The concepts and systems described herein relate generally to phased array antennas adapted for volume production at a relatively low cost and more particularly to Active Electronically Steered Arrays (AESAs) including a plurality of sub-array modules where each one of the sub-array modules are interchangeable.
Phased array antennas include a plurality of antenna elements spaced apart from each other by known distances coupled through a plurality of phase shifter circuits to either or both of a transmitter or receiver. There is a desire to lower acquisition and life cycle costs of radio frequency (RF) systems that utilize phased array antennas (or more simply “phased arrays”). One way to reduce costs when fabricating RF systems is to utilize printed wiring boards (PWBs) (also sometimes referred to as printed circuit boards or PCBs), which allow use of more effective manufacturing techniques.
As is known, phased array antenna systems are adapted to produce a beam of radio frequency energy (RE) and direct such beam along a selected direction by controlling the phase (via the phase shifter circuitry) of the RF energy passing between the transmitter or receiver and the array of antenna elements. In an electronically scanned phased array, the phase of the phase shifter circuits (and thus the beam direction) is selected by sending a control signal or word to each of the phase shifter sections. The control word is typically a digital signal representative of a desired phase shift, as well as a desired attenuation level and other control data.
Phased array antennas are often used in both defense and commercial electronic systems. For example, Active Electronically Scanned Arrays (AESAs) are in demand for a wide range of defense and commercial electronic systems such as radar surveillance, terrestrial and satellite communications, mobile telephony, navigation, identification, and electronic counter measures. Such systems are often used in radar for land base, ship and airborne radar systems and satellite communications systems. Thus, the systems are often deployed on a single structure such as a ship, aircraft, missile system, missile platform, satellite, or building where a limited amount of space is available.
AESAs offer numerous performance benefits over passive scanned arrays as well as mechanically steered apertures. However, the costs associated with deploying AESAs can limit their use to specialized military systems. An order of magnitude reduction in array cost could enable widespread AESA insertion into military and commercial systems for radar, communication, and electronic warfare (EW) applications. The performance and reliability benefits of AESA architectures could extend to a variety of platforms, including ships, aircraft, satellites, missiles, and submarines. Reducing fabrication costs and increasing the quantity of components being manufactured can drive down the costs of the components and thus the cost of the AESAs.
With the desire to reduce cost of antennas, and in particular the cost of antennas having relatively large apertures, it has become common to develop the antenna aperture as an array of active aperture sub-arrays. These sub-arrays typically have their own internal RF power dividers, driver amplifiers, time delay units, logic distribution networks, DC power distribution networks, DC/DC converters, and accessible ports for RF, logic, DC power, and thermal management interfaces. It would desirable if each of the sub-arrays could be manufactured the same and be used interchangeably in the fabrication of the complete array. But when the aperture is formed from sub-arrays, it has, heretofore, lacked flexibility because the RF distribution networks required for receive beam formation and exciter output distribution are hardwired into the aperture backplane and position dependent in detail. Thus, typical AESA apertures are not configured such that the sub-arrays are interchangeable.
To further complicate the problem, a tracking radar employing a highly directive antenna pattern (narrow main beam) seeks to keep the antenna electrical boresight aligned with a target of interest. The method typically used to track targets is monopulse beamforming where the angular location of a target is obtained by comparison of signals received simultaneously in two antenna patterns (called the “elevation monopulse pattern” and “azimuth monopulse pattern”).
Presently, there are two basic approaches for AESA monopulse beamforming, analog beamforming, and combined analog-digital beamforming. In analog beamforming, an analog RF feed network combines each AESA Transmit/Receive (T/R) channel into sub-arrays; each sub-array has a unique RF feed network that is designed to couple and weight T/R channel RF receive signals to produce an array-level monopulse pattern in elevation and azimuth angle.
In combined analog-digital beamforming, an analog RF feed network combines each AESA T/R channel into sub-arrays where each unique RF feed network is designed to couple and weight T/R channel RF receive signals. Analog to Digital (A/D) converters at each sub-array produce digital signals that are then combined to form the final array level monopulse pattern in elevation and azimuth angle.
Thus, elevation and azimuth monopulse patterns can be generated with analog beamforming techniques, digital beamforming techniques, or a combination of both analog and digital beamforming.
