Abstract:
A tunable frequency transmission line pulse forming network circuit for forming a waveform having a spectral content. The pulse forming network circuit comprises a dielectric material; a ground section; a stepped shaped charged section, with the charged section having a plurality of stages including a first stage; a power supply coupled to the pulse forming network circuit for charging the pulse forming network circuit; a switch coupled to the pulse forming network circuit for periodically discharging the pulse forming network circuit; and an antenna coupled to the pulse forming network circuit for propagating a high-power microwave signal from the pulse forming network circuit into the environment. At least the first stage of pulse forming network circuit has one of a tunable magnetic material and a nonlinear magnetic which facilitates adjusting the waveform and the spectral content of the waveform emitted by the pulse forming network circuit into the surrounding environment.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    1. Field of the Invention 
         [0002]    This invention relates to directed energy weapons, and more particularly, to high power microwave weapons. 
         [0003]    2. Brief Description of Related Art 
         [0004]    Conventional high power microwave (HPM) sources incorporating pulse forming networks (PFNs) based on segments of charged transmission lines (also known as a family of Darlington circuits) have fixed spectral content which is determined by the electrical length. However, potential customers indicate a lot of interest in frequency agile HPM sources and in sources capable of generating arbitrary waveforms since different targets are vulnerable to different frequencies and different waveforms. 
         [0005]    As is conventional in the art and used within this patent application, a pulse forming network (PFN) is an electric circuit that accumulates electrical energy over a comparatively long time, then releases this stored energy in the form of a relatively square pulse of a comparatively brief duration for various pulsed power applications. In the PFN circuit, the energy storage components, such as capacitors, inductors or transmission lines are charged by means of a high voltage power source, then rapidly discharged into a load via a high voltage switch, e.g., as a spark gap, a hydrogen thyratron or a photoconductive semiconductive switch. Repetition rates range from single pulses to about 10 4  per second. PFN circuits are used to produce precise nanosecond-length pulses of electricity to power devices such as klystron or magnetron tube oscillators in radar sets, pulsed lasers, particle accelerators, flashtubes, and high voltage utility test equipment. A lot of high energy research equipment is operated in a pulsed mode, both to keep heat dissipation down and because high energy physics often occur at short time scales, so large PFN circuits are widely used in high energy research. They have been used to produce nanosecond length pulses with voltages of up to 10 6 -10 7  volts and currents up to 10 6  amps, with peak power in the terawatt range, similar to lightning bolts. 
         [0006]    Conventional PFN circuits consist of the segments of transmission lines having the same electrical length but different impedances. An example of such pulse forming circuits is the Blumlein pulse-forming line. The Blumlein pulse-forming line is, in fact, the simplest member of the entire family of circuits known as the Darlington circuits. These circuits are capable of producing unipolar (Darlington) or bipolar (S. London) single-cycle rectangular pulses as well as trains of such pulses. These circuits also produce such pulses at potentials which can be many multiples of the potential to which the circuit is charged initially. The electrical length of the transmission line segments in conventional pulse-forming networks is fixed. This fixed electrical length, in turn, fixes duration of the generated pulses as well as their spectral content. 
         [0007]    With reference now to  FIG. 1 , a description concerning a conventional prior art circuit  2  will now be briefly described. As is conventional in the art, the central core component of such prior art circuit  2  is a block of dielectric material  4 , e.g., polypropylene, ceramics, etc. The dielectric material  4  is then cut or otherwise processed in order to remove undesired dielectric material  4  and thereby form the basic shape of the circuit  2 , i.e., both a generally linear surface  6 , along one elongate side of the dielectric material  4 , and a generally stepped shaped surface  8 , along an opposite elongate side of the dielectric material  4 , with the dielectric material  4  located therebetween. As shown in this Figure, the generally stepped shaped surface  8  is formed to produce a series of at least seven steps or stages  10  with each step or stage  10  being located progressively further away from the associated generally linear surface  6 . For example, the first step or stage  10 ′ may be spaced from the generally linear surface  6  by a distance of a few thousands of an inch or so, the second step or stage  10 ″ may be spaced from the generally linear surface  6  by a distance of 15 to 20 thousands of an inch or so, the third or stage  10 ′″ may be spaced from the generally linear surface  6  by a distance of 60 to 80 thousands of an inch or so, and so forth. 
