Broadband dual-polarization probe horn antenna loaded with arc-feed OMT structure

Abstract

A broadband dual-polarization probe horn antenna loaded with an arc-feed OMT structure comprises a circular four-ridge waveguide and a radiation boundary thereof; the circular four-ridge waveguide is composed of a circular waveguide and an arc-feed OMT structure arranged therein, the arc-feed OMT structure comprises four square waveguides, four straight waveguides and two feeding coaxial lines, the four square waveguides are centrally symmetrically distributed and unconnected, the adjacent square waveguides are vertical, a straight waveguide is loaded and connected below each square waveguide, the bottom end of the straight waveguide is located on the inner bottom surface short-circuit plate of the circular four-ridge waveguide, and the square waveguide and the straight waveguide constitute the four ridges of the circular four-ridge waveguide; one feeding coaxial line radially penetrates into two square waveguides located on the same straight line, and another feeding coaxial line radially penetrates into the other two square waveguides located on the same straight line, and the two feeding coaxial lines have an axial distance to realize dual polarization. The antenna of the present invention has the advantages of wide bandwidth, dual polarization, stable gain, good radiation main lobe characteristics, symmetrical characteristics, etc.

Description

Technical Field

[0001] The invention belongs to the technical field of antennas, and relates to a probe horn antenna applied to an antenna far-field test system, and in particular to a broadband dual-polarization probe horn antenna loaded with an arc-type feeding OMT structure. Background Art

[0002] In antenna test systems, far-field measurement technology is one of the earliest technologies. Far-field measurement technology uses a standard probe test antenna that applies far-field and is placed 2D away from the antenna to be tested. 2 / λ, (D is the radiation aperture size of the antenna to be measured, λ is the working wavelength of the antenna to be measured), and the corresponding far-field radiation characteristics are directly measured. Therefore, far-field measurement technology is widely used in the field of antenna measurement.

[0003] As an important component of the far-field measurement system, the performance of the probe horn antenna will directly affect the efficiency of the entire measurement system. During the antenna test process, we often need to mechanically rotate the test probe antenna to test different polarization results. Therefore, the dual-polarization probe horn antenna is widely used in antenna test systems. However, due to the four-ridge arrangement under the dual-polarization characteristics, its broadband characteristics are often limited. Compared with the probe horn antenna with a dual-ridge structure, its working bandwidth is stretched. Therefore, we hope that the probe horn antenna can provide dual-polarization characteristics while meeting the wider bandwidth characteristics, combined with good radiation pattern symmetry within the working frequency band and the corresponding main lobe characteristics to improve its efficiency in the antenna test system.

[0004] At present, dual-polarization probe horn antennas realized by loading quad-ridge structures are more common in antenna far-field measurement systems. In 2019, Shang Junping and other scholars designed a dual-polarization probe horn antenna with 9 times the frequency working at 2GHz~18GHz based on the Bessel curve structure, but the radiation pattern at the high frequency of 18GHz showed a saddle shape and collapsed; then in the same year, Zeng Qingsheng and other scholars designed a conical dual-polarization probe horn antenna with 8 times the frequency working at 5GHz~40GHz, and studied the influence of different back cavity structures on the overall voltage standing wave ratio. Finally, through the optimization of the reflection back cavity, the designed dual-polarization probe horn antenna has good radiation pattern characteristics, but the bandwidth is narrow. Although the above two have studied the dual-polarization probe horn antenna, the bandwidth characteristics are insufficient. Nowadays, with the rapid development of wireless communication technology, the research on ultra-wideband antennas has gradually become a hot spot. In particular, fields such as radar detection and electromagnetic compatibility testing require probe horn antennas to have characteristics such as wide bandwidth and dual polarization. Summary of the invention

[0005] In order to overcome the disadvantages of the above-mentioned existing technologies and achieve a breakthrough in the above-mentioned wide-band and dual-polarization existing technologies, the purpose of the present invention is to provide a broadband dual-polarization probe horn antenna loaded with an arc-fed OMT structure, which overcomes the problem of too small distributed capacitance value caused by the arrangement between the four ridges, thereby solving the problems of narrow bandwidth and deteriorated radiation characteristics in the high-frequency band of the existing dual-polarization probe horn antenna, and improving the test performance of the entire far-field test system from the perspective of improving the overall performance of the probe horn antenna.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is:

[0007] A broadband dual-polarization probe horn antenna loaded with an arc-fed OMT structure, comprising a circular four-ridge waveguide and its radiation boundary; the circular four-ridge waveguide is composed of a circular waveguide and an arc-fed OMT structure arranged therein, the arc-fed OMT structure includes four rectangular waveguides, four straight waveguides and two feeding coaxial cables, the four rectangular waveguides are symmetrically distributed at the center and not connected, adjacent rectangular waveguides are perpendicular, and a straight waveguide is loaded and connected below each rectangular waveguide, the bottom end of the straight waveguide is located on the inner bottom short-circuit plate of the circular four-ridge waveguide, and the rectangular waveguide and the straight waveguide form the four ridges of the circular four-ridge waveguide; one feeding coaxial cable penetrates radially into two rectangular waveguides on the same straight line, and the other feeding coaxial cable penetrates radially into the other two rectangular waveguides on the same straight line, and the two feeding coaxial cables have an axial distance to achieve dual polarization.

[0008] In one embodiment, the feeding coaxial cable is connected by an SMA connector, which is composed of a coaxial cable feeding connector and a feeding probe inner core contained in the coaxial cable feeding connector; for two rectangular waveguides on the same straight line, the feeding probe inner core penetrates through a through hole on one rectangular waveguide and extends into the other rectangular waveguide to form a monopole radiator structure. By adjusting the ratio of the diameter of the through hole to the diameter of the feeding probe inner core, the characteristic impedance of the feeding coaxial cable is made the same as or close to the characteristic impedance of the circular four-ridge waveguide, so as to achieve impedance matching from the feeding port to the probe horn antenna.