What is needed is an AESA phased array architecture that enables the use of a beamforming RF feed network that is identical for each sub-array, provides the basic monopulse function, and reduces non-recurring engineering (NRE) cost.
As indicated above, given a change in the active aperture dimension, sub-array dimension, or antenna sidelobe performance of a conventional Active Electronically Steered Array (AESA), it is necessary to completely re-design the feed network. This greatly increases AESA non-recurring engineering (NRE) cost as well as the time it takes to design and manufacture the AESA. In addition, regardless of whether a so-called “brick” or “panel architecture” is employed in the AESA, both the analog and digital beamforming approaches used in a typical AESA suffer from certain drawbacks themselves. For example, in analog beamforming architectures, the conventional approach is to design and fabricate a unique RF feed network for each sub-array. However, as noted above, this feed network must be completely re-designed given a change in the AESA active aperture dimension, sub-array dimension, or sidelobe performance.
Digital beamforming at the Transmit/Receive (T/R) element level generally provides design invariance to a change in AESA active aperture dimension, sub-array dimension, or sidelobe performance. However, digital beamforming at the T/R element level is presently cost prohibitive for any reasonably sized tracking AESA. And the combined analog-digital beamforming approach still suffers from the disadvantage of having to design unique RF feed networks for each sub-array.
In contrast to the above-described conventional approaches, exemplary embodiments of the concepts described herein are directed toward a common RF building block for an AESA array with the following attributes:
An array antenna manufactured in accordance with the concepts described herein is comprised of a plurality of substantially identical monopulse network sub-array building blocks. That is, modular construction is used. Each of the building blocks function independently of their particular location within the array and independently of a particular sidelobe performance. For a given RF band, an AESA aperture can be constructed as an m×n (m, n integers) array of identical RF monopulse network building blocks.
The monopulse network building block described herein is based on a mathematical formulation where the antenna element outputs are combined into a network. In one specific embodiment, each 2n inputs (n an integer) are combined to form three outputs, referred to herein as 2n:3 combining. The array scaling is controlled by the value chosen for n. Furthermore, the network can be optimized (that is, choosing “n”) to meet radar system requirements (e.g., system noise figure, beam pointing accuracy, cost). There is a trade-off between the size of the beamforming network, n, and the RF losses in that beamformer. A larger beamforming network reduces the number of parts and subassemblies in an array—this helps to reduce overall complexity and cost. However, the larger beamforming network has higher RF losses (prior to any second stage amplification) and therefore a higher system noise figure. Thus, the system described herein is a scalable RF design.
The present architecture produces a modular sub-assembly because the monopulse network building blocks are substantially identical. This architecture enables an interchangeable sub-array architecture that is independent of position in the AESA aperture and is independent of AESA receive sum channel sidelobe performance (or, equivalently, aperture illumination distribution). The scalable, analog monopulse network provided in accordance with the concepts described herein may comprise two RF sub-assemblies or modules that form a common building block. In one exemplary embodiment, the two RF sub-assemblies are designated as the Monopulse Beamformer and the Monopulse Processor.
The Monopulse Beamformer provides a passive, analog 2n:3 RF coupling/combining network. The Monopulse Processor may be implemented as an active RF network with three RF inputs and three RF outputs, corresponding to the receive sum signal, receive delta elevation signal and receive delta azimuth signals employed in the well-known monopulse tracking function. It follows the Monopulse Beamformer and performs the appropriate amplitude and phase weighting for each of the three RF inputs from the Monopulse Beamformer.
The present invention thus extends the mathematical beamforming formulation from one-dimension to two-dimensions, as is further discussed below. It also advantageously provides AESA design flexibility to optimize the number of T/R channels combined (the factor “n” in the combiner ration) versus AESA noise figure performance and beam pointing accuracy.
Accordingly, the present invention enables a phased array architecture that employs an identical beamforming RF feed network in each sub-array that provides the necessary monopulse tracking function while reducing NRE cost.
The foregoing and other objects, features and advantages of the invention will be apparent from the following description of particular embodiments of the invention, as illustrated in the accompanying drawings in which like reference characters refer to the same parts throughout the different views. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the invention.
Embodiments of the present system are directed to an apparatus and associated techniques for monopulse beamforming in a modular Active Electronically Steered Array (AESA) element that results in a scalable, reusable sub-array architecture suitable for use over a wide range of phased array applications without costly element- or sub-array-level redesign.
