EP2509156B1 - Electric PCB track - Google Patents

Description

Embodiments according to the invention relate to an electrical trace and its application as an antenna or line or in a distributed circuit as defined in the appended set of claims.

There are known antennas with many different shaped interconnects. For example, the shows US Pat. No. 6,476,766 B1 a well-known fractal antenna and a fractal circuit that uses a classic fractal structure. Such a fractal antenna is in Fig. 2 shown. Another example of a rat race hybrid (hybrid coupler) as a moor fractal in the second refinement after " Ghali, H .; Moselhy, TA "Miniaturized Fractal Rat-Race, Branch-Line and Coupled-Line Hybrids", IEEE Transactions on Microwave Theory and Techniques, Vol. 11, Nov. 2004, pp. 2513-2520 "is in Fig. 3 shown.

Similarly see antenna structures in US 2010/0177001 A1 out. These represent modified polygonal polya curves, as for example in Fig. 6 in the second to sixth iteration (n = 2-6). This type of known antennas have the disadvantage that strong reflections can occur at the corners and kinks in the high-frequency range (HF range). By using such curves, for example, delay lines can be miniaturized.

The patent US 2008/0084352 A1 shows a device with a non-conductive and a conductive material that forms an antenna. The antenna has the shape determined by a fractal curve based on a modified Peano-Gosper curve. Such a Gosper curve is defined in particular by the fact that in each case 60 ° angle segments and 120 ° angle segments are used.

The paper titled "A Novel Miniaturization Technique in Microstrip Feed Network Design" deals with microstrip antennas with S-sections and not with fractals.

The patent EP 1 699 110 A2 3 shows a space-filling curve geometry without curved elements.

The patent US 2010/0177001 A1 shows an antenna structure based on polygons.

The publication of Ghali et al. titled "Miniaturized Fractal Rat-Race, Branch-Line, and Coupled-Line Hybrids "shows a space-filling curve without fractal structures.

The patent US 6,452,553 shows a fractal antenna and arcuate segments. It is the object of the present invention to provide an electrical trace which allows a reduction of reflections and / or losses in the electrical trace when the electrical trace is used for RF signals.

This object is achieved by an electrical conductor according to claim 1.

According to the invention, an electrical trace provides an arcuate modification of a shape of at least a portion of a fractal, at least a second iteration. The fraction of the fractal is greater than twice a first iteration of the fractal. The arcuate modified shape has a radius of curvature for directional changes that is greater than a predefined minimum radius of curvature.

Embodiments according to the invention are based on the core idea of using electrical conductor tracks which have a shape (at least a part) of a fractal sen, wherein the electrical conductor track instead of corners has arcuate pieces. As a result, on the one hand, the use of fractal-shaped interconnects allows very space-saving interconnects of great length to be realized. On the other hand, by the arcuate modification (the corners of the fractal), the reflections and losses in the electrical conductor track when used with RF signals (high-frequency signals, eg greater than 1, 10, 100 or 1000 MHz) can be significantly reduced.

According to the invention, a Peano curve or box fractal is used as the shaping fractal.

According to the invention, the arcuate modified form fits on a grid of annular segments, which are arranged at a distance of their average diameter. By using such a grid, the electrical trace can be systematically given its shape without falling below the predefined minimum curve radius.

Fig. 1a

eine elektrische Leiterbahn;

Fig. 1b

eine bogenförmige Abwandlung der Form einer Peano-Kurve zweiter Iteration;

Fig. 1c

eine schematische Darstellung einer möglichen Definition für den vordefinierten minimalen Kurvenradius;

Fig. 2

eine bekannte Fraktal-Antenne;

Fig. 3

ein bekannter Rat-Race-Hybrid;

Fig. 4

ein Beispiel für eine bekannte Faltung einer geraden Leitung;

Fig. 5

ein weiteres Beispiel für eine Faltung einer geraden Leitung;

Fig. 6

eine modifizierte polygonförmige Polya-Kurve von zweiter bis sechster Iteration;

Fig. 7

eine Approximation einer Peano-Kurve erster Iteration durch bogenförmige Segmente;