[0009] In one embodiment, the rectangular waveguide has an axial length, a radial width and a third width perpendicular to the radial and axial directions. Taking the symmetry center of the four ridges as the origin o and the radial direction of the rectangular waveguide as the x-axis and y-axis, an xoy plane is established, and the relative end side walls of each rectangular waveguide are subjected to a secondary arc cutting transition; among them, for the rectangular waveguide in the positive y-axis direction, its secondary arc cutting transition method along the positive x-axis direction is as follows:

[0010] Take the first tangent point (hrr, d / 2) in its third width direction, where hrr < w1 / 2, w1 is the value of the third width, and d is the relative end spacing of two rectangular waveguides on the same straight line; let the center of the first tangent circle be (r q1, -d / 3), thus obtaining the expression of the first tangent circle structure in the positive direction of the y-axis and along the positive direction of the x-axis:

[0011] y1={[(r q1 -hrr) 2 +(d / 2+d / 3) 2 ]-(xr q1 ) 2} 0.5 -d / 3,x∈[hrr,d2 / 2]

[0012] Where d2 is the diameter of the through hole through which the inner core of the feeding probe passes;

[0013] Afterwards, a second cutting is performed based on the first cutting circle structure, and the center of the second cutting circle is set to (r q2 , -d / 3), thus obtaining the expression of the second tangent circle structure:

[0014] y2={[(r q2 -d2 / 2) 2 +t 2 ]-(xr q2 ) 2} 0.5 -d / 3,x∈[d2 / 2,w1 / 2]

[0015] where t 2 ={[(r q1 -hrr) 2 +(d / 2+d / 3) 2 ]-(d2 / 2-r q1 ) 2};

[0016] According to the symmetry about the y-axis, the square waveguide in the positive direction of the y-axis is cut along the negative direction of the x-axis by a secondary arc:

[0017] Take the first tangent point (-hrr, d / 2), and set the center of the first tangent circle to (-r q1 , -d / 3), thus obtaining the expression of the first tangent circle structure in the positive direction of the y-axis and along the negative direction of the x-axis:

[0018] y1={[(r q1 -hrr) 2 +(d / 2+d / 3) 2 ]-(x+r q1 ) 2} 0.5 -d / 3,x∈[-hrr,-d2 / 2]

[0019] Let the center of the second tangent circle be (-r q2, -d / 3), thus obtaining the expression of the second tangent circle structure:

[0020] y2={[(r q2 -d2 / 2) 2 +t 2 ]-(x+r q2 ) 2} 0.5 -d / 3,x∈[-d2 / 2,-w1 / 2]

[0021] The secondary arc cutting structure of the other square waveguides is the same.

[0022] In one embodiment, the square waveguide has a groove structure with a height of h on the lower side of one end close to the center of symmetry, so that it is L-shaped, that is, the axial length of the end away from the center of symmetry is h greater than the axial length of the end close to the center of symmetry, thereby forming a resonant matching circuit structure under two polarizations.

[0023] In one embodiment, a truncated cone metal ring reflective back cavity is provided in the circular quad-ridged waveguide, and the truncated cone metal ring reflective back cavity includes a truncated cone metal ring and a short-circuit plate. The outer wall of the truncated cone metal ring is in contact with the outer wall of the circular quad-ridged waveguide, and the interior is a funnel-shaped channel with a top surface larger than the bottom surface. The short-circuit plate is arranged on the short-circuit plate on the inner bottom surface of the circular quad-ridged waveguide, and the bottom end of the truncated cone metal ring is embedded in the short-circuit plate. The straight waveguide is embedded in the truncated cone metal ring, and the top extends into the inner wall of the truncated cone metal ring to be loaded with the square waveguide.

[0024] In one embodiment, the top radius of the truncated cone metal ring is consistent with the radius of the circular quad-ridged waveguide, both of which are r2. By adjusting the size of the bottom radius r3 of the truncated cone metal ring, the angle θ with the inner wall of the circular quad-ridged waveguide is changed. The angle θ controls the slope of the truncated cone metal ring reflection back cavity, thereby changing the transmission characteristics of the cavity to the radiation field.

[0025] In one embodiment, the radiation boundary adopts a conical open waveguide structure, connected to the top circular end face of the circular four-ridge waveguide, and its input port is consistent with the circular four-ridge waveguide in size, and the radius is r2, to ensure the continuity of radiation to the port surface; its output port radius is r1, which is the same as the composite type x p The spacing of the ridges remains consistent.

[0026] In one embodiment, four symmetrical composite ridges are arranged on the inner wall of the radiation boundary. The composite ridge is a flat plate structure, whose side edges are connected to the inner wall of the radiation boundary, the bottom edge is connected to the top of a square waveguide, and the remaining edges are arc-shaped transitions to form ridge edges and extend out of the mouth surface of the radiation boundary.

[0027] In one embodiment, the composite ridge is divided into two sections, which are a circular four-ridge waveguide transition section x pComposite ridge structure and oral-facial transition section p The composite ridge structure is connected and the coordinate system is established with the yoz plane where the cross section of the probe horn antenna is located. The composite ridge satisfies the continuity in mathematical form and realizes the following function form:

[0028]

[0029] In the above formula, A and p are constants. The constant A is used to adjust the curvature of the ridge structure near the feed end, and p is used to adjust the curvature of the ridge structure near the mouth surface. Looking along the y-axis, the starting point of the mouth surface arc surface is r1-r 11 , the end point is r1, r 11 Determines the relative spacing of the ridge structure at the mouth surface. Taking the overall structural plane of the composite ridge as the reference, the larger the A and p values, the more the overall ridge structure expands outward. 11 The larger the mouth, the smaller the distance between the ridges and the more obvious the curvature.

[0030] In one embodiment, the ridge edge of the composite ridge is loaded with a ridge transition groove structure, wherein the ridge transition groove structure is based on the cross section of the square waveguide with a length x p The ridge curve contour is formed by wrapping around, and finally forms a transition section x loaded on the circular four-ridge waveguide p The first ridge transition groove structure of the ridge structure and the composite x loaded on the transition section of the mouth surface p The second ridge transition groove structure of the type ridge structure, the ridge transition groove structure is consistent with the axial length of the radiation boundary.

[0031] Compared with the prior art, the present invention has the following beneficial effects:

[0032] First, the present invention improves the dual-polarization quad-ridged waveguide feeding OMT structure by designing a secondary arc cutting transition structure for the feeding through hole loaded by the quad-ridged waveguide and the side of the quad-ridged waveguide. The principle is that the quad-ridged waveguide cross section adopts the secondary arc cutting technology to increase the distributed inductance between the quad-ridged waveguides, thereby reducing the low-frequency cutoff frequency of the probe horn antenna, realizing the dual-polarization characteristics and widening the bandwidth characteristics.

