US3530486A - Offset-wound spiral antenna - Google Patents
Offset-wound spiral antenna Download PDFInfo
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- US3530486A US3530486A US778116A US3530486DA US3530486A US 3530486 A US3530486 A US 3530486A US 778116 A US778116 A US 778116A US 3530486D A US3530486D A US 3530486DA US 3530486 A US3530486 A US 3530486A
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- 230000005855 radiation Effects 0.000 description 20
- 230000007423 decrease Effects 0.000 description 4
- 238000003491 array Methods 0.000 description 3
- 238000002955 isolation Methods 0.000 description 3
- 238000000926 separation method Methods 0.000 description 3
- 229910052729 chemical element Inorganic materials 0.000 description 1
- 239000004020 conductor Substances 0.000 description 1
- 230000006866 deterioration Effects 0.000 description 1
- 230000010287 polarization Effects 0.000 description 1
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Classifications
-
- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01Q—ANTENNAS, i.e. RADIO AERIALS
- H01Q9/00—Electrically-short antennas having dimensions not more than twice the operating wavelength and consisting of conductive active radiating elements
- H01Q9/04—Resonant antennas
- H01Q9/16—Resonant antennas with feed intermediate between the extremities of the antenna, e.g. centre-fed dipole
- H01Q9/26—Resonant antennas with feed intermediate between the extremities of the antenna, e.g. centre-fed dipole with folded element or elements, the folded parts being spaced apart a small fraction of operating wavelength
- H01Q9/27—Spiral antennas
-
- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01Q—ANTENNAS, i.e. RADIO AERIALS
- H01Q25/00—Antennas or antenna systems providing at least two radiating patterns
- H01Q25/02—Antennas or antenna systems providing at least two radiating patterns providing sum and difference patterns
Definitions
- antenna elements are provided by offset-wound square or round Archimedean spirals or equiangular spirals, thereby to achieve a shift in the radiation center with frequency.
- Each pair of elements in an array are disposed with the respective radiation centers thereof for the various frequencies spaced a nominal one-half wavelength apart which requires that the elements be oriented in a manner such that separation between the radiation centers increases for decreases in frequency.
- This nominal separation of one-half Wavelength enables the array to maintain relatively constant patterns and gain over a frequency band that exceeds three octaves.
- Four elements may be arrayed by crossing two linear arrays to provide a system for monopulse tracking.
- FIG. 1 shows a perspective view of a two-element array of offset-wound, square Archimedean spirals
- FIG. 2 shows a plan view of a two-by-two planar array of offset-wound, square Archimedean spirals
- FIG. 3 shows a plan view of a two-element array of offset-wound circular Archimedean spirals
- FIG. 4 shows a plan view of a two-element array of ofiset-wound equiangular spirals.
- FIG. 1 of the drawings there is shown a perspective view of a two-element array of offset-wound square conductive spiral elements 12, 14.
- the offset-wound square spiral elements 12, 14 are disposed on square dielectric sheets 15, 16 respectively, which, in turn, are mounted on square base structures 17, 18 which are rigidly attached along one edge in a manner such that horizontal diagonals of the square diatent electric sheets 15, 16, as viewed in the drawing, form a straight line.
- the offset-square spiral elements 12, 14 each have, for example, eleven turns, the dimensions of which increase in size linearly with the portions of the respective turns nearest each other located side by side with only sufficient spacing consistent with electrical isolation.
- both of the spiral elements 12, 14 in order for both of the spiral elements 12, 14 to receive signals of consistent polarity, both elements, 12, 14 spiral in the same direction. As viewed in the drawing, both spiral elements 12, 14 spiral outwards in a counter-clockwise direction.
- Inputs to the spiral antenna elements 12, 14 are provided by coaxial lines 20, 21 which connect from input coaxial connectors 22, 23, respectively, to the inner extremities of spiral elements 12, 14.
- the outer conductors of coaxial lines 20, 21 may be connected to a ground plane spaced behind antenna elements 12, 14.
- the portion of the spiral elements 12, 14 that radiate is the parts thereof which have a circumference of one wavelengh.
- the center region of a turn of the spiral ele ment 12 or 14 which has a circumference of one wavelength is defined as the radiation center of that element 12 or 14, for that particular frequency.
