The subject matter disclosed herein relates to the field of quantum computing and more particularly relates to a cryostat system including printed flexible cables, vacuum sealing, and suspended sample board.
Quantum computing is a new paradigm that exploits fundamental principles of quantum mechanics, such as superposition and entanglement, to tackle problems in mathematics, chemistry and material science that are well beyond the reach of supercomputers. Its power is derived from a quantum bit (qubit), which can simultaneously exist as a superposition of both 0 and 1 states and can become entangled with other qubits. This leads to doubling the computational power with each additional qubit, which can be repeated many times. It has been already shown that quantum computers can speed up some of the algorithms and, potentially, model any physical process.
Operating electronics including quantum circuits under cryogenic conditions (i.e. temperatures below −180° C./93K) is useful for the operation of certain types of silicon devices, such as thermal detectors and quantum computer circuitry. Maintaining cryogenic conditions in an experimental or operational region requires a heat pump to remove the heat from that region, and a cryostat to minimize the heat transfer from the surroundings back into the region.
There is also a need to provide a path for electrical signals including data, control, and power lines to enter and exit the cold, low pressure region inside a vacuum chamber from the outside which is typically at room temperature and at atmospheric pressure while providing a sufficient seal to maintain the vacuum within the chamber.
The following summary is illustrative only and is not intended to be limiting in any way. That is, the following summary is provided to introduce concepts, highlights, benefits and advantages of the novel and non-obvious techniques described herein. Select implementations are further described below in the detailed description. Thus, the following summary is not intended to identify essential features of the claimed subject matter, nor is it intended for use in determining the scope of the claimed subject matter.
The present invention is a wiring apparatus and related techniques that address the need to feed power and electronic signals into and out of the cold, low pressure region in a vacuum chamber to the outside which is typically at room temperature and atmospheric pressure. The wiring apparatus also functions to balance electrical resistance with the thermal conductivity of the power and signal conductors. Copper is most often used to transmit electronic signals, but as stated supra, it is also used as a good thermal conductor. Note that thermal conductivity and electrical conductivity are related by the Wiedemann-Franz law which states that the ratio of the electronic contribution of the thermal conductivity (K) to the electrical conductivity (a) of a metal is proportional to the temperature (T).
In the development of cryo-electronic systems, it is preferable to produce wiring solutions that can be assembled consistently, and that can be modified quickly and cost effectively, in order to more quickly determine the correct balance between thermal and electronic performance. When mass producing such cryo-electronic systems, it is also important to maximize component functionality and reliability while minimizing complexity, part count and ultimately cost.
In one embodiment, both the TV flex printed circuit as well as the cryo flex printed circuit are multilayer and in one example embodiment comprise four layers. The two outer layers serve as electromagnetic shields while the two inner layers comprise the signal lines which typically require electromagnetic shielding, electrical isolation from each other and from external electromagnetic fields. In one embodiment, the electromagnetic shield is not solid and comprises a mesh pattern (e.g., diamond, hexagons, octagons, or other polygon shape) making it more flexible. Preferably, the RF cutoff frequency of the printed shield is high enough to act as a solid shield without creating too much conductance. The mesh preferably minimizes conductivity while still providing sufficient RF shielding. Thus, the cable enables effective shielding by optimizing the scale and size of the mesh, while minimizing the total cross sectional area of copper running up and down the flex cables, and therefore its thermal conductivity.
There is thus provided in accordance with the invention, a sample board apparatus for use in a cryostat, comprising a cold plate attached to a second stage of a cryostat and maintained at a first cryogenic temperature, a plurality of pillar spacers attached and thermally coupled to the cold plate, a contact plate attached and thermally coupled to the plurality of pillar spacers, a sample printed circuit board (PCB) incorporating a quantum integrated circuit (IC) die to be cooled to the first cryogenic temperature, and a first plurality of spring loaded mounting screws adapted to mechanically fasten the PCB to the contact plate suspending it therefrom to allow for differential thermal expansion and contraction and to provide a capability of adjusting an amount of force applied between the quantum integrated circuit (IC) die and the contact plate.