The scalable, analog monopulse network of the present invention is based upon the mathematical formulation given in the commonly-owned and co-pending U.S. patent application Ser. No. 12/757,371 filed on Apr. 9, 2010 and entitled, “An RF Feed Network for Modular Active Aperture Electronically Steered Arrays,” incorporated herein by reference in its entirety, further described hereinbelow.
Referring now to
Beamformer signal ports 120a, 120b (representing the sum and delta monopulse signals) are coupled to monopulse beamformer ports 130a, 130b of active monopulse processor 130 (also sometimes referred to herein as the monopulse board). Monopulse processor 130 is comprised of circulators 140, 142 and power divider circuits 141, 156 configured to combine and condition the signals fed to ports 130a, 130b from beamformer 120 so as to enable conventional tracking and electronic beam steering.
Sub-array module 100, comprising the component assemblies noted above, is also referred to herein as a monolithic assembly because, when arrayed together, a number of these modules 100 may form a complete AESA phased array antenna without re-design or customization of the individual monolithic assemblies.
It should, of course, be appreciated that passive monopulse beamformer 120 may be implemented using a variety of different circuit components and techniques other than as shown in
The passive monopulse beamformer 120 combines the signals from antenna elements 110 (as combined individually conditioned by T/R channel components 112) and forms the necessary monopulse function signals (delta elevation, delta azimuth, and sum) through techniques well-known in the RF arts.
Monopulse processor board 130 may then be used to condition either the delta azimuth or the delta elevation signals in addition to the sum signal; the same processor 130 may be simply duplicated to form both. Here, for clarity, only a single exemplary processor circuit is depicted, with the delta signal output labeled as “Δ” for illustration. The monopulse processor board 130 thus controls the sub-array weighting on the delta azimuth, delta elevation, and sum channels by amplifying and conditioning the monopulse signals from the beamformer and interfaces. Monopulse processor 130 also interfaces with a conventional beam steering computer to enable the full range of phased array functions.
In one exemplary embodiment, the sum signal processing branch of monopulse processor 130 comprises circulator 140, which receives the sum signal from beamformer 120 and provides the signal to a first port 141a of a divider circuit 141. Divider circuit 141 splits the signal evenly between ports 141b, 141c.
The signal propagating through port 141c is coupled to a first port of a circulator 142 and propagates through a second circulator port to a monopulse processor signal port 131a (or a sum (E) port 131a) at which a sum (E) signal is provided.
The delta (Δ) signal processing branch of monopulse processor 130 comprises amplifier 150, a weighting circuit 155 (which provides a weighting function) and a combiner circuit 156. The delta signal path from passive monopulse beamformer 120 is coupled to an input of RF amplifier 150. An output of amplifier 150 is coupled to a first input of combiner 156. A second input of combiner 156 is coupled through weighting circuit 155 to port 141b of divider circuit 141. Weighting circuit 155 selects the weighting level. The weighting levels are based on the physical location of the sub-array module 100 within the overall array aperture according to techniques well-known in the art.
The initial amplification in the delta signal path is initially set by the T/R channel components 112 at the output of the sub-array. RF amplifier 150 may act (in some exemplary embodiments) as a pad or buffer to further condition the signal level received from the output of monopulse beamformer 120.
The outputs of amplifier 150 and weighting circuit 155 are combined in combiner circuit 156 to form a delta (Δ) signal which propagates to a monopulse processor signal port 131b at which a delta signal output is provided. The delta signal processing branch provides delta azimuth signals when connected to the azimuth outputs of beamformer 120; a similar (but independently weighted) circuit, connected to the elevation outputs of beamformer 120 produces the delta elevation signal.
In a transmit mode, a transmit signal T is provided to the second port of the circulator 142 and the signal propagates through a third port of circulator 142 to an input of circulator 140. The transmit signal propagates through circulator 142 to beamformer 120. The transmit signal is coupled from the beamformer input through a series of combiner/divider circuits 122 and through circuits 112 until the transmit signal is emitted through antenna elements 110.