Fig. 8a

eine Peano-Kurve erster Iteration;

Fig. 8b

eine modifizierte Peano-Kurve erster Iteration;

Fig. 9a

eine Peano-Kurve zweiter Iteration vom Serpentinentyp 000 000 000;

Fig. 9b

eine modifizierte Peano-Kurve zweiter Iteration vom Serpentinentyp 000 000 000;

Fig. 10a

eine Peano-Kurve zweiter Iteration vom Serpentinentyp 111 111 111;

Fig. 10b

eine modifizierte Peano-Kurve zweiter Iteration vom Serpentinentyp 111 111 111;

Fig. 11a

eine Peano-Kurve zweiter Iteration vom Serpentinentyp 010 101 010;

Fig. 11b

eine modifizierte Peano-Kurve zweiter Iteration vom Serpentinentyp 010 101 010;

Fig. 12a

ein modifiziertes Box-Fraktal erster Iteration;

Fig. 12b

ein modifiziertes Box-Fraktal zweiter Iteration;

Fig. 12c

ein modifiziertes Box-Fraktal dritter Iteration;

Fig. 13a

ein Box-Fraktal mit berührungsfreier Führung durch abgekürzte Leitungen;

Fig. 13b

ein Box-Fraktal mit berührungsfreier Leitungsführung durch Ausrichtung auf Rundungsgitter;

Fig. 14a

eine konventionelle Butler-Matrix; und

Fig. 14b

eine miniaturisierte Butler-Matrix.

Embodiments according to the invention are explained below with reference to the accompanying figures.

Fig. 1a

an electrical conductor;

Fig. 1b

an arcuate modification of the form of a Peano curve second iteration;

Fig. 1c

a schematic representation of a possible definition for the predefined minimum curve radius;

Fig. 2

a known fractal antenna;

Fig. 3

a well-known rat race hybrid;

Fig. 4

an example of a known convolution of a straight line;

Fig. 5

another example of a convolution of a straight line;

Fig. 6

a modified polygonal polya curve from second to sixth iteration;

Fig. 7

an approximation of a peano curve of the first iteration by arcuate segments;

Fig. 8a

a Peano curve first iteration;

Fig. 8b

a modified Peano curve first iteration;

Fig. 9a

a second-serpentine curve of the serpentine type 000 000 000;

Fig. 9b

a modified Peano curve of the second iteration of serpentine type 000 000 000;

Fig. 10a

a serpentine type second iteration peano curve 111 111 111;

Fig. 10b

a modified peano curve of the second iteration of the serpentine type 111 111 111;

Fig. 11a

a Peano curve of the second iteration of serpentine type 010 101 010;

Fig. 11b

a modified Peano curve of the second iteration of serpentine type 010 101 010;

Fig. 12a

a modified box fractal of the first iteration;

Fig. 12b

a modified box fractal second iteration;

Fig. 12c

a modified box fractal of third iteration;

Fig. 13a

a box fractal with non-contact guidance through shortened lines;

Fig. 13b

a box fractal with non-contact cable routing by aligning with a rounding grid;

Fig. 14a

a conventional Butler matrix; and

Fig. 14b

a miniaturized Butler matrix.

Hereinafter, the same reference numerals are used in part for objects and functional units having the same or similar functional properties. Furthermore, optional features of the various embodiments may be combined with each other or interchangeable. Fig. 1a shows a schematic representation of an electrical conductor 100 according to an embodiment of the invention. The electrical trace 100 has at least partially an arcuate modification of a shape of at least a portion of a fractal at least second iteration. The fraction of the fractal is greater than twice a first iteration of the fractal. The arcuately modified form has a larger radius of curvature for changes in direction than a predefined minimum curve radius R _min .

Fig. 1a shows an example of an electrical conductor 100 having the shape of a part of a second-course Peano curve, as in arcuate form in FIG Fig. 1b is shown. In this case, the part of the Peano curve 150 used for the electrical conductor track 100 is marked by the drawn circle 160.

By using a fractal-based mold long electrical conductors can be realized in a small footprint. By the arcuate modification of the shape of the fractal or a portion of the fractal reflections or losses to otherwise existing corners or kinks can be significantly reduced or completely prevented.