There is also provided in accordance with the invention, a sample board apparatus for use in a cryostat, comprising a cold plate attached to a second stage of a cryostat and maintained at a first cryogenic temperature, a plurality of spacers attached and thermally coupled to the cold plate, a contact plate attached and thermally coupled to the plurality of pillar spacers, a sample printed circuit board (PCB) incorporating a quantum integrated circuit (IC) die to be cooled to the first cryogenic temperature, a first plurality of spring loaded mounting screws adapted to mechanically suspend the PCB from the contact plate to allow for differential thermal expansion and contraction whereby the amount of force applied between the quantum integrated circuit (IC) die and the contact plate is adjustable via the first plurality of spring loaded mounting screws, and a magnet assembly adapted to be adjustably positioned above and below the quantum IC for applying a magnetic field to control a spin of one or more particles in the quantum IC.
There is further provided in accordance with the invention, a sample board apparatus for use in a cryostat, comprising a cold plate attached to a second stage of a cryostat and maintained at a first cryogenic temperature, a contact plate attached and thermally coupled to the cold plate, a sample printed circuit board (PCB) incorporating a quantum integrated circuit (IC) die to be cooled to the first cryogenic temperature, a first plurality of spring loaded mounting screws adapted to mechanically fasten the sample PCB to the contact plate suspending it therefrom to allow for differential thermal expansion and contraction and to provide a capability of adjusting an amount of force applied between the quantum integrated circuit (IC) die and the contact plate, and a second plurality of spring loaded mounting screws adapted to mechanically fasten a flexible printed cable terminated with a PCB and connecter therein to the sample PCB.
The present invention is explained in further detail in the following exemplary embodiments and with reference to the figures, where identical or similar elements may be partly indicated by the same or similar reference numerals, and the features of various exemplary embodiments being combinable. The invention is herein described, by way of example only, with reference to the accompanying drawings, wherein:
In the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of the invention. It will be understood by those skilled in the art, however, that the present invention may be practiced without these specific details. In other instances, well-known methods, procedures, and components have not been described in detail so as not to obscure the present invention.
Among those benefits and improvements that have been disclosed, other objects and advantages of this invention will become apparent from the following description taken in conjunction with the accompanying figures. Detailed embodiments of the present invention are disclosed herein; however, it is to be understood that the disclosed embodiments are merely illustrative of the invention that may be embodied in various forms. In addition, each of the examples given in connection with the various embodiments of the invention which are intended to be illustrative, and not restrictive.
The subject matter regarded as the invention is particularly pointed out and distinctly claimed in the concluding portion of the specification. The invention, however, both as to organization and method of operation, together with objects, features, and advantages thereof, may best be understood by reference to the following detailed description when read with the accompanying drawings.
The figures constitute a part of this specification and include illustrative embodiments of the present invention and illustrate various objects and features thereof. Further, the figures are not necessarily to scale, some features may be exaggerated to show details of particular components. In addition, any measurements, specifications and the like shown in the figures are intended to be illustrative, and not restrictive. Therefore, specific structural and functional details disclosed herein are not to be interpreted as limiting, but merely as a representative basis for teaching one skilled in the art to variously employ the present invention. Further, where considered appropriate, reference numerals may be repeated among the figures to indicate corresponding or analogous elements.
Because the illustrated embodiments of the present invention may for the most part, be implemented using electronic components and circuits known to those skilled in the art, details will not be explained in any greater extent than that considered necessary, for the understanding and appreciation of the underlying concepts of the present invention and in order not to obfuscate or distract from the teachings of the present invention.
Any reference in the specification to a method should be applied mutatis mutandis to a system capable of executing the method. Any reference in the specification to a system should be applied mutatis mutandis to a method that may be executed by the system.
Throughout the specification and claims, the following terms take the meanings explicitly associated herein, unless the context clearly dictates otherwise. The phrases “in one embodiment,” “in an example embodiment,” and “in some embodiments” as used herein do not necessarily refer to the same embodiment(s), though it may. Furthermore, the phrases “in another embodiment,” “in an alternative embodiment,” and “in some other embodiments” as used herein do not necessarily refer to a different embodiment, although it may. Thus, as described below, various embodiments of the invention may be readily combined, without departing from the scope or spirit of the invention.
In addition, as used herein, the term “or” is an inclusive “or” operator, and is equivalent to the term “and/or,” unless the context clearly dictates otherwise. The term “based on” is not exclusive and allows for being based on additional factors not described, unless the context clearly dictates otherwise. In addition, throughout the specification, the meaning of “a,” “an,” and “the” include plural references. The meaning of “in” includes “in” and “on.”
