Fractal and space-filling transmission lines, resonators, filters and passive network elements

• US 20080011509A1
• Filed: 06/22/2007
• Published: 01/17/2008
• Est. Priority Date: 01/19/2000
• Status: Active Grant

• Current Assignee: Callahan Cellular LLC (Intellectual Ventures LLC)
• Original Assignee: Itrolamer Holdings AG LLC (Intellectual Ventures LLC)
• Inventors: Baliarda, Carles, O'Callaghan Castella, Juan, Collado Gomez, Juan, Rozan, Edouard, Duffo Ubeda, Nuria
• Granted Patent: US 7,538,641 B2
• Time in Patent Office: Days
• US Class Current: 174/261
• CPC Class Codes: H01P 1/20381 Special shape resonators
• CPC Class Codes: H01P 1/2039 Galvanic coupling between Input/Output
• CPC Class Codes: H01P 1/227 Strip line attenuators H01P1/23 takes precedence
• CPC Class Codes: H01P 3/003 Coplanar lines
• CPC Class Codes: H01P 3/023 Fin lines; Slot lines
• CPC Class Codes: H01P 3/026 Coplanar striplines [CPS]
• CPC Class Codes: H01P 3/06 Coaxial lines
• CPC Class Codes: H01P 3/081 Microstriplines
• CPC Class Codes: H01P 3/085 Triplate lines
• CPC Class Codes: H01P 3/16 Dielectric waveguides, i.e. without a longitudinal conductor
• CPC Class Codes: H01P 7/082 Microstripline resonators H01P7/088 takes precedence
• CPC Class Codes: H01P 7/084 Triplate line resonators H01P7/088 takes precedence
• CPC Class Codes: H01P 7/086 Coplanar waveguide resonators H01P7/088 takes precedence
• CPC Class Codes: H01Q 9/0407 Substantially flat resonant element parallel to ground plane, e.g. patch antenna dipole H01Q9/285; monopole H01Q9/40
• CPC Class Codes: H05K 1/0237 High frequency adaptations H05K1/0216 takes precedence
• CPC Class Codes: H05K 1/16 incorporating printed electric components, e.g. printed resistor, capacitor, inductor
• CPC Class Codes: H05K 1/162 incorporating printed capacitors
• CPC Class Codes: H05K 1/165 incorporating printed inductors
• CPC Class Codes: H05K 1/167 incorporating printed resistors
• CPC Class Codes: H05K 2201/09263 Meander

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.

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.

4. A slow-wave transmission line or electromagnetic guiding structure in which at least one of its parts is shaped as a SFC, Fractal, FSFC, Hilbert, Peano, SZ, ZZ, Dragon, Koch, HilbertZZ, Minkowski or Sierpinski curve as defined in claim 1.

5. A slow-wave transmission line or electromagnetic guiding structure formed by the periodic repetition of a SFC, Fractal, FSFC, Hilbert, Peano, SZ, ZZ, Dragon, Koch, HilbertZZ, Minkowski or Sierpinski curve as defined in claim 1.

6. A micro-strip transmission line comprising:

(A) a metallic or superconducting ground-plane,

(B) a metallic or superconducting strip parallel to said ground-plane,

(C) an optional set of dielectric material slabs placed between the strip and the ground-plane,

wherein at least a portion of said strip is shaped either as an SFC, Fractal, FSFC, Hilbert, Peano, SZ, ZZ, Dragon, Koch, HilbertZZ, Minkowski or Sierpinski curve as defined in claim 1.

7. A strip-line transmission line comprising:

(A) two parallel metallic or superconducting ground-planes,

(B) a metallic or superconducting strip placed between said ground-planes,

(C) an optional set of dielectric material slabs placed between said ground-planes, wherein at least a portion of said strip is shaped either as an SFC, Fractal, FSFC, Hilbert, Peano, SZ, ZZ, Dragon, Koch, Minkowski, HilbertZZ, or Sierpinski curve as defined in claim 1.

8. A co-planar transmission line comprising:

(a) two metallic or superconducting ground-strips laying on the same plane,

(b) a metallic or superconducting central strip lying on the same plane as said ground-strips wherein said strip is placed between said ground-strips,

(c) an optional set of dielectric material slabs supporting said ground-strips and said central strip,

wherein at least a portion of said central strip is shaped either as an SFC, Fractal, FSFC, Hilbert, Peano, SZ, ZZ, Dragon, Koch, HilbertZZ, Minkowski or Sierpinski curve as defined in claim 1.

9. A coaxial transmission line comprising:

(a) a metallic or superconducting shielding,

(b) a central metallic or superconducting strip or wire placed within said shielding,

(c) an optional dielectric material placed inside the shielding

wherein at least a portion of said central strip or wire is shaped either as an SFC, Fractal, FSFC, Hilbert, Peano, SZ, ZZ, Dragon, Koch, HilbertZZ, Minkowski or Sierpinski curves as defined in claim 1.

10. A parallel plate transmission line comprising:

(a) two parallel metallic or superconducting strips, wires or plates,

(b) an optional dielectric material placed between said strips wires or plates,

wherein at least a portion of said parallel strips, wires or plates are shaped either as an SFC, Fractal, FSFC, Hilbert, Peano, SZ, ZZ, Dragon, Koch, HilbertZZ, Minkowski or Sierpinski curve as defined in claim 1.

11. A dielectric wave-guide comprising:

(a) a dielectric slab,

(b) a dielectric strip etched over said slab with a dielectric permitivity larger than that of said slab,

wherein at least a portion of said strips, is shaped either as an SFC, Fractal, FSFC, Hilbert, Peano, SZ, Dragon, Koch, HilbertZZ, Minkowski or Sierpinski curve as defined in claim 1.

12. A slot-line transmission line comprising two metallic or superconducting strips laying on the same plane, wherein said strips are separated by a slot or gap shaped as an SFC, Fractal, FSFC, Hilbert, Peano, SZ, ZZ, Dragon, Koch, HilbertZZ, Minkowski or Sierpinski curve as defined in claim 1.

13. A distributed capacitor comprising a transmission line according to claim 1 wherein said transmission line has an open circuit at one end, and the electrical length of said transmission line is smaller than a quarter of the operating guided wave lengths.

14. A distributed capacitor comprising a transmission line according to claim 1 wherein said transmission line has a short-circuit at one end, and the electrical length of said transmission line is larger than an odd number of a quarter of the operating guided wave lengths.

15. A capacitor comprising two co-planar metallic or superconducting plates wherein at least part of the boundary between said plates is a gap shaped as a SFC, a FSFC or a fractal curve as defined in claim 1.

16. A distributed inductor comprising a transmission line according to claim 1 wherein said transmission line has a short-circuit at one end, and the electrical length of said transmission line is smaller than a quarter of the operating guided wave lengths.

17. A distributed inductor comprising a transmission line according to claim 1 wherein said transmission line has an open-circuit at one end, and the electrical length of said transmission line is larger than an odd number of a quarter of the operating guided wave lengths.

18. A distributed inductor comprising a metallic or superconducting strip shaped as an SFC, a FSFC or a fractal curve as defined in claim 1, wherein said strip lays down on a plane, being said plane the one including the characteristic strip of either a micro-strip, a strip-line, a co-planar transmission line or an SFC capacitor.

19. A one-port distributed electromagnetic resonator comprising a transmission line according to claim 1 wherein any of its ends is either short-circuited, open-ended, or connected to a reactive load and wherein the coupling is located at any point along said transmission-line.

20. A two-port distributed electromagnetic resonator comprising a transmission line according to claim 1 coupled by two input-output ports at any pair of points along the length of said transmission-line.

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.

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.