[0033] Second, the present invention breaks the conventional exponential ridge curve structure by adopting a new composite x p The ridge transition structure is designed based on the arc-shaped feed OMT structure, and the probe horn antenna aperture is processed with an arc transition structure to reduce the diffraction of electromagnetic waves at the probe horn antenna aperture. At the same time, the ridge transition groove structure between the composite ridge is designed based on the arc-shaped feed OMT structure, so that the characteristic impedance can be smoothly transitioned from the feed to the radiation aperture. Based on the shaping of the ridge curve, the voltage standing wave ratio of the dual-polarized probe horn antenna designed in this way is less than 2.1 in the working frequency band of 1.2GHz to 18GHz.

[0034] Third, the present invention loads a truncated cone metal ring reflective back cavity at the circular quad-ridge waveguide, and adjusts the distribution characteristics of the field in the cavity by changing the radius of the truncated cone metal ring embedded in the short-circuit plate. The continuity of the cross section suppresses the generation of high-order modes to a certain extent, thereby improving the directivity and stability of the radiation pattern of the probe horn antenna at high frequencies. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a perspective view of the overall structure of the present invention.

[0036] Figure 2 It is a cross-sectional view of the overall arrangement of the present invention along the axial direction.

[0037] Figure 3 It is the dimension mark of the circular quad-ridge waveguide of the present invention.

[0038] Figure 4 This is the arc-type feed OMT structure diagram of the present invention

[0039] Figure 5 It is the overall structure diagram of the coaxial converter of the present invention.

[0040] Figure 6 It is a cross-sectional view of the internal structure of the circular quad-ridged waveguide reflective back cavity of the present invention.

[0041] Figure 7 The composite type x of the present invention p Schematic diagram of the ridge structure.

[0042] Figure 8 It is a cross-sectional view of the ridge transition groove structure of the present invention.

[0043] Fig. 9 It is a schematic diagram of the voltage standing wave ratio of the present invention.

[0044] Fig.10 It is a schematic diagram of the gain of the present invention that varies with the operating frequency.

[0045] Fig.11 It is a schematic diagram of port isolation under the dual polarization characteristics of the present invention.

[0046] Fig.12 It is the radiation pattern of the E-plane and H-plane in the rectangular coordinate system at 2 GHz, 6 GHz, 12 GHz and 18 GHz of the present invention. DETAILED DESCRIPTION

[0047] In order to make the purpose, features and advantages of the present invention more obvious and easy to understand, the invention is further described in detail below with reference to the accompanying drawings and embodiments, but they are not intended to be a basis for limiting the invention in any way.

[0048] The present invention is a broadband dual-polarization probe horn antenna loaded with an arc-type feed OMT structure, and the operating frequency band is 1.2 GHz to 18 GHz. Figure 1 , Figure 2 and Figure 3 , which mainly includes a circular quad-ridged waveguide 2 and a radiation boundary 4 thereof, wherein the circular quad-ridged waveguide 2 is composed of a circular waveguide and an arc-type feeding OMT structure 3 disposed therein. For ease of description, in the present invention, the direction in which the short-circuit plate of the circular waveguide is located is defined as the "bottom" or "lower part", the direction in which the circular waveguide connects to the radiation boundary 4 is defined as the "top" or "upper part", and the axial direction of the circular waveguide is defined as the "axial direction" in the description of the present invention.

[0049] refer to Figure 4 and Figure 5 The arc-type feeding OMT structure 3 is located at the inner top surface of the circular quad-ridged waveguide 2, and mainly includes four square waveguides 31, four straight waveguides 32 and two feeding coaxial lines 35. The four square waveguides 31 are symmetrically distributed and have no connection. The adjacent square waveguides 31 are vertical, and the symmetry center is located in the axial direction of the circular waveguide. For the convenience of description, the center is defined as the origin o. A straight waveguide 32 is loaded and connected below each square waveguide 31. The top of the straight waveguide 32 is connected to the bottom under the square waveguide 31, and the bottom is located on the short-circuit plate on the inner bottom surface of the circular quad-ridged waveguide 2. The square waveguide 31 and the straight waveguide 32 constitute the "four ridges" of the circular quad-ridged waveguide 2. One feeding coaxial line 35 radially penetrates into two square waveguides 31 located on the same straight line, and another feeding coaxial line 35 radially penetrates into the other two square waveguides 31 located on the same straight line, and the two feeding coaxial lines 35 have an axial distance to achieve dual polarization.

[0050] In the present invention, the arc-feed OMT structure 3 realizes dual-polarization characteristics through the orthogonal symmetrical arrangement of four-ridged waveguides.

[0051] Reference Figure 3 In one embodiment of the present invention, the radius r2 of the mouth surface of the circular quad-ridge waveguide 2 is mainly determined by the operating cutoff frequency λ c The general circular waveguide works in the main mode and satisfies 2.62r2<λ c <3.41r2, but due to the loading ridge structure, the cutoff frequency of the main mode is reduced, and the cutoff wavelength of the main mode is greater than 3.41r2, and its bandwidth characteristics are improved, and its axial length l4 should be an integer multiple of 1 / 4 of the wavelength corresponding to the operating frequency. In this embodiment, r2=15.4mm, l4=20mm.

[0052] In some embodiments of the present invention, the feeding coaxial line 35 is connected by an SMA connector, and is composed of a coaxial cable feeding connector 351 and a feeding probe core 352 contained in the coaxial cable feeding connector 351; for two square waveguides 31 on the same straight line, the feeding probe core 352 passes through a through hole 353 on one square waveguide 31 and extends into the other square waveguide 31 to form a monopole radiator structure. By adjusting the ratio of the diameter of the through hole 353 to the diameter of the feeding probe core 352, the characteristic impedance of the feeding coaxial line 35 is made the same or similar to the characteristic impedance of the circular quad-ridged waveguide 2, thereby achieving impedance matching from the feeding port to the probe horn antenna.

[0053] Reference Figure 5 , its size d2 / d1=2.3, meets the characteristic impedance of 50Ω of the coaxial line. In this embodiment, d1=0.9mm, d2=2.1mm; while ensuring that the inner core 352 of the dual coaxial line does not short-circuit, the inner cores 352 of the feeding probes are 2mm apart to improve the isolation characteristics of the dual ports within the operating frequency range.