- radiation centers 25, 26 of elements 12, 14 respectively correspond to the highest frequency of operation and radiation centers 27, 28 thereof corespond to the lowest frequency of operation.
- the offset of the turns of spiral elements 12, 14 causes the radiation centers thereof to shift outwardly from the centers 25, 26 as the frequency decreases.
- the nominal spacing between radiation centers 25 and 26 and radiation centers 27 and 28 and between corresponding radiation centers for intermediate wavelengths is one-half wavelength at the frequency corresponding thereto.
- the center of radiation shifts continuously outwards from the centroid of the element 12 or 14 as the frequency decreases, thereby to maintain the nominal spacing therebetween of onehalf wavelength.
- a four-element array 30 including offset-wound square Archimedean spiral elements 31, 32, 33, 34.
- the spiral elements 31, 32, 33, 34 are offset in a manner such that the respective radiation centers shift diagonally outwards from the center of the array 30 for decreases in frequency.
- the nominal spacing between the respective radiation centers of the spiral elements 31 and 32 and between the respective radiation centers of spiral elements 33 and 34 is designed to be one-half wavelength.
- all of the spiral elements 31, 32, 33, 34 spiral outwards in the same direction, which as viewed in the drawing is clockwise, so as to receive waves of the same polarization.
- the four-element array 30 can be adapted to monopulse tracking through the addition of suitable sum and difference networks.
- the spiral elements 31, 32, 33, 34 are driven by appropriate connections (not shown) to the inner extremities thereof as in the case of the array 10 of FIG. 1.
- a two-element array 40 including offset-wound circular Archimedean spiral elements 42, 44.
- the radius of successive turns increases linearly with the angle of rotation.
- the portions of the turns between the centroids of the spiral elements 42, 44 are closely spaced consistent with electrical isolation whereby the elements 42, 44 are offset wound.
- high frequency radiation centers 45, 46 of elements 42, 44 respectively occur in the center of the turn having the smallest circumference and the low frequency radiation centers 47, 48 occur in the center of the outermost turn.
- a two-element array 50 includes offset-wound equiangular spiral elements 52, 54.
- An equiangular spiral is where the spiral always intersects a radius at equal angles. Portions of the turns of spiral elements 52, 54 between turns having the smallest circumference are closely spaced consistent with electrical isolation. Loci of radiation centers may intersect at an obtuse angle in order to more nearly achieve a nominal spacing of one-half wavelength between radiation centers corresponding to any one frequency. Operation is the same as for the devices in FIGS. 1 and 3.
- An antenna array for operation over a predetermined band of frequencies comprising a first spiral element having a selected number of turns which turns include an inner and an outer turn and rotate outwardly in a predetermined direction with the spacing thereof compressed on one side of said turns the circumference of said inner turn being equal to a wavelength at the high end of said predetermined band of frequencies and the circumference of said outer turn being equal to a wavelength at the low end of said predetermined band of frequencies; a second spiral element having a number of turns equal to said selected number of turns which turns include an inner and an outer turn and rotate outwardly in said predetermined direction with the spacing thereof compressed on the side of said turns of said sec ond spiral nearest said one side of said turns of said first spiral, the circumferences of said inner and outer turns of said second spiral being equal, respectively, to said circumstances of said inner and said outer turns of said first spiral and the center of said inner turn of said second spiral being spaced nominally one-half wavelength at the high end of said predetermined band of frequencies from the center of said inner turn of said first spiral; and
- a four-element planar antenna array having first and second bisecting orthogonal diagonals for operation over a predetermined band of frequencies, said array comprising first, second, third and fourth spiral elements, each having an equal number of turns of square configuration with the bisected halves of said first diagonal constituting diagonals for said first and second spiral elements and the bisected halves of said second diagonal constituting diagonals for said third and fourth spiral elements, said turns of each of said first, second, third and fourth spiral elements including an inner and an outer turn and rotating outwardly in like directions with the spacing thereof compressed on the sides of said turns nearest the point of intersection of said first and second orthogonal diagonals, the circumferences of said inner turns each being equal to a wavelength at the high end of said predetermined band of frequencies and the circumference of said outer turns each being equal to a wavelength at the low end of said predetermined band of frequencies and the centers of said inner turns of said first and third spiral elements being spaced, respectively, nominally one-half wavelength at the high end of said predetermined band of frequencies from the centers of said inner turns of
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Description
Sept. 22, 1970 c. A. STRIDER 3,530,486
\ I OFFSET-WOUND SPIRAL ANTENNA Filed Nov. 22, 1968 v 3 Sheets-Sheet 1 Zwawraz 6442.45: ,4 Sa /05g 4PM W Sept. 22, 1970 c. A. STRIDER 3,530,486
OFFSET-WOUND SPIRAL ANTENNA Filed Nov. 22, 1968 3 Sheets-Sheet 3 Sept. 22, 1970 c. A. STRIDER 3,530,486
OFFSET-WOUND SPIRAL ANTENNA Filed Nov. 22, 1968 3 Sheets-Sheet 5 ww/Aesaaawcy 240/4270 awrz! ZZZ-a4.