         [0008]    Next, both the generally linear surface  6  and the generally stepped shaped surface  8  are each covered with a thin layer of a copper material  12  (e.g., by an electroplating process for example) thereby to form a generally linear ground section  14  of the circuit  2  and also form a generally stepped shaped charged section  16  of the circuit  2 . Each step or stage, of the generally stepped shaped charged section  16  of the circuit  2 , typically has a thickness of between 0.003 and 0.008 of an inch, a width of between 2.75 inches (7 cm) and 3.15 inches (8 cm) and an axial length—depending upon the frequency—of between 0.39 inches (1 cm) and 15.75 inches (40 cm), for example. The ground section  14  of the circuit  2 , on the other hand, typically has a thickness of between 0.003 and 0.008 of an inch, a width of between 2.75 inches (7 cm) and 3.15 inches (8 cm) and an axial length, between 2.75 inches (7 cm) and 110.23 inches (280 cm) or more, for example. That is, the axial length of the ground section  14  of the circuit  2  is equal to a total combined axial length of each of the steps or stages. 
         [0009]    As shown in  FIG. 1 , a final step or stage Z 7′  of the generally stepped shaped charged section  16  of the circuit  2  and is spaced or otherwise separated from the last step or stage of the generally stepped shaped charged section  16 , e.g., the seventh step or stage Z 7  in this circuit  2 , by a layer of unremoved dielectric material  4 ′. The final step or stage Z 7′  typically has a thickness of between 0.003 and 0.008 of an inch, a width of 7 or 8 centimeters and an axial length, typically between 0.39 inches (1 cm) and 15.75 inches (40 cm), for example. As shown in  FIG. 1 , a left end beginning of the last step or stage Z 7′  of the charged section  16  of the circuit  2  is axially aligned with a left first end of the final step or stage Z 7  while the axial length of the final step or stage Z 7′  is axially longer than the axial length of the last step or stage Z 7  of the charged section  16  of the circuit  2  so that the right end of the final step or stage Z 7′  terminates at the same axial position as the ground section  14  of the circuit  2  terminates. 
         [0010]    As is conventional in the art, a switch  18  is coupled to a first (e.g., left end) axial end of both the ground section  14  and the charged section  16  to facilitate periodic discharge of the circuit  2 . This switch  18  may be periodically activated by a laser (not shown), for example, for discharging the circuit  2 , as desired. The circuit  2  is also typically charged, via a conventional power supply  19 , to a voltage of between 1,000 and 7,000 volts, for example, before being periodically discharged by the switch  18 , e.g., a laser being fired at the switch  18  in order to activate the switch  18  and discharge the circuit  2 . In a conventional manner, a first contact of the power supply  19  is coupled to the copper material  12  of the ground section  14  while a second contact of the power supply  19  is coupled to the copper material  12  of the charged section  16 . In order to complete the circuit  2 , a first end of an antenna Z L  is coupled to an opposite second (right) axial end of the ground section  14  while a second end of the antenna Z L  is coupled to an opposite (right) second end of the final step or stage Z 7′  to facilitate periodic propagation of the high power microwave energy from the circuit to the antenna Z L  and into the surrounding environment. As is conventional in the art, when the circuit  2  is discharged, this causes a high power microwave signal to be generated by the first step or stage Z 1 . Thereafter, this generated high power microwave signal propagates progressively along the circuit  2 , from left to right, and eventually to the antenna Z L  for transmission, e.g., from the first step or stage Z 1  to the second step or stage Z 2 , from the second step or stage Z 2  to the third step or stage Z 3 , from the third step or stage Z 3  to the fourth step or stage Z 4 , from the fourth step or stage Z 4  to the fifth step or stage Z 5 , from the fifth step or stage Z 5  to the six step or stage Z 6 , from the sixth step or stage Z 6  to the seven step or stage Z 7 , from the seven step or stage Z 7  to the last step or stage Z 7′ , and from the last step or stage Z 7′  into the antenna Z L  for transmission. The antenna Z L  then propagates the high-power microwave signal into the surrounding environment and typically toward a desired target  22 . 
         [0011]    While the above arrangement has worked satisfactory for some applications, there still exists a need for a way to vary the waveform and its spectral content in order to provide a more versatile high-power microwave signal for achieving the desired result. 
       BRIEF SUMMARY OF THE INVENTION 
       [0012]    Wherefore, it is an object of the present invention to overcome the above mentioned shortcomings and drawbacks associated with the prior art. 
         [0013]    One embodiment of the invention comprises a tunable-frequency transmission-line-based pulse forming network. It has been found that the waveform (and its spectral content) produced by PFN circuit can be changed if the dielectric filling for at least one, and possibly two or more transmission line segments, forming the PFN circuit, is replaced by nonlinear (or tunable) magnetic and/or dielectric material. Variation of the effective electrical length of one of more transmission line segments enables control of the generated pulse duration and hence its spectral content. As a result, frequency agility for the circuit is thereby obtained. 