[0054] In some embodiments of the present invention, in the arc-type feeding OMT structure 3, the secondary arc cutting technology is used to increase the cross-sectional area of ​​the ridge waveguide, that is, the opposite surfaces of the four square waveguides 31 are partially cut, mainly by performing secondary arc cutting transition on the through hole 353 of the inner core 352 of the feeding probe and the side walls of the four square waveguides 31, thereby increasing the distributed inductance value between the four ridge-arranged guides, thereby reducing the low-frequency cutoff frequency of the probe horn antenna. This structure is one of the technical means of the present invention to achieve dual-polarization characteristics, while widening the frequency band characteristics.

[0055] For ease of description, the square waveguide 31 is defined as having an axial length along the axial direction, a radial width along the radial direction of the circular waveguide, and a third width perpendicular to both the radial direction and the axial direction. The symmetry center of the four ridges is taken as the origin o, and the radial direction of the square waveguide 31 is taken as the x-axis and the y-axis, and an xoy plane is established, such as Figure 4 As shown in the figure, the right side is defined as the positive direction of the y-axis, and the downward side is defined as the positive direction of the x-axis, and a secondary arc cutting transition is performed on the opposite end side walls of each square waveguide 31. The arc cutting transition method and structure for the square waveguides 31 distributed on different coordinate axes are the same, but due to the coordinate system, the structural design expression will be slightly different, which needs to be explained here.

[0056] Based on the fact that the secondary arc cutting structures on the two square waveguides 31 along the y-axis are symmetrically distributed along the y-axis, the secondary arc cutting transition mode along the positive direction of the x-axis for the square waveguide 31 in the positive direction of the y-axis is described in detail as follows:

[0057] In order to eliminate the short circuit phenomenon caused by the ridge thickness, i.e., the third width w1, the first tangent point (hrr, d / 2) is taken in the third width direction, where hrr < w1 / 2, w1 is the value of the third width, and d is the distance between the opposite ends of the two square waveguides 31 on the same straight line; the center of the first tangent circle is (r q1 , -d / 3), thus obtaining the expression of the first tangent circle structure 33 in the positive direction of the y-axis and along the positive direction of the x-axis:

[0058] y1={[(r q1 -hrr) 2 +(d / 2+d / 3) 2 ]-(xr q1 ) 2} 0.5 -d / 3, x∈[hrr,d2 / 2]

[0059] Wherein d2 is the diameter of the through hole 353 through which the inner core 352 of the feeding probe passes;

[0060] Afterwards, in order to minimize the coupling effect in the air under the dual-feed structure, the edge of the square waveguide 31 is improved, and a second cut is performed on the basis of the first cut circle structure 33, and the center of the second cut circle is set to (r q2 , -d / 3), thus obtaining the expression of the second tangential circle structure 34:

[0061] y2={[(r q2 -d2 / 2) 2 +t 2 ]-(xr q2 ) 2} 0.5 -d / 3, x∈[d2 / 2,w1 / 2]

[0062] where t 2 ={[(r q1 -hrr) 2 +(d / 2+d / 3) 2 ]-(d2 / 2-r q1 ) 2};

[0063] According to the symmetry about the y-axis, the square waveguide 31 in the positive direction of the y-axis cuts the transition structure along the secondary arc in the negative direction of the x-axis:

[0064] The first tangent point is (-hrr, d / 2), and the center of the first tangent circle is (-r q1 , -d / 3), thus obtaining the expression of the first tangent circle structure 33 in the positive direction of the y-axis and along the negative direction of the x-axis:

[0065] y1={[(r q1 -hrr)2 +(d / 2+d / 3) 2 ]-(x+r q1 ) 2} 0.5 -d / 3, x∈[-hrr, -d2 / 2]

[0066] Let the center of the second tangent circle be (-r q2 , -d / 3), thus obtaining the expression of the second tangent circle structure (34):

[0067] y2={[(r q2 -d2 / 2) 2 +t 2 ]-(x+r q2 ) 2} 0.5 -d / 3, x∈[-d2 / 2, -w1 / 2]

[0068] The secondary arc cutting structures of the other square waveguides 31 are the same, which are described in detail as follows.

[0069] According to the secondary arc cutting transition expression of the square waveguide 31 along the positive direction of the y-axis, based on the symmetry of the x-axis, the secondary arc cutting transition structure of the square waveguide 31 in the negative direction of the y-axis along the positive direction of the x-axis is:

[0070] The first tangent point is (hrr, -d / 2), the center of the first tangent circle is (r q1 , d / 3), thereby obtaining the expression of the first tangent circle structure 33 in the negative direction of the y-axis and along the positive direction of the x-axis:

[0071] y1=-{[(r q1 -hrr) 2 +(d / 2+d / 3) 2 ]-(xr q1 ) 2} 0.5 +d / 3,x∈[hrr,d2 / 2]

[0072] The center of the second tangent circle is (r q2 , d / 3), thereby obtaining the expression of the second tangential circle structure 34:

[0073] y2=-{[(r q2 -d2 / 2) 2 +t 2 ]-(xr q2 ) 2} 0.5 +d / 3,x∈[d2 / 2,w1 / 2]

[0074] According to the symmetry about the y-axis, the square waveguide 31 in the negative direction of the y-axis cuts the transition structure along the negative direction of the x-axis in a secondary arc: the first tangent point is (-hrr, -d / 2), and the center of the first tangent circle is (-r q1 , d / 3), thereby obtaining the expression of the first tangent circle structure 33 in the negative direction of the y-axis and along the negative direction of the x-axis:

[0075] y1=-{[(r q1 -hrr) 2 +(d / 2+d / 3) 2 ]-(x+r q1 ) 2} 0.5 +d / 3,x∈[-hrr,-d2 / 2]

[0076] The center of the second tangent circle is (-r q2 , d / 3), thereby obtaining the expression of the second tangential circle structure 34:

[0077] y2=-{[(r q2 -d2 / 2) 2 +t 2 ]-(x+r q2 ) 2} 0.5 +d / 3,x∈[-d2 / 2,-w1 / 2]

[0078] The above is a design formula for the secondary arc transition structure of the square waveguide 31 in the y-axis direction, and the design formula for the secondary arc transition structure of the square waveguide 31 in the x-axis direction is further explained.

