REFLECTOR ANTENNA WITH MINIMAL FOCAL DISTANCE AND LOW CROSS-POLARIZATION
20210119351 ยท 2021-04-22
Inventors
Cpc classification
H01P1/161
ELECTRICITY
International classification
Abstract
A reflector antenna includes a reflector, a feed, and a beamforming network. The feed is spaced apart at a focal distance from the reflector. The feed includes an array of dual linear polarized elements. The beamforming network is operatively coupled to the feed. The beamforming network is configured to generate a Sigma pattern and a Delta pattern in a plane orthogonal to the reflector plane of symmetry.
Claims
1. A reflector antenna comprising: a reflector having a reflector plane of symmetry; a feed spaced apart at a focal distance from the reflector, the feed comprising an array of dual linear polarized elements; and a beamforming network operatively coupled to the feed and configured to generate a Sigma pattern and a Delta pattern in a plane orthogonal to the reflector plane of symmetry.
2. The reflector antenna of claim 1, wherein the reflector has a diameter and a ratio of the focal distance to the diameter is less than 0.55.
3. The reflector antenna of claim 1, wherein the beamforming network is configured to generate the Sigma pattern and the Delta pattern in orthogonal polarizations.
4. The reflector antenna of claim 1, wherein the Delta pattern is excited by power decoupled from the Sigma pattern.
5. The reflector antenna of claim 1, wherein the Delta pattern is normalized to a cross-polarization of the Sigma pattern.
6. The reflector antenna of claim 5, wherein the Delta pattern is out of phase to the cross-polarization of the Sigma pattern.
7. The reflector antenna of claim 6, wherein the Delta pattern is out of phase to the cross-polarization of the Sigma pattern across at least 50% of a bandwidth of the reflector antenna.
8. The reflector antenna of claim 6, wherein a power decoupling factor is maintained across at least 50% of a bandwidth.
9. The reflector antenna of claim 1, wherein the array of dual linear polarized elements each comprise an orthomode transducer.
10. The reflector antenna of claim 9, wherein the orthomode transducer is asymmetric.
11. The reflector antenna of claim 1, wherein the array of dual linear polarized elements each comprise an open ended waveguide.
12. The reflector antenna of claim 11, wherein the open ended waveguide is tapered.
13. The reflector antenna of claim 11, wherein the open ended waveguide has a square cross-sectional shape.
14. A feed for use with a reflector antenna, the feed comprising: an array of dual linear polarized orthomode transducers, wherein each dual linear polarized orthomode transducer is coupled to an open ended waveguide.
15. The feed of claim 14, wherein the open ended waveguide is tapered.
16. The feed of claim 14, wherein the open ended waveguide has a square cross-sectional shape.
17. A reflector antenna comprising: a reflector; and an array of dual linear polarized orthomode transducers spaced apart from the reflector, wherein each dual linear polarized orthomode transducer is coupled to an open ended waveguide.
18. The reflector antenna of claim 16, wherein the reflector has a diameter, the array of dual linear polarized orthomode transducers is spaced apart a focal distance from the reflector, and a ratio of the focal distance to the diameter is less than 0.55.
19. The reflector antenna of claim 16, wherein the open ended waveguide is tapered.
20. The reflector antenna of claim 16, wherein the open ended waveguide has a square cross-sectional shape.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
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DETAILED DESCRIPTION
[0043] As described herein, reflector antennas can be used to send and receive radio frequency signals. Conventional offset reflector antennas can utilize various approaches to minimize cross-polarization of fields.
[0044] In some applications, certain conventional offset reflector antennas can utilize a feed array with a large number of elements, a shaped reflector designed to cancel cross-polarization, and/or a polarization selective grip disposed between the feed and the reflector. In some applications, a conventional offset reflector antenna can utilize a conjugated feed wherein cross-polarization contributed by the offset geometry in the feed focal plane is similar to a combination of the higher order modes.