States 3,530,486 OFFSET-WOUND SPIRAL ANTENNA Charles A. Strider, Los Angeles, Calif, assignor t Hughes Aircraft Company, Culver City, Calif, a corporation of Delaware Filed Nov. 22, 1968, Ser. No. 778,116 Int. Cl. H011 l/38 U5. Cl. 343-895 6 Claims ABSTRACT OF THE DISCLOSURE BACKGROUND OF THE INVENTION Contemporary systems comprise standard Archimedean or equiangular spiral elements arranged in arrays. Although each such spiral element is individually capable of extremely broadband frequency coverage, arrays of these elements are not. The patterns and gain of such an array change appreciably with variation in frequency of the order of ten percent because of the fixed separation of the radiation centers of the respective elements in the array. Larger changes in frequency may result in a complete deterioration of pattern and gain.
SUMMARY OF THE INVENTION In accordance with the invention, antenna elements are provided by offset-wound square or round Archimedean spirals or equiangular spirals, thereby to achieve a shift in the radiation center with frequency. Each pair of elements in an array are disposed with the respective radiation centers thereof for the various frequencies spaced a nominal one-half wavelength apart which requires that the elements be oriented in a manner such that separation between the radiation centers increases for decreases in frequency. This nominal separation of one-half Wavelength enables the array to maintain relatively constant patterns and gain over a frequency band that exceeds three octaves. Four elements may be arrayed by crossing two linear arrays to provide a system for monopulse tracking.
BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 shows a perspective view of a two-element array of offset-wound, square Archimedean spirals;
FIG. 2 shows a plan view of a two-by-two planar array of offset-wound, square Archimedean spirals;
FIG. 3 shows a plan view of a two-element array of offset-wound circular Archimedean spirals; and
FIG. 4 shows a plan view of a two-element array of ofiset-wound equiangular spirals.
DESCRIPTION Referring now to FIG. 1 of the drawings, there is shown a perspective view of a two-element array of offset-wound square conductive spiral elements 12, 14. The offset-wound square spiral elements 12, 14 are disposed on square dielectric sheets 15, 16 respectively, which, in turn, are mounted on square base structures 17, 18 which are rigidly attached along one edge in a manner such that horizontal diagonals of the square diatent electric sheets 15, 16, as viewed in the drawing, form a straight line. The offset-square spiral elements 12, 14 each have, for example, eleven turns, the dimensions of which increase in size linearly with the portions of the respective turns nearest each other located side by side with only sufficient spacing consistent with electrical isolation.
In designing antennas of this type, the circumference of successive turns corresponds to the wavelengths at which the antenna will radiate. Thus, the wavelength of the band of frequencies through which the antenna 10 is designed to operate will extend from the circumference of the centroid area to the circumference of the outermost turn. Also, in order for both of the spiral elements 12, 14 to receive signals of consistent polarity, both elements, 12, 14 spiral in the same direction. As viewed in the drawing, both spiral elements 12, 14 spiral outwards in a counter-clockwise direction. Inputs to the spiral antenna elements 12, 14 are provided by coaxial lines 20, 21 which connect from input coaxial connectors 22, 23, respectively, to the inner extremities of spiral elements 12, 14. As would be obvious to one of ordinary skill in the art, the outer conductors of coaxial lines 20, 21 may be connected to a ground plane spaced behind antenna elements 12, 14.