[0079] Take the first tangent point (d / 2, hrr) in the third width direction, hrr<w1 / 2, w1 is the third width value, d is the distance between the opposite ends of the two square waveguides 31 on the same straight line; set the center of the first tangent circle to (-d / 3, r q1 ), thus obtaining the expression of the first tangent circle structure 33 in the positive direction of the x-axis and along the positive direction of the y-axis:

[0080] x1={[(r q1 -hrr) 2 +(d / 2+d / 3) 2 ]-(yr q1 ) 2} 0.5 -d / 3, y∈[htr,d2 / 2]

[0081] Wherein d2 is the diameter of the through hole 353 through which the inner core 352 of the feeding probe passes;

[0082] Afterwards, a second cutting is performed on the basis of the first cutting circle structure 33, and the center of the second cutting circle is set to (-d / 3, r q2 ), thereby obtaining the expression of the second tangential circle structure 34:

[0083] x2={[(r q2 -d2 / 2) 2 +t 2 ]-(yr q2 ) 2} 0.5 -d / 3, y∈[d2 / 2,w1 / 2]

[0084] where t 2 ={[(r q1 -hrr) 2 +(d / 2+d / 3) 2 ]-(d2 / 2-r q1 ) 2}

[0085] According to the symmetry about the x-axis, for the secondary arc transition structure of the square waveguide 31 in the positive direction of the x-axis along the negative direction of the y-axis: the first tangent point is (d / 2, -hrr), and the center of the first tangent circle is (-d / 3, -r q1 ), thus obtaining the expression of the first tangent circle structure 33 in the positive direction of the x-axis and along the negative direction of the y-axis:

[0086] x1={[(r q1 -hrr) 2 +(d / 2+d / 3) 2 ]-(y+r q1 ) 2} 0.5 -d / 3, y∈[-hrr, -d2 / 2]

[0087] The center of the second tangent circle is (-d / 3, -r q2 ), thereby obtaining the expression of the second tangential circle structure 34:

[0088] x2={[(r q2 -d2 / 2) 2 +t 2 ]-(y+r q2 ) 2} 0.5 -d / 3, y∈[-d2 / 2, -w1 / 2]

[0089] According to the design expression of the secondary arc cutting transition of the square waveguide 31 along the positive direction of the x-axis, based on the y-axis symmetry, the secondary arc cutting structure of the square waveguide 31 along the negative direction of the x-axis and along the positive direction of the y-axis: the first tangent point is (-d / 2, hrr), the center of the first tangent circle is (d / 3, r q1), thus obtaining the expression of the first tangent circle structure 33 in the negative direction of the x-axis and along the positive direction of the y-axis:

[0090] x1=-{[(r q1 -hrr) 2 +(d / 2+d / 3) 2 ]-(yr q1 ) 2} 0.5 +d / 3,y∈[hrr,d2 / 2]

[0091] The center of the second tangent circle is (d / 3, r q2 ), thereby obtaining the expression of the second tangential circle structure 34:

[0092] x2=-{[(r q2 -d2 / 2) 2 +t 2 ]-(yr q2 ) 2} 0.5 +d / 3,y∈[d2 / 2,w1 / 2]

[0093] According to the symmetry about the x-axis, for the secondary arc transition structure of the square waveguide 31 in the negative direction of the x-axis along the negative direction of the y-axis: the first tangent point is (-d / 2, -hrr), the center of the first tangent circle is (d / 3, -hrr q1 ), thus obtaining the expression of the first tangent circle structure 33 in the negative direction of the x-axis and along the negative direction of the y-axis:

[0094] x1=-{[(r q1 -hrr) 2 +(d / 2+d / 3) 2 ]-(y+r q1 ) 2} 0.5 +d / 3,y∈[-hrr,-d2 / 2]

[0095] The center of the second tangent circle is (d / 3, -r q2 ), thereby obtaining the expression of the second tangential circle structure 34:

[0096] x2=-{[(r q2 -d2 / 2) 2 +t 2 ]-(y+r q2 ) 2} 0.5 +d / 3,y∈[-d2 / 2,-w1 / 2]

[0097] The above is a detailed description of the arc transition structure design in the arc feed OMT structure 3. q1 , rq2 It is a variable, and the overall performance is adjusted by changing the two. In practice, its value is: r q1 =2.0mm, r q2 =7.5mm. Combined Figure 4 , the ridge spacing d = 1 mm, the ridge width w1 = 4 mm. Looking along the x-axis, the first tangent point hrr = 0.46 mm, the radius r of the first tangent circle structure 33 q1 =2mm, the radius r of the second cutting circle structure 34 q2 =6mm.

[0098] In this embodiment, the cross-sectional area of ​​the ridge waveguide section is increased by the secondary arc transition structure, the overall distributed inductance between the four ridge waveguides is increased, and the low-frequency cutoff frequency is reduced, thereby achieving bandwidth expansion. The design of the first cut-circle structure 33 mainly avoids the short circuit phenomenon caused by the ridge spacing and ridge width due to the size; the design of the second cut-circle structure 34 mainly reduces the coupling degree between the dual probe cores 352. Thus, dual polarization characteristics are achieved while taking into account broadband characteristics.

[0099] Reference Figure 6 In some embodiments of the present invention, a truncated cone metal ring reflective back cavity 7 is provided in the circular quad-ridged waveguide 2. The truncated cone metal ring reflective back cavity 7 is loaded at the short-circuit plate on the inner bottom surface of the circular quad-ridged waveguide 2, and the whole presents a funnel-shaped structure, which mainly includes a truncated cone metal ring 71 loaded along the wall of the circular quad-ridged waveguide 2 and a short-circuit plate 72 loaded on the short-circuit surface. Specifically, the outer wall of the truncated cone metal ring 71 fits with the outer wall of the circular quad-ridged waveguide 2, and the interior is a funnel-shaped channel with a top surface larger than the bottom surface. The short-circuit plate 72 is provided on the short-circuit plate on the inner bottom surface of the circular quad-ridged waveguide 2, and the bottom end of the truncated cone metal ring 71 is embedded in the short-circuit plate 72. The straight waveguide 32 is embedded in the truncated cone metal ring 71, and the top extends into the inner wall of the truncated cone metal ring 71, and is loaded with the square waveguide 31.

