Abstract:
An in-line resonator filter has a linear array of three or more conductors. A first pair of adjacent conductors has inductive main coupling and oppositely signed capacitive main coupling, while a second pair of non-adjacent conductors has inductive cross-coupling. The first and second pairs have one conductor in common. Between the second pair of non-adjacent conductors, there is no direct ohmic connection that provides the corresponding inductive cross-coupling. The oppositely signed capacitive main coupling compensates for at least a portion of the inductive main coupling between the first pair of adjacent conductors. The in-line resonator filter is able to provide one or more transmission zeros without requiring any discrete bypass connectors that provide direct ohmic connection between pairs of non-adjacent conductors. As such, the in-line resonator filters can be smaller, less complex, and less susceptible to damage.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application claims the benefit of the filing date of U.S. provisional application No. 62/091,696, filed on Dec. 15, 2014, the teachings of which are incorporated herein by reference in their entirety. 
     
    
     BACKGROUND 
     Field of the Invention 
       [0002]    The present invention relates to electronics and, more specifically but not exclusively, to resonator filters for radio frequency (RF) applications. 
       Description of the Related Art 
       [0003]    This section introduces aspects that may help facilitate a better understanding of the invention. Accordingly, the statements of this section are to be read in this light and are not to be understood as admissions about what is prior art or what is not prior art. 
         [0004]    One type of filter for RF applications is a resonator filter comprising an assemblage of coaxial resonators, where the overall transfer function of the resonator filter is a function of the responses of the individual resonators as well as the electromagnetic coupling between different pairs of resonators within the assemblage. 
         [0005]    U.S. Pat. No. 5,812,036 (“the &#39;036 patent”), the teachings of which are incorporated herein by reference, discloses a number of different resonator filters having different configurations and topologies of coaxial resonators. 
         [0006]      FIG. 1  of this specification corresponds to  FIG. 3  of the &#39;036 patent, which depicts a top sectional view of a six-stage resonator filter  200  having a (2×3) array of coaxial resonators R 1 -R 6  between input terminal  204  and output terminal  206 . The resonator filter  200  has five coupling holes H 1 -H 5  between the five sequential pairs of resonators R 1 -R 6  that enable main coupling between the sequential pairs. In addition, the resonator filter  200  has a first bypass coupling aperture A C1  that enables cross-coupling between the non-sequential pair of resonators R 2  and R 5 . The resonator filter  200  also has a second bypass coupling aperture A C2  that enables cross-coupling between the non-sequential pair of resonators R 1  and R 6 . The main couplings between the five sequential pairs of resonators and the cross-couplings between the two non-sequential pairs of resonators contribute to the overall transfer function of the resonator filter  200 . 
         [0007]      FIGS. 2A and 2B  of this specification correspond respectively to  FIGS. 1A and 1B  of the &#39;036 patent, which depict overhead and side sectional views of a four-stage in-line resonator filter  1  having a linear array of four coaxial resonators  5 - 8  between input terminal  30  and output terminal  40 . The resonator filter  1  has three coupling holes A 1  -A 3  between the three sequential pairs of resonators  5 - 8  that enable main coupling between the sequential pairs. To achieve cross-coupling between the non-sequential pair of resonators  5  and  8 , the resonator filter  1  has a discrete, external, bypass connector C C  represented in phantom in the figures that provides a direct ohmic connection between resonators  5  and  8 . The term “direct ohmic connection” means that the external bypass connector physically interconnects resonator  5  to resonator  8  without physically contacting any of the intervening resonators (i.e., resonators  6  and  7 ). As explained in the &#39;036 patent, this type of external bypass connector increases filter size and complexity, and renders the resonator filter  1  susceptible to damage. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0008]    Other embodiments of the invention will become more fully apparent from the following detailed description, the appended claims, and the accompanying drawings in which like reference numerals identify similar or identical elements. 
