US3740755A - Microwave antenna with radome - Google Patents

Microwave antenna with radome Download PDF

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Publication number
US3740755A
US3740755A US00217158A US3740755DA US3740755A US 3740755 A US3740755 A US 3740755A US 00217158 A US00217158 A US 00217158A US 3740755D A US3740755D A US 3740755DA US 3740755 A US3740755 A US 3740755A
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Prior art keywords
reflector
radome
antenna according
shroud
parabolic
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Expired - Lifetime
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US00217158A
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R Grenzeback
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SYS RESOURCES CORP
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SYS RESOURCES CORP
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    • HELECTRICITY
    • H01ELECTRIC ELEMENTS
    • H01QANTENNAS, i.e. RADIO AERIALS
    • H01Q1/00Details of, or arrangements associated with, antennas
    • H01Q1/42Housings not intimately mechanically associated with radiating elements, e.g. radome
    • HELECTRICITY
    • H01ELECTRIC ELEMENTS
    • H01QANTENNAS, i.e. RADIO AERIALS
    • H01Q19/00Combinations of primary active antenna elements and units with secondary devices, e.g. with quasi-optical devices, for giving the antenna a desired directional characteristic
    • H01Q19/10Combinations of primary active antenna elements and units with secondary devices, e.g. with quasi-optical devices, for giving the antenna a desired directional characteristic using reflecting surfaces
    • H01Q19/12Combinations of primary active antenna elements and units with secondary devices, e.g. with quasi-optical devices, for giving the antenna a desired directional characteristic using reflecting surfaces wherein the surfaces are concave
    • HELECTRICITY
    • H01ELECTRIC ELEMENTS
    • H01QANTENNAS, i.e. RADIO AERIALS
    • H01Q19/00Combinations of primary active antenna elements and units with secondary devices, e.g. with quasi-optical devices, for giving the antenna a desired directional characteristic
    • H01Q19/10Combinations of primary active antenna elements and units with secondary devices, e.g. with quasi-optical devices, for giving the antenna a desired directional characteristic using reflecting surfaces
    • H01Q19/12Combinations of primary active antenna elements and units with secondary devices, e.g. with quasi-optical devices, for giving the antenna a desired directional characteristic using reflecting surfaces wherein the surfaces are concave
    • H01Q19/13Combinations of primary active antenna elements and units with secondary devices, e.g. with quasi-optical devices, for giving the antenna a desired directional characteristic using reflecting surfaces wherein the surfaces are concave the primary radiating source being a single radiating element, e.g. a dipole, a slot, a waveguide termination

Abstract

A microwave antenna having a parabolic reflector with a confocal parabolic radome. The coincident foci of the reflector and radome cause reflections from the latter to be incident upon the reflector in the same direction as the energy directly incident thereon from the feed. The antenna is integrally formed in nestable segments each comprising portions of the reflector, the radome and any interconnecting shroud.

