BACKGROUND

[001] Known coaxial cables include a cable center conductor within a cable outer conductor. A dielectric is provided between the cable center conductor and the cable outer conductor.

[002] Connections to and between known cables are made with coaxial connectors, which also include a connector center conductor within a connector outer conductor. A dielectric is also provided between the connector center conductor and the connector outer conductor.

Additionally, the connector center conductor is provided with an opening to receive the cable center conductor.

[003] FIG. 1 shows a profile view of a known coaxial cable 101 connected to a known cable connector 102. In FIG. 1, the coaxial cable 101 includes cable center conductor 111 and cable outer conductor 114, with a dielectric layer 103 disposed therebetween. The cable connector 102 includes connector center conductor 121 and connector outer conductor collar 122, with a dielectric layer 104 therebetween. The cable center conductor 111 fits into an opening of the connector center conductor 121 where the cable center conductor 111 and the connector center conductor 121 overlap in the length direction.

[004] As shown in Fig. 1, at certain locations at the interface between the coaxial cable 101 and the cable connector 102 discontinuities occur, where a discontinuity is a sharp change in directionality of a profile of the cable connector. FIG. 1 shows examples of discontinuities as “steps” in the profile of the connector center conductor 121 by the 90° changes in x-y dimensions of the coordinate system shown to reflect sharp changes in diameter. The steps correspond to sharp changes in diameter over, for example, less than 10% or even 5% of the total length (x- dimension of the coordinate system of Fig. 1) of the cable connector 102. A sharp change in directionality of a profile of a cable connector may therefore be considered, for example, a change in directionality of the profile on the order of 45° to 90° occurring over less than 10% of the total length of the cable connector. The“steps” shown in the profile in FIG. 1 are provided to accommodate the opening for the cable center conductor 111, and the steps reflect discontinuities in two separate places along the length of the interconnected combination of the cable center conductor 111 and the connector center conductor 121, as the diameter of the connector center conductor 121 sharply changes twice in the length direction.

[005] The discontinuities shown in FIG. 1 are typical of known cable to connector transitions. At lower frequencies, the discontinuities do not significantly affect radio frequency (RF) performance enough to cause problems that require redress. However, at higher frequencies such as those being increasingly relied upon in communications, these discontinuities deleteriously impact performance of the coaxial signal transmission line.

BRIEF DESCRIPTION OF THE DRAWINGS

[006] The example embodiments are best understood from the following detailed description when read with the accompanying drawing figures. It is emphasized that the various features are not necessarily drawn to scale. In fact, the dimensions may be arbitrarily increased or decreased for clarity of discussion. Wherever applicable and practical, like reference numerals refer to like elements.

[007] FIG. 1 illustrates a profile view of a known coaxial cable connected to a known cable connector.

[008] FIG. 2A illustrates cross-sectional view of an inner conductor of a signal transmission line connector in accordance with a representative embodiment.

[009] FIG. 2B illustrates a cross-sectional view of a coaxial cable connected to a signal transmission line connector, in accordance with a representative embodiment.

[010] FIGs. 3A to 3E illustrate a process for manufacturing and assembling a combined coaxial cable and a signal transmission line connector, in accordance with a representative embodiment.

[Oil] FIG. 4 illustrates a profile view of a coaxial cable connected to a signal transmission line connector, in accordance with a representative embodiment.

[012] FIG. 5 illustrates a profile view of a coaxial cable connected to a signal transmission line connector, in accordance with a representative embodiment.

[013] FIG. 6 illustrates a profile view of another two coaxial cables connected to a signal transmission line connector, in accordance with a representative embodiment.

[014] FIG. 7 illustrates a profile view of a coaxial cable connected to a signal transmission line connector, in accordance with a representative embodiment.

DETAILED DESCRIPTION

[015] In the following detailed description, for purposes of explanation and not limitation, representative embodiments disclosing specific details are set forth in order to provide a thorough understanding of the embodiments according to the present teachings. Descriptions of known systems, devices, materials, methods of operation and methods of manufacture may be omitted so as to avoid obscuring the description of the representative embodiments.

Nonetheless, systems, devices, materials and methods that are within the purview of one of ordinary skill in the art are within the scope of the present teachings and may be used in accordance with the representative embodiments. It is to be understood that the terminology used herein is for purposes of describing particular embodiments only, and is not intended to be limiting. The defined terms are in addition to the technical and scientific meanings of the defined terms as commonly understood and accepted in the technical field of the present teachings.

[016] It will be understood that, although the terms first, second, third etc. may be used herein to describe various elements or components, these elements or components should not be limited by these terms. These terms are only used to distinguish one element or component from another element or component. Thus, a first element or component discussed below could be termed a second element or component without departing from the teachings of the present disclosure.

[017] The terminology used herein is for purposes of describing particular embodiments only, and is not intended to be limiting. As used in the specification and appended claims, the singular forms of terms‘a’,‘an’ and‘the’ are intended to include both singular and plural forms, unless the context clearly dictates otherwise. Additionally, the terms "comprises", and/or "comprising," and/or similar terms when used in this specification, specify the presence of stated features, elements, and/or components, but do not preclude the presence or addition of one or more other features, elements, components, and/or groups thereof. As used herein, the term "and/or" includes any and all combinations of one or more of the associated listed items. [018] Unless otherwise noted, when an element or component is said to be“connected to”, “coupled to”, or“adjacent to” another element or component, it will be understood that the element or component can be directly connected or coupled to the other element or component, or intervening elements or components may be present. That is, these and similar terms encompass cases where one or more intermediate elements or components may be employed to connect two elements or components. However, when an element or component is said to be “directly connected” to another element or component, this encompasses only cases where the two elements or components are connected to each other without any intermediate or intervening elements or components.

[019] In view of the foregoing, the present disclosure, through one or more of its various aspects, embodiments and/or specific features or sub-components, is thus intended to bring out one or more of the advantages as specifically noted below. For purposes of explanation and not limitation, representative embodiments disclosing specific details are set forth in order to provide a thorough understanding of an embodiment according to the present teachings. However, other embodiments consistent with the present disclosure that depart from specific details disclosed herein remain within the scope of the appended claims. Moreover, descriptions of well-known apparatuses and methods may be omitted so as to not obscure the description of the example embodiments. Such methods and apparatuses are within the scope of the present disclosure.