           [0009]      FIG. 1 , which corresponds to  FIG. 3  of the &#39;036 patent, depicts a top sectional view of a six-stage resonator filter having a 2×3 array of coaxial resonators; 
           [0010]      FIGS. 2A and 2B , which correspond respectively to  FIGS. 1A and 1B  of the &#39;036 patent, depict overhead and side sectional views of a four-stage in-line resonator filter having a linear array of four coaxial resonators; 
           [0011]      FIG. 3  is a side sectional view of a resonator filter; 
           [0012]      FIG. 4  is a side sectional view of an in-line resonator filter according to one embodiment of the invention; 
           [0013]      FIG. 5  is a side sectional view of an in-line resonator filter according to another embodiment of the invention; 
           [0014]      FIGS. 6-10  depict the Halma topologies of six-stage, two-port, in-line resonator filters having six inner conductors and two input/output (I/O) ports according to different embodiments of the invention; 
           [0015]      FIG. 11  depicts the Halma topology of an 11-stage, three-port, diplexer, in-line resonator filter having eleven inner conductors and three I/O ports according to another embodiment of the invention; and 
           [0016]      FIG. 12  depicts the Halma topology of a 6-stage, three-port, arrow-diplexer, in-line resonator filter having six inner conductors and three I/O ports according to another embodiment of the invention. 
       
    
    
     DETAILED DESCRIPTION 
       [0017]    Detailed illustrative embodiments of the present invention are disclosed herein. However, specific structural and functional details disclosed herein are merely representative for purposes of describing example embodiments of the present invention. The present invention may be embodied in many alternate forms and should not be construed as limited to only the embodiments set forth herein. Further, the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments of the invention. 
         [0018]    As used herein, the singular forms “a,” “an,” and “the,” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It further will be understood that the terms “comprises,” “comprising,” “includes,” and/or “including,” specify the presence of stated features, steps, or components, but do not preclude the presence or addition of one or more other features, steps, or components. It also should be noted that in some alternative implementations, the functions/acts noted may occur out of the order noted in the figures. For example, two figures shown in succession may in fact be executed substantially concurrently or may sometimes be executed in the reverse order, depending upon the functionality/acts involved. 
         [0019]      FIG. 3  is a side sectional view of a resonator filter  300 . Filter  300  has a bottom ground plane  302 , a top ground plane  304 , and a lateral ground plane  306 . Although not specified in  FIG. 3 , filter  300  typically has a cylindrical or rectilinear 3D shape. 
         [0020]    The interior structure of filter  300  includes a single, inner conductor  310  consisting of (i) a high-impedance (cylindrical or rectilinear) base  312  that is shorted to the bottom ground plane  302  and (ii) a low-impedance, cup-shaped head  314  that does not contact the top ground plane  304 . Depending on the amount of self and mutual capacitance needed, instead of being cup-shaped, head  314  may be shaped like a tuning fork. In addition, filter  300  has a cylindrical tuning element  320  that extends from the top ground plane  304  into the inner volume  316  defined by the cup-shaped head  314 . The shapes, dimensions, locations, and compositions of the various elements of the inner conductor  310  define the inherent transfer function of the resonator filter  300 . 
         [0021]    In certain embodiments, the position of the tuning element  320 , which might or might not be shorted to the top ground plane  304 , can be adjusted (e.g., by rotating the tuning element when the tuning element is a threaded screw engaging a tapped screw hole in the top ground plane  304 ) to change the degree to which the tuning element vertically extends within the inner volume  316  in order to alter the coupling within the resonator and thereby tune the overall transfer function of the single-resonator filter  300  to be different from the filter&#39;s inherent transfer function. 
         [0022]      FIG. 4  is a side sectional view of an in-line resonator filter  400  according to one embodiment of the invention. Like resonator filter  300  of  FIG. 3 , resonator filter  400  has a bottom ground plane  402 , a top ground plane  404 , and a lateral ground plane  406 . Although not specified in  FIG. 4 , filter  400  would typically have a rectilinear 3D shape. 
         [0023]    Unlike resonator filter  300  of  FIG. 3  which has only a single inner conductor  310 , in-line resonator filter  400  has five inner conductors  410 ( 1 )- 410 ( 5 ), each of which having (i) a high-impedance base  412 (i) that is shorted to the bottom ground plane  402  and (ii) a low-impedance, shaped head  414 (i) that does not contact the top ground plane  404 . In some implementations, the inner conductors  410  are designed to function as stepped impedance resonators (SIRs). 
         [0024]    Like prior-art in-line resonator filter  1  of  FIGS. 2A-2B , the five inner conductors  410 ( 1 )- 410 ( 5 ) of in-line resonator filter  400  are linearly arranged to form a one-dimensional array of conductors. Note, however, that the inner conductors  410  can, but do not have to be perfectly aligned. One or more of the inner conductors  410  may be displaced towards the front or back of the resonator filter  400  (i.e., into or out of the page). Note further that, unlike prior-art in-line resonator filter  1 , there are no intervening walls between adjacent inner conductors  410  in the resonator filter  400 . As explained further below, this enables more-substantial cross-coupling to occur between pairs of non-adjacent inner conductors  410 . 