[0045] Alternatively, in some applications, certain conventional offset reflector antennas can utilize a long focal distance offset reflector design to reduce cross-polarization (on the order of approximately 30 dB). For example, a Ku-band offset reflector antenna can have a diameter of 100 inches, a focal length of 140 inches, a focal length to diameter ratio of 1.4 and an offset of 20 inches. The feed of the Ku-band offset reflector antenna can be a corrugated horn feed with a feed aperture radius of 3.3 inches. The feed can include four ports that are used, including transmission (horizontal polarization), transmission (vertical polarization), receiving (horizontal polarization), and receiving (vertical polarization). The feed offset angle can be approximately 27 degrees and the reflector illumination cone can be approximately +/19.2 degrees. The waveguide run can be approximately 200-300 inches.
[0046] In another example, a C-band offset reflector antenna can have a diameter of 100 inches, a focal length of 140 inches, a focal length to diameter ratio of 1.4 and an offset of 30 inches. The feed of the C-band offset reflector antenna can be a corrugated horn feed with a feed aperture radius of 7.5 inches and a length of approximately 30 inches. The feed can include four ports that are used, including transmission (horizontal polarization), transmission (vertical polarization), receiving (horizontal polarization), and receiving (vertical polarization). The feed offset angle can be approximately 30 degrees and the reflector illumination cone can be approximately +/19.2 degrees. The waveguide run can be approximately 200-300 inches.
[0047] The approaches described in above offset reflector antennas can be large in size, heavy, expensive, and may not suitable to size and weight sensitive applications, such as space satellite applications.
[0048] Therefore, it is desirable to reduce the size (a focal length to diameter ratio of approximately less than 0.55), weight, and cost of the antenna without degrading the performance of the antenna, for example in cross polarization. Further, in some applications, it is desirable to reduce or eliminate cross-polarization across a wide bandwidth.
[0049] As appreciated by the present disclosure, embodiments of the reflector antenna disclosed herein include features to reduce or eliminate cross-polarization while reducing the size weight and cost of the antenna. Various aspects of the present disclosure provide an antenna with a reduced focal length to diameter ratio compared to conventional offset reflector antennas (a focal length to diameter ratio of approximately less than 0.55). Further, various aspects of the present disclosure provide antenna that allows for a reduction or elimination of cross-polarization across a wide bandwidth (in excess of 50%).
[0050] The present description relates in general reflector antennas, and more particularly to, for example, without limitation, reflector antennas with an array of dual linear polarized elements.
[0051]
[0052] In the depicted example, the reflector antenna 100 includes a feed 110 formed from an array of dual linear polarized elements 112. As illustrated, the dual linear polarized elements 112 can be arranged in a 22 array to form the feed 110. The dual linear polarized elements 112 can include an open-ended waveguide or any other suitable waveguide or other type of antennas.
[0053] Advantageously, as described herein, the feed 110 can be disposed a short focal distance (focal length to diameter ratio less than 0.55) from the reflector 104. As can be appreciated, the feed array aperture of the feed 110 can be 5-6 times smaller than in conventional applications and the length of the array element of the feed 110 could be approximately 8-10 times shorter than in conventional applications. As can be appreciated, conventional applications may utilize a long reflector focal distance and a corrugated horn as a feed.
[0054] In the depicted example, the beamforming network 102, as illustrated in
[0055] In some applications, the decoupling factors are configured such that a far field Delta pattern would be normalized and opposite to the cross-polarization of the Sigma pattern, allowing the cross-polarization to be canceled or at least significantly reduced. As can be appreciated, the decoupling factors can be configured to minimize either the cross-polarization of the Sigma pattern, cross-polarization discrimination, and/or left hand circular polarization/right hand circular polarization squint in circular polarized applications and across a wide frequency band. While delivering these features, the decoupling factors can be configured to be constant across a considered bandwidth.
