US6452553B1
Expired / Lapsed
US
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Fractal antennas and fractal resonators
Assignee: Fractal Antenna Systems Inc
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Filing: 1995-08-09
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Granted: 2002-09-17
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Expires: 2015-08-09
Abstract
Abstract An antenna includes at least one element whose physical shape is at least partially defined as a second or higher iteration deterministic fractal. The resultant fractal antenna does not rely upon an opening angle for performance, and may be fabricated as a dipole, a vertical, or a quad, among other configurations. The number of resonant frequencies for the fractal antenna increases with iteration number N and more such frequencies are present than in a prior art Euclidean antenna. Further, the resonant frequencies can include non-harmonically related frequencies. At the high frequencies associated with wireless and cellular telephone communications, a second or third iteration, preferably Minkowski fractal antenna is implemented on a printed circuit board that is small enough to fit within the telephone housing. A fractal antenna according to the present invention is substantially smaller than its Euclidean counterpart, yet exhibits at least similar gain, efficiency, SWR, and provides a 50Ω termination impedance without requiring impedance matching.
Inventors
- 👤 Nathan Cohen
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-11-08 14:22
CPC Classifications
H; H01; H01Q; H01Q21/00; H01Q21/06; H01Q21/20; H01Q21/205; H01Q1/00; H01Q1/12; H01Q1/22; H01Q1/24; H01Q1/241; H01Q1/246; H01Q1/36; H01Q1/38; H01Q21/28
Claims Analysis
Total Claims: 12
Claim 1
Independent Claim
226 words
An antenna including a first element having a portion that includes at least a first motif and a first replication of said first motif and a second replication of said first motif such that a point chosen on a geometric figure represented by said first motif will result in a corresponding point on said first replication and on said second replication of said first motif, wherein there exists at least one non-straight line locus connecting each said point; and wherein a replication of said first motif is a change selected from a group consisting of (a) a rotation and change of scale of said first motif, (b) a linear displacement translation and a change of scale of said first motif, and (c) a rotation and a linear displacement translation and a change of scale of said first motif, wherein said fractal is defined as a superposition over at least N=2 iterations of a fractal generator motif, an iteration being placement of said fractal generator motif upon a base figure through at least one positioning selected from the group consisting of (i) rotation, (ii) stretching, and (iii) translation, and wherein each of said first and second motifs is selected from a family consisting of (i) Koch, (ii) Minkowski, (iii) Cantor, (iv) torn square, (v) Mandelbrot, (vi) Caley tree, (vii) monkey's swing, (viii) Sierpinski gasket, and (ix) Julia.
Claim 2
Dependent Claim
226 words
An antenna including a first element having a portion that includes at least a first motif and a first replication of said first motif and a second replication of said first motif such that a point chosen on a geometric figure represented by said first motif will result in a corresponding point on said first replication and on said second replication of said first motif, wherein there exists at least one non-straight line locus connecting each said point; and wherein a replication of said first motif is a change selected from a group consisting of (a) a rotation and change of scale of said first motif, (b) a linear displacement translation and a change of scale of said first motif, and (c) a rotation and a linear displacement translation and a change of scale of said first motif, wherein said fractal is defined as a superposition over at least N=2 iterations of a fractal generator motif, an iteration being placement of said fractal generator motif upon a base figure through at least one positioning selected from the group consisting of (i) rotation, (ii) stretching, and (iii) translation, and wherein each of said first and second motifs is selected from a family consisting of (i) Koch, (ii) Minkowski, (iii) Cantor, (iv) torn square, (v) Mandelbrot, (vi) Caley tree, (vii) monkey's swing, (viii) Sierpinski gasket, and (ix) Julia.
Claim 3
Dependent Claim
229 words
An antenna including a first element having a portion that includes at least a first motif and a first replication of said first motif and a second replication of said first motif such that a point chosen on a geometric figure represented by said first motif will result in a corresponding point on said first replication and on said second replication of said first motif, wherein there exists at least one non-straight line locus connecting each said point; and wherein a replication of said first motif is a change selected from a group consisting of (a) a rotation and change of scale of said first motif, (b) a linear displacement translation and a change of scale of said first motif, and (c) a rotation and a linear displacement translation and a change of scale of said first motif, and wherein said antenna has a perimeter compression parameter (PC) defined by: PC = full - sized antenna element length Fractal - reduced antenna element length where: PC=A −log {N ( D+C )} in which A and C are constant coefficients for said first motif, N is an iteration number, and D is a fractal dimension given by log(L)/log(r), where L and r are one-dimensional lengths of said first element before and after fractalization, respectively.