         [0025]    Like resonator filter  300  of  FIG. 3 , each inner conductor  410 (i) in resonator filter  400  has a corresponding tuning element  420 (i). Resonator filter  400  also has four additional tuning elements  422 ( 1 )- 422 ( 4 ) located between corresponding adjacent inner conductors  410 , where additional tuning elements  422 ( 1 ) and  422 ( 2 ) extend from the top ground plane  404 , while additional tuning elements  422 ( 3 ) and  422 ( 4 ) extend from the bottom ground plane  402 . 
         [0026]    As shown in  FIG. 4 , resonator filter  400  also has four conductive connectors  418 ( 1 )- 418 ( 4 ), each providing a physical (i.e., ohmic) connection between a different one of the four pairs of adjacent inner conductors  410 . 
         [0027]    Note that some of the heads  414  of the inner conductors  410  of resonator filter  400  have different shapes and that the inter-conductor spacing between the inner conductors  410  varies from adjacent pair to adjacent pair. In  FIG. 4 , heads  414 ( 1 ) and  414 ( 5 ) may be either cup-shaped or fork-shaped, while heads  414 ( 2 )- 414 ( 4 ) are necessarily fork-shaped. In addition, the height of the inter-conductor connectors  418  also varies from adjacent pair to adjacent pair. Note further that the resonator filter  400  is asymmetric along its lateral dimension in that a 180-degree rotation about, for example, the vertical axis of base  412 ( 3 ) of inner conductor  410 ( 3 ) results in a view that is different from the view of the resonator filter  400  shown in  FIG. 4 . All of these different and varying features of the resonator filter  400  contribute to its overall filter transfer function. The features can therefore by specifically designed to achieve a desired filter transfer function. 
         [0028]    In general, based on the particular design of resonator filter  400 , there is both inductive and capacitive main coupling between each of the four pairs of adjacent inner conductors  410 , where, for each pair, the sign of the capacitive main coupling is the opposite of the sign of the inductive main coupling, such that the capacitive and inductive main couplings compensate for one another to at least some degree. In addition, resonator filter  400  has been designed such that there is non-negligible (e.g., inductive) cross-coupling between certain pairs of non-adjacent inner conductors  410 , where that non-negligible cross-coupling is achieved without employing discrete bypass connectors that ohmically connect non-adjacent inner conductors  410 , whether those bypass connectors are internal or external to the resonator filter  400 . For example, there may be non-negligible cross-coupling between inner conductor  410 ( 1 ) and inner conductor  410 ( 3 ). In addition, there may be smaller, but still non-negligible cross-coupling between inner conductors  410 ( 1 ) and  410 ( 4 ) or even between inner conductors  410 ( 1 ) and  410 ( 5 ). In general, the greater the separation distance between two inner conductors, the smaller the coupling strength. 
         [0029]    Two basic coupling mechanisms take place, both contributing to the amount of coupling between adjacent and non-adjacent inner conductors: capacitive coupling and inductive coupling. 
         [0030]    Capacitive coupling can be controlled by adjusting the length and/or the impedance of the capacitive head  414  of each inner conductor  410  (e.g., by independently adjusting the dimensions A, B, and C of inner conductor  410 ( 3 )). This kind of interaction will contribute with a negative amount of capacitive coupling for adjacent pairs of inner conductors  410  and a positive amount of capacitive coupling for non-adjacent pairs of inner conductors. 
         [0031]    Inductive coupling can be controlled by adjusting the lengths (D in  FIG. 4 ) and/or the heights (E in  FIG. 4 ) of the inter-conductor connections  418  connecting the different pairs of adjacent inner conductors, where the distance and height might vary from connection to connection. This kind of interaction will contribute with a positive amount of inductive coupling for both adjacent and non-adjacent pairs of inner conductors  410 . 
         [0032]    The capacitive and inductive contributions of the main couplings (i.e., between adjacent conductors) and the cross-couplings (i.e., between non-adjacent conductors) can be designed to meet prescribed coupling values, at least within a certain range of prescribed coupling values. The sign of the cross-couplings is always positive for the structure considered, while the sign of the main couplings can be conveniently set according to the specific blend of capacitive and inductive couplings. It is then possible to realize networks of coupled resonators and mixed signed couplings. 
