Fractal and space-filling transmission lines, resonators, filters and passive network elements
First Claim
1. An electromagnetic transmission-line in which at least one of its parts is shaped as a space-filling curve (hereafter SFC), being said SFC defined as a curve composed by at least ten connected straight segments, wherein said segments are smaller than a tenth of the operating free-space wave length and they are spatially arranged over a surface in such a way that none of said adjacent and connected segments form another straight segment, wherein none of said segments intersect to each other except optionally at the tips of the curve, and wherein the corners formed by each pair of said adjacent segments can be optionally rounded or smoothed otherwise.
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Accused Products
Abstract
A high frequency electromagnetic circuit is disclosed as being patterned on a metallic or superconducting film on top of a dielectric in a plurality of configurations. A part of the circuit such as the characteristic strip or slot of the configurations is shaped in a novel space-filling geometry which allows a significant size reduction of a circuital component. Miniature transmission lines, capacitors, inductors, resistors, filters, and oscillators can be manufactured this way.
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Citations
20 Claims
- 1. An electromagnetic transmission-line in which at least one of its parts is shaped as a space-filling curve (hereafter SFC), being said SFC defined as a curve composed by at least ten connected straight segments, wherein said segments are smaller than a tenth of the operating free-space wave length and they are spatially arranged over a surface in such a way that none of said adjacent and connected segments form another straight segment, wherein none of said segments intersect to each other except optionally at the tips of the curve, and wherein the corners formed by each pair of said adjacent segments can be optionally rounded or smoothed otherwise.
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2. An electromagnetic transmission-line in which at least one of its parts is shaped as a fractal curve, being said fractal curve constructed after an Iterated Function System (IFS), a Multi Reduction Copy Machine (MRCM) or a Networked Multi Reduction Copy Machine (NMRCM), wherein said IFS, MRCM and NMRCM algorithms comprise a characteristic set of affine linear transformations, being said transformations selected from the following:
- rotation, translations, scaling, skewing and mirroring, wherein said set of transformations are applied in a first stage to a set of points A0, comprising at least a curve, to obtain a set of points A1;
in a second stage to said resulting set A1 to obtain a set A2, and so on until a set An is obtained after as many stages as required to obtain a fractal curve of a physical length larger than a tenth of the operating wave-length.
- rotation, translations, scaling, skewing and mirroring, wherein said set of transformations are applied in a first stage to a set of points A0, comprising at least a curve, to obtain a set of points A1;
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3. An electromagnetic transmission-line in which at least one of its parts is shaped as a fractal space-filling curve (hereafter FSFC), being said FSFC defined as a curve with a box-counting dimension larger than one, wherein such a box-counting dimension is computed as usual over the FSFC as the slope of the straight portion of a log-log graph, wherein such a straight portion is substantially defined as a straight segment over an octave of scales on the horizontal axes of the log-log graph.
Specification