A perspective view diagram illustrating a first example cryostat system constructed in accordance with the present invention is shown in
In one embodiment, the cryostat employs a vacuum (or partial vacuum) to remove the gases that would conduct and convect external heat back into the region, polished surfaces, gold plating to minimize heat radiation into the region, certain materials such as stainless steel (a poor heat conductor) to minimize conduction where needed, and copper (an excellent heat conductor) to maximize heat conduction where needed.
In another embodiment, the TV flex circuit is mounted on the top of the vacuum chamber. The top of the chamber is where the cryogenic cooler apparatus passes through a hole in the vacuum chamber as well as a corresponding hole in the TV flex circuit. Vacuum sealing utilizes O-rings to seal against the annular sealing region portion of the flex circuit. A spiral tab extending into the vacuum chamber is adapted to have a path around the cryogenic cooler head assembly.
A trans-vacuum (TV) flexible circuit or wiring apparatus 66 functions to provide electrical connections between outside the vacuum chamber via connector 68 and the sample board via PCB assembly 92. The TV flex circuit has an annular ring portion 70 that forms part of the vacuum seal. Electrical connections cross the annular ring and form a spiral path 72 around the cooling shaft 80 to a PCB assembly 76. A plurality of holes 74 allow for fasteners to secure a cover plate. A second flexible circuit cable 86 (also referred to as a cryo-flex cable) is coupled to the TV flex cable via PCB assembly 84 and connector 82. In one embodiment, the PCB assembly 76 is mounted to the first stage cold plate 78 which is held at approximately degrees K. To address convention and radiative heat loss, the first and second stage cold plates 78, 90 are solid copper and plated with gold to make them very reflective.
The cryo-flex cable passes through a thermal anchor 88 that clamps the temperature at that point in the cable to the first stage temperature of approximately 30 degrees K. The cryo-flex cable forms a loop between the thermal anchor 88 and the connector 82. The connector is adapted to provide good electrical conductivity but poor thermal conductivity to provide a degree of thermal isolation between the two flex cables. The cryo-flex cable 86 continues downward along the cooling shaft 96 to the cold mounting/fastening plate 94 and second stage which is maintained at 3K. In addition, since the PCB assembly 76 is clamped to the first cooling stage which has far more cooling capacity (e.g., 50 W) than the second cooling stage (e.g., 200 mW), it is preferable to place at the first stage location any power hungry circuitry such as RF attenuators, amplifiers, and/or power supply regulators which are used to reduce noise in the RF signals. Other circuitry such as transceiver circuits or intermediate amplifier circuits for high speed communication can also be placed at this location.
It is noted that using two flex cables with a thermal break and electrical connection between them (i.e. two stage design of TV-flex and cryo-flex cables) versus using a single cable is far more energy efficient. Use of two cables in going from 300K to 30K and then 30K to 3K lowers the energy loss than use of a single cable with the same temperature span of 300K to 3K. This is because any kind of thermal contact that must be cooled to 3K consumes much more energy compared with being cooled first to 30K and then to 3K. Note that the thermal conductivity of copper increases as it is cooled and has a peak at approximately 20K. Although copper is a good electrical conductor it is also a good thermal conductor which is not desirable in this case inside the cryostat vacuum chamber. This is because the 3K at the second stage sample board can creep along the copper traces of the printed flexible cable. As each further region of copper is cooled, its thermal conductivity increases and losses would also increase along the path of the cable. Thus, the thermal anchor stops this process from continuing along the cable.
In one embodiment, the flex circuits comprise four layers with the two outer layers functioning as RF shielding. The electromagnetic shielding layers may be solid metal but to improve flexibility at low temperatures they preferably have a non-solid pattern. For example a honeycomb, diamond, octagonal, hexagonal, or other polygon shaped pattern of relatively thin traces can be used, which yield a minimum amount of metal (e.g., copper) to provide RF shieling while retaining flexibility at low temperatures and also minimizing thermal conductivity along the cable. The multiple layers of the cable provide electrical isolation between the individual signal traces whether single ended or balanced, differential, as well as isolation from external electromagnetic fields. Further, the RF and microwave lines of the flex cables can be impedance controlled and well isolated from each other in left, right, up, and down directions in relation to their position in the cable, which improves performance. Thus, the cable can enable effective shielding by optimizing the scale and size of the mesh, while minimizing the total cross sectional area of copper running up and down the flex cables, and therefore its thermal conductivity.