The electrical conductor may comprise, for example, copper, aluminum or another conductive material. Furthermore, in addition to the part which is formed as an arcuate modification of at least one part of a fractal, the electrical conductor track 100 can also have other parts with a different shape. The electrical conductor 100 may, as in Fig. 1a shown have open ends, with which they can be connected, for example, to electrical circuits. Alternatively, the electrical trace 100 may also form a closed curve and be connected at arbitrary points of the closed curve.

The fractal can in principle be any fractal and depends, for example, on the particular application of the electrical conductor 100. The fractal property of the curve can be recognized, for example, by a self-similarity. For example, the fractal may be a Peano curve or a box fractal. For example, serpentine Peano curves can be used. By using box fractals or peano curves (serpentine type), a rectangular or square area can already be filled out of the iteration, whereas in Pòlya curves only a triangular area is occupied.

Fractals are preferably used in which the number of line segments at least triples between two iteration steps (ie in an iteration), which is the case with box fractals and peano curves (of the serpentine type). In other words, the number of line segments changed in one iteration step is set to at least 3, for example. On the other hand, in Pólya curves, the number of line segments only doubles for each iteration step.

In order to realize an electrical conductor 100 as space-saving as possible, the fractal may be, for example, a space-filling fractal, which in this context may also be called space-filling curve.

aus dem Einheits-Intervall I = [0,1] in den Euklidischen Raum

deren Bild f(I) eine Fläche ausfüllt, d.h. ein Jordan-Maß J(f(I)) > 0 besitzt.In general, a space-filling curve is a continuous image $f:I\to {\mathbb{<figure-callout\; id="2"\; label="R"\; filenames="imgf0008.png"\; state="\{\{state\}\}">R</figure-callout>}}^2$

from the unit interval I = [0,1] into the Euclidean space

whose image f (I) fills an area, ie has a Jordan measure J ( f ( I ))> 0.

Such space-filling curves can be iteratively described by an initiator (initial figure, "base") and a generator (formation specification, "motif"). By (infinitely) repeated application of this educational rule, the space-filling property of the curve described is achieved.

In a practical application, the iteration must be aborted after N levels, which means that the curve is not yet space-filling according to the definition. However, it is (theoretically) possible to continue the iteration as far as possible at smaller scale levels by means of the educational instruction. The presence of such a formation rule is therefore crucial to the question of whether a curve has room-filling properties.

The space-filling property is fulfilled by means of this iteration rule (with infinite continuation). However, the curve does not yet have to have a fractal property because there may not be self-similarity between the iteration steps. Also, between the iteration steps, only anisotropic scaling in e.g. vertical direction.

By contrast, the structures used according to the described concept are fractal curves, for example, with the isotropic scaling necessary for exact self-similarity between the iterations. These then also differ, for example, from curves with quasi-self-similarity or statistical self-similarity.

By "at least part of a fractal" is meant that it can also be the entire fractal of a particular iteration. In other words, the part of the fractal does not have to be a true subset of the fractal, but part of the fractal may also mean the entire fractal. In other words, an entire fractal is part of a higher iteration fractal anyway (for example, an entire fractal of the third iteration is part of a fractal of the fourth iteration).

However, the fraction of the fractal must be greater than at least two times the first iteration of the fractal, since fractals in the first iteration often have very simple structures, and otherwise the advantage of space-saving routing in the use of fractals does not yet come to fruition. Here, the phrase "the fraction of the fractal is greater than twice a first iteration of the fractal" means that the electrical trace within the portion of the fractal more than twice takes the form of the first iteration of the fractal (in its arcuate variation). In other words, the part of the fractal contains more than twice (the shape) of the fractal in the first iteration.