Description

Baa-e72, SR
United States Patent 1 Grenzeback 1' June 19, 1973 MICROWAVE ANTENNA WITH RADOME Robert J. Grenzeback, c/o Systems Resources Corp., 7 Corporation Way Ext, Medford, Mass. 02155 Filed: Jan. 12, 1972 Appl. No.: 217,158
Inventor:
US. Cl. 343/840, 343/872 Int. Cl. l-l0lq 19/12 Field of Search 343/840, 872, 873,
[56] References Cited UNITED STATES PATENTS 3,430,245 2/1969 Wolcott .5 343/872 Dunlap 343/872 Suliteanu 343/872 Primary ExaminerEli Lieberman Att0mey-Herbert W. Kenway, Melvin R. .lerrey,
' Richard R. Hildreth 57 ABSTRACT 14 Claims, 5 Drawing Figures Pmmwm 3740.755
SHEEI 1 0f 2 FIG. I
1 MICROWAVE ANTENNA WITH RADOME BRIEF SUMMARY OF THE INVENTION This invention relates generally to microwave antennas, and more particularly to antennas having radomes. For protection of the parabolic electrically conductive inner surface of the reflector against damage including icing and other weather effects, it is customary to provide an electrically nonconductive radome of curved shape to form an enclosure with the reflector. Radomes in common use are frequently of conical shape with .rounded noses. Antennas having radomes are constructed with or without shrouds, which are usually of cylindrical shape and having electrically conductive inner surfaces. A shroud is useful to prevent stray reflections and, leakage of energy at the annular rim of the reflector, including diffraction effects and crosstalk between closely adjacent antennas having substantially the same directions of transmission.
Reflector-type antennas in common use frequently have a focal length which is approximately four-tenths of thediameter measured at the annular peripheral rim of the reflector. The aperture size of the antenna, which in the case of a 'paraboloidal reflector corresponds to its diameter, determines the radiating area of the antenna which in turn determines its gain. With large antennas equipped with radomes, difficulties arise from problems of fabrication and shipping because of the large volume of the assembled enclosure and the necessity to provide structural rigidity and integrity both in transit and in use.
Difficulties are also commonly encountered as a result of the fact that the radome is only imperfectly transparent to incident microwave energy, and in practice it may reflect as much as percent of such energy. This results in a reduction in transmission effiindependent device, its combination with the usual radome results in making it more frequency-dependent.
The improved antenna embodying this invention is characterized by a predetermined structural relationship between the inner reflector and radome surfaces. In the preferred embodiment the reflector and radome are both parabolic in shape with coincident foci, the feed being located to radiate energy from the common focal position.
As a means of fixing the reflector and radome surfaces in accurate spacial relationship, these parts preferably comprise .portions of an integrally formed, segmental structure, whereby-the segmental portions are nestable for space conservation in shipping and the antenna is assembled at the site of installation by joining the segments to form a complete enclosure.
An antenna according to this invention may be constructed with or without a shroud, depending upon end use considerations. If a shroud is employed, each integral antenna segment includes a shroud portion interconnecting corresponding reflector and randome portions.
BRIEF DESCRIPTION OF THE DRAWING FIG. 1 is a back elevation of an antenna embodying the invention.
FIG. 2 is a side elevation in section taken on line 22 of FIG. 1.
FIG. 3 is an elevation showing a number of antenna segments nested for storage and shipment.
FIG. 4 is a schematic diagram corresponding to the embodiment of FIGS. 1 and 2, for illustrating the spacial relationship of the several parts.
FIG. 5 is a schematic diagram similar to FIG. 4 and illustrating an alternative embodiment without a shroud.
DETAILED DESCRIPTION Referring to FIGS. 1 and 2, a preferred embodiment of the invention employing a shroud between a dishshaped reflector and randome is shown generally at 12.
The assembly comprises a number. of substantially identical segments 14, 16, 18 and 20, each of which is an integrally formed rigid structure.
According to one form of fabrication each segment is formed by a thermosetting resin saturated fiberglas fabric draped over 'a rigid form and heated to set the resin, thereby forming a rigid structure. The resin may be of the polyester type or the epoxy type, or it may consist of any other material that is substantially transparent to microwave radiation. Alternatively, the structure may be vacuum formed or formed by'other techniques familiar to those in the art.
' Referring to FIG. 2, the detailed structure of the segment 20 is described in furthe detail, the other segments being substantially identical thereto. As shown, the segment 20 is a quarter segment but it will be obvious that the angle which it subtends may be greater or less than The total of all of the angles subtended by the segments equals 360 in the embodiment shown, although it will be evident from this description that the teachings of this invention are fully applicable to antennas utilizing reflectors that are only fragmental or partial paraboloids of revolution.
The segment 20 includes a reflector portion 22, a
shroud portion 24 and a radome portion 26, the portions 22 and 26 having parabolic shaped interior surfaces 28 and 30, respectively. The foci of the surfaces 28 and 30 are coincident at a point P. The shroud portion 24 is preferably of generally cylindrical shape having a diameter equal to or slightly greater than that of the reflector and radome portions at the respective circular lines of intersection therewith. An integral flange 32 extends around the segment along the lines abutting contiguous segments, and holes 34 are formed in the flange for receiving bolts 36 or other equivalent fasteners. Suitable brackets 38 or other hardware for mounting the antenna may be bolted or otherwise secured to the flanges of the segments or to other convenient parts of the assembly.
A microwave antenna feed, designated generally at 40, is mounted in position to direct energy against the parabolic surface 28 of the reflector from the point P. To this end, any known type of feed, microwave emitter or radiator may be employed and positioned so that the apparent point source of radiation is coincident with the point P. In the illustrated embodiment a microwave conductor 42 is led in through a flanged sleeve 44 and terminates in a horn 46. A support 48 is preferably attached to the conductor 42 and secured to a sleeve 50 similar in configuration to the sleeve 44. If desired, other alternative forms of feed may be employed and may be supported at positions other than those defined by the axial sleeves 44 and 50.
