Compact dual-band linear polarization orthogonal mode converter

Abstract

To make a broadband-compatible orthogonal mode transducer smaller than conventional types. The present invention relates to a broadband linearly polarized orthomode converter obtained by additive manufacturing, the linearly polarized orthomode converter comprising: a first waveguide having a first input port and a first output port for single polarization; a second waveguide having a second input port and a second output port for single polarization; a coupling portion connecting the first waveguide and the second waveguide; A two-element coupler comprising: The orthogonal mode converter comprises: a single-polarized third input port coupled to the first output port; a single-polarized fourth input port coupled to the second output port; The third output port The optical fiber polarizer further includes a septum polarizer comprising: a first waveguide and a second waveguide, the first waveguide and the second waveguide being arranged symmetrically with respect to a symmetry plane that includes the septum of the septum polarizer.

Description

[Technical Field]

[0001] The present invention relates to a compact, dual-band linearly polarized orthogonal mode converter. [Background technology]

[0002] Orthomode transducers (OMTs) are passive components widely used in radio frequency antennas to enable both receiving and transmitting operations.

[0003] Their use is particularly prevalent in onboard antennas on communications satellites, so keeping the weight and volume of such antennas down is a key challenge. The ability of the antenna (and therefore the OMT) to transmit and receive in multiple frequency bands is also a crucial factor.

[0004] However, conventional OMTs have the drawback of being difficult to make compact (miniaturized) while maintaining wide transmission and reception bandwidths. Other OMTs, such as side-arm OMTs, are compact but have narrow bandwidths. While the side arm can be extended to operate in a second frequency band (dual-band), this extension is only possible for one of the two polarizations. Other OMTs, such as the "Boifot" junction (a technology that influences signal quality and broadband performance) and the "Turnstile" junction (a technology for processing signals with different polarization states using five ports), are broadband compatible but are not compact because they have an aperture larger than the wavelength λ of the wave with the OMT's highest operating frequency.

[0005] EP2330681A1 describes a single-wave orthogonal mode converter with a septum polarizing section, which septum provides a 180° phase shift to produce a 45° polarization.

[0006] Patent document 2 (US2012 / 0319799A1) describes an orthogonal mode converter that connects a first septum polarization section to a second wave polarization section to cancel the circular polarization generated by the first polarization section and generate a 45° polarization. Increasing the length of the converter and increasing the overall dimensions theoretically allows for wider bandwidth performance.

[0007] EP 2047564 B1 describes an orthogonal mode transducer with a coupling in the form of a side arm coupled to the transducer via a slot, allowing for a 90° rotation of the transverse waveguide. The side arm increases the footprint of the transducer. Furthermore, broadband performance has not been demonstrated with this type of transducer. [Prior art documents] [Patent documents]

[0008] [Patent Document 1] European Patent Application Publication No. 2330681 [Patent Document 2] US Patent Application Publication No. 2012 / 319799 [Patent Document 3] European Patent No. 2047564 Summary of the Invention [Problem to be solved by the invention]

[0009] It is an object of the present invention to provide an orthomode transducer that is not subject to the limitations of known orthomode transducers.

[0010] Another object of the present invention is to provide a broadband orthomode transducer with a small footprint. [Means for solving the problem]

[0011] These objects are achieved by the subject matter of the claims, in particular by a broadband linearly polarized orthomode converter which is obtainable by additive manufacturing, comprising: a first waveguide having a first input port and a first output port for single polarization; a second waveguide having a second input port and a second output port for single polarization; a coupling portion connecting the first waveguide and the second waveguide; Two-element coupler (hybrid coupler) The orthogonal mode converter comprises: a single-polarized third input port coupled to the first output port; a single-polarized fourth input port coupled to the second output port; Single polarized third output port and The optical fiber polarizer further includes a septum polarizer comprising: a first waveguide and a second waveguide, the first waveguide and the second waveguide being arranged symmetrically with respect to a symmetry plane that includes the septum of the septum polarizer.

[0012] The symmetrical arrangement of the first and second waveguides of the coupler described above allows for a limited footprint of the transducer, i.e. a compact cross section over the entire length of the transducer, which allows for a more dense and compact construction of such devices, for example in antenna arrays.

[0013] In the first embodiment, the coupling portion connects a first lateral surface of the first waveguide and a second lateral surface of the second waveguide, the first lateral surface and the second lateral surface being arranged in the same plane.