bestimmt werden, wobei W die Breite der elektrischen Leiterbahn und D_min ein minimaler Abstand zwischen zwei in den Eckpunkten eines Quadrats, diagonal zu einander angeordneter Ringe eines Rasters, wie er in Fig. 1c gezeigt ist, ist und weiter unten noch ausführlicher beschrieben wird.Many fractals have an angular shape in their familiar presentation. The arcuate modified form has in comparison to these known forms of fractals a predefined minimum curve radius R _min for changes in direction of the electrical conductor, which is not exceeded. In this case, the predefined, minimum radius of curvature is at least three times (or 1 times, 1.5 times, twice, four times or more) the width of the electrical conductor track 100. Alternatively, the predefined minimum curve radius can be $${\mathrm{R}}_{\min }=\mathrm{W}/\left(\mathrm{2}\left(\mathrm{\surd }\mathrm{2}-\mathrm{1}\right)\right)+{\mathrm{D}}_{\min }/\left(\mathrm{2}\left(\mathrm{\surd }\mathrm{2}-\mathrm{1}\right)\right)$$

where W is the width of the electrical trace and D _{min is} a minimum distance between two rings of a grid arranged diagonally to one another in the corner points of a square, as shown in FIG Fig. 1c is shown, and will be described in more detail below.

The radius of curvature of a change in direction of the electrical trace, for example, refers to the inner radius, the mean radius or the outer radius of the electrical trace in the corresponding portion of the change in direction.

In general, for example, a length of the electric wiring 100 is greater than 10 times (or 20x, 50x, 100x or more) a width of the electrical wiring 100 and greater than 10 times (or 20x, 50x, 100x or more) a height of the electrical trace. The electrical conductor 100 takes in its longitudinal extent (direction of its largest extension) to the arc-shaped modified form.

The electrical trace 100 may have a constant width (or height) along its length, or alternatively have different widths (or heights) in different sections. This may vary depending on the requirement of the particular application.

Normally, the electrical conductor 100 is in a plane, so that the arcuate modified form is easily visible. By this is meant that the electrical conductor extends in its longitudinal extent and its width extension in the plane. However, it is also possible that a three-dimensional structure is formed with the electrical conductor track 100, so that parts of the electrical conductor track 100 can lie in different planes.

The electrical conductor track 100 may also have an arcuate modification of a shape of at least part of a fractal at least twice iteration. These can be parts of the same fractal or fractals. For example, to achieve a large space-saving effect, it may be determined that the electrical trace 100 is at least 50% (or 20%, 30%, 70%, 80% or more) of its length simply or multiply an arcuate variation of a shape of at least one Part of a fractal has at least second iteration.

In some embodiments according to the invention, the electrical trace has an arcuately modified shape that includes only direction changes with the same curve radius (which is greater than the predefined minimum curve radius). This may also relate to the entire electrical trace, if it is greater than that part corresponding to an arcuate modified form of at least a portion of a fractal at least second iteration.

One way to construct such structures is to adapt the electrical trace to a grid consisting of annular segments. In other words, the arcuate modified form fits for example on a grid of annular segments (eg Fig. 1c ), which are arranged at a distance of their average diameter. The mean diameter of the annular segment is the mean of the inner diameter (2 * R ₁ ) and the outer diameter (2 * R ₂ ) of the annular segment. The annular segments of the grid are the same size.

Some embodiments according to the invention relate to an antenna, a line or a distributed circuit having an electrical conductor track according to the described concept.

As a result, an antenna or, for example, a delay line can be realized in a very space-saving manner and with little reflection and / or low loss.

Some other embodiments according to the invention relate to a method for producing an electrical conductor, wherein the electrical conductor is produced with the described shape (on a substrate).

Some embodiments according to the invention relate to antennas, lines and / or distributed circuits using space-filling curves and fractals (arcuate modification of the shape) modified on rounding gratings (raster with annular segments). In this case, electrical conductor tracks are used according to the described concept.

The distributed circuits may be, for example, high frequency circuits. In other words, the antennas, lines and / or passive high frequency circuits can be constructed using modified space filling curves and (or) fractals.