The surface 28 of the reflector is made electrically conductive by any one of a number of known techniques such as metallic spraying or securing thereto a screen, metallic foil or sheet metal. Similarly, an interior surface 52 of the shroud portion 24 is made electrically conductive, the conducting surfaces 28 and 52 being electrically continuous and electrically interconnected along the circular line 54 defined by the peripheral rim of the reflector portion 22. The surface 52 is preferably undulating so as to cause diffusion of stray reflections impinging thereon. In the illustrated embodiment the shroud portion 24 is fabricated over a corrugated form, but other alternative types of nobby surfaces may be substituted, if desired. Therefore, as used herein the word undulating" is intended to include any irregular, corrugated, nobby or otherwise shaped or deformed surface having an equivalent property. The corrugated shape has the further advantage of imparting mechanical stiffness to the structure, thereby permitting it to be formed of lighter materials without loss of dimensional integrity. In any case, there is no gap at the peripheral edge of the reflector portion 22 and shroud 24 where energy might leak and cause diffraction or back radiation.
As shown in FIG. 3, the segments l4, l6, l8 and may be conveniently nested, thereby materially reducing the volume of the components for purpose of storage and shipment. It is also apparent that, since the reflector, shroud and radome portions of each segment are formed as parts of an integral structure under factory conditions, it is assured that the foci of the reflector and radome portions are precisely coincident.
The foregoing structural features and advantages readily permit the construction of large antennas having high gain and performance. This can be attributed to the novel segmental construction which affords structural strength, dimensional integrity and precision, and provision for reducing the shipping volume of the antenna.
Further features of the above-described antenna arising from from the confocal geometry may be understood by reference to the schematic diagram of FIG. 4, wherein the parabolic reflector surface 28 is shown as having a focal length f and the parabolic radome surface 30 is shown as having a focal length f The overall diameter has the value D, and the axial length of the shroud surface 52 is L. The point P lies at the intersection of the common axis 58 of the two parabolic surfaces and a common focal plane 60 normal to this axis.
Typically, the value of D is determined preliminarily according to the gain required of the antenna. The value f, is also given and it is usually in the vicinity of four-tenths of the value D, although the invention is in no way limited to this precise relationship. With given values of D and f,, it will be apparent that the depth d of the reflector surface 28 is defined by the: parabolic equation The length L of the shroud may then be determined by the expression L =f H-d and d =f I-l, the following quadratic equation may be derived:
for which the quadratic formula provides the solution 2 was Once the value f is determined the value d is readily found from equation (3).
In some applications a shroud is not required, in which case the structure defined with reference to FIGS. 1 to 3 may be simplified as illustrated in the schematic diagram of FIG. 5. In this figure, since and since equations l and (3) above also hold for this figure, it may be shown that d =f and f d,.
By reason of the foregoing relationships, it will be apparent that any energy from the focus P that is reflected from the parabolic surface 28 will impinge on the surface 30 in a direction parallel to the axis 58 and that any energy reflected from the latter surface will be directed through the focus P, and that this energy will again impinge upon the surface 28 for a second reflection from the latter in the same direction as the first rcflection. In fact, this relationship holds for any number of reflections and for any frequency of transmission.
Further, it may be shown that the total path length from the focus P to the reflector surface 28, thence to the radome surface 30 and back to the point P, is given by the expression and therefore reflection from all portions of the radome surface return to the point P in phase with each other and with the original signal. This results from a fundamental property of a parabola, namely, that the confocal relationships can be realized in alternative practical configurations, for example parabolic cylinradiating from a line or other locus rather than from a point, and the reflector and radome may have parabolic 'cross sections which are uniform along all sections transverse to such radiating line or locus, and FIGS. 4 and 5 are illustrative of such cross sections. For this reason the word parabolic as used herein refers only to a cross sectional configuration of the parts and ders. Thusthe reflector may be illuminated by a feed does not necessarily imply any limitations in the dimension normal to such cross section.
I claim:
1. A microwave antenna having, in combination,
a reflector having a parabolic inner electrically conductivesurface,
a microwave feed in position to radiate energy to and from thefocus of said electrically conductive surface,
and a radome having a parabolicinner electrically nonconductive surface connected with the reflector in a position with its focus coincident with that of said electrically conductive surface.
2. An antenna according to claim 1, in which the reflector and radome are dish shaped and connected by means of their peripheral rims.
3. An antenna according to claim 2, including a 4. An antenna according to claim 2, in which said coincident foci are spaced from the plane defined by the rim of the reflector and on the side of said plane opposite to the reflector.
5. An antenna-according to claim 2, in which said coincident foci are located in the plane defined by the rim of the reflector.
6. An antenna according to claim 3, in which said coincident foci are spaced from the plane defined by the rim of the reflector and on the side or said plane opposite to the reflector.
7. A microwave antenna having, in combination,
a plurality of segments, each segment including a fragmental parabolic reflector portion and a fragmental radomeportion, said portions of each seg ment being integrally formed, said segments having provision for interconnection at their periphery to form an enclosure.
8. An antenna according to claim 7, in which the ra dome portion is of fragmental parabolic shape.
9. An antenna according to claim 8, in which the foci of the reflector and radome portions are coincident.
10. An antenna according to claim 7, in which each segment includes a fragmental shroud portion integrally formed with'and interconnecting the reflector and radome portions. 7
11. An antenna according to claim 10, which is electrically continuous at the line of intersection between the shroud and the parabolic periphery of the reflector portion. 7
12. An antenna according to claim 11, in which the surfaces of the reflector and shroud portions have electrically conducting surfaces. I
13. An antenna according-to claim 10, in which the shroud portion has an undulating surface.
14. An antenna according to claim 9, including a feed supported for radiation reciprocally in relation. to a point located at said coincident foci. :k