[0014] If the first transverse surface corresponds to one of the smallest dimensions of the first waveguide, then the second transverse surface corresponds to one of the smallest dimensions of the second waveguide.

[0015] This configuration can be further reduced in bulk by placing the two waveguides with their largest sides facing each other, thereby reducing the footprint of the coupler.

[0016] In one embodiment, the coupling portion comprises a trapezoidal base prism, with a first portion of the rectangular face of the prism abutting a first lateral face of the first waveguide and a second portion of the rectangular face of the prism abutting a second lateral face of the second waveguide.

[0017] This coupling geometry facilitates additive manufacturing of the coupler by limiting protrusions (cantilevered portions).

[0018] The coupling may include an impedance matching element.

[0019] In the second embodiment, the coupling portion connects the first horizontal surface of the first waveguide and the second horizontal surface of the second waveguide, and the first horizontal surface and the second horizontal surface are arranged on different planes that are parallel to each other.

[0020] This arrangement advantageously limits the footprint of the transducer by placing the coupling between the two waveguides: indeed, the outer faces of the coupler, i.e., the faces of the waveguides that are not directly opposite the faces of the other waveguides, do not contain any protruding elements that would increase the footprint of the transducer.

[0021] Advantageously, the coupling portion may comprise a plurality of branches, where a first end of each branch is connected to the first waveguide and a second end of each branch is connected to the second waveguide.

[0022] In one embodiment, each branch forms a two-sided roof, where a first side of the roof is adjacent to a first lateral surface (of the first waveguide) and a second side of the roof is adjacent to a second lateral surface (of the second waveguide). This branch geometry facilitates additive manufacturing by limiting the cantilevered portion.

[0023] The edge of the roof created by the junction of the first side and the second side may lie in a plane perpendicular to the print direction.

[0024] To facilitate additive manufacturing, the first side may form an angle of 35° to 55° with a first lateral plane of the first waveguide, and the second side may form an angle of 35° to 55° with a second lateral plane of the second waveguide.

[0025] To further limit the cantilevered section of the joint, each branch may form two two-sided roofs: a first two-sided roof with a first side adjacent to the first lateral face and a second side adjacent to the second lateral face, and a second two-sided roof with a third side adjacent to the first lateral face and a fourth side adjacent to the second lateral face.

[0026] The first and third sides of the roof may be formed at an angle of 35° to 55° with the first lateral plane, and the second and fourth sides of the roof may be formed at an angle of 35° to 55° with the second lateral plane.

[0027] The edge formed by the junction of the first side and second side of the first roof may be at an angle of 35° to 55° with respect to the printing direction, and the edge formed by the junction of the third side and fourth side of the second roof may be at an angle of 35° to 55° with respect to the printing direction.

[0028] Several embodiments of the invention are set forth in the following description taken in conjunction with the accompanying drawings. [Brief explanation of the drawings]

[0029] [Figure 1] FIG. 1 shows a schematic representation of an orthomode transducer according to the present invention. [Figure 2] FIG. 2 shows a septum polarization section. [Figure 3] FIG. 3 shows a two-element coupler with a trapezoidal coupling. [Figure 4a] FIG. 4a shows an orthogonal mode transducer comprising the two-element coupler of FIG. [Figure 4b] FIG. 4b shows an orthogonal mode transducer comprising the two-element coupler of FIG. [Figure 5a]FIG. 5a shows a two-element coupler with multiple prongs where the coupling is suitable for additive manufacturing. [Figure 5b] FIG. 5b shows a two-element coupler with multiple prongs where the coupling is suitable for additive manufacturing. [Figure 6a] FIG. 6a shows a two-element coupler with multiple prongs suitable for additive manufacturing. [Figure 6b] FIG. 6b shows a two-element coupler with multiple prongs suitable for additive manufacturing. [Figure 7a] FIG. 7a shows an orthogonal mode transducer comprising the two-element coupler shown in FIG. 6a. [Figure 7b] FIG. 7b shows an orthogonal mode transducer comprising the two-element coupler shown in FIG. 6b. DETAILED DESCRIPTION OF THE INVENTION

[0030] As shown in Figure 1, the orthogonal mode converter of the present invention comprises a two-element coupler 1 (hybrid coupler) and a septum polarizer 2 connected to the two-element coupler 1. The two-element coupler 1 comprises two waveguides (10, 11) arranged in parallel and connected to each other by a coupling part 12. The septum polarizer 2 is connected to the output port of the two-element coupler 1 via two input ports.