[0100] In some embodiments of the present invention, the top radius of the truncated cone metal ring 71 is consistent with the radius of the circular quad-ridged waveguide 2, both of which are r2, and its bottom end is directly embedded in the short-circuit plate 72. By adjusting the size of the bottom radius r3 of the truncated cone metal ring 71, the angle θ with the inner wall of the circular quad-ridged waveguide 2 is changed. The angle θ controls the slope of the truncated cone metal ring reflection back cavity 7, thereby changing the transmission characteristics of the cavity to the radiation field. Its main function is to eliminate the discontinuity of the structure, to a certain extent suppress the generation of high-order modes, improve the distribution characteristics of the radiation field in the cavity, suppress the generation of high-order modes, and achieve the directionality and stability of the radiation pattern.

[0101] In this embodiment, the radius of the truncated cone metal ring 71 is consistent with the radius of the circular quad-ridge waveguide 2, r2 = 15.4 mm, and the radius r3 of the truncated cone metal ring 71 embedded in the short-circuit plate structure 72 is 7 mm, and the inclination angle θ of the formed curved surface is 25°. Figure 6 , wherein h1 = 5 mm, h2 = 1.7 mm, h3 = 6.8 mm, h4 = 6 mm. The height l3 of the frustum-shaped metal ring 71 is 14.3 mm.

[0102] In this embodiment, a truncated cone metal ring reflective back cavity 71 is designed in the circular quad-ridge waveguide 2. This structure suppresses electromagnetic waves radiated in high-order modes at high frequencies, so that the main mode radiation is concentrated in the ridge structure, thereby improving the directionality and stability of the E-plane and H-plane radiation patterns within the frequency band.

[0103] Reference Figure 5 In a linear polarization port of an embodiment of the present invention, a square waveguide 31 has a slot structure with a height of h on the lower side of one end close to the symmetry center, so that it is L-shaped, that is, the axial length of the end away from the symmetry center is greater than the axial length of the end close to the symmetry center by h, thereby forming a resonant matching circuit structure under two polarizations. For example, h=1.67 mm.

[0104] In this embodiment, the slotted structure mainly plays a role in forming a good resonant circuit between the circular quad-ridge waveguide 2 under the polarization, the truncated cone metal ring reflective back cavity 7 and the probe inner core 352. The problem of impedance mismatch at high frequencies caused by the spacing between the probe inner core structures 352 is overcome.

[0105] In some embodiments of the present invention, the radiation boundary 4 adopts a conical open waveguide structure, connected to the top circular end face of the circular four-ridge waveguide 2. In order to make the radiation boundary 4 have a good transition to the radiated electromagnetic wave, its input port is consistent with the size of the circular four-ridge waveguide 2, that is, the root radius of the radiation boundary 4 and the radius of the circular four-ridge waveguide 2 are both r2, ensuring the continuity of radiation to the mouth surface; its output port radius, that is, the radiation aperture radius, is consistent with the longitudinal spacing of the ridge end (that is, the spacing of the composite ridge 5), both of which are r1. For example, r2 = 15.4mm, r1 = 65mm; at the same time, the thickness of the radiation boundary 4 also meets the requirements of processing rivets to fix the internal ridge structure.

[0106] Reference Figure 7 In some embodiments of the present invention, four symmetrical composite ridges 5 are arranged on the inner wall of the radiation boundary 4. The composite ridge 5 is a flat plate structure, whose side edges are connected to the inner wall of the radiation boundary 4, the bottom edge is connected to the top of a square waveguide 31, and the remaining edges are formed by arc transition to form ridge edges. The composite ridge 5 is one of the structures for the probe horn antenna to achieve wide-band characteristics. It extends out of the mouth of the radiation boundary 4 and adopts an arc transition structure, which reduces the diffraction of electromagnetic waves at the end of the ridge structure.

[0107] In some embodiments of the present invention, the conventional exponential ridge curve form is broken, and the composite ridge 5 is divided into two sections, which are the circular four-ridge waveguide transition section x p Ridge structure 51 and mouth surface transition section composite x p The composite ridge structure 52 is connected to form a coordinate system in the yoz plane where the cross section of the probe horn antenna is located, and the composite ridge 5 satisfies the continuity in mathematical form to achieve the following function form:

[0108]

[0109] In the above formula, A and p are both constants. The constant A is mainly used to adjust the curvature of the ridge structure near the feed end, and p is mainly used to adjust the curvature of the ridge structure near the mouth surface. Looking along the y-axis, the mouth surface arc surface, i.e., the mouth surface transition section composite x p The starting point of the ridge structure 52 is r1-r 11 , the end point is r1, r 11 Determines the relative spacing of the ridge structure at the mouth surface. Taking the overall structural plane of the composite ridge 5 as the reference, the larger the A and p values, the more the overall ridge structure expands outward. 11 The larger the mouth, the smaller the distance between the ridges and the more obvious the curvature.

[0110] For example, in the circular quad-ridge waveguide transition section x p The length of the ridge structure 51 is l1 = 200 mm, and the length of the ridge structure extending from the radiation aperture is l2 = 15 mm. The curvature of the aperture arc is determined by r 11 To avoid the diffraction of electromagnetic waves at the aperture, 11 =29mm, and set A=0.99, p=3.2.

[0111] In this embodiment, the composite ridge 5 reduces the diffraction of the radiated electromagnetic wave at the end of the ridge by imparting properties to the ridge curve and adopting an arc transition treatment on the aperture surface of the probe horn antenna.

[0112] Reference Figure 8 In some embodiments of the present invention, the ridge edge of the composite ridge 5 is loaded with a ridge transition groove structure 6, and the ridge transition groove structure 6 is based on the cross section of the square waveguide 31 with x p The ridge curve contour is formed by wrapping around, and finally forms a transition section x loaded on the circular four-ridge waveguide p The first ridge transition groove structure 61 of the ridge structure 51 and the composite x loaded on the mouth surface transition section p The second ridge transition groove structure 62 of the ridge structure 52 is designed to avoid structural mutation caused by digging out the ridge transition groove structure 6 of the composite ridge 5. Therefore, the axial length of the ridge transition groove structure 6 is consistent with that of the radiation boundary 4, which is l1, l1=200 mm.

[0113] The ridge transition groove structure 6 realizes the transition of the characteristic impedance from the arc-type feeding OMT structure 3 to the composite ridge 5, that is, realizes the smooth transition of the characteristic impedance from the feeding point to the radiation aperture.