         [0014]    It has, therefore, been demonstrated both analytically and by numerical simulations that tunable-frequency variant of the pulse-forming network can be implemented if the dielectric material filling at least the first stage, or possibly both the first and second stages of PFN circuit, is replaced by nonlinear or tunable magnetic and/or dielectric material. 
         [0015]    Another object of the present invention is to provide an adjustable current, to at least the first step or stage of the of PFN circuit to permit variation of the current supplied thereto and thus vary the magnetic field applied to the first step or stage of the of PFN circuit. 
         [0016]    The present invention also relates to a tunable frequency transmission line pulse forming network circuit for forming a waveform having a spectral content, the pulse forming network circuit comprising: a dielectric material; a ground section being formed on one side of the dielectric material; a stepped shaped charged section being formed on an opposite side of the dielectric material, and the charged section having a plurality of stages including a first stage; a power supply being coupled to the pulse forming network circuit for charging the pulse forming network circuit; a switch being coupled to the pulse forming network circuit for periodically discharging the pulse forming network circuit; and an antenna being coupled to the pulse forming network circuit for propagating a high-power microwave signal from the pulse forming network circuit into a surrounding environment; wherein at least the first stage of pulse forming network circuit has one of a tunable magnetic material and a nonlinear magnetic which facilitates adjusting the waveform and the spectral content of the waveform emitted by the pulse forming network circuit into the surrounding environment. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0017]    The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate various embodiments of the invention and together with the general description of the invention given above and the detailed description of the drawings given below, serve to explain the principles of the invention. The invention will now be described, by way of example, with reference to the accompanying drawings in which: 
           [0018]      FIG. 1  is a diagrammatic representation showing a conventional single-cycle pulse forming network according to the prior art; 
           [0019]      FIG. 2  is a diagrammatic representation showing a single-cycle pulse forming network according to the present invention; 
           [0020]      FIG. 2A  is a diagrammatic representation showing the dielectric material being formed into the basic shape for forming the single-cycle pulse forming network according to the present invention; 
           [0021]      FIG. 2B  is an enlarged section A of  FIG. 2A  showing a hollow space or void formed in the first step or stage of the single-cycle pulse forming network; 
           [0022]      FIG. 2C  is a diagrammatic representation showing a tunable magnetic material completely filling the hollow space or void formed in the first step or stage of the single-cycle pulse forming network; 
           [0023]      FIG. 2D  is a diagrammatic representation showing a wire wrapped around the first step or stage of the charged section to form an external magnetic field source; 
           [0024]      FIG. 3  is a graph showing typical dependence of the transient propagation velocity versus bias magnetic field; 
           [0025]      FIG. 4A  is a graph showing the generated voltage waveform of the circuit shown in  FIG. 1  while  FIG. 4B  is a graph showing the spectrum at the output of the circuit shown in  FIG. 1 ; 
           [0026]    FIG.  5 A 1  is a graph showing the generated voltage waveform of the circuit according to  FIG. 2 , while FIG.  5 A 2  is a graph showing the spectrum at an output of the tunable-frequency PFN circuit, according to  FIG. 2 , biased with an external magnetic field of (a) H ext =100 kA/m; 
           [0027]    FIG.  5 B 1  is a graph showing the generated voltage waveform of the circuit according to  FIG. 2 , while FIG.  5 B 2  is a graph showing the spectrum at an output of the tunable-frequency PFN circuit, according to  FIG. 2 , biased with an external magnetic field of (a) H ext =80 kA/m; 
           [0028]    FIG.  5 C 1  is a graph showing the generated voltage waveform of the circuit according to  FIG. 2 , while FIG.  5 C 2  is a graph showing the spectrum at an output of the tunable-frequency PFN circuit, according to  FIG. 2 , biased with an external magnetic field of (a) H ext =60 kA/m; 
           [0029]    FIG.  5 D 1  is a graph showing the generated voltage waveform of the circuit according to  FIG. 2 , while FIG.  5 D 2  is a graph showing the spectrum at an output of the tunable-frequency PFN circuit, according to  FIG. 2 , biased with an external magnetic field of (a) H ext =10 kA/m; and 
           [0030]      FIG. 6  is a diagrammatic representation showing a single-cycle pulse forming network, according to a further embodiment of the present invention, in which both the first and the second stages are tunable. 
       