[020] In accordance with a representative embodiment, a signal transmission line connector comprises: an inner electrical conductor comprising a first male portion at an end, a second male portion at an opposing end, and a tapered portion between the first male portion and the second male portion; an outer electrical conductor; and a dielectric region disposed between the inner electrical conductor and the outer electrical conductor. The dielectric region has a taper along a length. The signal transmission line connector has a first cross-sectional area at the end, and a second cross-sectional area at the opposing end. The second cross-sectional area is smaller than the first cross-sectional area.

[021] In accordance with another representative embodiment, an apparatus comprises: a first electrical connector comprising: an inner electrical conductor comprising a first male portion at an end, a second male portion at an opposing end, and a tapered portion between the first male portion and the second male portion; an outer electrical conductor; and a dielectric region disposed between the inner electrical conductor and the outer electrical conductor, the dielectric region having a taper along a length. The first electrical connector has a first cross- sectional area at the end, and a second cross-sectional area at the opposing end, and the second cross-sectional area is smaller than the first cross-sectional area. The apparatus further comprises a second electrical connector comprising a female portion adapted to receive the second male portion.

[022] FIGs. 2A and 2B are a cross-sectional view, and a profile view, respectively, of a connector inner conductor 221 in accordance with a representative embodiment. The connector inner conductor 221 comprises a first male portion 221A, and a second male portion 221B on an opposing side of the connector inner conductor 221.

[023] As depicted in Figs. 2A and 2B, the connector inner conductor 221 has a tapered profile reflected in a tapered circumference of the connector inner conductor 221 between the first male portion 221A and the second male portion 221B. The angle (Q) of this taper between the termination of the first male portion 221 A and second male portion 221B is described more fully below. Notably, the taper of the connector inner conductor 221 is substantially symmetric about a center axis 201 shown in Fig. 2C.

[024] In an embodiment, the taper in a connector center conductor may also increase rather than decrease while still avoiding significant steps and discontinuities in the profile. In such an embodiment, the signal transmission line center conductor (sometimes referred to as“inner conductor”) may meet a connector inner conductor where the signal transmission line center conductor has its smallest cross-sectional area and its smallest cross sectional profile length.

[025] FIG. 2C illustrates a cross-sectional view of a first coaxial signal transmission line 210 connected to a first coaxial signal transmission line connector 220, in accordance with a representative embodiment.

[026] The first coaxial signal transmission line 210 comprises a signal transmission line inner conductor 211, a signal transmission line dielectric layer 223a, and a signal transmission line outer conductor (sometimes referred to as“outer conductor”) 214. The signal transmission line inner conductor 211 comprises a female portion 211 A, which is configured to receive the first male portion 221 A of the connector inner conductor 221.

[027] In a representative embodiment, an electrically thin resistive layer 225 is disposed in the signal transmission line dielectric layer 223a. Further details of the electrically thin resistive layer 225 may be found in commonly owned U.S. Patent Application No. 14/823,997 to Dove, et al. entitled“Coaxial Transmission Line Including Electrically Thin Resistive Layer and

Associated Methods” filed on August 11, 2015. The disclosure of U.S. Patent Application No. 14/823,997 is hereby incorporated by reference in its entirety.

[028] The first coaxial signal transmission line connector 220 comprises the connector inner conductor 221, a connector dielectric layer 223b, and a connector outer conductor collar 222a. Between the connector inner conductor 221 and a connector tapered barrel outer conductor collar 222b, the first coaxial signal transmission line connector 220 is shown connected to a signal transmission line inner conductor 211 of the first coaxial signal transmission line 210 through the mating of the first male portion 221A to the female portion 211A of the signal transmission line inner conductor 211.

[029] As depicted in Fig. 2C, the connector inner conductor 221 is connected to a second coaxial signal transmission line connector 230 on the right side. The second coaxial signal transmission line connector 230 comprises an inner pin 232, an air dielectric 245, and an outer pin 243. The use of air as a dielectric is merely illustrative, and other dielectric materials are contemplated. As shown, when air is used as the dielectric, supports 250 are provided between the inner pin 232 and the outer pin 243.

[030] The inner pin 232 of the second coaxial signal transmission line connector 230 comprises a female portion 232a that is adapted to receive the second male portion 22 IB of the connector inner conductor 221. The second coaxial signal transmission line connector 230 has smaller dimensions than the first coaxial signal transmission line 210. As such, the first coaxial signal transmission line connector 220 has a first cross-sectional area at the end of the first male portion 221A, and a second (smaller) cross-sectional area at the opposing end where the second male portion 221B is located, with the change in cross-sectional area being made across the length (x- dimension of the coordinate system of Fig. 2C) of the first coaxial signal transmission line connector 220. FIG. 2C shows the inner pin 232 between the air dielectric 245, and an outer pin 231 on the other side of the air dielectric 245 from the inner pin 232.

[031] It is noted that rather than being connected to the second coaxial signal transmission line connector 230, the first coaxial signal transmission line connector 220 may be connected to another coaxial signal transmission line. To this end, the components of the second coaxial signal transmission line connector 230 depicted in Fig. 2C compose a second coaxial signal transmission line having a smaller cross-sectional area than that of the first coaxial signal transmission line 210, and rather than terminate as the second coaxial signal transmission line connector 230 as shown, continues. As such, the first coaxial signal transmission line connector 220 is an adapter enabling the connection of coaxial signal transmission lines having different cross-sectional areas and dimensions, without discontinuities that plague known devices.

[032] The connector inner conductor 221 is tapered inward from the left to the right in Fig. 2C. On the left, the tapered part of the connector inner conductor 221 starts at the rightmost extreme of the signal transmission line inner conductor 211. The widest part of the connector inner conductor 221 is where the tapered portion has the greatest height in FIG. 2C, and this corresponds to both the largest cross-sectional area of the connector inner conductor 221, and the largest outer perimeter of any cross-section of the connector inner conductor 221. By comparison, the signal transmission line inner conductor 211 will have a wider or substantially equivalent maximum cross-sectional area, and a larger or substantially equivalent maximum profile length, compared to the connector inner conductor 221 in the region where the connector inner conductor 221 and the signal transmission line inner conductor 211 overlap in the length (x-direction in the depicted coordinate system). That is, when the connector inner conductor 221 is connected to signal transmission line inner conductor 211 by the engagement of the first male portion 221A and a female portion of the signal transmission line inner conductor 211, an extremity of the signal transmission line inner conductor 211 will meet the connector inner conductor 221 where the connector inner conductor 221 has its largest cross-sectional area and its greatest outermost cross-sectional profile length.