[0031] When a radio frequency device including an orthogonal mode converter of the present invention is operating in a transmitting mode, electromagnetic waves propagate from the two-element coupler 1 to the septum polarizer 2, and when operating in a receiving mode, electromagnetic waves propagate from the septum polarizer to the two-element coupler. Terms used in the present invention, such as "input port" and "output port," refer to the transmitting mode of operation, even though the converter can operate in either the transmitting or receiving mode of operation.

[0032] Thereby, the direction of wave propagation in the transducer is parallel to the longitudinal direction of the guided wave of the coupler 1 and the polarizer 2 .

[0033] The orthomode transducers of the present invention are manufactured by additive manufacturing. Additive manufacturing refers to any manufacturing method in which a part is manufactured by adding material according to computer data stored on a computer medium that defines a model of the part. In addition to stereolithography, the term refers to other manufacturing methods that rely on the hardening or solidification of a liquid or powder, including: Binder jetting, DED (Direct Energy Deposition), EBFF (Electron beam freeform fabrication), FDM (Fused Additive Manufacturing), PFF (Plastic Free Forming), Aerosol, BPM (Ballistic Particle Manufacturing), Powder Bed, SLS (Selective Laser Sintering), ALM (Additive Manufacturing), PolyJet, EBM (Electron Beam Melting), Photopolymerization, etc. shall be included.

[0034] Thus, the orthogonal mode converter comprises two elements with different functions, namely a two-element coupler (hybrid coupler) and a septum polarizer, but its fabrication does not require any assembly after the three-dimensional (3D) printing process. The coupler and polarizer are typically molded as a single unit.

[0035] A two-element coupler is a four-port directional coupler used to separate or combine waves with a specific phase relationship. There are two main types of two-element couplers: those that create a 90° phase difference between the two output ports, and those that create a 180° phase difference between the two output ports. Two-element couplers also function as wave power dividers, since the waves are typically attenuated by 3 dB, so that the power of the wave transmitted by each output port is 50% of the power of the input wave.

[0036] FIG. 2 shows a conventional rib-type (riblet) two-element coupler in which two waveguides are coupled to each other through openings in the walls adjacent to the two waveguides.

[0037] As shown schematically in Figure 1, the first waveguide 10 has a first input port 100 and a first output port 101, and the second waveguide has a second input port 110 and a second output port 111. The phase difference at the output ports is determined by the coupling section 12. Each of these four ports handles a single polarization.

[0038] The coupling section 12 of the coupler 1 allows waves propagating in the first waveguide 10 to pass at least partially through the second waveguide 11, and allows waves propagating in the second waveguide 11 to pass at least partially through the first waveguide 10.

[0039] Thus, for example, a wave propagating through the first input port 100 of the first waveguide 10 is split into the first and second waveguides (10, 11) via the coupling section 12, and is thereby output from the first output port (100) and the second output port (101) of the two-element coupler 1.

[0040] The output ports (101, 111) of the dual-element coupler are connected to a septum polarizer 2 via a third input port 200 and a fourth input port 210 of the polarizer, respectively. The other end of the polarizer 2 is provided with a third output port 201. The third output port is connected to a radiating element of an antenna or, in certain embodiments, functions as a radiating element itself. The third and fourth input ports (200, 210) of the polarizer are both for single polarization. The third output port 201 of the polarizer is for dual polarization.

[0041] Although the various embodiments shown in the figures show waveguides with rectangular cross sections, the invention is not limited to these geometries. Indeed, the first and second waveguides (10, 11) and the septum polarizer 2 may have cross sections that are circular, elliptical, polygonal (regular or irregular), such as triangular, pentagonal, hexagonal, or octagonal.

[0042] The dual-element coupler 1 is used to simultaneously excite the third and fourth input ports of the polarizer 2 to generate two circularly polarized waves, which are combined by the polarizer septum to generate a linearly polarized wave at the third output port 201.

[0043] The septum 22 of the polarizer 2 is arranged in a plane parallel to the direction of wave propagation in the transducer. The septum typically has a varying height (rather than a constant height), with the highest part of the septum located at one end of the polarizer that includes the third and fourth input ports (200, 210). The height of the septum typically decreases linearly or in steps. Figure 2 shows a polarizer 2 with a septum 22 that decreases in height like a step.