Note that the shielding is solid and planar and not a mesh in the outer two layers of the cable in the region of the annular vacuum seal of the TV flex circuit. This is because the O-rings that provide the sealing prefer to seal against a solid planar surface and not the thin mesh pattern of the shield.
Note further that the width and thickness of the copper traces used in the flex cables may be fabricated having any desired size in order to manage their electrical and thermal conductivity in accordance with the particular implementation of the invention.
A perspective view diagram illustrating a second example cryostat system constructed in accordance with the present invention is shown in
A diagram illustrating a top (and bottom) layer of a first example trans-vacuum flexible printed circuit having rigid printed circuit board tabs is shown in
The trans-vacuum (TV) flexible circuit or wiring apparatus, generally referenced 10, comprises an annular sealing region 12 adapted to receive one or more O-rings to create a vacuum seal around the perimeter of an opening in a vacuum chamber. The TV flex circuit also comprises a plurality of electrical traces 15 that run between two rigid printed circuit board (PCB) edge connectors 18, 20. The electrical traces 15 extend through a flex tab 16, cross the annular sealing region 12 through a gap 13 in the RF shielding mesh 17 and continue through tab 14 to rigid PCB connector 20.
The TV flex circuit uses well-known printed circuit board flex circuit technology to integrate a vacuum seal with the electrical conductors that need to pass through from the air side to the vacuum side of a cryostat. In one embodiment, the TV flex circuit enables the feedthrough of up to 84 separate signals with less than 50 mW thermal power penalty.
Note that in this example embodiment, the electrical traces cross axially or perpendicular to the annular sealing region. In alternative embodiments, the electrical traces cross tangentially at any desired angle depending on the particular application. In addition, flex tab 14 is shown having a shape of a spiral in order to maximize the length of the flex tab during manufacture. Alternatively, the flex tab 14 can have any desired shape and is not limited to a spiral shape.
As described supra, the TV flex cable comprises an RF shield mesh 17 on its two outer layers. In the area of the annular sealing region delineated by the dashed concentric circles 11 and extending to the edges of the flex circuit, however, a solid or semi-solid pattern 19 replaces the mesh 17 in order to enable better vacuum sealing against the O-rings. On the signal layers, a gap 13 in the solid or semi-solid pattern 19 is placed on either side of the signal traces 15.
A diagram illustrating a top view of a second example trans-vacuum flexible printed circuit having rigid printed circuit board tabs is shown in
A diagram illustrating a cross sectional view of a first example trans-vacuum flexible printed circuit is shown in
A diagram illustrating a cross sectional top view of a first example trans-vacuum (TV) flexible printed circuit rigid printed circuit board tabs is shown in
A diagram illustrating a top view of a cryostat flexible printed circuit having rigid printed circuit board tabs is shown in
Similar to the TV flex printed cable described supra, several PCB layers surround the ends of the cryostat flexible printed cable to form the rigid PCB assemblies 84, 92. Electrical connections between the signal traces in the cryostat flexible cable and the copper conductor PCB layers are made using a plurality of vias. This typically requires accurate alignment of the flex circuit and PCB layers during manufacturing.
A diagram illustrating a side view of the example cryostat system that uses two printed flexible circuits is shown in
This figure highlights the spiral path 72 of the TV-flex cable 66 around the first stage cooling shaft 80. The annular sealing region is clamped between the vacuum cover and the housing. Also highlighted is the thermal anchor consisting of matched thermally conductive components 88, 89 that clamp the cryo-flex cable 86 to the first stage temperature of 30K. For example, the matched thermally conductive components may comprise matched concave and convex components such as a saddle and matching complimentary anvil. Electrical connector 82 also provides thermal isolation or discontinuity between the two flex cables.
A diagram illustrating a side view of the example cryostat system using a single printed flexible cable is shown in
A diagram illustrating a cross sectional view of the example cryostat system including heat shield and cooling tower is shown in
It is noted that both the PCB assembly 92 at the end of the cryo-flex cable 86 and the sample board 106 are suspended to allow for differential thermal expansion and contraction between temperature changes from low working temperatures (i.e. 3K) to room temperature (i.e. 300K).
