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US 7,256,751 B2Granted
Fractal antennas and fractal resonators
OwnerNathan Coheninventor
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OwnerNathan Coheninventor
Estimating the term…
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.
An apparatus comprising:
An apparatus comprising:
A fractal resonating system, comprising:
An apparatus comprising:
An apparatus comprising:
Dependencies are inferred from the claim text.
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From the US filing history. Foreign family members aren’t listed.
The units being spaced along or adjacent to a curvilinear path: providing an omnidirectional coverage
Used in mobile communications, e.g. GSM: specially adapted for base stations
Details of, or arrangements associated with, antennas: structural form of radiating elements, e.g. cone, spiral, umbrella; Particular materials…
Structural form of radiating elements, e.g. cone, spiral, umbrella; Particular materials used therewith: formed by a conductive layer on an…
Term ended 5 Sep 2016 (estimated)
The present invention relates to antennas and resonators, and more specifically to the design of non-Euclidian antennas and non-Euclidian resonators.
Antenna are used to radiate and/or receive typically electromagnetic signals, preferably with antenna gain, directivity, and efficiency. Practical antenna design traditionally involves trade-offs between various parameters, including antenna gain, size, efficiency, and bandwidth.
Antenna design has historically been dominated by Euclidean geometry. In such designs, the closed antenna area is directly proportional to the antenna perimeter. For example, if one doubles the length of an Euclidean square (or “quad”) antenna, the enclosed area of the antenna quadruples. Classical antenna design has dealt with planes, circles, triangles, squares, ellipses, rectangles, hemispheres, paraboloids, and the like, (as well as lines). Similarly, resonators, typically capacitors (“C”) coupled in series and/or parallel with inductors (“L”), traditionally are implemented with Euclidian inductors.
FIG. 1A depicts a base element for an antenna or an inductor, according to the prior art;
FIG. 1B depicts a triangular-shaped Koch fractal motif, according to the prior art;
FIG. 1C depicts a second-iteration fractal using the motif of FIG. 1B, according to the prior art;
In overview, the present invention provides an antenna having at least one element whose shape, at least is part, is substantially a fractal of iteration order N>2. The resultant antenna is smaller than its Euclidean counterpart, provides a 50Ω termination impedance, exhibits at least as much gain and more frequencies of resonance than its Euclidean counterpart, including non-harmonically related frequencies of resonance, exhibits a low Q and resultant good bandwidth, acceptable SWR, a radiation impedance that is frequency dependent, and high efficiencies.
In contrast to Euclidean geometric antenna design, fractal antenna elements according to the present invention have a perimeter that is not directly proportional to area. For a given perimeter dimension, the enclosed area of a multi-iteration fractal area will always be at least as small as any Euclidean area.
Using fractal geometry, the antenna element has a self-similar structure resulting from the repetition of a design or motif (or “generator”), which motif is replicated using rotation, translation, and/or scaling (or any combination thereof). The fractal portion of the element has x-axis, y-axis coordinates for a next iteration N+1 defined by xN+1=f(xN, ybN) and yN+1=g(xN, yN), where xN, yN are coordinates of a preceding iteration, and where f(x,y) and g(x,y) are functions defining the fractal motif and behavior.