    
    
       [0031]    It should be understood that the drawings are not necessarily to scale and that the disclosed embodiments are sometimes illustrated diagrammatical and in partial views. In certain instances, details which are not necessary for an understanding of this disclosure or which render other details difficult to perceive may have been omitted. It should be understood, of course, that this disclosure is not limited to the particular embodiments illustrated herein. 
       DETAILED DESCRIPTION OF THE INVENTION 
       [0032]    The present invention will be understood by reference to the following detailed description, which should be read in conjunction with the appended drawings. It is to be appreciated that the following detailed description of various embodiments is by way of example only and is not meant to limit, in any way, the scope of the present invention. 
         [0033]      FIG. 2  is a diagrammatic Fig. showing, as an example, a single-cycle PFN circuit  2 ′ according to the present invention. In order to form such single-cycle PFN circuit  2 ′, the dielectric material  4  is first cut or otherwise shaped into the basic shape of the single-cycle PFN circuit  2 ′ as generally shown in  FIG. 2A . Next, the dielectric material  4 , located between the first step or stage Z 1  of the charged section  16  and the ground section  14  of the circuit  2 ′, is substantially cut out and/or removed, as generally shown in  FIG. 2B . As shown in this Figure, a substantial portion of the entire dielectric material  4 , located between the first step or stage Z′ 1  of the charged section  16  and the ground section  14  is substantially completely removed so as to form a hollow space or void  24  located between the ground section  14  and the charged section  16  of the circuit  2 ′. That is, only a very thin layer of the dielectric material  4  still remains to define a perimeter of the hollow space or void  24 . Thereafter, as shown in  FIG. 2C , a suitable tunable magnetic material  26 , such as ferroelectric ceramics (e.g., lead zirconate titanate (PZT)), is inserted into or otherwise completely fills and occupies the hollow space or void  24  formed in the dielectric material  4 . It is to be appreciated that, in some applications for example, the layer of the dielectric material  4 , located between the first step or stage  10 ′ of the charged section  16  and the ground section  14 , may be removed and replaced with the tunable magnetic material which may be secured or affixed, e.g., gluing, fusing, etc., to the remainder of the dielectric material  4  without departing form the spirit and scope of the present invention. 
         [0034]    Thereafter, a thin wire  28 , e.g., having a diameter of 0.2 and 1.0 mm, for example, is then wrapped around the ground section  14 , the tunable magnetic material  26 , the remaining thin layer of the dielectric material  4 , and the first step or stage Z′ 1  of the charged section  16  of the circuit  2 ′ to form an external magnetic field source  30 , as diagrammatically shown  FIG. 2D . It is to be appreciated that the wire  28  may be wrapped one or more times around the ground section  14 , the tunable magnetic material  26 , the remaining thin layer of the dielectric material  4 , and the first step or stage Z′ 1  of the charged section  16  of the circuit  2 ′. By providing additional wraps of the wire  28 , this facilitates the generation of a large magnetic field, by the formed external magnetic field source  30  which thereby results in an increased tuning range according to the present invention. 
         [0035]    In order to complete the external magnetic field source  30 , as shown in  FIG. 2D  a first end of the wire  28 , which loops or wraps around the first step or stage Z′ 1  of the charged section  16  of the circuit  2 ′ in order to create a magnetic field, is connected to a first contact of a current supply  32  while a second opposite and the wire is connected to a second contact of the current supply  32 . Typically a current of between 2 to 5 amps, for example, is supplied to the external magnetic field source  30  in order to vary the current applied thereto and thereby vary the pulse and the frequency produced by the single-cycle PFN circuit  2 ′. It is to be appreciated that, depending upon the particular application, a current supply may supply either a greater or lesser amount of current to the external magnetic field source  30 . The current supply  32  has a rotatable knob, or some other current supply adjustment mechanism  34 , which permits an operator of the current supply to readily alter the current or fixed pulse being supplied to the external magnetic field source  30  of the single-cycle PFN circuit  2 ′ and thereby alter and/or vary the frequency of the outputted high power microwave to be emitted by the transformer or module  36 . 
         [0036]    The single-cycle PFN circuit  2 ′ of  FIG. 2D  is then equipped with both a switch  18  and an antenna Z L , as described above and generally shown in  FIG. 2 , in order to complete formation of the transformer or module  36  according to the present invention. 
         [0037]    It is to be appreciated that the electrical length (propagation constant) of the first transmission line segment can be varied if the ferrite is placed into a saturating external static magnetic field perpendicular to the magnetic field in the transient (discharge) pulse so that the magnetization vector in ferrite initially aligned with the static external magnetic field (bias field). The pulsed magnetic field, produced by the discharge of the transmission line, causes the magnetization vector to rotate. It is to appreciated that the rotation of the magnetization vector is described by the Landau-Lifshitz equation: 
         [0000]    
       