Claims (14)

1. A microwave antenna having, in combination, a reflector having a parabolic inner electrically conductive surface, a microwave feed in position to radiate energy to and from the focus of said electrically conductive surface, and a radome having a parabolic inner electrically nonconductive surface connected with the reflector in a position with its focus coincident with that of said electrically conductive surface.
2. An antenna according to claim 1, in which the reflector and radome are dish shaped and connected by means of their peripheral rims.
3. An antenna according to claim 2, including a shroud spacing and interconnecting the reflector and radome at their peripheral rims.
4. An antenna according to claim 2, in which said coincident foci are spaced from the plane defined by the rim of the reflector and on the side of said plane opposite to the reflector.
5. An antenna according to claim 2, in which said coincident foci are located in the plane defined by the rim of the reflector.
6. An antenna according to claim 3, in which said coincident foci are spaced from the plane defined by the rim of the reflector and on the side or said plane opposite to the reflector.
7. A microwave antenna having, in combination, a plurality of segments, each segment including a fragmental parabolic reflector portion and a fragmental radome portion, said portions of each segment being integrally formed, said segments having provision for interconnection at their periPhery to form an enclosure.
8. An antenna according to claim 7, in which the radome portion is of fragmental parabolic shape.
9. An antenna according to claim 8, in which the foci of the reflector and radome portions are coincident.
10. An antenna according to claim 7, in which each segment includes a fragmental shroud portion integrally formed with and interconnecting the reflector and radome portions.
11. An antenna according to claim 10, which is electrically continuous at the line of intersection between the shroud and the parabolic periphery of the reflector portion.
12. An antenna according to claim 11, in which the surfaces of the reflector and shroud portions have electrically conducting surfaces.
13. An antenna according to claim 10, in which the shroud portion has an undulating surface.
14. An antenna according to claim 9, including a feed supported for radiation reciprocally in relation to a point located at said coincident foci.
US00217158A 1972-01-12 1972-01-12 Microwave antenna with radome Expired - Lifetime US3740755A (en)

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US21715872A 1972-01-12 1972-01-12

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JP (1) JPS544587B2 (en)
CA (1) CA963109A (en)
DE (1) DE2262810A1 (en)
FR (1) FR2167958B1 (en)
GB (2) GB1411780A (en)
IT (1) IT974307B (en)