In the operation of the two-element array 10 of FIG. 1, the portion of the spiral elements 12, 14 that radiate is the parts thereof which have a circumference of one wavelengh. The center region of a turn of the spiral ele ment 12 or 14 which has a circumference of one wavelength is defined as the radiation center of that element 12 or 14, for that particular frequency. In this respect, radiation centers 25, 26 of elements 12, 14 respectively, correspond to the highest frequency of operation and radiation centers 27, 28 thereof corespond to the lowest frequency of operation. The offset of the turns of spiral elements 12, 14 causes the radiation centers thereof to shift outwardly from the centers 25, 26 as the frequency decreases. In general, the nominal spacing between radiation centers 25 and 26 and radiation centers 27 and 28 and between corresponding radiation centers for intermediate wavelengths is one-half wavelength at the frequency corresponding thereto. Thus, the center of radiation shifts continuously outwards from the centroid of the element 12 or 14 as the frequency decreases, thereby to maintain the nominal spacing therebetween of onehalf wavelength.
Referring now to FIG. 2 of the drawings, there is shown a four-element array 30 including offset-wound square Archimedean spiral elements 31, 32, 33, 34. The spiral elements 31, 32, 33, 34 are offset in a manner such that the respective radiation centers shift diagonally outwards from the center of the array 30 for decreases in frequency. As in the array 10 of FIG. 1, the nominal spacing between the respective radiation centers of the spiral elements 31 and 32 and between the respective radiation centers of spiral elements 33 and 34 is designed to be one-half wavelength. Also, all of the spiral elements 31, 32, 33, 34 spiral outwards in the same direction, which as viewed in the drawing is clockwise, so as to receive waves of the same polarization. The four-element array 30 can be adapted to monopulse tracking through the addition of suitable sum and difference networks. The spiral elements 31, 32, 33, 34 are driven by appropriate connections (not shown) to the inner extremities thereof as in the case of the array 10 of FIG. 1.
Referring to FIG. 3, there is shown a two-element array 40 including offset-wound circular Archimedean spiral elements 42, 44. In an Archimedean spiral, the radius of successive turns increases linearly with the angle of rotation. The portions of the turns between the centroids of the spiral elements 42, 44 are closely spaced consistent with electrical isolation whereby the elements 42, 44 are offset wound. As before, high frequency radiation centers 45, 46 of elements 42, 44 respectively, occur in the center of the turn having the smallest circumference and the low frequency radiation centers 47, 48 occur in the center of the outermost turn. The nominal spacing between radiation centers of the spiral elements 42, 44 corresponding to a specific frequency is one-half wavelength at that frequency. Operation of the array 40 is the same as for the array 10 of FIG. 1 with feeds being connected to the innermost extremities of the spiral elements 42, 44.
Referring to FIG. 4, there is shown an alternate embodiment of the invention wherein a two-element array 50 includes offset-wound equiangular spiral elements 52, 54. An equiangular spiral is where the spiral always intersects a radius at equal angles. Portions of the turns of spiral elements 52, 54 between turns having the smallest circumference are closely spaced consistent with electrical isolation. Loci of radiation centers may intersect at an obtuse angle in order to more nearly achieve a nominal spacing of one-half wavelength between radiation centers corresponding to any one frequency. Operation is the same as for the devices in FIGS. 1 and 3.
What is claimed is:
1. An antenna array for operation over a predetermined band of frequencies, said array comprising a first spiral element having a selected number of turns which turns include an inner and an outer turn and rotate outwardly in a predetermined direction with the spacing thereof compressed on one side of said turns the circumference of said inner turn being equal to a wavelength at the high end of said predetermined band of frequencies and the circumference of said outer turn being equal to a wavelength at the low end of said predetermined band of frequencies; a second spiral element having a number of turns equal to said selected number of turns which turns include an inner and an outer turn and rotate outwardly in said predetermined direction with the spacing thereof compressed on the side of said turns of said sec ond spiral nearest said one side of said turns of said first spiral, the circumferences of said inner and outer turns of said second spiral being equal, respectively, to said circumstances of said inner and said outer turns of said first spiral and the center of said inner turn of said second spiral being spaced nominally one-half wavelength at the high end of said predetermined band of frequencies from the center of said inner turn of said first spiral; and means connected to the inner extremities of said first and second spiral elements for providing terminals for said array.