[033] FIGs. 3A to 3E illustrate a process for manufacturing and assembling a combined coaxial signal transmission line and signal transmission line conductor, in accordance with a representative embodiment. FIG. 3A shows a profile of a signal transmission line inner conductor prior to processing. FIG. 3B shows the signal transmission line inner conductor 311 once a gap/hole 312 is formed on the right side. The gap/hole 312 may be formed by, for example, drilling. In FIG. 3B, context is shown for the signal transmission line inner conductor 311 being arranged within a signal transmission line outer conductor 314, and the signal transmission line outer conductor 314 is shown connected to a connector outer conductor collar 322.

[034] FIG. 3C shows solder paste 313 being applied to the gap/hole 312 of the signal transmission line inner conductor 311. A male portion at the left end of the connector inner conductor 321 is inserted into the gap/hole 312 with the solder paste 313 applied. The connector inner conductor 321 has the same taper as the connector inner conductor 221 in FIGs. 2A-2B. Similar to the connector inner conductor 221 in FIGs. 3A and 3B, the connector inner conductor 321 has a sub-connector portion on the right side that can be inserted into a female portion of an inner pin (not shown).

[035] At an interface where the signal transmission line inner conductor 311 is at an extremity on the right, the connector inner conductor 321 has the same or substantially the same (e.g., within 5%) outermost cross-sectional circumference, diameter and perimeter as the closest parallel portion of the signal transmission line inner conductor 311. The interface between the signal transmission line inner conductor 311 and the connector inner conductor 321 here can be considered a planar interface or a substantially planar interface.

[036] FIG. 3D shows the addition of a connector outer conductor collar 322b around the connector inner conductor 321. FIG. 3E shows the addition of an inner pin 332 and an outer pin 331 on the other side of dielectric 343 from the inner pin 332. A female portion on the left side of the inner pin 332 is configured to receive the sub-connector portion of the connector inner conductor 321.

[037] As shown in FIGs. 3A-3E, a signal transmission line to connector transition with continuity characteristics can be constructed starting by modifying a signal transmission line inner conductor 311 from FIG. 3A by, for example, drilling an opening or gap/hole 312 into an end. Any such opening or gap/hole 312 should be centered about a center axis along the length of the signal transmission line inner conductor 311 assuming that the signal transmission line inner conductor 311 is symmetric about such a center axis, such as by having a circular or elliptical cross-section.

[038] In any event, the connector inner conductor 321 in FIG. 3E will have a maximum cross- sectional area that is substantially the same (e.g., within 5%) as the maximum cross-sectional area of the signal transmission line inner conductor 311 in the entirety of the region shown in FIG. 3E where the signal transmission line inner conductor 311 and connector inner conductor 321 overlap in the length direction. Additionally, the cross-sectional area of the connector inner conductor 321 decreases from the maximum area with the tapering of the connector inner conductor 321 as the cross-sectional diameter decreases. The grade of the connector inner conductor 321 in FIG. 3E results from the decreasing diameter of the cross-section, and may be in the order of 5-30° as compared to the steep grades around 90° for the steps of the connector inner conductor 121 shown in FIG. 1A. The tapering of the connector inner conductor 321 corresponds to the grade, and more than 50% of the length of the connector inner conductor 321 may be tapered, compared to the changes in FIG. 1 which occur over less than 5% of the length of the connector inner conductor 121 that is conventional. Accordingly, the connector inner conductor 321 provides both a smooth transition from the signal transmission line inner conductor 311, and avoids discontinuities of the type known to cause problems at higher frequencies.

[039] As alluded to above, the representative embodiments described in connection with FIGs. 2A-2C and 3A-3E can be used for transitioning from a large signal transmission line center conductor 211/311 to a small connector center conductor 321/321. This is useful for transitioning larger cables to smaller high-frequency connector classes such as, for example, 1.85 mm and 1 mm connectors.

[040] Additionally, although not discussed above, the dielectric 343 in FIG. 3E is itself tapered in two ways. First, the dielectric 343 is tapered around the connector center conductor 421 that is itself tapered. Additionally, the dielectric 343 is tapered within the tapered interior of the connector outer conductor collar 322b.

[041] FIG. 4 illustrates a profile view of another coaxial signal transmission line connected to another signal transmission line connector, in accordance with a representative embodiment. In the embodiment of FIG. 4, a hollow signal transmission line center conductor 411 is connected to a connector center conductor 421 that is tapered. Compared to previous embodiments, there is no need to drill an opening centered on a center axis of the hollow signal transmission line center conductor 411 simply in order to fit a male portion on the left side of the connector center conductor 421.

[042] As shown, the connector center conductor 421 in FIG. 4 has a smaller outer diameter than the outer diameter of the hollow signal transmission line center conductor 411 throughout the regions shown in FIG. 4. However, the connector center conductor 421 runs flush with the hollow signal transmission line center conductor 411 at the horizontal extremity of the hollow signal transmission line center conductor 411 on the right where it interfaces the connector center conductor 421. As a result, the maximum cross-sectional area of the connector center conductor 421 is substantially the same as (e.g., within 5% of) the cross-sectional area of any portion of the hollow signal transmission line center conductor 411 shown in FIG. 4. Other than those aspects described above, the embodiment of FIG. 4 is similar or identical to the embodiment of FIGs. 3A-3E. In other embodiments, the connector center conductor 421 may have a smaller diameter that is only partially flush with the hollow signal transmission line center conductor 411 at the horizontal extremity of the hollow signal transmission line center conductor 411 on the right where it interfaces the connector center conductor 421. In these embodiments, the maximum cross-sectional area of the connector center conductor 421 is less than the cross-sectional area of any portion of the hollow signal transmission line center conductor 411.

[043] At an interface where the hollow signal transmission line center conductor 411 is at an extremity on the right, the connector center conductor 421 has the same or substantially the same (e.g., within 5%) outermost cross-sectional circumference, diameter and perimeter as the closest parallel portion of the hollow signal transmission line center conductor 411. The interface between the hollow signal transmission line center conductor 411 and the connector center conductor 421 here can be considered a planar interface or a substantially planar interface.

[044] FIG. 5 illustrates a profile view of another coaxial signal transmission line connected to another signal transmission line connector, in accordance with a representative embodiment. In FIG. 5, the signal transmission line center conductor 511 has a male portion on the right side, and the connector center conductor 521 has a female portion on the left side. When connected, the male portion of the signal transmission line center conductor 511 is inserted into the female portion of the connector center conductor 521.