[0056] As can be appreciated, the portion of power decoupled from the Sigma channel does not reduce the peak gain of the reflector antenna 100. During operation, once the Delta pattern cancels out the cross-polarization in far field, the cross polarization of the Delta pattern is in phase with the Sigma pattern, recovering the decoupled portion of the power back to the pattern peak, across a wide frequency range.
[0057] Advantageously, the configuration of the reflector antenna 100 described herein allows for low cross polarization (greater than 28 dB) in at least 50% of the considered bandwidth with constant decoupling factors.
[0058] For example, a reflector antenna in accordance with embodiment described herein can be a Ku-band (10.7 GHz-14.7 GHz) offset reflector antenna. The example antenna can have a circular dual linear polarized open waveguide radiating element with an aperture diameter of 0.375 inches. The feed can be a 22 array fed by a beamforming network. The reflector can have a diameter of 100 inches, a focal length of 55 inches, a focal length to diameter ratio of 0.55, and an offset of 37.5 inches. The feed offset angle can be approximately 70 degrees. As can be appreciated, the coupling parameters or factors (APHor, AAHor, APver, AAver) can be configured to minimize cross polarization in far field.
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TABLE-US-00001 10.7 GHz to 12.75 GHz Co Pattern Co Pattern Peak Frequency X-pol dB WC X-pol dB WC Peak dBi Peak dBi Difference GHz Polar. Uncompensated Compensated Uncompensated Compensated 10.7 H 17.79 33.87 46.53 46.55 0.02 11.7 H 18.09 37.49 47.16 47.21 0.05 12.75 H 18.45 34.99 47.59 47.67 0.08 10.7 V 17.78 32.36 46.53 46.56 0.03 11.7 V 18.02 36.92 47.16 47.22 0.06 12.75 V 18.33 33.48 47.59 47.68 0.09
TABLE-US-00002 Coupling at 10.7 GHz to 12.75 GHz dB Deg H-pol 12.51 89.9 V-pol 12.85 89.9
TABLE-US-00003 13.5 GHz to 14.7 GHz Co Pattern Co Pattern Peak Frequency X-pol dB WC X-pol dB WC Peak dBi Peak dBi Difference GHz Polar. Uncompensated Compensated Uncompensated Compensated 13.5 H 18.74 32.53 47.78 47.92 0.14 14.2 H 19.02 31.77 47.9 48.05 0.15 14.7 H 19.25 30.9 47.94 48.1 0.16 13.5 V 18.6 32.63 47.79 47.92 0.13 14.2 V 18.85 31.82 47.9 48.05 0.15 14.7 V 19.07 30.9 47.94 48.1 0.16
TABLE-US-00004 Coupling at 13.5 GHz to 14.7 GHz dB Deg H-pol 15.39 89.9 V-pol 15.37 89.9
TABLE-US-00005 10.7 GHz to 14.7 GHz Co Pattern Co Pattern Peak Frequency X-pol dB WC X-pol dB WC Peak dBi Peak dBi Difference GHz Polar. Uncompensated Compensated Uncompensated Compensated 10.7 H 17.79 28.55 46.53 46.58 0.05 11.7 H 18.09 32.31 47.16 47.24 0.08 12.75 H 18.45 34.62 47.59 47.69 0.1 13.5 H 18.75 33.41 47.79 47.91 0.12 14.2 H 19.02 31.88 47.9 48.05 0.15 14.7 H 19.25 30.07 47.94 48.1 0.16 10.7 V 17.78 28.08 46.53 46.58 0.05 11.7 V 18.02 31.61 47.16 47.24 0.08 12.75 V 18.33 34.44 47.59 47.7 0.11 13.5 V 18.6 33.39 47.79 47.92 0.13 14.2 V 18.85 31.36 47.9 48.05 0.15 14.7 V 19.07 29.6 47.94 48.1 0.16
TABLE-US-00006 Coupling at 10.7 GHz to 14.7 GHz dB Deg H-pol 14.02 89.78 V-pol 14.21 89.78
[0061] In summary, for transmission bands only, cross-polarization is improved from 17.8 dB before compensation to up to 32.3 dB after compensation, while peak gain remains generally unchanged through the band or even increased by approximately 0.1 dB at high end of transmitting band. For receiving bands only, cross-polarization is improved from 18.6 dB before compensation to up to 30.9 dB after compensation, while peak gain is increased by more than 0.1 dB at the highest frequencies. For transmission and receiving bands combined, cross-polarization is improved from 17.8 dB before compensation to up to 28.1 dB after compensation, while peak gain is increased by about 0.05 dB at the lower end of the band and up to 0.15 dB at the higher end of the band. Advantageously, embodiments of the reflector antenna described herein do not increase insertion losses compared to conventional antennas. Further, in some applications, embodiments of the reflector antenna with shorter transmission lines (less than 100 inches) may have reduced insertion losses compared to conventional antennas.