Cited By (20)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4263599A (en) * 1978-05-11 1981-04-21 Cselt-Centro Studi E Laboratori Telecomunicazioni S.P.A. Parabolic reflector antenna for telecommunication system
US4282530A (en) * 1979-12-26 1981-08-04 Bell Telephone Laboratories, Incorporated Cylindrical paraboloid weather cover for a horn reflector antenna with wave absorbing means
US4355316A (en) * 1980-09-22 1982-10-19 Ford Aerospace & Communications Corp. Offset J-hook reflector antenna
US4786915A (en) * 1985-04-26 1988-11-22 British Telecommunications Public Limited Company Attenuation of microwave signals
EP0305518A1 (en) * 1987-02-24 1989-03-08 SCHUDEL, Conrad, R. Monocoque antenna structure
US5451972A (en) * 1994-05-12 1995-09-19 Paul Dean Franklin Satellite antenna dish cover
US5528253A (en) * 1994-05-12 1996-06-18 Paul Dean Franklin Satellite dish utility cover
USD387356S (en) * 1996-09-13 1997-12-09 W. L. Gore & Associates, Inc. Satellite dish cover
US5815125A (en) * 1997-02-05 1998-09-29 W. L. Gore & Associates, Inc. Satellite dish cover
US5963176A (en) * 1997-04-14 1999-10-05 The United States As Represented By The Secretary Of Commerce Antenna system with edge treatment means for diminishing antenna transmitting and receiving diffraction, sidelobes, and clutter
US5999143A (en) * 1994-08-31 1999-12-07 Glynn; James J. Antenna system parabolic reflector, flat plate shroud and radome
US6072440A (en) * 1997-05-02 2000-06-06 Bowman; Francis E. Satellite receiving dish feed horn or LNB cover
US20080150822A1 (en) * 2006-12-26 2008-06-26 Samsung Electronics Co., Ltd Antenna apparatus
CN1979954B (en) * 2005-12-06 2010-09-29 阿尔卡特公司 Radio communication antenna fitted with a radome and method of assembling same
EP2234204A1 (en) * 2007-12-07 2010-09-29 NEC Corporation Parabolic antenna
US20100315307A1 (en) * 2009-06-12 2010-12-16 Andrew Llc Radome and Shroud Enclosure for Reflector Antenna
CN101212079B (en) * 2006-12-26 2013-03-27 三星电子株式会社 Antenna apparatus
US20130088409A1 (en) * 2010-06-15 2013-04-11 Intellian Technologies Inc. Reflector assembly for satellite antenna and manufacturing method thereof
CN107667450A (en) * 2015-05-21 2018-02-06 康普技术有限责任公司 Sectional antenna cover
RU184248U1 (en) * 2018-03-29 2018-10-19 Владимир Евгеньевич Гершензон FULL-ROTARY ANTENNA WITH RADIO-TRANSPARENT CIRCLE

Families Citing this family (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
GB8431800D0 (en) * 1984-12-17 1985-01-30 Shamah Plastics Ltd M Antenna systems
FR2671235B1 (en) * 1990-12-28 1993-08-20 Cgti OFFSET ANTENNA WITH RADOME.
JP6971611B2 (en) 2017-04-06 2021-11-24 キヤノン株式会社 Radiation imaging system, radiography equipment, radiography method, and program

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US2560218A (en) * 1950-04-22 1951-07-10 Rca Corp Submarine antenna structure
US3296685A (en) * 1962-05-31 1967-01-10 Sylvania Electric Prod Method of making dielectric foam antenna
US3430245A (en) * 1965-05-19 1969-02-25 Whittaker Corp Spherical reflector with lens to convert to parabolic surface

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US3056131A (en) * 1956-10-01 1962-09-25 Collins Radio Co Inflatable antenna
FR1289120A (en) * 1961-05-10 1962-03-30 New realization of Hertzian wave reflectors

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Publication number Priority date Publication date Assignee Title
US2560218A (en) * 1950-04-22 1951-07-10 Rca Corp Submarine antenna structure
US3296685A (en) * 1962-05-31 1967-01-10 Sylvania Electric Prod Method of making dielectric foam antenna
US3430245A (en) * 1965-05-19 1969-02-25 Whittaker Corp Spherical reflector with lens to convert to parabolic surface