Although a sub-array comprised of a plurality of antenna elements and two assemblies or modules (i.e., the beamformer and the monopulse processor) is described, those skilled in the art will realize that functional and/or mechanical partitions other than that described can be used. Accordingly, the concepts, systems, and techniques described herein are not limited to any particular partition of these functions onto one, two, three or more modules. Likewise, although an amplifier function providing 3 dB of gain is illustrated, more or less gain (or even attenuation), dependant on the actual circuit implementation and system configuration, may be necessary. In general, a low noise amplifier may be used to set the gain level. This may, in some embodiments, be the same LNA as is used in circuit 112. One of ordinary skill in the art will appreciate that this is not a restriction and that one is free to choose a different LNA with different gain and noise figure parameters. In general, using the same LNA in circuit 112 and in monopulse processor 130 simplifies DC power distribution and logic control in the array. Such variations are well within the skill level of an ordinary practitioner and can be readily determined without undue experimentation. Accordingly, the amount of gain provided by amplifier 150 should not be considered as limiting the scope of the present invention.
As noted above, beamformer 120 comprises, in one exemplary embodiment, an RF coupling network that forms the basic delta elevation and delta azimuth RF signals. Signal formation is based on the fundamental (one-dimensional) relationships, shown in Equations (1A), (1B) and (1C) and well-known in the art, between the array illumination function on the receive sum channel, f(x), and the far-field pattern g(y) (i.e., the receive sum pattern) at position y in the far-field. The derivative illumination is obtained from the Fourier transform relations:
Equation (1A) represents the Fourier transform of the function f(x), which is g(y). Equation (1B) is the well known result that the nth derivative of g(y) is the Fourier transform of the original function f(x) multiplied by xn. Equation (1C) is the case for the first derivative of g(y):
Thus, the derivative illumination is given by the anti-symmetric function: x*f(x).
The derivative illumination distribution for the phased array is simply the position of the element within the array aperture, xm,n, multiplied by the sampled receive sum channel distribution illumination, fm,n. For a discrete phased array, the integrals become sums: the sampled, derivative difference distribution at point xm,n, with inter-element spacing dx is given by the general result in Equation (1D):
Upon re-arranging, we arrive at:
The first term is a weighting that depends only on the position of the element n within the sub-array; this term determines the attenuator weighting for the beamformer “coupled” signal. The second term is a weighting that depends only on the position of the sub-array, m, within the array aperture; this term determines the attenuator weighting for the “replica” signal. This is a function of the sub-array's position indices m, n, where:
Thus, for every sub-array, m, Equation (2) defines the theoretical weightings for the coupled and replica signals.
In one exemplary embodiment, the first term within the brackets of Equation (2) may be implemented solely by coupler circuits 124 within the beamformer 120, where the elements are coupled passively, dependant on their respective index (or location) within the array. The second term within the brackets, which controls the weighting of the monopulse signals for the entire sub-array, may be likewise dependant only on the sub-array index. This term may be implemented in the weighting circuit 155 of the monopulse processor 130.
The monopulse beamformer 120 may be a passive, RF coupling network. One of ordinary skill in the art will appreciate that the present formulation may be generalized for any 2n:3 beamforming network. In the mathematical formulation, combining is one dimensional, as a sub-array of T/R channels. In one exemplary embodiment, the monopulse beamformer may be implemented as two-dimensional RF network combining eight rows of 16 T/R channels to form a 128:3 monopulse beamformer network. One of ordinary skill in the art will recognize that combinations of more or fewer elements may also be employed subject only to the 2n:3 limitation herein described. Accordingly, the present invention should be understood as not limited by the exemplary depictions of the number of elements shown and described herein. In general, the present apparatus may combine multiple rows of multiple T/R channels to form a two-dimensional beamformer network of any size.
Exemplar coupled weightings for a representative monopulse beamformer 120 are given by the first bracketed term in Equation (2).
Note that beamformer 120 may also be implemented using eight elevation coupling networks (combining eight T/R Channels) and one azimuth coupling network (combining the 16 columns of elevation coupling networks). Such flexibility in implementation is part and parcel of the present invention.
As described above with respect to
Referring now to
The coupled port weightings of circuit 350 (depicted as coupler circuits 124 within the T/R channel front end,
Note that the coupler value depends only on the element position, n, within the sub-array.
and applied electronically by controllers 440A-440D. Note that the replica attenuation depends only on the sub-array index, m, within the array. Addition of active electronic components 440A and 440B provides design flexibility by allowing a relatively wide range of electronic attenuator weighting as well as electronic insertion phase. Addition of active electronic components 440C and 440D provides another degree of freedom to correct for amplitude differences between the replica and coupled paths due to manufacturing, material and component tolerances in circuits 120 and 130 and electronic insertion phase. Addition of active electronic component 440A is used to drive power amplifier 450A during the transmit pulse; in receive, attenuation may be added to minimize the overall weighting on the T/R channels in sub-array module 100. Controllers 440A-440D thus provide amplitude and phase level adjustment for each signal path in the monopulse processor.