[0114] In a complete structure of the present invention, the antenna mainly includes a flange fixing structure 1, a circular four-ridge waveguide 2, a truncated cone metal ring reflective back cavity 7, a radiation boundary structure 4, a composite x p The ridge structure 5 and the ridge transition groove structure 6 have an operating frequency band of 1.2 GHz to 18 GHz, reaching 15 times the frequency, and have good port isolation, gain, radiation pattern stability, and good main lobe characteristics and directivity.

[0115] The effect of the present invention can be further illustrated by the following simulation:

[0116] like Fig. 9 The figure shows the voltage standing wave ratio of the broadband dual-polarization probe horn antenna of this embodiment. In the working frequency band of 1.2 GHz to 18 GHz, the overall voltage standing wave ratio is less than 2.1, but in the working frequency band of 2 GHz to 3 GHz and 16 GHz to 18 GHz, the voltage standing wave ratio is as high as about 2.1. The bandwidth is widened under the dual-polarization characteristic, achieving a 15-fold frequency effect.

[0117] like Fig.10 As shown, this is a gain curve of the broadband dual-polarization probe horn antenna of this embodiment that varies with frequency. Within the operating frequency band range of 1.2GHz to 18GHz, the gain is between 5.0dBi and 24.0dBi. The gain consistency is good under the dual-polarization characteristics and there is no gain drop in the full frequency band. The gain has good stability and a wide gain bandwidth.

[0118] like Fig.11 As shown, it is a schematic diagram of the port isolation of the broadband dual-polarization probe horn antenna of this embodiment. The port isolation is greater than 30dB in the operating frequency band range of 1.2GHz to 18GHz. The designed arc-feed OMT structure achieves the reduction of the coupling effect of the dual-feed probe in the air to a certain extent.

[0119] like Fig.12 As shown in the figure, it is the radiation pattern of the broadband dual-polarization probe horn antenna in the rectangular coordinate system of this embodiment. The E-plane and H-plane radiation patterns at 2GHz, 6GHz, 14GHz, and 18GHz are selected. It can be seen that there is no split lobe or high side lobe phenomenon on the E-plane and H-plane, and the maximum level difference between the main lobe and the side lobe is greater than 10dBi, which meets the application of the probe horn antenna in the test system.

[0120] In summary, the broadband dual-polarization probe horn antenna of the present invention firstly designs the feeding structure innovatively and designs the arc-type feeding OMT structure, which realizes the increase of the cross-sectional area of ​​the ridge waveguide through the design of the secondary arc transition cutting structure, reduces the low-frequency cutoff frequency by increasing the distributed inductance between ridges, and also ensures the dual-polarization characteristics; secondly, the ridge structure that plays a major transmission role in the radiation characteristics is improved by shaping, breaking the conventional exponential ridge curve and adopting a composite x p The curve structure is designed, and the ridge transition groove structure is designed according to the new OMT structure, which realizes a good transition of the characteristic impedance from the feed port to the ridge end; finally, by loading a truncated cone metal ring on the reflective back cavity of the dual-polarization probe horn antenna, the slope of its cross section is changed by changing the radius of the embedded short-circuit plate. The continuity of the structure avoids the generation of abrupt structures, improves defects such as the split lobes of the radiation pattern, and improves the overall radiation directivity and stability of the probe horn antenna. By optimizing various structural parameters, a broadband dual-polarization probe horn antenna with good radiation characteristics is finally realized.

[0121] The above is a composite x-based p The broadband dual-polarization probe horn antenna loaded with a ridge arc feed OMT structure is introduced in detail, and the principle and implementation of the present invention are explained and implemented by applying a detailed structural design. The description of the above embodiment is only used to help understand the method and core idea of ​​the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A broadband dual-polarization probe horn antenna loaded with an arc-type feed (OMT) structure, comprising a circular quad-ridge waveguide (2) and a radiation boundary (4) thereof; characterized in that: The circular four-ridged waveguide (2) is composed of a circular waveguide and an arc-type feeding structure (3) arranged therein. The arc-type feeding structure (3) comprises four square waveguides (31), four straight waveguides (32) and two feeding coaxial lines (35). The four square waveguides (31) are centrally symmetrically distributed and unconnected. Adjacent square waveguides (31) are perpendicular. A straight waveguide (32) is loaded and connected below each square waveguide (31). The bottom end of the straight waveguide (32) is located on a short-circuit plate on the inner bottom surface of the circular four-ridged waveguide (2). The square waveguides (31) and the straight waveguides (32) constitute four ridges of the circular four-ridged waveguide (2). One feeding coaxial line (35) radially penetrates into two square waveguides (31) located on the same straight line, and another feeding coaxial line (35) radially penetrates into another two square waveguides (31) located on the same straight line. The two feeding coaxial lines (35) have an axial distance to achieve dual polarization.

2. According to the broadband dual-polarization probe horn antenna loaded with the circular arc feed (OMT) structure of claim 1, it is characterized in that: The feeding coaxial line (35) is connected by an SMA connector and is composed of a coaxial cable feeding connector (351) and a feeding probe inner core (352) contained in the coaxial cable feeding connector (351); for two square waveguides (31) on the same straight line, the feeding probe inner core (352) passes through a through hole (353) on one square waveguide (31) and then extends into the other square waveguide (31), forming a monopole radiator structure; by adjusting the ratio of the diameter of the through hole (353) and the feeding probe inner core (352), the characteristic impedance of the feeding coaxial line (35) is made the same as or close to the characteristic impedance of the circular quad-ridged waveguide (2), thereby achieving impedance matching from the feeding port to the probe horn antenna.