[045] Additionally, in FIG. 5 the connector center conductor 521 has a tapered profile, so that the cross-sectional diameter of the connector center conductor 521 decreases away from the signal transmission line center conductor 511. The maximum cross-sectional area of the connector center conductor 521 is substantially the same (e.g., within 5%) as the maximum cross-sectional area of the signal transmission line center conductor 511. However, the cross- sectional area of the signal transmission line center conductor 511 is consistent along the length of the signal transmission line center conductor 511 in FIG. 5 except where the signal transmission line center conductor 511 overlaps the connector center conductor 521. On the other hand, the maximum-cross-sectional area of the connector center conductor 521 is at the leftmost extremity of the connector center conductor 521, and decreases to the right in the length direction.

[046] At an interface where the signal transmission line center conductor 511 is at an extremity on the right, the connector center conductor 521 has the same or substantially the same (e.g., within 5%) outermost cross-sectional circumference, diameter and perimeter as the closest parallel portion of the signal transmission line center conductor 511. The interface between the signal transmission line center conductor 511 and the connector center conductor 521 here can be considered a planar interface or a substantially planar interface.

[047] In the embodiments of FIG. 6 and FIG. 7 described below, electrically thin resistive layers are provided within dielectric layers in/of coaxial cables and signal transmission line connectors. As context for these embodiments, it is generally desirable for transmission lines such as coaxial cables to support a single eigenmode (‘single mode’) of signal propagation. Multi-mode signal propagation is problematic because the desired propagation mode and higher- order modes may interfere with each other to provide a received signal that is severely frequency-dependent in an uncontrolled and usually un-interpretable manner. The lowest order mode for coaxial cables and signal transmission line connectors may be a substantially transverse electric magnetic (TEM) mode of transmission, and the electrically thin resistive layer is configured to be substantially transparent to the substantially TEM mode, and yet to substantially attenuate (i.e., almost completely) higher order modes of transmission. The TEM mode is typically desired, and features a substantially radially directed electric field, which is not true of the transverse electric (TE) or transverse magnetic (TM) higher order modes. The TEM mode is somewhat of an idealization that follows from solutions to Maxwell’s Equations. In reality, at any nonzero frequency the TEM mode actually has small deviations from a purely transverse electric field due to the imperfect nature of the conductors of the coaxial cables and signal transmission line conductors. Also, inhomogeneity in the dielectric region(s) will lead to dispersion and deviation from the behavior of an‘ideal’ TEM mode (which is technically dispersionless) in coaxial cables and signal transmission line conductors at higher frequencies.

As such, the term“substantially TEM mode" accounts for such deviations from the ideal behavior due to the environment of the cables and signal transmission line conductors of the representative embodiments described below. Electrically thin resistive layers contemplated for the present teachings are described in the following commonly assigned patent applications, the disclosures of which are hereby incorporated by reference in their entireties: U.S. Patent Application No. 15/594,996, filed May 15, 2017, and entitled "Coaxial Transmission Line Including Electrically Thin Resistive Layer and Associated Method;” International Application No. PCT/US2016/039593, filed June 26, 2016 and entitled "Electrical Connectors for Coaxial Transmission Lines Including Taper and Electrically Thin Resistive Layer"; U.S. Patent Application No. 15/008,368, filed January 27, 2016 and entitled "Signal Transmission Line and Electrical Connector Including Electrically Thin Resistive Layer and Associated Methods", and U.S. Patent Application No. 14/823,997, filed August 11, 2015 and entitled "Coaxial

Transmission Line Including Electrically Thin Resistive Layer and Associated Methods.”

[048] FIG. 6 illustrates a profile view of another two coaxial cables connected to another signal transmission line connector, in accordance with a representative embodiment. Notably, many aspects and details of the signal transmission line connectors of the representative embodiments described above are common to the signal transmission line connector in FIG. 6. These common aspects and details are often not repeated in the presently described representative embodiment.

[049] In FIG. 6, a coaxial signal transmission line 610 includes signal transmission line inner conductor 611, signal transmission line outer conductor 614, and dielectric layers 643, 641 disposed between the signal transmission line inner conductor 611 and signal transmission line outer conductor 614. An electrically thin resistive layer 642 is provided between the dielectric layers 643, 641. A coaxial signal transmission line 615 includes signal transmission line inner conductor 616, signal transmission line outer conductor 619, and dielectric layers 643, 641 disposed between the signal transmission line inner conductor 616 and signal transmission line outer conductor 619. The dielectric layers 643, 641 and electrically thin resistive layer 642 are also provided in the coaxial signal transmission line 615.

[050] Also in FIG. 6, a signal transmission line connector includes an inner conductor and an outer connector. The inner conductor includes female inner conductor 62 la and male inner conductor 621b, and the outer connector includes connector outer conductor collars 622a, 622b, one a connector outer conductor collar 622a for the female inner conductor 62 la, and the other a connector outer conductor collar 622b for the male inner conductor 62lb. The inner conductor (i.e., 62la, 62lb) has a common propagation axis with the connector outer conductor collars 622a, 622b. A dielectric region between the inner conductor and the outer connector includes the dielectric layers 643, 641, and an electrically thin resistive layer 642 between the dielectric layers 643, 641. The electrically thin resistive layer 642 is concentric with the inner conductor and the outer connector.

[051] In FIG. 6, the coaxial signal transmission lines 610, 615 differ from other shielded signal transmission line used for carrying lower-frequency signals, such as audio signals. Specifically, dimensions of the coaxial signal transmission lines 610, 615 are controlled to give a substantially precise, substantially constant spacing between the signal transmission line inner conductors 611, 616 and the signal transmission line outer conductors 614, 619.

[052] Coaxial signal transmission lines 610, 615 are often used as tran mi ion lines for radio frequency signals. Applications of coaxial signal transmission lines 610, 615 include feedlines connecting radio transmitters and receivers with their antennas. In radio-frequency applications, the electric and magnetic signals propagate primarily in the substantially transverse electric magnetic (TEM) mode, which is the single desired mode to be supported by the coaxial signal transmission lines 610, 615 and signal transmission line connector. In a substantially TEM mode, the electric and magnetic fields are both substantially perpendicular to the direction of propagation. However, above a certain cutoff frequency, transverse electric (TE) or transverse magnetic (TM) modes, or both, can also propagate, as they do in a waveguide. It is usually undesirable to transmit signals above the cutoff frequency, since it may cause multiple modes with different phase velocities to propagate, interfering with each other. The average of the circumference between the signal transmission line inner conductors 611, 616 and the inside of the signal transmission line outer conductors 614, 619 is roughly inversely proportional to the cutoff frequency.