         [0033]    Depending on the number and location of the input/output (I/O) ports coupled to suitably selected inner conductors, different types of in-line resonator filters can be implemented. In-line resonator filters of the invention, such as in-line resonator filter  400  of  FIG. 4 , can be represented by Halma topologies that indicate the non-negligible main and cross-couplings between adjacent and non-adjacent conductors. 
         [0034]      FIG. 5  is a side sectional view of an in-line resonator filter  500  according to another embodiment of the invention. In-line resonator filter  500  is similar to in-line resonator filter  400  of  FIG. 4 , with analogous elements identified using analogous labels. Note that, in resonator filter  500 , the four conductive connectors  518 ( 1 )- 518 ( 4 ) that provide physical connections between different pairs of adjacent inner conductors  510  are wall-shaped elements that extend downward to the bottom ground plane  502  with the tuning elements  522  emerging over those connectors. 
         [0035]      FIG. 6  depicts the Halma topology of a six-stage, two-port, in-line resonator filter  600  having six inner conductors  610 ( 1 )- 610 ( 6 ) and two input/output (I/O) ports  630 ( 1 ) and  630 ( 2 ) according to one embodiment of the invention. Note that, although the Halma topology is depicted as a two-dimensional distribution of inner conductors, that is only to indicate the various couplings within the resonator filter  600 . The physical implementation of the resonator filter  600  involves the six inner conductors  610 ( 1 )- 610 ( 6 ) arranged linearly. 
         [0036]    The inter-conductor links in  FIG. 6  represent the non-negligible couplings within resonator filter  600 . In particular, link  632 ( 1 , 2 ) represents the main coupling between adjacent conductors  610 ( 1 ) and  610 ( 2 ), while link  632 ( 2 , 3 ) represents the main coupling between adjacent conductors  610 ( 2 ) and  610 ( 3 ), and analogously for links  632 ( 3 , 4 ),  632 ( 4 , 5 ), and  632 ( 5 , 6 ). On the other hand, link  632 ( 1 , 3 ) represents the cross-coupling between non-adjacent conductors  610 ( 1 ) and  610 ( 3 ), link  632 ( 2 , 4 ) represents the cross-coupling between non-adjacent conductors  610 ( 2 ) and  610 ( 4 ), and analogously for links  632 ( 3 , 5 ) and  632 ( 4 , 6 ). 
         [0037]    As depicted in  FIG. 6 , I/O port  630 ( 1 ) is connected to inner conductor  610 ( 1 ) via I/O link  634 ( 1 ), while I/O port  630 ( 2 ) is connected to inner conductor  610 ( 6 ) via I/O link  634 ( 2 ). Depending on the particular implementation, I/O links  634 ( 1 ) and  634 ( 2 ) may be ohmic or non-ohmic connections between the corresponding I/O ports  630  and inner conductors  610 . 
         [0038]    Although in-line resonator filter  600  has six inner conductors, in general, in-line resonator filters of this type can be implemented with a linear array having any number N&gt;2 of inner conductors with two I/O ports respectively connected to the first and last inner conductors in the linear array. When the number N of inner conductors is odd, the in-line resonator filter can be designed to provide up to (N−1)/2 transmission zeros. When the number N of inner conductors is even, the in-line resonator filter can be designed to provide up to N/2−1 transmission zeros. 
         [0039]    As an advantage, asymmetric responses exhibiting transmission zeros can be implemented using a linear arrangement of N inner conductors without the need of discrete bypass connectors that provide direct ohmic connection to pairs of non-adjacent inner conductors. At least in principle, there is no restriction on the location of the transmission zeros, which may be located above as well as below the pass-band. 
         [0040]      FIG. 7  depicts the Halma topology of a six-stage, two-port, folded, in-line resonator filter  700  having six inner conductors  710 ( 1 )- 710 ( 6 ) and two I/O ports  730 ( 1 ) and  730 ( 2 ) according to another embodiment of the invention. Folded, in-line resonator filter  700  is similar to in-line resonator filter  600  of  FIG. 6  with analogous main and cross-couplings between adjacent and non-adjacent conductors  710 , except that, in resonator filter  700 , the second I/O port  730 ( 2 ) is connected to the second inner conductor  710 ( 2 ) instead of the last inner conductor  710 ( 6 ). With its quasi-canonical folded topology, in-line resonator filter  700  can provide up to four transmission zeros. In general, an N-stage, folded, in-line resonator filter of the invention can provide up to N-2 transmission zeros. Again there is, at least in principle, no limit on the location of such transmission zeros. 