In known circuits or antennas lines are guided so that wrinkles arise. If the resulting kinks are not bevelled, the transmission behavior of the line is disturbed, resulting in additional losses. The lowest loss is a (double-sided) arcuate transition, the bending radius should be at least three times the width of the conductor. This is related to the fact that the characteristic impedance of the arc with the radius, which falls below the above-mentioned value, noticeably changes and represents a discontinuity. In Popugaev, AE; Wansch, R. "Novel Miniaturization Technique in Microstrip Feed Network Design", 3rd European Conference on Antennas and Propagation (EuCAP 2009), Proceedings, CD-ROM: 23 - 27 March 2009, Berlin, Germany, Berlin: VDE-Verlag, 2009, pp. 2309-2313 It has been shown that circuits to be miniaturized can be made completely arcuate, so that no discontinuities of the straight line - arc type arise. As an aid, a grid may be used which consists of annular segments which are arranged at a distance of their mean diameter, each segment being divided into four equal quarter-circle rings. There are some wire routing curves shown which are aligned on a rounding grid, but which are not fractals or space-filling curves, nor an iteration rule is specified. These curves were created freehand, an iteration rule for the transition to the next lower scale level is neither specified nor recognizable. The curves shown are therefore no space-filling curves. Fig. 4 and 5 illustrates such a grid for folding straight lines.

For example, For example, a delay line can be effectively miniaturized using fractal round segments.

The proposed concept allows e.g. the construction of fractal antennas and circuits, based on a Peano curve, which has been modified so that no kinks arise. As a result, optimal transmission properties with respect to reflections can be ensured, for example, particularly in the case of microstrip line circuits.

For example, a peano curve modified on a roundness grid shows, if you look at the grid Fig. 4 and 5 takes and draws the in Fig. 7 If you rotate the curve with the grid by 45 °, you can see that this curve is very similar to the Peano curve of the 1st iteration Fig. 8a and 8b is shown. Fig. 8a shows a Peano curve first iteration and Fig. 8b shows a modified Peano curve first iteration. The modified curve can be considered as an approximation of the Peano curve through arcuate segments.

By continued redivision of the in Figs. 8A and 8B It is also possible to obtain modified serpentine-type peano curves using the modified Peano curve. Fig. 9A Serpentine type second 000,000,000 Peano curve and 9B (modified second-serpentine peano curve 000,000,000) Fig. 10A (Peano curve of the second iteration of serpentine type 111 111 111) and 10B (modified Peano curve of the second iteration of serpentine type 111 111 111) and Fig. 11A (Peano curve of the second iteration of serpentine type 010 101 010) and 11B (modified Peano curve of the second iteration of serpentine type 010 101 010) show 2nd iterations of the three different variants.

Alternatively, for example, a round box-modified box fractal (Vicsek fractal, Minkowski island) may be used. In the Fig. 2 The fractal antenna shown can also be modified on a rounding grid. The first three iterations are in Figs. 12A-12C illustrated.

With the described technique (the described concept for electrical interconnects) it is possible to build antennas, lines and / or complex circuits which make use of the advantages of fractal structures, but which can be realized simpler, faster and / or above all reflection and / or low loss. By aligning on a rounding grid, it is possible to realize non-contact routing without having to manually shorten sections of the original fractal structure ( Figs. 13A and 13B ).

For example, For a 2x2 antenna arrangement, a Butler matrix was developed and then miniaturized. The circuit should realize a uniform amplitude assignment and the following phase assignments (depending on the gate combination): -180 ° / -90 ° / -180 ° / -270 °; -90 ° / -180 ° / -270 ° / -180 °; -180 ° / -270 ° / -180 ° / -90 ° and -270 ° / -180 ° / -90 ° / -180 °.

A direct comparison of the constructed Butler matrices is in Figs. 14a and 14b to see. It is in Fig. 14b an electrical trace 1400 having multiple arcuate modification of a shape of at least a portion 1410 of a fractal at least second iteration is shown.

In the Fig. 14a and Fig. 14b shown electrical conductor tracks have different widths in different sections.

It can be seen that the miniaturized feed network (in Fig. 14b ) is almost three times as small as the conventional design ( Fig. 14a ). The circuits include 90 ° hybrids, cross couplers and delay lines. The miniaturized cross-coupler was designed as two miniaturized 90 ° hybrids connected in series, with each miniaturized 90 ° hybrid (one part) following the modified Peano curve Fig. 11b represents. Measurement results of the manufactured Butler matrix are summarized in the following table.