[053] The signal transmission line connector in FIG. 6 is shown in the drawings as a coaxial signal transmission line connector. The signal transmission line connector in FIG. 6 is a male-to- male connector, comprising a male inner conductor 62lb with male characteristics on both the right side and left side, and a female inner conductor 62 la with male characteristics on the left side. As will be appreciated by one of ordinary skill in the art, all aspects of signal transmission line connectors of the present teachings are provided through the presently described

representative embodiment.

[054] In operation, the male side of the female inner conductor 62 la is inserted into an opening of the signal transmission line inner conductor 611 of the coaxial signal transmission line 610. The right side of the male inner conductor 62 lb is inserted into an opening of the signal transmission line inner conductor 616 of the coaxial signal transmission line 615. When the male inner conductor 62 lb is inserted into the female side of the female inner conductor 62 la, the signal transmission line connector connects the coaxial signal transmission lines 610, 615 via signal tran mi ion line inner conductors 611, 616. That is, as in FIG. 2C, the signal transmission line connector of FIG. 6 has two separate pieces that can be separated and joined, i.e., the female inner conductor 62 la and connector outer conductor collar 622a, and the male inner conductor 62lb and connector outer conductor collar 622b. The signal transmission line connector of FIG. 6B can connect two otherwise separated coaxial signal transmission lines or coaxial signal transmission line segments.

[055] The size and shape parameters of the embodiment of FIG. 6 are the same as in the embodiment of FIG. 2C. That is, diameters, cross-sectional areas, profile lengths, and other characteristic sizes of the components of FIG. 6 that are common to components of FIG. 2C, are the same as for the components of FIG. 2C. The same is true of shapes for the common components of FIGs. 2C and 7. The coaxial signal tran mi sion lines 610, 615 are signal transmission lines that include terminating regions where the signal transmission line inner conductors 611, 616 respectively overlap the female inner conductor 621a and the male inner conductor 621b.

[056] In representative embodiments, the electrically thin resistive layer 642 is continuous and extends along the length of the signal transmission line connector. The continuity of the electrically thin resistive layer 642 may be common to the coaxial signal transmission lines 610, 615, as well as coaxial signal transmission lines of other representative embodiments described herein. Alternatively, the electrically thin resistive layer 642, as well the electrically thin resistive layer of other representative embodiments may be discontinuous, and thereby have gaps along the length of the particular coaxial signal transmission line and/or signal transmission line connector. The electrically thin resistive layer 642 may be an electrically thin resistive coating on the dielectric layer 643. The electrically thin resistive layer 642 illustratively includes at least one of TaN, WSiN, resistively-loaded polyimide, graphite, graphene, transition metal dichalcogenide (TMDC), nichrome (NiCr), nickel phosphorus (NiP), indium oxide, and tin oxide. Notably, however, other materials within the purview of one of ordinary skill in the art having the benefit of the present teachings, are contemplated for use as the electrically thin resistive layer 642. Transition metal dichalcogenides (TMDCs) include: HfSe2, HfS2, SnS2, ZrS2, MoS2, MoSe2, MoTe2, WS2, WSe2, WTe2, ReS2, ReSe2, SnSe2, SnTe2, TaS2, TaSe2, MoSSe, WSSe, MoWS2, MoWSe2, PbSnS2. The chalcogen family includes the Group VI elements S, Se and Te. The electrically thin resistive layer 642 may have an electrical sheet resistance between 20-2500 ohms/sq and preferably between 20-200 ohms/sq.

[057] The inner conductor (i.e., 62la, 62lb) has a common propagation axis with the outer connector (i.e., connector outer conductor collars 622a, 622b). Similarly, the inner conductor and the outer connector share a common geometric center (e.g., a point on the common propagation axis). Moreover, the signal transmission line connector in FIG. 6 may be substantially circular in cross-section. Generally, the term‘coaxial’ means the various layers/regions of a coaxial signal transmission line and signal transmission line connector have a common propagation axis.

Likewise, the term‘concentric’ means layers/regions of a coaxial signal transmission line and signal transmission line connector have the same geometric center. The signal transmission line connectors of some representative embodiments may be coaxial and concentric, whereas in other representative embodiments the signal transmission line connectors may not be concentric. Finally, the signal transmission line connectors of the representative embodiments are not limited to those circular in cross-section. Rather, signal transmission line connectors with other cross- sections are contemplated, including but not limited to, rectangular and elliptical cross-sections.

[058] As depicted in FIG. 6, the male inner conductor 62 lb extends beyond the terminus of the body of the signal transmission line connector to facilitate connection with the female inner conductor 621a. In this manner, the signal transmission line connector in FIG. 6 can function as a termination of a coaxial signal transmission line 610 or a coaxial signal transmission line 615, each comprising an electrically thin resistive layer 642. Additionally, the signal transmission line connector in FIG. 6 can be used to terminate coaxial signal transmission lines 610, 615 in the manner described and shown, with each of the two coaxial signal transmission lines 610, 615 comprising one or more electrically thin resistive layer 642. The signal transmission line connector in FIG. 6 can also be used to interconnect coaxial signal transmission lines 610, 615 in the manner described and shown, with each of the two coaxial signal transmission lines 610, 615 comprising one or more electrically thin resistive layer 642.

[059] At an interface where the signal transmission line inner conductor 611 is at an extremity on the right, the female inner conductor 62 la has the same or substantially the same (e.g., within 5%) outermost cross-sectional circumference, diameter and perimeter as the closest parallel portion of the signal transmission line inner conductor 611. The interface between the signal transmission line inner conductor 611 and the female inner conductor 62la here can be considered a planar interface or a substantially planar surface. Similarly, at an interface where the signal transmission line inner conductor 616 is at an extremity on the left, the female inner conductor 621a has the same or substantially the same (e.g., within 5%) outermost cross- sectional circumference, diameter and perimeter as the closest parallel portion of the signal transmission line inner conductor 616. The interface between the signal transmission line inner conductor 616 and the female inner conductor 62 la here may also be considered a planar interface or a substantially planar interface.

[060] Adding a second electrically thin resistive layer, such as 2/3 of the way in from the connector outer conductor collars 622a, 622B may be better positioned to attenuate some higher order modes, and may be beneficial in the presence of multiple discontinuities or with a poorly matched load. It may also be useful to allow a signal transmission line to be bent multiple times. So, it may be desired to include more than one electrically thin resistive layer 642 between the one shown in FIG. 6 and the connector outer conductor collars 622a, 622b. However, the benefits of another electrically thin resistive layer 642 must be weighed against the possible disadvantage that another electrically thin resistive layer 642 may add some insertion loss for the dominant substantially TEM mode.