         [0041]      FIG. 8  depicts the Halma topology of a six-stage, two-port, extended-box, in-line resonator filter  800  having six inner conductors  810 ( 1 )- 810 ( 6 ) and two I/O ports  830 ( 1 ) and  830 ( 2 ) according to another embodiment of the invention. Extended-box, in-line resonator filter  800  is similar to in-line resonator filter  600  of  FIG. 6 , except that, in resonator filter  800 , the main couplings between adjacent conductors  810 ( 2 ) and  810 ( 3 ) and between adjacent conductors  810 ( 4 ) and  810 ( 5 ) are negligible or even non-existent. Each negligible or non-existent main coupling may be achieved by having the negative capacitive coupling between the two corresponding conductors negate the positive inductive coupling between those same two conductors. 
         [0042]    In general, for an N-stage resonator filter, where N is even, when (i) the two I/O ports are coupled to the first and last inner conductors and (ii) the main couplings from conductor 2k to conductor 2k+1 (k=1, . . . , N/2−1) are designed to be as small as possible (ideally zero), an extended-box topology of degree N results with the ability to accommodate up to N/2−1 transmission zeros. Again there is, at least in principle, no limit on the location of such transmission zeros. 
         [0043]      FIG. 9  depicts the Halma topology of a six-stage, two-port, extracted-poles, in-line resonator filter  900  having six inner conductors  910 ( 1 )- 910 ( 6 ) and two I/O ports  930 ( 1 ) and  930 ( 2 ) according to another embodiment of the invention. Extracted-poles, in-line resonator filter  900  is similar to in-line resonator filter  600  of  FIG. 6 , except that, in resonator filter  900 , (i) all of the inter-conductor couplings are negligible or zero and (ii) each inner conductor  910 (i) is connected to a corresponding non-resonating node  942 (i) of an external network  940  via a corresponding (ohmic) connection  944 (i), where the two I/O ports  930 ( 1 ) and  930 ( 2 ) are connected to the first and last non-resonating nodes  942 ( 1 ) and  942 ( 6 ) of the external network  940 . In that case, an extracted pole topology of degree N=6 results with the ability to accommodate up to N=6 transmission zeros. The external coupling network  940  needs to realize a manifold-like connection between the I/O ports  930  and the resonating nodes (i.e., the inner conductors  910 ) and might be implemented on a printed circuit board in microstrip technology, for example. The non-resonating nodes  942  might then be implemented as stubs of suitable length. 
         [0044]      FIG. 10  depicts the Halma topology of a six-stage, two-port, transversal, in-line resonator filter  1000  having six inner conductors  1010 ( 1 )- 1010 ( 6 ) and two I/O ports  1030 ( 1 ) and  1030 ( 2 ) according to another embodiment of the invention. Transversal, in-line resonator filter  1000  is similar to in-line resonator filter  900  of  FIG. 9  with negligible or zero inter-conductor coupling, except that, in resonator filter  1000 , each inner conductor  1010 (i) is connected to both I/O ports  1030 ( 1 ) and  1030 ( 2 ). In that case, a transversal topology of degree N=6 results with the ability to accommodate up to N−1=5 transmission zeros. Transversal, in-line resonator filter  1000  has two external coupling networks, where each external coupling network realizes a star-like connection between the corresponding I/O port  1030 (i) and the inner conductors  1010 , where both external coupling networks might be implemented on a single printed circuit board in microstrip technology, for example. 
         [0045]      FIG. 11  depicts the Halma topology of an 11-stage, three-port, diplexer, in-line resonator filter  1100  having eleven inner conductors  1110 ( 1 )- 1110 ( 11 ) and three I/O ports  1130 ( 1 ),  1130 ( 2 ),  1130 ( 3 ) according to another embodiment of the invention. Diplexer, in-line resonator filter  1100  is analogous to in-line resonator filter  600  of  FIG. 6 , except that, in resonator filter  1100 , an intermediate inner conductor  1110 ( 6 ) is connected to the intermediate, third I/O port  1130 ( 3 ). 