A diagram illustrating a side view of the example cryostat system showing the cryostat cable in more detail is shown in
A diagram illustrating the connector interface between the two flex cables in more detail is shown in
A diagram illustrating the suspended sample board mechanism in more detail is shown in
The magnet assembly 100 is adapted to be adjustably positioned above and below the quantum integrated circuit (IC) and functions to apply a magnetic field to control the spin of one or more quantum particles in the quantum IC.
Alternatively, the magnets may be omitted and the pillar spacers in this case would not be needed and the contact plate would be fastened directly to the cold plate 90. In another embodiment, the magnets are mounted so as not to apply a vertical magnetic field as shown in
Wheel assembly 128 enables adjustment of the height of the magnet assembly 100 above and below the integrated circuit. Plate 130 and pillars 132 provide mechanical support for the magnet assembly. In addition, RF connectors 120 receive RF signal inputs to the integrated circuit on the sample board.
In an alternative embodiment, the TV flex circuit is mounted on the side of the vacuum chamber rather than the top. The TV flex circuit uses the same vacuum sealing utilizing 0-rings to seal against the annular sealing region portion of the flex circuit. A spiral tab extends into the vacuum chamber and is terminated in a thermally isolating electrical connector.
A diagram illustrating an outside view of an example trans-vacuum flexible printed circuit installed in a vacuum chamber with a rigid printed circuit board tab extending outward is shown in
In the configuration shown, the annular sealing region 12 (
A diagram illustrating a forward cutaway view of an example trans-vacuum flexible printed circuit installed in a vacuum chamber with an O-ring seated against an annular sealing region is shown in
A diagram illustrating a rear cutaway view of an example trans-vacuum flexible printed circuit installed in a vacuum chamber with an O-ring seated against an annular sealing region is shown in
A diagram illustrating a side sectional view of a first example trans-vacuum flexible printed circuit installed in a vacuum chamber with an annular sealing region sandwiched between two O-rings is shown in
Since the cover plate 30 is exposed to air it typically sits at room temperature 300K. This is the temperature that the TV flex cable gets anchored. The temperature inside the vacuum chamber is maintained at 30K. Thus, there is a gradient along the TV-flex cable tab to the first stage rigid PCB connector. Note that heat convection is minimal because of the vacuum maintained inside the chamber. Radiated heat is handled by the first stage cooler which in one embodiment is rated at 50 W. Radiated heat is received and reflected via the heat shield made of gold plated copper.
The flexible printed circuits of the present invention are typically constructed from well-known materials used such as Kapton, polyimide, etc. Any material used should preferably have low outgassing, be suitable for use in a vacuum and at low temperatures, have good electrical performance, exhibit low insertion loss and good isolation.
In one embodiment, the annular flex material sealing region is sufficiently wide for annular vacuum seals (e.g., elastomeric O-rings 36, 40, etc.) to seal off on both its top side and bottom side, creating vacuum seals between the outer sealing surface of the hole into the vacuum chamber and the underside of the flex material sealing region 12, and the top side of the flex material sealing region and the underside sealing surface of the vacuum cover plate 30.
Note that in one embodiment, the annular vacuum seals can be concentric, and they can be the same size so they compress the TV flex material sealing region directly between them. Alternatively, the centers of the annular vacuum seals can be offset and/or their diameters can be different to each other, so that they compress the flex material sealing region between themselves and a rigid component surface opposite them, i.e. (1) the outer sealing surface of the hole into the vacuum chamber, (2) the underside sealing surface of the vacuum cover plate, or (3) other intermediate sealing components or features. In addition, the two O-ring seals do not necessarily have the same diameter as one may have a larger diameter than the other to improve sealing. This alternative embodiment is shown in
Moreover, the annular vacuum seals (e.g., O-rings) can employ different shaped cross-sections, such as round, oval, square, rectangular, X-shaped or any combination of these cross-section shapes. Further, the annular vacuum seals are not limited to elastomeric seals and may comprise non-elastomeric seals such as crush seals. In addition, the TV flex circuit and/or the annular vacuum seals can be non-circular in plan view.