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[0063] In some embodiments, the reflector antenna 200 can be configured to be an extended C-band (3.4-3.65 GHz transmission, 6.425-6.675 receiving) offset reflector antenna. The example antenna can have a disc-rod dual linear polarized antenna radiating element with an aperture diameter of 1.12 inches and a height of 4.375 inches. The feed can be a 22 array with an aperture diameter of 2.64 inches. The reflector can have a diameter of 100 inches, a focal length of 70 inches, a focal length to diameter ratio of 0.7, and an offset of 30 inches. The feed offset angle can be approximately 55 degrees. As can be appreciated, the coupling parameters or factors (PHor, AHor, Pver, Aver) of the transmission and receiving bands can be configured to minimize cross polarization discrimination for regular and shaped reflection applications for regional low cross polarization discrimination shaped beams.
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[0065] As illustrated, and shown in the tables below, embodiments of the reflector antenna allow for improved cross polarization discrimination.
TABLE-US-00007 Transmission Performance EOC X-pol Freq MHz Pol Peak W.C EOC Min XPD Before Compensation 3400 h 36.94 18.92 34.52 18.65 3650 h 37.29 19.03 34.59 17.96 3400 v 36.95 19.25 34.47 19.07 3650 v 37.3 19.63 34.54 18.84 After Compensation 3400 h 36.886 26.42 34.36 30.37 3650 h 37.269 26.8 34.45 29.87 3400 v 36.957 26.59 34.45 30.31 3650 v 37.327 26.608 34.48 29.98
TABLE-US-00008 Receiving Performance EOC X-pol Freq MHz Pol Peak W.C EOC Min XPD Before Compensation 6425 h 40.272 23.78 36.31 20.73 6675 h 38.52 22.41 35.32 19.81 6425 v 40.267 23.94 36.37 20.49 6675 v 38.56 22.96 35.21 21.97 After Compensation 6425 h 40.44 26.054 36.44 24.68 6675 h 38.805 24.406 35.48 23.93 6425 v 40.438 27.295 36.37 27.28 6675 v 38.828 25.2052 35.49 26.95
[0066] In summary, the transmission performance after compensation was improved with AHor=14.563 dB (0.15 dB transmission co-polarization loss, PHor=85.399 deg and AVer=13.205 dB (0.21 dB transmission co-polarization loss), PVer=265.935 deg. Similarly receiving performance after compensation was improved with AHor=27.685 dB (0.007 dB in receiving co-polarization loss), PHor=134.306 deg and AVer=26.183 dB (0.01 dB in receiving co-polarization loss), PVer=314.505 deg. Further, for transmission bands, cross polarization discrimination performance was improved from 18.0 dB before compensation to 29.9 dB after compensation, while peak gain remained unchanged across the band. Similarly, for receiving bands, cross polarization discrimination performance was improved from 19.8 dB before compensation to 24.0 dB after compensation, while peak gain increased by more than 0.16 dB across the band after compensation.