Cited By (28)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4263599A (en) * 1978-05-11 1981-04-21 Cselt-Centro Studi E Laboratori Telecomunicazioni S.P.A. Parabolic reflector antenna for telecommunication system
US4282530A (en) * 1979-12-26 1981-08-04 Bell Telephone Laboratories, Incorporated Cylindrical paraboloid weather cover for a horn reflector antenna with wave absorbing means
US4355316A (en) * 1980-09-22 1982-10-19 Ford Aerospace & Communications Corp. Offset J-hook reflector antenna
US4786915A (en) * 1985-04-26 1988-11-22 British Telecommunications Public Limited Company Attenuation of microwave signals
EP0305518A1 (en) * 1987-02-24 1989-03-08 SCHUDEL, Conrad, R. Monocoque antenna structure
EP0305518A4 (en) * 1987-02-24 1990-04-10 Conrad R Schudel Monocoque antenna structure.
US5451972A (en) * 1994-05-12 1995-09-19 Paul Dean Franklin Satellite antenna dish cover
US5528253A (en) * 1994-05-12 1996-06-18 Paul Dean Franklin Satellite dish utility cover
US5999143A (en) * 1994-08-31 1999-12-07 Glynn; James J. Antenna system parabolic reflector, flat plate shroud and radome
USD387356S (en) * 1996-09-13 1997-12-09 W. L. Gore & Associates, Inc. Satellite dish cover
US5815125A (en) * 1997-02-05 1998-09-29 W. L. Gore & Associates, Inc. Satellite dish cover
US5963176A (en) * 1997-04-14 1999-10-05 The United States As Represented By The Secretary Of Commerce Antenna system with edge treatment means for diminishing antenna transmitting and receiving diffraction, sidelobes, and clutter
US6072440A (en) * 1997-05-02 2000-06-06 Bowman; Francis E. Satellite receiving dish feed horn or LNB cover
CN1979954B (en) * 2005-12-06 2010-09-29 阿尔卡特公司 Radio communication antenna fitted with a radome and method of assembling same
US7812778B2 (en) * 2006-12-26 2010-10-12 Samsung Electronics Co., Ltd Antenna apparatus
US20080150822A1 (en) * 2006-12-26 2008-06-26 Samsung Electronics Co., Ltd Antenna apparatus
CN101212079B (en) * 2006-12-26 2013-03-27 三星电子株式会社 Antenna apparatus
US8638267B2 (en) * 2007-12-07 2014-01-28 Nec Corporation Parabolic antenna
EP2234204A4 (en) * 2007-12-07 2010-12-22 Nec Corp Parabolic antenna
US20100245187A1 (en) * 2007-12-07 2010-09-30 Norihiko Omuro Parabola antenna
EP2234204A1 (en) * 2007-12-07 2010-09-29 NEC Corporation Parabolic antenna
US20100315307A1 (en) * 2009-06-12 2010-12-16 Andrew Llc Radome and Shroud Enclosure for Reflector Antenna
US8077113B2 (en) * 2009-06-12 2011-12-13 Andrew Llc Radome and shroud enclosure for reflector antenna
US20130088409A1 (en) * 2010-06-15 2013-04-11 Intellian Technologies Inc. Reflector assembly for satellite antenna and manufacturing method thereof
CN107667450A (en) * 2015-05-21 2018-02-06 康普技术有限责任公司 Sectional antenna cover
US20180145403A1 (en) * 2015-05-21 2018-05-24 Commscope Technologies Llc Segmented antenna radome
EP3298655A4 (en) * 2015-05-21 2019-01-16 Commscope Technologies LLC Segmented antenna radome
RU184248U1 (en) * 2018-03-29 2018-10-19 Владимир Евгеньевич Гершензон FULL-ROTARY ANTENNA WITH RADIO-TRANSPARENT CIRCLE

Also Published As

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JPS544587B2 (en) 1979-03-08
FR2167958A1 (en) 1973-08-24
GB1411780A (en) 1975-10-29
IT974307B (en) 1974-06-20
JPS4882750A (en) 1973-11-05
DE2262810A1 (en) 1973-07-19
FR2167958B1 (en) 1976-05-14
GB1411779A (en) 1975-10-29
CA963109A (en) 1975-02-18

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