The results of the conventional and miniaturized Butler matrices are almost identical, with the area requirement of the miniaturized Butler matrix being only one third.

Some embodiments according to the invention relate to antennas, lines, and / or distributed circuits created using space-filling fractal-arced curves, the fractal structure having exact self-similarity or scale invariance, at least one iteration step, or one or more Sections of such a fractal curve are used, and the resulting curve has been modified by means of a roundness grating so that a non-contact and uncut routing is achieved, so that line sections of the original fractal structure for a non-contact guidance need not be shortened manually, whereby compared to conventional Design a significantly simplified routing is possible, and optimum transmission properties can be ensured with respect to reflections.

Although some aspects have been described in the context of a device, it will be understood that these aspects also constitute a description of the corresponding method, so that a block or a component of a device is also to be understood as a corresponding method step or as a feature of a method step. Similarly, aspects described in connection with or as a method step also represent a description of a corresponding block or detail or feature of a corresponding device.

The embodiments described above are merely illustrative of the principles of the present invention. It will be understood that modifications and variations of the arrangements and details described herein will be apparent to others of ordinary skill in the art. Therefore, it is intended that the invention be limited only by the scope of the appended claims and not by the specific details presented in the description and explanation of the embodiments herein.

Claims (8)

1. Electric conductive trace (100) comprising an arch-shaped variation of a shape of at least a portion of a fractal of at least second iteration, wherein the arch-shaped variation consists of one or several ring-shaped segments,
   wherein the electric conductive trace within the portion of the fractal includes more than twice the shape of the first iteration of the fractal,
   wherein the shape varied to be arch-shaped fits onto a raster consisting of ring-shaped segments, arranged at the distance of their mean diameter,
   wherein the shape varied to be arch-shaped comprises, for changes of direction, a bending radius, that is larger than a predefined minimum bending radius (R_min),
   wherein the predefined minimum bending radius is equal to $${\mathrm{R}}_{\min }=\frac{\mathrm{W}}{2\left(\sqrt{2}-1\right)}+\frac{{\mathrm{D}}_{\min }}{2\left(\sqrt{2}-1\right)},$$

   

   wherein W is the width of the electric conductive trace and D_min is a minimum distance between two rings of the raster that are arranged by means of their centers in the corner points of a square and are diagonally arranged toward one another, and wherein the difference between an outer radius of the electric conductive trace (R₂) and an inner radius of the electric conductive trace (R₁) in a ring-shaped segment of the raster corresponds to the width W of the electric conductive trace, wherein the latitudinal extension and the longitudinal extension of the electric conductive trace extend in a common plane,
   wherein the fractal is a Peano curve or a box fractal.
2. Electric conductive trace as claimed in claim 1, wherein the fractal is a space-filling fractal.
3. Electric conductive trace as claimed in any of claims 1 or 2, wherein the electric conductive trace (100) lies in a plane.
4. Electric conductive trace as claimed in any of claims 1 to 3, wherein a length of the electric conductive trace (100) is larger than 10 times a width of the electric conductive trace (100) and larger than 10 times a height of the electric conductive trace (100), wherein the electric conductive trace (100) comprises in its longitudinal extension the shape varied to be arch-shaped, wherein the latitudinal extension and the longitudinal extension of the electric conductive trace extend in a common plane.
5. Electric conductive trace as claimed in any of claims 1 to 4, wherein the shape varied to be arch-shaped comprises exclusively changes of direction with a same bending radius.
6. Electric conductive trace as claimed in any of claims 1 to 5, wherein the electric conductive trace (100) comprises several times an arch-shaped variation of a shape of at least a portion of a fractal of at least second iteration.
7. Electric conductive trace as claimed in any of claims 1 to 6, wherein the electric conductive trace (100) comprises, over at least 50% of its length, one or several arch-shaped variations of a shape of at least a portion of a fractal of at least second iteration.
8. Antenna, line or distributed circuit comprising an electric conductive trace (100) as claimed in any of claims 1 to 7.

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