2. The antenna array for operation over a predetermined band of frequencies as defined in claim 1 where successive turns of said first and second spiral elements have rectangular configurations.
3. The antenna array for operation over a predetermined band of frequencies as defined in claim 1 wherein the radius from center of curvature of successive turns of said first and second spiral elements increases linearly with the angle of rotation.
4. The antenna array for operation over a predetermined mand of frequencies as defined in claim 1 wherein successive turns of said first and second spiral elements intersect respective radiuses thereof from center of curvature at equal angles.
5. The antenna array for operation over a predeter mined band of frequencies as defined in claim 1 wherein successive turns of said first and second spiral elements have square configurations and wherein a diagonal through said first spiral element forms an obtuse angle with a corresponding diagonal through said second spiral element.
6. A four-element planar antenna array having first and second bisecting orthogonal diagonals for operation over a predetermined band of frequencies, said array comprising first, second, third and fourth spiral elements, each having an equal number of turns of square configuration with the bisected halves of said first diagonal constituting diagonals for said first and second spiral elements and the bisected halves of said second diagonal constituting diagonals for said third and fourth spiral elements, said turns of each of said first, second, third and fourth spiral elements including an inner and an outer turn and rotating outwardly in like directions with the spacing thereof compressed on the sides of said turns nearest the point of intersection of said first and second orthogonal diagonals, the circumferences of said inner turns each being equal to a wavelength at the high end of said predetermined band of frequencies and the circumference of said outer turns each being equal to a wavelength at the low end of said predetermined band of frequencies and the centers of said inner turns of said first and third spiral elements being spaced, respectively, nominally one-half wavelength at the high end of said predetermined band of frequencies from the centers of said inner turns of said second and fourth spiral elements; and means connected to the inner extremities of said first, second, third and fourth spiral elements for providing terminals for said array.
References Cited UNITED STATES PATENTS 2,953,781 9/1960 Donnellan et al. 343895 X 3,034,121 5/1962 Riblet 343-895 X 3,152,330 10/1964 Chatelain 343-895 X PAUL L. GENSLER, Primary Examiner US. Cl. X.R. 343-908 *zgz g g UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent No. 3 ,530 ,486 a d September-22 1970 Inventor(s) CHARLES A. STRIDER It is certified that error appears in the above-identified patent and that said Letters Patent are hereby corrected as shown below:
Claim 1, column 3, line 44 change "circumstances to circumferences;
Claim 4, column 4, line 7, change "mand" to band-.
Signed and sealed this 1st day of May 1973.
fattest:
31051 .11 1i. FLEICHER, J3. ROBERT GOTTSCHAIK -lttesring Officer Commissioner of Patents
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| US77811668A | 1968-11-22 | 1968-11-22 |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| US3530486A true US3530486A (en) | 1970-09-22 |
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| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| US778116A Expired - Lifetime US3530486A (en) | 1968-11-22 | 1968-11-22 | Offset-wound spiral antenna |
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| Country | Link |
|---|---|
| US (1) | US3530486A (en) |
Cited By (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| FR2440089A1 (en) * | 1978-10-27 | 1980-05-23 | Dassault Electronique | Double spiral radar antenna - uses wires of varying expansion rates to enable direction finding without reference to wavelength of utilised signal |