[0067] Advantageously, embodiments of the reflector antennas described herein can be used in applications requiring low cross polarization over broad coverage (e.g. C, Ku, Ka band), allowing long focal distance offset reflector antennas to be replaced by shorter focal distance antennas as described herein. Advantageously, the use of the reflector antennas described herein allow for increased flexibility in spacecraft design as the described antennas may occupy a smaller volume, have a smaller mass, and may be placed on a deck without a tall faring. Further, the described antennas can be utilized for a shaped reflector design for a regional low cross polarization discrimination coverage. Additionally, the dual polarizing elements used within the feed may have lower power handling requirements, as power used is distributed among the array of elements.
[0068] As can be appreciated, embodiments of the reflector antenna described herein can utilize a 22 array including square tapered waveguides with orthomode transducers configured to illuminate a short focal distance (e.g. F/D=0.53, =75.5 deg) single offset reflector. Antennas utilize the arrays described herein can produce peak directivity comparable or favorable to long focal distance single offset reflector antennas (e.g. F/D>=1.4, =29.5 deg.) across significant bandwidth (greater than 32%). The antennas described herein can be used with a beamforming network that produces low cross-polarization and/or cross polarization discrimination in far field across a wide frequency band, for example, greater than 32% of bandwidth (e.g. 10.7-14.7 GHz at Ku band).
[0069] For example, a reflector antenna in accordance with embodiments described herein can be a Ku-band (10.7 GHz-14.7 GHz) offset reflector antenna. The reflector can have a diameter of 100 inches, a focal length of 53.5 inches, a focal length to diameter ratio of 0.535, and an offset of 36 inches. The feed of the antenna can include an array of square rectangular waveguides with orthomode transducers (OMT) attached thereto. The feed can be a 22 array fed by a beamforming network. The array element aperture dimensions can be 0.66 inches by 0.66 inches. The array aperture dimensions can be 1.32 inches by 1.32 inches. The array envelope can be 1.32 inches by 2.16 inches by 3.6 inches including the dual linear OMT. The feed can include eight ports, with four ports transmission/receiving (horizontal polarization) and four ports transmission/receiving (vertical polarization). The feed offset angle can be approximately 75.5 degrees. The reflector illumination cone can be approximately +/33.5 degrees.
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[0071] Optionally, the orthomode transducer 320 can be coupled to a waveguide 330. The waveguide 330 can be an open ended waveguide. Further, the cross-sectional profile of the waveguides 330 can be square. In some embodiments, the cross-sectional profile of the waveguides can be tapered. For example, for a Ku-Band application, the orthomode transducer 320 can have an envelope of 0.55 inches wide, 1.0325 inches height, and 1.56 inches length.
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TABLE-US-00009 Freq H_Short V_Short H, V_Long H_diff V_diff dif. w.c. dif_AV 10.7 47.26 47.21 10.95 47.43 47.35 47.64 0.21 0.29 0.29 0.25 11.2 47.6 47.51 47.82 0.22 0.31 0.31 0.265 11.45 47.71 47.67 47.99 0.28 0.32 0.32 0.3 11.7 47.81 47.83 48.16 0.35 0.33 0.35 0.34 12.5 48.3 48.4 48.66 0.36 0.26 0.36 0.31 12.75 48.56 48.61 48.81 0.25 0.2 0.25 0.225 13.5 49.45 49.44 13.75 49.05 49.03 49.32 0.27 0.29 0.27 0.28 14 49.53 49.46 49.44 0.09 0.02 0.09 0.055 14.25 49.89 49.76 49.56 0.33 0.2 0.33 0.265 14.5 49.77 49.85 49.68 0.09 0.17 0.17 0.13 14.7 49.33 48.98
[0076] Advantageously, the embodiments described herein can maximize cross polarization discrimination in far field, as described in the tables below.