3. According to claim 2, the broadband dual-polarization probe horn antenna loaded with an arc-type feed (OMT) structure is characterized in that: The square waveguide (31) has an axial length, a radial width and a third width perpendicular to the radial and axial directions. The symmetry center of the four ridges is taken as the origin o, the radial direction of the square waveguide (31) is taken as the x-axis and the y-axis, and an xoy plane is established. Secondary arc cutting and transition are performed on the side walls of the opposite ends of each square waveguide (31); wherein, for the square waveguide (31) in the positive direction of the y-axis, the secondary arc cutting and transition along the positive direction of the x-axis is performed as follows: Take a first tangent point (hrr, d / 2) in its third width direction, where hrr < w1 / 2, w1 is the value of the third width, and d is the relative end spacing of two square waveguides (31) on the same straight line; let the center of the first tangent circle be (r q1 , -d / 3), thereby obtaining the expression of the first tangent circle structure (33) in the positive y-axis direction and along the positive x-axis direction: y1={[(r q1 -hrr) 2 +(d / 2+d / 3) 2 ]-(x-r q1 ) 2 } 0.5 -d / 3,x∈[hrr,d2 / 2] Wherein d2 is the diameter of the through hole (353) through which the inner core (352) of the feeding probe passes; Afterwards, a second cutting is performed on the basis of the first cutting circle structure (33), and the center of the second cutting circle is set to (r q2 , -d / 3), thus obtaining the expression of the second tangent circle structure (34): y2={[(r q2 -d2 / 2) 2 +t 2 ]-(x-r q2 ) 2 } 0.5 -d / 3,x∈[d2 / 2,w1 / 2] where t 2 ={[(r q1 -hrr) 2 +(d / 2+d / 3 2 )]-d(2 / 2-r q1 2 ); According to the symmetry about the y-axis, the square waveguide (31) in the positive direction of the y-axis is cut and transitioned in the secondary arc along the negative direction of the x-axis: Take the first tangent point (-hrr, d / 2), and set the center of the first tangent circle to (-r q1 , -d / 3), thus obtaining the expression of the first tangent circle structure (33) in the positive direction of the y-axis and along the negative direction of the x-axis: y1={[(r q1 -hrr) 2 +(d / 2+d / 3) 2 ]-(x+r q1 ) 2 } 0.5 -d / 3,x∈[-hrr,-d2 / 2] Let the center of the second tangent circle be (-r q2 , -d / 3), thus obtaining the expression of the second tangent circle structure (34): y2={[(r q2 -d2 / 2) 2 +t 2 ]-(x+r q2 ) 2 } 0.5 -d / 3,x∈[-d2 / 2,-w1 / 2] The secondary arc cutting structure of the remaining square waveguides (31) is the same.

4. The broadband dual-polarization probe horn antenna loaded with an arc-type feed (OMT) structure according to claim 2 or 3, characterized in that: The square waveguide (31) is provided with a slot structure with a height of h on the lower side of one end close to the symmetry center, so that it is L-shaped, that is, the axial length of the end away from the symmetry center is greater than the axial length of the end close to the symmetry center by h, thereby forming a resonant matching circuit structure under two polarizations.

5. The broadband dual-polarization probe horn antenna loaded with an arc-type feed (OMT) structure according to claim 1, characterized in that: A truncated cone metal ring reflective back cavity (7) is arranged in the circular four-ridged waveguide (2), and the truncated cone metal ring reflective back cavity (7) comprises a truncated cone metal ring (71) and a short-circuit plate (72). The outer wall of the truncated cone metal ring (71) is in contact with the outer wall of the circular four-ridged waveguide (2), and the interior is a funnel-shaped channel with a top surface larger than a bottom surface. The short-circuit plate (72) is arranged on the short-circuit plate on the inner bottom surface of the circular four-ridged waveguide (2), and the bottom end of the truncated cone metal ring (71) is embedded in the short-circuit plate (72). The straight waveguide (32) is embedded in the truncated cone metal ring (71), and the top extends into the inner wall of the truncated cone metal ring (71) to be loaded with the square waveguide (31).

6. The broadband dual-polarization probe horn antenna loaded with an arc-type feed (OMT) structure according to claim 5, characterized in that: The top radius of the truncated cone metal ring (71) is consistent with the radius of the circular quad-ridged waveguide (2), both being r2. By adjusting the size of the bottom radius r3 of the truncated cone metal ring (71), the included angle θ with the inner wall of the circular quad-ridged waveguide (2) is changed. The included angle θ controls the slope of the truncated cone metal ring reflection back cavity (7), thereby changing the transmission characteristics of the cavity to the radiation field.

7. The broadband dual-polarization probe horn antenna loaded with an arc-type feed (OMT) structure according to claim 5, characterized in that: The radiation boundary (4) adopts a conical open waveguide structure, connected to the top circular end surface of the circular four-ridge waveguide (2), and its input port is consistent in size with the circular four-ridge waveguide (2), and the radius is r2, so as to ensure the continuity of radiation to the port surface; The radius of the output port is r1, which is consistent with the spacing of the composite ridge (5).

8. The broadband dual-polarization probe horn antenna loaded with an arc-type feed (OMT) structure according to claim 1 or 7, characterized in that: Four symmetrical composite ridges (5) are arranged on the inner wall of the radiation boundary (4). The composite ridge (5) is a flat plate structure, with its side edges connected to the inner wall of the radiation boundary (4), its bottom edge connected to the top of a square waveguide (31), and the remaining edges transitioned into arcs to form ridge edges and extending out of the mouth surface of the radiation boundary (4).

9. The broadband dual-polarization probe horn antenna loaded with an arc-type feed (OMT) structure according to claim 8, characterized in that: The composite ridge (5) is divided into two sections, a circular four-ridge waveguide transition section x p The ridge structure (51) and the mouth-face transition section are combined p The composite ridge (5) is connected to form a ridge structure (52), and a coordinate system is established with the yoz plane where the cross section of the probe horn antenna is located, so that the composite ridge (5) satisfies the continuity in mathematical form and realizes the following function form: In the above formula, A and p are constants. The constant A is used to adjust the curvature of the ridge structure near the feed end, and p is used to adjust the curvature of the ridge structure near the mouth surface. Looking along the y-axis, the starting point of the mouth surface arc surface is r1-r 11 , the end point is r1, r 11 Determines the relative spacing of the ridge structure at the mouth surface. Taking the overall structural plane of the composite ridge (5) as the reference, the larger the A and p values, the more the overall ridge structure expands outward. 11 The larger the mouth, the smaller the distance between the ridges and the more obvious the curvature.

10. The broadband dual-polarization probe horn antenna loaded with an arc-type feed (OMT) structure according to claim 9, characterized in that: The ridge edge of the composite ridge (5) is loaded with a ridge transition groove structure (6), and the ridge transition groove structure (6) is based on the cross section of the square waveguide (31) with a length x p The ridge curve contour is formed by wrapping around, and finally forms a transition section x loaded on the circular four-ridge waveguide p The first ridge transition groove structure (61) of the ridge structure (51) and the composite x p The second ridge transition groove structure (62) of the ridge structure (52) is consistent in axial length with the ridge transition groove structure (6) and the radiation boundary (4).

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