Fractal and space-filling transmission lines, resonators, filters and passive network elements
This invention relates to high frequency electromagnetic circuits, in particular to those made on planar or quasi-planar substrates, where the circuit is patterned on a metallic or superconducting film on top of a dielectric in any of the configurations known to those skilled in the art (for instance micro-strip, strip-line, co-planar, parallel plate or slot-line configurations). A part of the circuit such as the characteristic strip or slot of said configurations is shaped in a novel space-filling geometry which allows a significant size reduction of the circuital component. Miniature transmission lines, capacitors, inductors, resistors, filters and oscillators can be manufactured this way.
1. An electromagnetic transmission line, comprising:
a plurality of cascaded transmission line segments, each of the cascaded transmission line segments forming a space-filling curve (SFC),
said SFC including at least twenty ( 20 ) connected straight segments, wherein said straight segments are each smaller than a tenth of the operating free-space wave length of the electromagnetic transmission line, wherein said straight segments are spatially arranged such that no two adjacent and connected segments form another longer straight segment, and wherein none of said straight segments intersect with another straight segment, wherein each pair of adjacent straight segments forms a corner; and
wherein each pair of adjacent straight segments are generally orthogonal to each other and comprise segments of a Hilbert curve.
2. The electromagnetic transmission line of claim 1 , wherein one or more of the corners formed by adjacent straight segments in the SFC are rounded.
3. The electromagnetic transmission line of claim 1 , wherein one or more of said SFC has a Haussdorf dimension (D) larger than unity.
4. The electromagnetic transmission line of claim 1 , wherein one or more of said SFC is a fractal space-filling curve (FSFC).
5. The electromagnetic transmission line of claim 1 , wherein the electromagnetic transmission line is included in an electromagnetic resonator.
6. The electromagnetic transmission line of claim 1 , wherein one or more of said SFC forms a HilbertZZ curve.
7. The electromagnetic transmission line of claim 1 , wherein each of the plurality of cascaded transmission line segments comprises four (4) cascaded Hilbert curves.
8. The electromagnetic transmission line of claim 1 , wherein two or more of the plurality of cascaded transmission line segments are separated by a capacitive gap.