The Receive Sum Channel (RX Σ) signal 401 passes through circulator 410A and is amplified by Low Noise Amplifier (LNA) 420A and split into the Receive Sum signal 404 and Replica Channel signal 405. The Replica Channel signal 405 is again split into the following signals:
The Transmit Channel input 410 proceeds first through controller 440E, power amplifier 450, through isolator 430I and finally through circulator 410A before leaving the module as TX signal Output 411. Controller 440E provides drive power amplification to PA 450 on transmit; on receive, Controller 440E provides phase and attenuation control for the Receive Sum channel output. Controller 440E does not differ from controllers 440A-440D in terms of phase and attenuation control in receive mode; 440A-440D have the capability to also provide drive power amplification in transmit mode, but this function may not be used in some implementations.
Circuit DM1 of
Each output 408, 409, 410 goes to a uniform combiner: one for the Transmit Channel Input/RX Sum Channel Output 410, one for the Receive Delta Elevation Channel Output 409, and one for the Receive Delta Azimuth Channel Output 408.
In some embodiments, the active controller devices 440A-440E may be employed to correct amplitude and phase imbalances in each signal path. This is desirable because, since each monopulse processor combines a number of T/R channels, the amplitude and phase errors have a de-correlation based on the number of sub-arrays.
Manufacturing considerations require that the range of coupler weightings and the range of variable attenuator weightings (Equation (2), first and second term, respectively) are realizable. This is accomplished by moving the reference point (i.e., the “center” of the sub-array) of Equation (2) by adding (refsub−1)/(M*N) to the first term and subtracting (refsub−1)/(M*N) from the second term in Equation (2). The choice of refsub is any real number from n=1 to N. The bracketed term in Equation (3) is the foundation employed in the design for circuits 120 and 130.
Equation (3) provides a trade-off between manufacturable coupler values versus a larger range in variable attenuator weighting. The first term determines the T/R signal weighting in coupler circuits 124; the second term the variable attenuator weighting in weighting circuit 155. Specifically, electronic components 440A through 440E offer a range of electronic attenuation settings and a range of electronic insertion phase shift. For example, in some embodiments, the SiGe Common Leg Circuit can provide attenuation in a range of 0 dB to 31 dB in 1 dB steps and insertion phase shift over a range of 5.625° to 354.375° in 5.625° steps. A large range in electronic attenuation (as determined by the second term in Equation (3)) enables manufacturable coupler values (as determined by the first term in Equation (3)).
In some implementations of the present systems and methods, the insertion phase of the Coupled El path (or Coupled Az path) is electronically adjusted using 440C (440D) to be in phase with the Receive Sum output insertion phase 410. The insertion phase of the El Replica signal 407 (or Az Replica signal 406) is then adjusted by 440B (440A) to be either in phase with the Coupled El path (or Coupled Az path) or 180° out of phase with the Coupled El path (Coupled Az path), depending on the relative sign between the first and second terms.
In one exemplary embodiment, transmit-side controller 440E may be implemented with a SiGe Common Leg Circuit (CLC) in conjunction with a 6-bit phase shifter and a 5-bit attenuator control.
In some embodiments, active controllers 440A-44E may be implemented in one or more Silicon-Germanium (SiGe) monolithic microwave integrated circuits (MMICs) devices, utilizing methods well-known to those of skill in the arts. Likewise, other implementations are also possible and known to the ordinary practitioner. Accordingly, the present invention is to be understood as not limited by the manner in which the controller function may be implemented and includes all such implementations.
In an alternate embodiment, the SiGe controller MMIC may be replaced by a controller implementing similar functionality in Gallium Arsenide (GaAs). In one exemplary embodiment, controllers 440A-440E may be implemented using Raytheon Company part number SSM1886 for all or some of controllers 440A-440E. In an alternate embodiments, a similar controller implemented in GaAs may also be used for controllers 440A-44E. Likewise, the PA and LNA functions of T/R channel components 112 and/or monopulse processor 130 may be implemented in GaAs using Raytheon part numbers PA-0608 and LN-0211, respectively. Drain modulator DM1 may be implemented using Raytheon Company part number SSM1860.