[061] As may be appreciated by those skilled in the art, the center connector and the outer connector may be any suitable electrical conductor such as a copper wire, or other metal, metal alloy, or non-metal electrical conductor. In certain embodiments, the dielectric material for dielectric layers 641, 643 is air. In such embodiments, in order to provide structural support, and thereby ensure separation of the center connector, the electrically thin resistive layer 642, and the outer connector, dielectric beads may be disposed between the center connector and the outer connector. These dielectric beads may be formed of a known material suitable for the intended purposed of the signal transmission line connector, for example a dielectric material described below.

[062] Alternatively, if air is not used as the dielectric material one or more layers of dielectric material may be provided for dielectric layers 641, 643. Such materials contemplated for use include, but are not limited to glass fiber material, plastics such as

_2 polytetrafluoroethylene (PTFE), low-k dielectric material with a reduced loss tangent (e.g., 10 ), ceramic materials, liquid crystal polymer (LCP), or any other suitable dielectric material, including air, and combinations thereof. Notably, the number of dielectric layers described in the various representative embodiments is generally illustrative, and more than two dielectric layers 641, 643 are contemplated. However, generally the dielectric constants of the dielectric layers 641, 643 are substantially the same in order to propagate substantially transverse- electromagnetic (TEM) modes of propagation.

[063] The signal transmission line connector of FIG. 6 may be used to connect coaxial signal transmission lines for radio frequency (RF) signals and higher. To this end, the signal transmission line connector of FIG. 6 is configured for use in RF, microwave and millimeter wave applications. Applications of the signal transmission line connector in FIG. 6 include terminating or interconnecting coaxial signal transmission lines used for computer network (Internet) connections, distributing signal transmission line television signals, routing high frequency signals in an electronic test and measurement instrument, and connecting between an electronic test and measurement instrument and a DUT (device under test). In radio-frequency applications, the electric and magnetic signals propagate primarily in the substantially TEM mode.

[064] The electrically thin resistive layer 642 is an electrically resistive layer selected and configured to be substantially transparent to a substantially TEM mode of transmission, while substantially completely attenuating higher order modes of transmission. Generally, as described above in connection with various coaxial signal transmission line and signal transmission line connectors of representative embodiments, substantially completely attenuating means the signal transmission line connector of FIG. 6 is designed to accommodate a predetermined threshold of relative attenuation between the desired substantially TEM mode and the undesired higher order modes. As will be appreciated, among other design considerations, this predetermined threshold is realized through the selection of the appropriate thickness (e.g., via the skin depth and resistivity) of the electrically thin resistive layer 642. For example, in an application where RF frequencies up to 10 GHz are relevant and the transmission length is on the order of 10 cm, the threshold of relative attenuation requires a TEM attenuation constant of approximately 0.1 m ¹ , but attenuation of the higher order modes by more than approximately 100 m ¹ , and usefully over approximately 1000 m ¹ is contemplated. On the other hand, in an application where the highest frequency of operation is only a few GHz (or less) and the transmission length is tens of meters, the threshold of relative attenuation requires a TEM attenuation constant of approximately 0 m ¹ to approximately 0.01 m ¹ , while attenuating the higher order modes by at least approximately 1.0 m ¹ , but usefully by more than approximately 10 m ¹ is contemplated. It is emphasized that these examples are merely illustrative, and are not intended to be limiting of the present teachings.

[065] Additionally, an“electrically thin” layer is one for which the layer thickness is less than the skin depth d at the (highest) signal frequency of interest. This insures that the substantially TEM mode is minimally absorbed. The skin depth is given by d = 1 N (pίms), where d is in meters, f is the frequency in Hz, m is the magnetic permeability of the layer in Henrys/meter, and s is the conductivity of the layer in Siemens/meter.

[066] So, for the discussion herein, if t is the physical thickness of the electrically thin resistive layer 642, it is“electrically thin” if t < d _{ii ii} = l/V (pί^ _c ms), where d _PIIII is the skin depth calculated at the maximum frequency f _max . For example, suppose f _max = 200 GHz, the layer is nonmagnetic and hence m = mo = the vacuum permeability = 4p*10-7 Henrys/meter, and the conductivity is 100 Siemens/meter. Then 6 _min = 112.5 pm, so a resistive layer thickness t of 25 pm would be considered electrically thin in this case. Recapitulating, the electrically thin resistive layer 642 is electrically thin when its thickness is less than a skin depth at a maximum operating frequency of the signal transmission line connector in FIG. 6. [067] The dielectric layer 643 may be an inner dielectric material between the center connector and the electrically thin resistive layer 642, and the dielectric layer 641 may be an outer dielectric material between the electrically thin resistive layer 642 and the outer connector. In various embodiments, the inner dielectric material between the center connector and the electrically thin resistive layer 642, and the outer dielectric material between the electrically thin resistive layer 642 have approximately the same thickness. In some embodiments, a thickness of the inner dielectric material is approximately twice a thickness of the outer dielectric material.

[068] FIG. 7 illustrates a profile view of another coaxial signal transmission line connected to another signal transmission line connector, in accordance with a representative embodiment.

[069] In FIG. 7, a coaxial signal transmission line includes signal transmission line inner conductor 711 and signal transmission line outer conductor 714, along with dielectric layers 731 , 733 provided in a dielectric region, with an electrically thin resistive sheet 732 provided between the dielectric layers 731, 733. A signal transmission line connector includes inner conductor 721 and outer conductors 722a, 722b, along with the dielectric layers 731, 733 and electrically thin resistive sheet 732.

[070] The dielectric layers 731, 733 and the electrically thin resistive sheet 732 have the same or similar characteristics as described above with respect to dielectric layers 641, 643 and electrically thin resistive layer 642 in FIG. 6. However, the embodiment of FIG. 7 also corresponds structurally to the embodiment of FIG. 3D, and relative sizes and shapes of components in FIG. 7 may have the same characteristics as in FIG. 3D.