Claim 4
Dependent Claim
229 words
An antenna including a first element having a portion that includes at least a first motif and a first replication of said first motif and a second replication of said first motif such that a point chosen on a geometric figure represented by said first motif will result in a corresponding point on said first replication and on said second replication of said first motif, wherein there exists at least one non-straight line locus connecting each said point; and wherein a replication of said first motif is a change selected from a group consisting of (a) a rotation and change of scale of said first motif, (b) a linear displacement translation and a change of scale of said first motif, and (c) a rotation and a linear displacement translation and a change of scale of said first motif, and wherein said antenna has a perimeter compression parameter (PC) defined by: PC = full - sized antenna element length Fractal - reduced antenna element length where: PC=A −log {N ( D+C )} in which A and C are constant coefficients for said first motif, N is an iteration number, and D is a fractal dimension given by log(L)/log(r), where L and r are one-dimensional lengths of said first element before and after fractalization, respectively.
Claim 5
Dependent Claim
170 words
An antenna including a first element having a portion that includes at least a first motif and a first replication of said first motif and a second replication of said first motif such that a point chosen on a geometric figure represented by said first motif will result in a corresponding point on said first replication and on said second replication of said first motif, wherein there exists at least one non-straight line locus connecting each said point; and wherein a replication of said first motif is a change selected from a group consisting of (a) a rotation and change of scale of said first motif, (b) a linear displacement translation and a change of scale of said first motif, and (c) a rotation and a linear displacement translation and a change of scale of said first motif, and wherein said antenna is a Minkowski fractal quad having a lowest resonant frequency ranging from about 850 MHz to 900 MHz, and having a side length KS approximately 1.2″ (3 cm).
Claim 6
Dependent Claim
170 words
An antenna including a first element having a portion that includes at least a first motif and a first replication of said first motif and a second replication of said first motif such that a point chosen on a geometric figure represented by said first motif will result in a corresponding point on said first replication and on said second replication of said first motif, wherein there exists at least one non-straight line locus connecting each said point; and wherein a replication of said first motif is a change selected from a group consisting of (a) a rotation and change of scale of said first motif, (b) a linear displacement translation and a change of scale of said first motif, and (c) a rotation and a linear displacement translation and a change of scale of said first motif, and wherein said antenna is a Minkowski fractal quad having a lowest resonant frequency ranging from about 850 MHz to 900 MHz, and having a side length KS approximately 1.2″ (3 cm).
Claim 7
Dependent Claim
180 words
A fractal antenna coupleable to a transceiver unit, the antenna comprising: a first element having a portion that includes at least a first motif and a first replication of said first motif and a second replication of said first motif such that a point chosen on a geometric figure represented by said first motif will result in a corresponding point on said first replication and on said second replication of said first motif, wherein there exits at least one non-straight line locus connecting each said point; and wherein a replication of said first motif is a change selected from a group consisting of (a) a rotation and change of scale of said first motif, (b) a linear displacement translation and a change of scale of said first motif, and (c) a rotation and a linear displacement translation and a change of scale of said first motif; wherein said first motif is selected from a family consisting of (i) Koch, (ii) Minkowski, (iii) Cantor, (iv) torn square, (v) Mandelbrot, (vi) Caley tree, (vii) monkey's swing, (viii) Sierpinski gasket, and (ix) Julia.
Claim 8
Dependent Claim
180 words
A fractal antenna coupleable to a transceiver unit, the antenna comprising: a first element having a portion that includes at least a first motif and a first replication of said first motif and a second replication of said first motif such that a point chosen on a geometric figure represented by said first motif will result in a corresponding point on said first replication and on said second replication of said first motif, wherein there exits at least one non-straight line locus connecting each said point; and wherein a replication of said first motif is a change selected from a group consisting of (a) a rotation and change of scale of said first motif, (b) a linear displacement translation and a change of scale of said first motif, and (c) a rotation and a linear displacement translation and a change of scale of said first motif; wherein said first motif is selected from a family consisting of (i) Koch, (ii) Minkowski, (iii) Cantor, (iv) torn square, (v) Mandelbrot, (vi) Caley tree, (vii) monkey's swing, (viii) Sierpinski gasket, and (ix) Julia.