One of ordinary skill in the art will readily appreciate that the components and functions of the present system may also be implemented using COTS parts for one or more of the controllers 440A-440E, T/R channel components 112, PAs, LNAs, and/or DM1. Such implementations are well within the skill of an ordinary practitioner in these arts.
Overall AESA noise performance may be improved by the noted use of appropriate LNAs in each of the Receive Sum Channel, Receive Delta Elevation Channel, and Receive Delta Azimuth Channel RF paths. In some embodiments, one or more of low noise amplifiers 420A-420D may be implemented in a Gallium Arsenide (GaAs) MMIC, although alternatives will be readily apparent to those of ordinary skill in the art. Furthermore, these components may be fabricated as part of a MMIC or may be separate components.
Isolation devices (e.g., isolators) are placed at the input and output in each signal path of the monopulse processor, thus greatly improving RF isolation between signal paths and improving the RF match in each signal path. Isolators 430A-430H reduce unwanted coupling as a function of frequency, which may be critical given the higher degree of correlated errors between monopulse processors. In some embodiments, one or more of isolators 430A-430H may be implemented as embedded circulators with a terminated port and may be fabricated as part of a MMIC or may be separate components.
In some embodiments, power amplifier 450 may be implemented in a Gallium Nitride (GaN) MMIC, although alternatives will be readily apparent to those of ordinary skill in the art. Furthermore, these components may be fabricated as part of a MMIC or may be separate components.
The active controllers 440A-44E, low noise amplifiers 420A-420D, and power amplifier 450 in the monopulse processor may be implemented as flip-chip MMICs, according to techniques commonly used in the art. This enables using the same brazement to heat sink the MMICs on the monopulse processor and any associated circuitry. In some embodiments, the T/R channel components may be mounted on a separate printed wiring board or daughter-cards for convenience in handling and test. This may be advantageous for improving gain and phase stability for all MMICs, especially for those used in the monopulse processor.
Overall AESA noise performance may be improved by the noted use of appropriate LNAs in each of the Receive Sum Channel, Receive Delta Elevation Channel, and Receive Delta Azimuth Channel RF paths.
Panel brazement assembly 530 forms the mounting surface for a plurality of monopulse processors 550. Monopulse processor 550 may, in some embodiments, be comprised of: carrier plate 561; thermal “gap-pad” material 564 used to heat sink the MMICs on the monopulse processor 550 to panel brazement assembly 530; RF connection 562 (one of the three RX Channels) to the 128 T/R channel sub-array module 520; monopulse processor circulator/isolator sub-assembly 569; and monopulse processor printed wiring board 567. Note that the monopulse processor comprises two active beamforming networks; each network is shown as reference 130 in
Each 128 T/R channel sub-array module 520 may be mounted to one side of panel brazement (or similar support structure, without limitation) 530 which may be, in some embodiments, a liquid-cooled heat sink. The monopulse beamformer 510 may be a 128:3 printed wiring board network and physically part of the 128 T/R channel sub-array 520. In some embodiments, the monopulse processor(s) 550 may be mounted to the other side of panel brazement 530 (opposite the sub-array modules 520) with the controllers (not shown) attached to the monopulse processor disposed so as to dissipate their waste heat to brazement 530 through conventional means.
Advantageously, both the monopulse beamformer module and the monopulse processors modules can be RF tested prior to assembly.
It should be appreciated that the concepts described herein may be embodied in hardware, software, or any combination thereof, as those terms are currently known in the art. In particular, portions of the present apparatus may be implemented in software, firmware, and/or microcode operating on a computer or computers of any type. Additionally, software embodying the present invention may comprise computer instructions in any form (e.g., source code, object code, and/or interpreted code, etc.) stored in any computer-readable medium and used with the devices disclosed herein. Accordingly, the present invention is not limited to any particular platform, unless specifically stated otherwise in the present disclosure.
While particular embodiments of the present invention have been shown and described, it will be apparent to those skilled in the art that various changes and modifications in form and details may be made therein without departing from the spirit and scope of the invention as defined by the following claims. Accordingly, the appended claims encompass within their scope all such changes and modifications.
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