor  916 . In some embodiments, the inductances of inductors  904 ,  906 , and  916  are all approximately the same, but in other embodiments the inductances of inductors  904 ,  906 , and  916  can be different from each other as long as the resultant impedance of inductors  904  and  906  and capacitor  908  is approximately equal to the impedance of inductor  916 . 
         [0111]    Matching the impedance of inductor  916  to inductors  904  and  906  and capacitor  908  is important, but those sets of components must also be tuned such that the impedance of the audio signal source is approximately equal to the impedance of the array of speakers. To make such a match easier to achieve, in some embodiments the various components can be variable (e.g., variable capacitors and/or variable inductors such as capacitors and inductors that can be either manually or electronically varied). By making components  904 ,  906 ,  908 , and/or  916  variable, the circuit can be tuned to provide improved impedance matching. Tuning can be accomplished by either a computer controlled system, or it can be accomplished by hand via, for example, a screwdriver to manipulate the variable component(s). 
         [0112]    The circuit  900  is also configured to reduce quantization noise in an audio signal. Audio signals that have been reconstructed from a digital format often include high frequency noise that, if reproduced by a speaker, would be inaudible to a human listener. Removing this type of noise is advantageous in that it allows a speaker to reproduce primarily sounds that are audible to a human listener. To reduce quantization noise, this circuit  900  includes capacitor  908 . When an audio signal is passed from the audio signal source via terminal  902  into the circuitry, which includes inductors  904  and  906  as well as capacitor  908 , the audio signal is caused to branch into both paths of the circuitry. 
         [0113]    In the top path, the audio signal source encounters inductor  904  and capacitor  908 , while in the bottom path it encounters only inductor  906 . Since inductors resist change in current, when high frequency spikes in the audio signal reach the inductors  904  and  906 , the inductors  904  and  906  help to smooth the signal. In the top path, the signal passes through inductor  904  to reach capacitor  908 . Capacitor  908  absorbs charge from the audio signal that passed through inductor  904  and then releases charge into the audio signal that passed through inductor  916 . Charge absorbed into capacitor  908  is released into the audio signal having experienced a phase shift (e.g., energy from the signal at time x is released back into the signal at time x+Δx, where Δx is on the order of picoseconds, nanoseconds, microseconds, or milliseconds). By releasing energy back into the audio signal, the capacitor  908  helps to eliminate quantization noise. Rereleased charge from the capacitor, in essence, fills in gaps that represent the absence of information caused by digitally encoding an analog audio signal. 
         [0114]      FIG. 10  shows a circuit  1000  having the components depicted in  FIG. 9  and also having a resistor  1014  and capacitor  1016  in parallel with the array of speakers  1012 . This configuration is similar to that of  FIG. 3 , which also has a resistor and capacitor in parallel with an array of speakers. When placed in parallel with the array of speakers  1012 , the resistor  1014  and capacitor  1016  act as a bypass for high frequency signals. Impedance of capacitors is a function of frequency such that as frequency approaches infinity, the impedance of a capacitor approaches zero. So when a high frequency signal reaches the capacitor  1016  at least a portion of the signal passes through the capacitor  1016  based on the capacitor&#39;s  1016  impedance. This effect is desirable because it prevents the array of speakers  1012  from reproducing portions of a signal that are attributable to quantization noise, allowing the array of speakers  1012  to reproduce predominantly sounds in a desired range (e.g., a range of frequencies audible to humans). 
         [0115]      FIG. 11  shows a diagram of a circuit  1100  that is similar to circuit  1000  of  FIG. 10 . The circuit  1100  has switches  1110 ,  1116 , and  1124  similar to the switches of circuit  400  of  FIG. 4 , which enable phase shifting of an audio signal passing through the circuit  1100 . Operating switches  1110 ,  1116 , and  1124  in a coordinated manner can cause a phase shift, and by inducing a phase shift in the audio signal the performance of the array of speakers  1114  can be improved. Introducing the right amount of phase shifting results in speaker(s) of the array of speakers  1114  vibrating in phase with the audio signal—in other words, the speaker(s) of the array of speakers  1114  are enabled to produce better quality sound because the vibration of the speaker(s) in the array of speakers  1114  is better synchronized with the audio signal. 