[0044] The orthomode transducer of the present invention can be implemented in a variety of radio frequency devices for a variety of frequency bands depending on the application. The present invention can typically be implemented in devices for the X, Ku, Ka, QV, Ku / Ka, and Ka / QV bands.

[0045] Preferably, the first and second waveguides (10, 11) of the two-element coupler 1 are arranged symmetrically with respect to a plane of symmetry comprising the septum 22 of the polarizer 2.

[0046] Preferably, the cross section of the polarizer with septum 2 measured perpendicular to the direction of wave propagation in the orthomode transducer is the same as the cross section of the two-element coupler 1 measured perpendicular to the same direction of propagation. This results in the diameter of the orthomode transducer (or transducer footprint) being approximately constant along the direction of propagation when measured in a plane perpendicular to the direction of propagation. This property improves the compactness of the transducer, allowing its size to be reduced, especially for use in compact antenna arrays.

[0047] As described above, depending on the coupling section 12, the two-element coupler 1 generates a phase difference of 90° or 180°. This means that during transmission, an electromagnetic wave propagating from the first or second input port (100, 110) of the two-element coupler is split into two waves that are 90° or 180° out of phase with each other between the first and second output ports (101, 111). Furthermore, each of the two output waves is attenuated by -3 dB relative to the input wave. During reception, the two-element coupler receives two waves that are 90° or 180° out of phase and combines them to double the power of the output wave (3 dB increase). Two main embodiments corresponding to the two phase differences are described below.

[0048] A two-element coupler 1 according to a first embodiment is shown in Figure 3. A first waveguide 10 and a second waveguide 11 are joined by a coupling 12.

[0049] During transmission, this coupler splits a wave propagated by the first or second input port (100, 110) into two waves that are 90° out of phase with each other via the coupling section 12. As a result, the two input ports of the septum polarizer 2 are simultaneously excited by the two waves that are 90° out of phase with each other, generating two circularly polarized waves that are 90° out of phase with each other.

[0050] The two circularly polarized waves are then combined in the septum polarizer 2 to produce a linearly polarized wave at the output port 201 of the septum polarizer, which is inclined at 45° with respect to the input wave of the two-element coupler 1 .

[0051] In this first embodiment, the first (10) and second (11) waveguides of the two-element coupler 1 have rectangular cross-sections and are arranged parallel to each other, as shown in Figure 3. Advantageously, one of the long sides of the rectangular cross-section of the first waveguide is parallel to one of the long sides of the rectangular cross-section of the second waveguide, so that the larger rectangular sidewalls of the first and second waveguides are arranged in parallel planes.

[0052] The two waveguides (10, 11) are connected to each other by a coupling 12. More specifically, this coupling 12 connects one of the small rectangular sidewalls of the first waveguide 10 to one of the small rectangular sidewalls of the second waveguide 11. The two small rectangular walls are arranged in the same plane, which is perpendicular to the large rectangular sidewall of each waveguide. Each small wall has an opening at the coupling that allows waves to propagate from the first waveguide to the second waveguide or from the second waveguide to the first waveguide. The coupling includes a portion of the waveguide that extends between these two openings, allowing waves to propagate between the two openings.

[0053] In the particular embodiment shown in Figure 3, the waveguide portion of the coupling portion 12 is trapezoidal in shape. More specifically, this waveguide portion has a rectangular base adjacent to the smaller sidewalls of the first and second waveguides (10, 11). The waveguide extends in a direction perpendicular to the rectangular base, and its cross section parallel to the base tapers toward the base, forming a rectangular top surface opposite the base. This results in the dimensions of the rectangle being smaller than the dimensions of the base.

[0054] The coupling section 12 may be provided with one or more impedance matching elements, such as grooves, internal protrusions, or openings in the walls of the coupling section, to optimize signal transmission at the coupling section. As shown in Figure 3, an opening may be provided on the top surface of the coupling section to improve signal transmission between the first waveguide (10) and the second waveguide (11).

[0055] Figures 4a and 4b show an orthomode converter according to the first embodiment described above. The two-element coupler 1 and the septum polarizer 2 are integrally formed by additive manufacturing, so no assembly is required to obtain the converter of the present invention.