         
           
             
               
                  
                 M 
               
               
                  
                 x 
               
             
             = 
             
               
                 
                   γμ 
                   0 
                 
                  
                 
                   ( 
                   
                     M 
                     × 
                     H 
                   
                   ) 
                 
               
               - 
               
                 
                   
                     αγμ 
                     0 
                   
                   
                     M 
                     s 
                   
                 
                  
                 
                   ( 
                   
                     M 
                     × 
                     
                       ( 
                       
                         M 
                         × 
                         H 
                       
                       ) 
                     
                   
                   ) 
                 
               
             
           
         
       
     
         [0038]    where M is the magnetization vector, 
         [0039]    M s  is the saturation magnetization, 
         [0040]    g is the gyromagnetic ratio, and 
         [0041]    H is the magnetic field. 
         [0042]    The applied pulsed magnetic field exerts a torque on magnetization vector. The basic response to this torque is, therefore, that M precesses around H. However, damping effects mean that, in the longer term, M becomes aligned with H. When coupled to the propagation of the transient along transmission line, this magnetization vector rotation causes a delay in propagation which depends on both 1) the magnitude of the bias magnetic field and 2) the pulsed magnetic field so that the transient propagation velocity along transmission line is expressed as follows: 
         [0000]    
       
         
           
             1 
             
               
                 1 
                 + 
                 
                   
                     b 
                      
                     
                         
                     
                      
                     
                       μ 
                       0 
                     
                      
                     
                       M 
                       s 
                     
                   
                   
                     
                       
                         H 
                         2 
                       
                       + 
                       
                         H 
                         ext 
                         2 
                       
                     
                   
                 
               
             
           
         
       