TABLE-US-00010 Uncompensated Freq Peak Xpl X-pol GHz Pol dBi dBi W.C. dB 10.7 H 47.26 30.401 16.859 11.2 H 47.6 30.578 17.022 11.7 H 47.81 31.024 16.786 12.75 H 48.56 31.635 16.925 13.5 H 49.45 31.983 17.467 14.25 H 49.89 32.28 17.61 14.7 H 49.33 31.958 17.372 10.7 V 47.21 30.582 16.628 11.2 V 47.51 30.388 17.122 11.7 V 47.83 30.367 17.463 12.75 V 48.61 31.321 17.289 13.5 V 49.44 32.285 17.155 14.25 V 49.76 32.063 17.697 14.7 V 48.98 30.78 18.2
TABLE-US-00011 Compensated Freq Peak Xpl X-pol GHz Pol dBi dBi W.C. dB Diff_Dir 10.7 H 47.289 21.797 25.492 0.0293 11.2 H 47.653 21.009 26.644 0.0534 11.7 H 47.876 21.979 25.897 0.0656 12.75 H 48.642 21.976 26.665 0.0816 13.5 H 49.55 17.253 32.297 0.0998 14.25 H 50.012 16.357 33.655 0.1218 14.7 H 49.477 21.977 27.5 0.1468 10.7 V 47.212 21.262 25.95 0.0018 11.2 V 47.536 18.349 29.187 0.0262 11.7 V 47.869 18.191 29.678 0.0389 12.75 V 48.66 17.665 30.996 0.0504 13.5 V 49.504 17.319 32.185 0.0644 14.25 V 49.867 18.768 31.098 0.1065 14.7 V 49.108 22.684 26.424 0.1281
TABLE-US-00012 Coupling Freq GHz Pol Real Image dB deg 10.7 H 0.1017 0.19 13.33 61.84 11.2 H 0.1017 0.19 13.33 61.84 11.7 H 0.1017 0.19 13.33 61.84 12.75 H 0.1017 0.19 13.33 61.84 13.5 H 0.1017 0.19 13.33 61.84 14.25 H 0.1017 0.19 13.33 61.84 14.7 H 0.1017 0.19 13.33 61.84 10.7 V 0.0845 0.2273 12.31 69.602 11.2 V 0.0845 0.2273 12.31 69.602 11.7 V 0.0845 0.2273 12.31 69.602 12.75 V 0.0845 0.2273 12.31 69.602 13.5 V 0.0845 0.2273 12.31 69.602 14.25 V 0.0845 0.2273 12.31 69.602 14.7 V 0.0845 0.2273 12.31 69.602
[0077] Further, cross polarization discrimination can be maximized in far field within a circle of 0.35 degrees, as shown in the tables below.
TABLE-US-00013 Uncompensated XPD Freq Peak Xpl X-pol @0.35 deg GHz Pol dBi dBi W.C. dB rad, dB 10.7 H 47.26 30.401 16.859 16.1331 11.2 H 47.6 30.578 17.022 15.733 11.7 H 47.81 31.024 16.786 15.122 12.75 H 48.56 31.635 16.925 14.6188 13.5 H 49.45 31.983 17.467 14.7212 14.25 H 49.89 32.28 17.61 14.71 14.7 H 49.33 31.958 17.372 13.8958 10.7 V 47.21 30.582 16.628 16.0561 11.2 V 47.51 30.388 17.122 16.332 11.7 V 47.83 30.367 17.463 16.5123 12.75 V 48.61 31.321 17.289 15.2216 13.5 V 49.44 32.285 17.155 14.375 14.25 V 49.76 32.063 17.697 14.7494 14.7 V 48.98 30.78 18.2 15.7122
TABLE-US-00014 Compensated Freq Peak Xpl X-pol Diff_Dir GHz Pol dBi dBi W.C. dB XPD @0.35 deg rad, dB 10.7 H 47.268 20.141 27.128 26.1105 0.0083 11.2 H 47.636 18.798 28.838 27.7241 0.0356 11.7 H 47.86 20.523 27.337 26.8257 0.0495 12.75 H 48.623 22.603 26.02 26.0708 0.0634 13.5 H 49.536 15.29 34.246 36.2753 0.0863 14.25 H 50.001 15.176 34.825 37.2007 0.1108 14.7 H 49.47 22.208 27.262 2.1492 0.14 10.7 V 47.233 21.503 25.73 25.2327 0.0228 11.2 V 47.551 19.842 27.71 27.7744 0.0412 11.7 V 47.882 19.813 28.069 29.7654 0.0516 12.75 V 48.676 18.875 29.801 28.3998 0.0659 13.5 V 49.518 19.217 30.301 29.0068 0.0783 14.25 V 49.88 16.894 32.986 35.1178 0.1203 14.7 V 49.123 22.771 26.352 25.2298 0.1427