The flexible tabs into and out of the TV flex circuit annular sealing region can be otherwise advantageously shaped. It can be shaped as a spiral on the inside, for example, to extend the service length of the inner flex tab or otherwise control its path into the vacuum chamber. Similarly for the outward pointing tab, but with greater design freedom because of the unlimited space around the outside of the annular vacuum seal.
Note that the flexible tabs into and out of the trans-vacuum sealing region need not traverse the vacuum seal shape axially, but can advantageously traverse the seal at other angles from axial to tangential, and/or along indirect paths around the annular vacuum sealing region.
Note also that the electrical traces that traverse the trans-vacuum sealing region can be split to form multiple connectors and connector types into and out of the vacuum chamber. Thus, any number of connectors may extend out of the annular sealing region into the air side as well as extend out of the annular sealing region into the vacuum chamber side.
Note that in one embodiment, the connector connecting the TV-flex and cryo-flex cables are not fabricated from copper but rather from copper beryllium or copper phosphor bronze. Both of these metals are poor electrical conductors at 30K thus the connector contacts are gold plated. Preferably, the connector is also a good thermal isolator making a high thermal ‘impedance’ connection to prevent any heat present on the flex cable from traveling toward the sample board. Typically, there is a thermal gradient along the TV-flex cable. Thus, a thermal break point is placed along the path of the TX-flex cable, cryo-flex cable, or both cables. It is noted that the copper that is used for the traces of the cables gets more conductive as it gets colder. Therefore, the largest gradient occurs near the 300K side (i.e. the air side) of the cable. Both the connector and the thermal anchor provide a needed thermal break, hence the use of two cables rather than one where the thermal isolation helps to keep the heat away from the sample board.
In one embodiment, one or more RF signals pass from outside the vacuum chamber, through the wall of the chamber via connectors mounted in holes to the one or more RF connectors 120 (
In an alternative embodiment, the RF signals are generated within the vacuum chamber via circuitry on the rigid PCB terminal end of the TV flex cable. A diagram illustrating example RF signal cables extending from the trans-vacuum flexible printed circuit to the suspended sample board is shown in
Any arrangement of components to achieve the same functionality is effectively “associated” such that the desired functionality is achieved. Hence, any two components herein combined to achieve a particular functionality may be seen as “associated with” each other such that the desired functionality is achieved, irrespective of architectures or intermediary components. Likewise, any two components so associated can also be viewed as being “operably connected,” or “operably coupled,” to each other to achieve the desired functionality.
Furthermore, those skilled in the art will recognize that boundaries between the above described operations merely illustrative. The multiple operations may be combined into a single operation, a single operation may be distributed in additional operations and operations may be executed at least partially overlapping in time. Moreover, alternative embodiments may include multiple instances of a particular operation, and the order of operations may be altered in various other embodiments.
The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. 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 will be further understood that the terms “comprises” and/or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.
In the claims, any reference signs placed between parentheses shall not be construed as limiting the claim. The use of introductory phrases such as “at least one” and “one or more” in the claims should not be construed to imply that the introduction of another claim element by the indefinite articles “a” or “an” limits any particular claim containing such introduced claim element to inventions containing only one such element, even when the same claim includes the introductory phrases “one or more” or “at least one” and indefinite articles such as “a” or “an.” The same holds true for the use of definite articles. Unless stated otherwise, terms such as “first,” “second,” etc. are used to arbitrarily distinguish between the elements such terms describe. Thus, these terms are not necessarily intended to indicate temporal or other prioritization of such elements. The mere fact that certain measures are recited in mutually different claims does not indicate that a combination of these measures cannot be used to advantage.
The corresponding structures, materials, acts, and equivalents of all means or step plus function elements in the claims below are intended to include any structure, material, or act for performing the function in combination with other claimed elements as specifically claimed. The description of the present invention has been presented for purposes of illustration and description, but is not intended to be exhaustive or limited to the invention in the form disclosed. As numerous modifications and changes will readily occur to those skilled in the art, it is intended that the invention not be limited to the limited number of embodiments described herein. Accordingly, it will be appreciated that all suitable variations, modifications and equivalents may be resorted to, falling within the spirit and scope of the present invention. The embodiments were chosen and described in order to best explain the principles of the invention and the practical application, and to enable others of ordinary skill in the art to understand the invention for various embodiments with various modifications as are suited to the particular use contemplated.
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