         [0116]    Switches  1110 ,  1116 , and  1124  can be operated either mechanically or electronically. Mechanical operation involves mechanically changing the state of a switch (e.g., a relay), while electronic operation involves changing the state of a switch using electricity (e.g., a transistor). When switches  1110  and  1124  are closed, an audio signal is able to bypass inductors  1104 ,  1106 ,  1108 , and  1126  so the audio signal can travel directly to the array of speakers. In addition, when switch  1116  is open, no part of an audio signal will reach resistor  1120  or capacitor  1118 . 
         [0117]      FIG. 12  shows a diagram of a circuit  1200  that provides improved impedance matching between an audio signal source and an array of speakers  1212 , as well as reduced quantization noise in an audio signal passing through the circuit  1200 . To do this, the circuitry coupling the positive terminals of the audio signal source  1202  and the array of speakers  1210  has the same components as the circuitry coupling the negative terminals of the audio signal source  1202  and the array of speakers  1210 . This circuit  1200  provides the benefits of quantization noise reduction from the circuit of  FIG. 9  while maintaining balance in the circuit. By having both circuitries (i.e., the circuitry between the positive terminals including inductors  1204  and  1206  and capacitor  1208  and the circuitry between the negative terminals including inductors  1218  and  1220  and capacitor  1216 ) include the same component configurations, the overall circuit  1200  is balanced on both the positive and negative sides of the array of speakers. Unlike a circuit where only one circuitry coupling the array of speakers to the audio signal source has two inductors and a capacitor, a circuit where both circuitries have two inductors and a capacitor is balanced not only in that the impedances of each circuitry can be substantially the same, but the behavior of each circuitry when subject to an audio signal is substantially the same as well. This design results in improved impedance matching as well as improved speaker performance in the array of speakers  1212 . 
         [0118]      FIG. 13  shows a circuit diagram of a circuit  1300  that is substantially similar to the circuit of  FIG. 12 , except that it also includes a resistor and a capacitor as the circuit  1000  shown in  FIG. 10 . This configuration provides all the advantages of the circuit of  FIG. 12 , with the additional advantages of including a resistor  1314  and a capacitor  1316  as in the circuit of  FIG. 10 . Resistor  1314  and capacitor  1316 , as with the circuit of  FIG. 12 , provide improved impedance matching by effectively reducing the impedance of the array of speakers  1312  by some degree. The degree of impedance reduction can be tuned by either careful selection of the resistor  1314  and the capacitor  1316 , or by implementing a variable resistor, a variable capacitor, or both (e.g., a mechanically or electronically varied resistor and/or capacitor). The resistance and capacitance of the resistor  1314  and capacitor  1316  determine the resultant impedance of those two components, which in turns affects the resultant impedance of the array of speakers  1312  when combined with the resistor  1314  and capacitor  1316 . 
         [0119]    In addition, the resistor  1314  and capacitor  1316  act as a high pass filter. As described above with regard to the circuit of  FIG. 10 , as the frequency of an audio signal approaches infinity, capacitance tends toward zero. By selecting a capacitor  1316  having a desirable capacitance, frequencies above a certain range can be allowed to pass (e.g., 20 kHz, 22 kHz, 24 kHz, 26 kHz, 20-22 kHz, 22-24 kHz, or 24-26 kHz), while still forcing frequencies of the audio signal below that range to pass through the array of speakers  1312 . 
         [0120]      FIG. 14  shows a circuit diagram of a circuit  1400  that is similar to the circuit of  FIG. 13  except that it includes switches  1408 ,  1416 , and  1428  to allow for phase shifting. This embodiment has all the advantages of having symmetric circuitries to couple the positive terminal of the array of speakers  1412  to the positive terminal of the audio signal source  1402 , and to couple the negative terminal of the array of speakers  1432  to the negative terminal of the audio signal source  1422 , as described with regard to  FIG. 12 . Switching to produce a phase shift is accomplished exactly as described above with respect to  FIG. 11 . 
         [0121]    It should be apparent to those skilled in the art that many modifications besides those already described are possible without departing from the inventive concepts herein. The inventive subject matter, therefore, is not to be restricted except in the spirit of the appended claims. Moreover, in interpreting both the specification and the claims, all terms should be interpreted in the broadest possible manner consistent with the context. In particular, the terms “comprises” and “comprising” should be interpreted as referring to elements, components, or steps in a non-exclusive manner, indicating that the referenced elements, components, or steps may be present, or utilized, or combined with other elements, components, or steps that are not expressly referenced. Where the specification claims refers to at least one of something selected from the group consisting of A, B, C . . . and N, the text should be interpreted as requiring only one element from the group, not A plus N, or B plus N, etc.