[0056] In one embodiment, the printing direction of the additively manufactured layers is aligned with the wave propagation direction in the orthomode transducer. To reduce or eliminate the use of printing supports during manufacturing, certain portions of the transducer are adapted for additive manufacturing. In particular, protruding portions (cantilevered portions) are angled at an angle significantly less than 90° relative to the printing direction.

[0057] As shown in FIG. 3, the coupling portion 12 of the two-element coupler may have sides that are angled at 35° to 55° with respect to the direction of propagation to eliminate the use of a print substrate.

[0058] In a second main embodiment, the orthomode converter comprises a two-element coupler 1 which produces a phase difference of 180° between the two waves at the output of the coupler when the device is in transmission mode.

[0059] In this second main embodiment, the coupling section 12 of the two-element coupler 1 connects a first transverse surface of the first waveguide 10 with a second transverse surface of the second waveguide 11, the first and second transverse surfaces being arranged in different planes that are parallel to each other.

[0060] In transmission mode, this two-element coupler 1 splits a wave propagated by the first or second input port (100, 110) into two waves with a 180° phase difference via the coupling section 12. As a result, the two input ports of the septum polarizer 2 are simultaneously excited by these two waves with a 180° phase difference, respectively, to generate two circularly polarized waves with a 180° phase difference.

[0061] 5a and 5b, the coupling portion 12 comprises a plurality of branches 121, each branch having one end connected to a first lateral face of the first waveguide 10 and the other end connected to a second lateral face of the second waveguide 11. Each branch 121 therefore intersects the plane of symmetry of the first and second waveguides (10, 11).

[0062] Each branch 121 comprises a waveguide that propagates waves from an opening in the first waveguide 10 to an opening in the sidewall of the second waveguide 11, or vice versa.

[0063] In an embodiment not shown, each branch 121 has a waveguide extending perpendicular to the sides of the first and second waveguides (10, 11). The cross section of this waveguide may be triangular, square, rectangular, pentagonal, hexagonal, or more generally polygonal. The cross section of this waveguide may also comprise curved sections in addition to or instead of straight sections.

[0064] As mentioned above, in order to reduce the use of printing substrates, certain portions of the two-element coupler according to the second main embodiment are tilted with respect to the printing direction, which is indicated by the z-axis in Figures 5a and 5b and corresponds to the direction of signal propagation within the coupler.

[0065] In particular, the branches 121 may include angled portions to limit the cantilevered portion and facilitate or enable additive manufacturing of the device.

[0066] In one embodiment shown in Figures 5a and 5b, each branch 121 advantageously forms a two-sided roof, with each side adjacent to either the first or second waveguide (10, 11), and the edge of the roof formed by the intersection of the two sides generally lies in a plane perpendicular to the printing direction z.

[0067] The two sides (of the roof) can be sloped so that the edges of the roof point towards the septum polarizer 2 or towards the first and second inlet ports (100, 110). That is, the two-sided roof has a V-shaped cross section pointing in one direction or the other along the printing direction of the z-axis. Such a branch 121 geometry advantageously reduces the cantilevered beam sections, and therefore facilitates its additive manufacturing, in particular by eliminating the need for a printing support.

[0068] Each branch forms an angle of 35° to 55°, preferably 40° to 50° with the side of the adjacent waveguide.

[0069] In one embodiment, the branches 121 are symmetrical about the plane of symmetry of the first and second waveguides (10, 11), i.e., the sides of the roof are symmetrical to each other about the plane of symmetry of the first and second waveguides.

[0070] In one embodiment shown in Figures 6a and 6, each branch 121 advantageously forms two two-sided roofs. More specifically, each branch 121 has: a first two-sided roof (first roof), each side of which is adjacent to a first waveguide or a second waveguide (10, 11); a second two-sided roof (second roof), each side of which is adjacent to the first or second waveguide (10, 11); The first two-sided roof and the second two-sided roof are connected to each other so that the edges of the first roof and the second roof are contained in the same plane. The edge of the first roof forms an angle with the edge of the second roof at the joint of the two roofs.

[0071] In other words, the embodiment shown in Figures 6a and 6b is similar to the embodiment shown in Figures 5a and 5b, except that each branch of the joint forms a bend in a plane that includes the sides of the branch.

[0072] Each of the two sides forms an angle of 35° to 55° with respect to the printing direction, and the angle between the two sides is 70° to 110°.