| FR2466879A1 (en) * | 1979-10-05 | 1981-04-10 | Thomson Csf | BIFILAR FLAT ANTENNA WITH TRANSVERSAL RADIATION AND ITS APPLICATION TO RADAR AIRS |
| US4559539A (en) * | 1983-07-18 | 1985-12-17 | American Electronic Laboratories, Inc. | Spiral antenna deformed to receive another antenna |
| US4804965A (en) * | 1985-07-09 | 1989-02-14 | Agence Spatiale Europeenne | Flat wide-band antenna |
| US5227807A (en) * | 1989-11-29 | 1993-07-13 | Ael Defense Corp. | Dual polarized ambidextrous multiple deformed aperture spiral antennas |
| US20040113862A1 (en) * | 2002-12-13 | 2004-06-17 | Broadcom Corporation | Eccentric spiral antenna and method for making same |
| US9733353B1 (en) | 2014-01-16 | 2017-08-15 | L-3 Communications Security And Detection Systems, Inc. | Offset feed antennas |
| US10172491B2 (en) | 2004-04-08 | 2019-01-08 | Parallax Group International, Llc | Floor matting |
| US12011910B2 (en) | 2021-09-16 | 2024-06-18 | The Parallax Group International, Llc | Mat and method for manufacturing the same |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US2953781A (en) * | 1959-11-30 | 1960-09-20 | John R Donnellan | Polarization diversity with flat spiral antennas |
| US3034121A (en) * | 1959-12-23 | 1962-05-08 | Henry B Riblet | Broad band spherical antenna |
| US3152330A (en) * | 1961-03-27 | 1964-10-06 | Ryan Aeronautical Co | Multi-spiral satellite antenna |
-
1968
- 1968-11-22 US US778116A patent/US3530486A/en not_active Expired - Lifetime
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US2953781A (en) * | 1959-11-30 | 1960-09-20 | John R Donnellan | Polarization diversity with flat spiral antennas |
| US3034121A (en) * | 1959-12-23 | 1962-05-08 | Henry B Riblet | Broad band spherical antenna |
| US3152330A (en) * | 1961-03-27 | 1964-10-06 | Ryan Aeronautical Co | Multi-spiral satellite antenna |
Cited By (16)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| FR2440089A1 (en) * | 1978-10-27 | 1980-05-23 | Dassault Electronique | Double spiral radar antenna - uses wires of varying expansion rates to enable direction finding without reference to wavelength of utilised signal |
| FR2466879A1 (en) * | 1979-10-05 | 1981-04-10 | Thomson Csf | BIFILAR FLAT ANTENNA WITH TRANSVERSAL RADIATION AND ITS APPLICATION TO RADAR AIRS |
| EP0027067A1 (en) * | 1979-10-05 | 1981-04-15 | Thomson-Csf | Planar bifilar antenna with transversal radiation and its use in radar aerials |
| US4559539A (en) * | 1983-07-18 | 1985-12-17 | American Electronic Laboratories, Inc. | Spiral antenna deformed to receive another antenna |
| US4804965A (en) * | 1985-07-09 | 1989-02-14 | Agence Spatiale Europeenne | Flat wide-band antenna |
| US5227807A (en) * | 1989-11-29 | 1993-07-13 | Ael Defense Corp. | Dual polarized ambidextrous multiple deformed aperture spiral antennas |
| US20050083244A1 (en) * | 2002-12-13 | 2005-04-21 | Broadcom Corporation | Eccentric spiral antenna |
| US6862004B2 (en) * | 2002-12-13 | 2005-03-01 | Broadcom Corporation | Eccentric spiral antenna and method for making same |
| US20040113862A1 (en) * | 2002-12-13 | 2004-06-17 | Broadcom Corporation | Eccentric spiral antenna and method for making same |
| US6947010B2 (en) | 2002-12-13 | 2005-09-20 | Broadcom Corporation | Eccentric spiral antenna |
| US10172491B2 (en) | 2004-04-08 | 2019-01-08 | Parallax Group International, Llc | Floor matting |
| US10258179B2 (en) | 2004-04-08 | 2019-04-16 | Parallax Group International, Llc | Floor matting |
| US10390647B2 (en) | 2004-04-08 | 2019-08-27 | Parallax Group International, Llc | Floor matting |
| US9733353B1 (en) | 2014-01-16 | 2017-08-15 | L-3 Communications Security And Detection Systems, Inc. | Offset feed antennas |
| US12011910B2 (en) | 2021-09-16 | 2024-06-18 | The Parallax Group International, Llc | Mat and method for manufacturing the same |
| US12565034B2 (en) | 2021-09-16 | 2026-03-03 | The Parallax Group International, Llc | Mat and method for manufacturing the same |
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