[071] A center axis runs through the interior of the signal transmission line connector in FIG. 7. The inner conductor 721, outer conductor 722b, and dielectric layers 731, 733 are substantially azimuthally symmetric about the center axis in Figure 8. Additionally, the inner conductor 721, the inner periphery of the outer conductor 722b, and the dielectric layers 731, 733 are tapered along their respective lengths lengthwise in the region that includes the inner conductor 721. That is, the inner conductor 721, the inner periphery of the outer conductor 722b, and dielectric layers 731, 733 have smaller radiuses (from the center axis) to the right and larger radiuses (from the center axis) to the left in FIG. 7. As a result, each of the inner conductor 721 and the inner periphery of the outer conductor 722b have a larger cross-sectional area at one end than at another end. The same is true of the dielectric layers 731, 733. [072] At an interface where the signal transmission line inner conductor 711 is at an extremity on the right, the inner conductor 721 has the same or substantially the same (e.g., within 5%) outermost cross-sectional circumference, diameter and perimeter as the closest parallel portion of the signal transmission line inner conductor 711. The interface between the signal transmission line inner conductor 711 and the inner conductor 721 here can be considered a planar interface or a substantially planar interface.

[073] In FIG. 7, the taper may have a length sufficient to maintain a skew between the inner conductor 721 and the outer conductor 722b of less than approximately 25 electrical degrees at a highest operating frequency of the electrical conductors. Alternatively, the taper may have a length sufficient to maintain a skew between the inner conductor 721 and the outer conductor 722b of less than approximately 20 electrical degrees at a highest operating frequency of the electrical conductors. The skew (Dy) in degrees is approximated by Df = 360(G/n] [^' (L ² + (a ₂ - a ² ) - / (L ² + [b ₂ -bi] ² ]], where f is the frequency in Hz, v is the phase velocity corresponding to the dielectric region, L is the axial length of the taper, al is an outer conductor radius of the first electrical conductor , bl is a inner conductor radius of the first electrical conductor, a2 is an outer conductor radius of the second electrical conductor, and b2 is an inner conductor radius of the second electrical conductor.

[074] Additionally, for shallow taper angles which may be useful for low skews, the skew length between the signal and ground paths can be approximated as ( a,, ² - 0C _I ² )L/2, where the outer and inner half-angles oc ₀ and cq are measured in radians, not degrees. Using the fact that 20° = p/9 radians, a rule of thumb is

Here e, is the relative dielectric constant in the taper, f _max is the maximum desired operation frequency, and c is the speed of light in vacuum.

[075] Due to the fact that oc ₀ and cq are not independent, if 50 ohms is to be maintained throughout the taper, then the outer conductor/inner conductor radius ratio may be maintained at ai/bi - a ₂ /b ₂ = exp((5/6)* (Ve _r )) where exp(x) is the exponential function e ^x . Thus, the small half-angles also satisfy the following equation: Oί _o /ai = exp( ( 5/6) * (Ve _{r) )}

The above-noted equations may be used to fully describe constraints on the taper.

[076] Additionally, a delay skew concern may be raised in a departure from a perfect cylindrical coaxial signal transmission line or connector. In such a departure, a length difference (and hence skew) will exist between the path that the signal/inner conductor takes and the path that the ground return/outer conductor takes. A commercial, stepped adapter can introduce such skew because the step discontinuity in the outer conductor is significantly larger than step

discontinuity in the inner conductor due to the need to preserve diameter ratios in order to preserve characteristic impedance of the TEM mode. Using a tapered adapter, skew can be easily calculated from Pythagorean geometry. Referring to taper half-angles, e.g., for a conical taper, a planar CPW taper, or a coupled-line taper, a _mner and a _outer for the respective inner and outer conductors, path skew is given by

d i .— L*(sec(oi _outer )-sec(ai _nner ))

where L is the axial length of the taper and sec is the secant function.

[077] For shallow half-angles, path skew can be approximated as

d _L ~ (L/2)*(( a _outer ) ² -(ai _nner ) ² )

where the half-angles are measured in radians, not degrees.

[078] A rule of thumb is to keep the phase delay skew < 20 degrees (= pi/9 radians) at the highest frequency of interest f _max . This means that

2ra*f _max *d _L *V ^r (E _r )/c < p/9

Substituting the above estimate of d _L ,

Here e _G is the relative dielectric constant in the taper. In the case where air is the constant, e _r would be 1.0 and c is the speed of light in a vacuum.

[079] The electrically thin resistive sheet 732 is provided also between the inner conductor 721 and the outer conductor 722b. The electrically thin resistive sheet 732 may be provided along the entire lengths of the inner conductor 721 and outer conductor 722b, or may be provided along a portion such as the portions where the inner conductor 721 and outer conductor 722b are wider to the left in FIG. 7. For example, the electrically thin resistive sheet 732 may be disposed along the entire length of a taper, and less than the entire length of the signal transmission line connector in FIG. 7. Indeed, the electrically thin resistive sheet 732 may not be particularly required or beneficial for a narrower portion of a signal transmission line connector in FIG. 7, such as when the narrower portion of such a signal transmission line connector does not propagate higher order modes that would be attenuated. In another example, a second electrically thin resistive layer (not shown in FIG. 7) may be also disposed between the inner conductor 721 and outer conductor 722b.

[080] The dielectric layers 731, 733 can be split into, e.g., four total pieces. The four pieces can include two inner pieces between an inner conductor and the electrically thin resistive sheet 732, and two outer pieces between the electrically thin resistive sheet 732 and an outer conductor. The inner pieces can be easily assembled first, and the outer pieces can be easily assembled around the inner pieces. Alternatively, the dielectric layers 731, 733 can be split into two pieces, i.e., an inner piece, and an outer piece. The two pieces can be assembled by sliding the inner piece into place (from a narrower end) of the signal transmission line connector, and then sliding the outer piece into place (from the narrower end).

[081] The electrically thin resistive sheet 732 may have curved comers and a slight gap between the ends of the sheet. The electrically thin resistive sheet 732 may have a seam indicating where the electrically thin resistive sheet 732 begins and ends, and the curved comers appear at the seam on both ends of the signal transmission line connector. The curved corners and gap will not cause a significant problem in attenuating higher order modes as explained herein.

[082] The inner conductor 721 and outer conductor 722b, and dielectric layers 731, 733, may be substantially azimuthally symmetric around a center axis. Azimuthal symmetry is a rotational symmetry around the center axis of a structure. As described more fully below, this azimuthal symmetry substantially prevents mode conversion of a transverse electromagnetic (TEM) mode to either a higher-order transverse electric (TE) mode, or a higher order transverse magnetic (TM) mode.