[0073] In one embodiment, each branch 121 has a two-fold symmetry: in fact, each branch has a first symmetry relative to the plane of symmetry of the first (10) and second (11) waveguides, and a second symmetry relative to a plane perpendicular to the plane of symmetry of the first and second waveguides and containing the printing direction Z.

[0074] As shown in FIGS. 7a and 2b, the orthomode transducer with branch couplers has overall symmetry along the plane containing the septum 22. [Explanation of symbols]

[0075] 1 Two-element coupler 10 First waveguide 11 Second waveguide 100 First input port 101 First output port 110 Second input port 111 Second output port 12 Joint 121 branches 122 Side 123 sides 2 Septum polarizer 200 3rd input port 210 4th input port 201 Third output port 22 Septum z Print direction

Claims

1. a first waveguide (10) with a first input port (100) and a first output port (101) for single polarization; a second waveguide (11) with a second input port (110) and a second output port (111) for single polarization; a coupling portion (12) connecting the first waveguide (10) to the second waveguide (11); Two-element coupler (1) 1. A broadband, linearly polarized orthomode converter obtained by additive manufacturing, comprising: a third input port (200) of single polarization coupled to the first output port (101); a fourth input port (210) of single polarization coupled to the second output port (111); a third output port (201) for single polarization; The septum polarizer (2) further comprises: The first waveguide and the second waveguide (10, 11) are arranged symmetrically with respect to a symmetry plane that includes the septum of the septum polarizer (2). Broadband, linearly polarized orthomode converter obtained by additive manufacturing.

2. 2. The orthogonal mode converter of claim 1, wherein the coupling portion (12) connects a first lateral surface of the first waveguide (10) and a second lateral surface of the second waveguide (11), and the first lateral surface and the second lateral surface are arranged in the same plane.

3. 3. The orthogonal mode converter of claim 2, wherein the first transverse surface corresponds to one of the smallest dimensions of the first waveguide (10) and the second transverse surface corresponds to one of the smallest dimensions of the second waveguide (11).

4. The coupling portion (12) comprises a prism having a trapezoidal base, a first portion of the rectangular face of the prism is in contact with the first lateral face of the first waveguide; a second portion of the rectangular face of the prism is tangent to the second lateral face of the second waveguide; 4. The orthogonal mode transducer of claim 3.

5. The orthomode transducer of claim 4, wherein the coupling portion (12) comprises an impedance matching element.

6. 2. The orthogonal mode converter of claim 1, wherein the coupling portion (12) connects a first lateral surface of the first waveguide (10) to a second lateral surface of the second waveguide (11), the first lateral surface and the second lateral surface being disposed in separate and parallel planes.

7. 7. The orthogonal mode converter of claim 6, wherein the coupling portion (12) comprises a plurality of branches (121), a first end of each branch being connected to the first waveguide (10) and a second end of each branch being connected to the second waveguide (11).

8. 8. The orthogonal mode transducer of claim 7, wherein each branch (121) forms a two-sided roof, a first side of the roof being adjacent to the first lateral surface and a second side of the roof being adjacent to the second lateral surface.

9. The orthogonal mode transducer of claim 8 , wherein an edge of the roof formed by the junction of the first side and the second side is contained in a plane perpendicular to the print direction (Z).

10. the first side forms an angle between 35° and 55° with the first lateral surface of the first waveguide; the second side forms an angle of between 35° and 55° with the second lateral surface of the second waveguide; 10. An orthogonal mode transducer according to claim 8 or 9.

11. Each branch (121) forms two two-sided roofs, and the two two-sided roofs are: a first two-sided roof having a first side adjacent the first lateral surface and a second side adjacent the second lateral surface; a second two-sided roof having a third side adjacent the first lateral surface and a fourth side adjacent the second lateral surface; The orthomode transducer of claim 7 comprising:

12. 12. The orthogonal mode transducer of claim 11, wherein the first and third sides form an angle of 35° to 55° with the first lateral plane, and the second and fourth sides form an angle of 35° to 55° with the second lateral plane.

13. 13. An orthogonal mode converter as described in claim 11 or 12, wherein a first roof edge formed by the junction of the first side portion and the second side portion is at an angle of 35° to 55° with respect to the printing direction (Z), and a second roof edge formed by the junction of the third side portion and the fourth side portion is at an angle of 35° to 55° with respect to the printing direction (Z).

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