Claim 9
Dependent Claim
247 words
A fractal antenna coupleable to a transceiver unit, the antenna comprising: a first element having a portion that includes at least a first motif and a first replication of said first motif and a second replication of said first motif such that a point chosen on a geometric figure represented by said first motif will result in a corresponding point on said first replication and on said second replication of said first motif, wherein there exists at least one non-straight line locus connecting each said point; and wherein a replication of said first motif is a change selected from a group consisting of (a) a rotation and change of scale of said first motif, (b) a linear displacement translation and a change of scale of said first motif, and (c) a rotation and a linear displacement translation and a change of scale of said first motif; and wherein said antenna has a perimeter compression parameter (PC) defined by: where: PC = full - sized antenna element length fractal - reduced antenna element length PC = A · log { N ( D + C ) } in which A and C are constant coefficients for said fractal generator motif, N is an iteration number, and D is a fractal dimension given by log(L)/log(r), where L and r are one-dimensional lengths of said element before and after fractalization, respectively.
Claim 10
Dependent Claim
247 words
A fractal antenna coupleable to a transceiver unit, the antenna comprising: a first element having a portion that includes at least a first motif and a first replication of said first motif and a second replication of said first motif such that a point chosen on a geometric figure represented by said first motif will result in a corresponding point on said first replication and on said second replication of said first motif, wherein there exists at least one non-straight line locus connecting each said point; and wherein a replication of said first motif is a change selected from a group consisting of (a) a rotation and change of scale of said first motif, (b) a linear displacement translation and a change of scale of said first motif, and (c) a rotation and a linear displacement translation and a change of scale of said first motif; and wherein said antenna has a perimeter compression parameter (PC) defined by: where: PC = full - sized antenna element length fractal - reduced antenna element length PC = A · log { N ( D + C ) } in which A and C are constant coefficients for said fractal generator motif, N is an iteration number, and D is a fractal dimension given by log(L)/log(r), where L and r are one-dimensional lengths of said element before and after fractalization, respectively.
Claim 11
Dependent Claim
210 words
A fractal antenna coupleable to a transceiver unit, the antenna comprising: a first element having a portion that includes at least a first motif and a first replication of said first motif and a second replication of said first motif such that a point chosen on a geometric figure represented by said first motif will result in a corresponding point on said first replication and on said second replication of said first motif, wherein there exists at least one non-straight line locus connecting each said point; and wherein a replication of said first motif is a change selected from a group consisting of (a) a rotation and change of scale of said first motif, (b) a linear displacement translation and a change of scale of said first motif and (c) a rotation and a linear displacement translation and a change of scale of said first motif; and wherein said transceiver unit is a self-contained handheld telephone operating in a frequency range of about 850 MHz to 900 MHz, said antenna is a Minkowski fractal quad having a lowest resonant frequency ranging from about 850 MHz to 900 MHz with a side length KS approximately 1.2″ (3 cm), and wherein said antenna is disposed within a housing of said handheld telephone.
Claim 12
Dependent Claim
210 words
A fractal antenna coupleable to a transceiver unit, the antenna comprising: a first element having a portion that includes at least a first motif and a first replication of said first motif and a second replication of said first motif such that a point chosen on a geometric figure represented by said first motif will result in a corresponding point on said first replication and on said second replication of said first motif, wherein there exists at least one non-straight line locus connecting each said point; and wherein a replication of said first motif is a change selected from a group consisting of (a) a rotation and change of scale of said first motif, (b) a linear displacement translation and a change of scale of said first motif and (c) a rotation and a linear displacement translation and a change of scale of said first motif; and wherein said transceiver unit is a self-contained handheld telephone operating in a frequency range of about 850 MHz to 900 MHz, said antenna is a Minkowski fractal quad having a lowest resonant frequency ranging from about 850 MHz to 900 MHz with a side length KS approximately 1.2″ (3 cm), and wherein said antenna is disposed within a housing of said handheld telephone.
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