         [0046]    The 11-stage, diplexer, in-line resonator filter  1100  has a first in-line path of degree 6−1=5 from the first I/O port  1130 ( 1 ) to the intermediate I/O port  1130 ( 3 ) and a second in-line path of degree 11−6=5 from the intermediate I/O port  1130 ( 3 ) to the second I/O port  1130 ( 2 ). In general, an N-stage, three-port, diplexer, in-line resonator filter of the invention having the Kth inner conductor, 1&lt;K&lt;N, connected to the intermediate I/O port will have a first in-line path of degree K-1 from the first I/O port to the intermediate I/O port and a second in-line path of degree N-K from the intermediate I/O port to the second I/O port. The number of available transmission zeros for each path is computed in the same way as in the case of in-line filter  600  of  FIG. 6 . Note that, for N odd, K can, but does not have to, equal (N+1)/2. In other words, the degrees of the two in-line paths can be the same or different. 
         [0047]      FIG. 12  depicts the Halma topology of a 6-stage, three-port, arrow-diplexer, in-line resonator filter  1200  having six inner conductors  1210 ( 1 )- 1210 ( 11 ) and three I/O ports  1230 ( 1 ),  1230 ( 2 ),  1230 ( 3 ) according to another embodiment of the invention. Arrow-diplexer, in-line resonator filter  1200  is similar to folded, in-line resonator filter  600  of  FIG. 6 , except that, in resonator filter  1200 , conductors  1210 ( 5 ) and  1210 ( 6 ) are both connected to the I/O port  1230 ( 3 ). Note that, in alternative embodiments, more than two inner conductors  1210  can be connected to the I/O port  1230 ( 3 ), which will affect the number of available transmission zeros. 
         [0048]    Resonator filters of the present invention may include air-filled cavity resonators, such as resonators having all-metal cavities, or dielectric-loaded resonators, such as TEM dielectric resonators. 
         [0049]    Although the invention has been described in terms of resonator filters having an adjustable tuning element for each inner conductor and additional tuning elements located between adjacent conductors and extending from either the top or bottom ground plane, the invention is not so limited. In general, resonator filters of the present invention may have zero, one, or more tuning elements, where each tuning element is independently adjustable or fixed and extends from the top, bottom, and lateral ground plane. 
         [0050]    Although the invention has been described in terms of resonator filters having inter-conductor connectors between each adjacent pair of inner conductors, the invention is not so limited. In general, one or more or all of the inter-conductor connectors can be omitted. 
         [0051]    For purposes of this description, the terms “couple,” “coupling,” “coupled,” “connect,” “connecting,” or “connected” refer to any manner known in the art or later developed in which energy is allowed to be transferred between two or more elements, and the interposition of one or more additional elements is contemplated, although not required. Conversely, the terms “directly coupled,” “directly connected,” etc., imply the absence of such additional elements. 
         [0052]    Unless explicitly stated otherwise, each numerical value and range should be interpreted as being approximate as if the word “about” or “approximately” preceded the value or range. 
         [0053]    It will be further understood that various changes in the details, materials, and arrangements of the parts which have been described and illustrated in order to explain embodiments of this invention may be made by those skilled in the art without departing from embodiments of the invention encompassed by the following claims. 
         [0054]    In this specification including any claims, the term “each” may be used to refer to one or more specified characteristics of a plurality of previously recited elements or steps. When used with the open-ended term “comprising,” the recitation of the term “each” does not exclude additional, unrecited elements or steps. Thus, it will be understood that an apparatus may have additional, unrecited elements and a method may have additional, unrecited steps, where the additional, unrecited elements or steps do not have the one or more specified characteristics. 
         [0055]    The use of figure numbers and/or figure reference labels in the claims is intended to identify one or more possible embodiments of the claimed subject matter in order to facilitate the interpretation of the claims. Such use is not to be construed as necessarily limiting the scope of those claims to the embodiments shown in the corresponding figures. 
         [0056]    Reference herein to “one embodiment” or “an embodiment” means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the invention. The appearances of the phrase “in one embodiment” in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments necessarily mutually exclusive of other embodiments. The same applies to the term “implementation.” 
         [0057]    The embodiments covered by the claims in this application are limited to embodiments that (1) are enabled by this specification and (2) correspond to statutory subject matter. Non-enabled embodiments and embodiments that correspond to non-statutory subject matter are explicitly disclaimed even if they fall within the scope of the claims.