[083] An example of the benefits of the electrically thin resistive sheet 632 and the electrically thin resistive sheet 732 can be explained for a 1.85-mm cable. Such a signal transmission line is single-mode up to approximately 73 GHz, but can be extended almost threefold to 220 GHz, for example, by identifying how many and which TE and TM modes between 73 GHz and 220 GHz have to be attenuated. A simple way to do this accounting is to compute the dimensionless eigenvalues kca for the higher-order modes, where kc is the cutoff wavenumber = 2 p/lo and 2a is the outer electrical conductor ID. Here Xc is the free-space cutoff wavelength = c/fc, where fc is the cutoff frequency and c is the speed of light in vacuum. The lowest eigenvalue corresponds to the ~73 GHz cutoff of the first higher-order mode, which happens to be the TE11 mode. Any eigenvalue within a factor of 3 of the lowest eigenvalue indicates a mode that should be attenuated. Eigenvalues more than a factor of 3 greater than the lowest eigenvalue correspond to modes that are still in cutoff, even at 220 GHz.

[084] The reason for using dimensionless eigenvalues is that the same reasoning can be scaled to other cases. For example, it may be desired to extend the operating frequency of l-mm cable, which is single-mode to -120 GHz, to -360 GHz. The lowest eigenvalue then

corresponds to the -120 GHz cutoff of the TE11 mode in l-mm cable. Beneficially, the sheet resistance and radius of the resistive cylinder can be selected to minimally attenuate the substantially TEM mode while maximally attenuating higher order modes (e.g., the TE11 mode).

[085] Let r be the radius of the resistive cylinder. The designer can hone the sheet resistance and the dimensionless ratio a/r, where 2a is the inner diameter ID of the outer conductor 722b. Sheet resistance in the range of approximately 20 W/sq to approximately 200 W/sq and a/r values in the range approximately 1.2 to approximately 2.4 are effective. The resistive cylinder may be substantially midway between the inner conductor 721 and outer conductor 722b.

[086] Accordingly, a signal transmission line connector may be used to terminate and interconnect coaxial signal transmission lines with substantially the same impedance as the signal transmission line connector, and with reduced reflections. All embodiments of FIGs. 1-8 include such signal transmission line connectors with cross-sectional characteristics substantially the same or smaller than the corresponding coaxial signal transmission lines and without the steps that appear in profiles when diameters are significantly reduced over a small portion of the length of a signal transmission line connector. The embodiments of FIGs. 7-8 include signal transmission line connectors with additional features of a resistive layer that is substantially transparent to a substantially TEM mode of transmission while substantially completely attenuating higher order modes of transmission.

[087] One or more embodiments of the disclosure may be referred to herein, individually and/or collectively, by the term“invention” merely for convenience and without intending to voluntarily limit the scope of this application to any particular invention or inventive concept. Moreover, although specific embodiments have been illustrated and described herein, it should be appreciated that any subsequent arrangement designed to achieve the same or similar purpose may be substituted for the specific embodiments shown. This disclosure is intended to cover any and all subsequent adaptations or variations of various embodiments. Combinations of the above embodiments, and other embodiments not specifically described herein, will be apparent to those of skill in the art upon reviewing the description.

[088] While the invention has been illustrated and described in detail in the drawings and foregoing description, such illustration and description are to be considered illustrative or exemplary and not restrictive; the invention is not limited to the disclosed embodiments.

[089] Other variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed invention, from a study of the drawings, the disclosure, and the appended claims. In the claims, the word "comprising" does not exclude other elements or steps, and the indefinite article "a" or "an" does not exclude a plurality. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to an advantage.

[090] While representative embodiments are disclosed herein, one of ordinary skill in the art appreciates that many variations that are in accordance with the present teachings are possible and remain within the scope of the appended claim set. The invention therefore is not to be restricted except within the scope of the appended claims.

[091] Accordingly, signal transmission line to connector transition with continuity

characteristics enables smooth transitions without significant steps in the profile of an inner conductor for a signal transmission line connector.

[092] Although signal transmission line to connector transition with continuity characteristics has been described with reference to several exemplary embodiments, it is understood that the words that have been used are words of description and illustration, rather than words of limitation. Changes may be made within the purview of the appended claims, as presently stated and as amended, without departing from the scope and spirit of signal transmission line to connector transition with continuity characteristics in its aspects. Although signal transmission line to connector transition with continuity characteristics has been described with reference to particular means, materials and embodiments, signal transmission line to connector transition with continuity characteristics is not intended to be limited to the particulars disclosed; rather signal transmission line to connector transition with continuity characteristics extends to all functionally equivalent structures, methods, and uses such as are within the scope of the appended claims.

[093] The illustrations of the embodiments described herein are intended to provide a general understanding of the structure of the various embodiments. The illustrations are not intended to serve as a complete description of all of the elements and features of the disclosure described herein. Many other embodiments may be apparent to those of skill in the art upon reviewing the disclosure. Other embodiments may be utilized and derived from the disclosure, such that structural and logical substitutions and changes may be made without departing from the scope of the disclosure. Additionally, the illustrations are merely representational and may not be drawn to scale. Certain proportions within the illustrations may be exaggerated, while other proportions may be minimized. Accordingly, the disclosure and the figures are to be regarded as illustrative rather than restrictive.

[094] One or more embodiments of the disclosure may be referred to herein, individually and/or collectively, by the term“invention” merely for convenience and without intending to voluntarily limit the scope of this application to any particular invention or inventive concept. Moreover, although specific embodiments have been illustrated and described herein, it should be appreciated that any subsequent arrangement designed to achieve the same or similar purpose may be substituted for the specific embodiments shown. This disclosure is intended to cover any and all subsequent adaptations or variations of various embodiments. Combinations of the above embodiments, and other embodiments not specifically described herein, will be apparent to those of skill in the art upon reviewing the description.

[095] The Abstract of the Disclosure is provided to comply with 37 C.F.R. § 1.72(b) and is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims. In addition, in the foregoing Detailed Description, various features may be grouped together or described in a single embodiment for the purpose of streamlining the disclosure. This disclosure is not to be interpreted as reflecting an intention that the claimed embodiments require more features than are expressly recited in each claim. Rather, as the following claims reflect, inventive subject matter may be directed to less than all of the features of any of the disclosed embodiments. Thus, the following claims are incorporated into the Detailed Description, with each claim standing on its own as defining separately claimed subject matter.

[096] The preceding description of the disclosed embodiments is provided to enable any person skilled in the art to practice the concepts described in the present disclosure. As such, the above disclosed subject matter is to be considered illustrative, and not restrictive, and the appended claims are intended to cover all such modifications, enhancements, and other embodiments which fall within the true spirit and scope of the present disclosure. Thus, to the maximum extent allowed by law, the scope of the present disclosure is to be determined by the broadest permissible interpretation of the following claims and their equivalents, and shall not be restricted or limited by the foregoing detailed description.