     
         [0043]    where b is geometry factor (ferrite filling factor), 
         [0044]    H ext  is the magnitude of the external bias magnetic field, 
         [0045]    H is the magnitude of the pulsed (transient) magnetic field, and 
         [0046]    v 0  is the phase velocity in the transmission line when ferrite is saturated in the direction of the pulsed magnetic field (linear case). 
         [0047]      FIG. 3  shows typical dependence of the transient propagation velocity versus the bias applied by the magnetic field which is generated by the external magnetic field source  30 . 
         [0048]      FIG. 4A  is a graph showing the generated voltage waveform of the circuit  2 ′, according to the prior art circuit  2  of  FIG. 1 , while  FIG. 4B  is a graph showing the spectrum at the output of the prior art circuit  2  according to  FIG. 1 . 
         [0049]    The initial modeling results, according to the present invention, are shown in  FIGS. 5A, 5B, 5C and 5D .  FIGS. 5A, 5B, 5C and 5D , respectively, show waveforms and their spectra for the tunable PFN circuit  2 ′, according to the present invention for four different values of the external bias magnetic field. FIG.  5 A 1  is a graph showing the generated voltage waveform while FIG.  5 A 2  is a graph showing the spectrum at an output of the tunable-frequency PFN circuit  2 ′, according to  FIG. 2 , biased with an external magnetic field of (a) H ext =100 kA/m. FIG.  5 B 1  is a graph showing the generated voltage waveform while FIG.  5 B 2  is a graph showing the spectrum at an output of the tunable-frequency PFN circuit  2 ′, according to  FIG. 2 , biased with an external magnetic field of (a) H ext =80 kA/m. FIG.  5 C 1  is a graph showing the generated voltage waveform while FIG.  5 C 2  is a graph showing the spectrum at an output of the tunable-frequency PFN circuit  2 ′, according to  FIG. 2 , biased with an external magnetic field of (a) H ext =60 kA/m. FIG.  5 D 1  is a graph showing the generated voltage waveform while FIG.  5 D 2  is a graph showing the spectrum at an output of the tunable-frequency PFN circuit  2 ′, according to  FIG. 2 , biased with an external magnetic field of (a) H ext =40 kA/m. 
         [0050]    As can readily be seen from  FIGS. 5A, 5B, 5C and 5D , the peak output voltage remains constant for each of the four tuning points, although the pulse shape and total number of pulses changes as the transformer or module  36  is tuned by an external bias magnetic field which is generated by the external magnetic field source  30 . 
         [0051]    The non-tunable prior art circuit  2  was initially designed to produce an ideal bipolar single-cycle waveform. Application of the external magnetic field, which is generated by the external magnetic field source  30 , results in variation of the electrical length of at least the first step or stage Z′ 1  leading to tunable-frequency waveform generation. However, it also results in impedance variation and thus introduces mismatch into the circuit  2 ′ leading to distortion of the ideal single-cycle waveform. As a result, it is desirable to generate a train of oscillations instead of a single pulse. This can be partly compensated by replacing the dielectric material  4 —which is non-tunable—with a tunable material in one or more additional steps or stages Z′ 1 , Z′ 2  etc., of the circuit  2 ′. For example, as generally shown in  FIG. 6 , both the first and the second steps or stages Z′ 1  and Z′ 2  of the generally stepped shaped charged section  16  of the circuit  2 ′ are each provided with a separate external magnetic field source  30 . 
         [0052]    According to this embodiment, in addition to the separate external magnetic field source  30  being formed for the first step of stage Z′ 1 , as described above, the dielectric material  4  located between the ground section  14  and the charged section  16  of the circuit  2 ′, for the second step or stage Z′ 2 , is substantially cut out or completely removed and replaced with a tunable magnetic material  26 . Thereafter, as described above, a thin wire  28 ′ wraps around the ground section  14 , the tunable magnetic material  26 , the remaining thin layer of the dielectric material  4 , and the second step or stage Z′ 2  of the charged section  16  of the circuit  2 ′ to form a second external magnetic field source  30 ′. Lastly, a first end of the wire  28 ′, which loops or wraps around the second step or stage Z′ 2  of the charged section  16  of the circuit  2 ′ in order to create a magnetic field, is connected to a first contact of a second current supply  32 ′ while a second opposite and the wire is connected to a second contact of the second current supply  32 ′. The second current supply  32 ′ has a rotatable knob, or some other current supply adjustment mechanism  34 ′, which permits an operator of the second current supply  32 ′ to readily alter the current or fixed pulse being supplied to the second external magnetic field source  30 ′ of the single-cycle PFN circuit  2 ′ and thereby alter and/or vary the frequency of the outputted high power microwave. 
         [0053]    If desired, one or more additional steps or stages, e.g., the third step or stage, the fourth step or stage, etc., of the transformer or module  36  may also be similarly equipped with a separate external magnetic field source  30  which facilitates individual tuning of each of those steps or stages of the single-cycle PFN circuit  2 ′, as described above, without departing from the spirit and scope of the present invention. However, it is to be appreciated that providing individual tuning of both the first and the second steps or stages Z′ 1  and Z′ 2  of the single-cycle PFN circuit  2 ′ generally provides about 90% of the overall total tunability range of adjustment for the high power microwave to be emitted by the single-cycle PFN circuit  2 ′. 
         [0054]    Furthermore, similar tunability can be enabled by utilizational. As a of nonlinear and tunable dielectrics like BST materials. 
         [0055]    While the present invention has been described in connection with the preferred embodiments of various Figures, it is to be understood that other similar embodiments may be used or modifications or additions may be made to the described embodiment for performing the same function of the present invention without deviating therefrom. Therefore, the present invention should not be limited to any single embodiment, but rather construed in breadth and scope in accordance with the recitation of the appended claims. 
         [0056]    While various embodiments of the present invention have been described in detail, it is apparent that various modifications and alterations of those embodiments will occur to and be readily apparent to those skilled in the art. However, it is to be expressly understood that such modifications and alterations are within the scope and spirit of the present invention, as set forth in the appended claims. Further, the invention(s) described herein is capable of other embodiments and of being practiced or of being carried out in various other related ways. In addition, it is to be understood that the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. The use of “including,” “comprising,” or “having,” and variations thereof herein, is meant to encompass the items listed thereafter and equivalents thereof as well as additional items while only the terms “consisting of” and “consisting only of” are to be construed in a limitative sense.