TABLE-US-00015 Coupling Freq GHz Pol Real Image dB deg 10.7 H 0.1244 0.203 12.45 58.55 11.2 H 0.1244 0.203 12.45 58.55 11.7 H 0.1244 0.203 12.45 58.55 12.75 H 0.1244 0.203 12.45 58.55 13.5 H 0.1244 0.203 12.45 58.55 14.25 H 0.1244 0.203 12.45 58.55 14.7 H 0.1244 0.203 12.45 58.55 10.7 V 0.1133 0.1946 12.95 59.791 11.2 V 0.1133 0.1946 12.95 59.791 11.7 V 0.1133 0.1946 12.95 59.791 12.75 V 0.1133 0.1946 12.95 59.791 13.5 V 0.1133 0.1946 12.95 59.791 14.25 V 0.1133 0.1946 12.95 59.791 14.7 V 0.1133 0.1946 12.95 59.791
[0078] As can be appreciated, the antenna illuminated by the arrays described herein can be scaled in dimensions within the same frequency band (maintaining the focal distance ratio or F/D, the feed offset angle and/or offset/diameter). Advantageously, the frequency of the antenna can be scaled or changed without effecting or changing the broadband cross-polarization performance achieved with the power decoupling factor, as presented in the above tables.
[0079] Terms such as top, bottom, front, rear, above, and below and the like as used in this disclosure should be understood as referring to an arbitrary frame of reference, rather than to the ordinary gravitational frame of reference. Thus, a top surface, a bottom surface, a front surface, and a rear surface may extend upwardly, downwardly, diagonally, or horizontally in a gravitational frame of reference.
[0080] A phrase such as an aspect does not imply that such aspect is essential to the subject technology or that such aspect applies to all configurations of the subject technology. A disclosure relating to an aspect may apply to all configurations, or one or more configurations. A phrase such as an aspect may refer to one or more aspects and vice versa. A phrase such as an embodiment does not imply that such embodiment is essential to the subject technology or that such embodiment applies to all configurations of the subject technology. A disclosure relating to an embodiment may apply to all embodiments, or one or more embodiments. A phrase such an embodiment may refer to one or more embodiments and vice versa.
[0081] The word exemplary is used herein to mean serving as an example or illustration. Any aspect or design described herein as exemplary is not necessarily to be construed as preferred or advantageous over other aspects or designs.
[0082] All structural and functional equivalents to the elements of the various aspects described throughout this disclosure that are known or later come to be known to those of ordinary skill in the art are expressly incorporated herein by reference and are intended to be encompassed by the claims. Moreover, nothing disclosed herein is intended to be dedicated to the public regardless of whether such disclosure is explicitly recited in the claims. No claim element is to be construed under the provisions of 35 U.S.C. 112, sixth paragraph, unless the element is expressly recited using the phrase means for or, in the case of a method claim, the element is recited using the phrase step for. Furthermore, to the extent that the term include, have, or the like is used in the description or the claims, such term is intended to be inclusive in a manner similar to the term comprise as comprise is interpreted when employed as a transitional word in a claim.