A Chebyshev tilt distribution leaky coaxial cable and a method of making the same

Abstract

The present application relates to a kind of Chebyshev tilt angle distribution leaky coaxial cable and its preparation method.The present application includes inner conductor;Insulating layer, covered in the inner conductor outer;Slot outer conductor, covered in the insulating layer outer, the slot outer conductor is equipped with multiple radiation slot holes along the equidistant arrangement of axial direction, the slot width of each radiation slot hole is uniform;Outer sheath, covered in the slot outer conductor outer;Wherein, the tilt angle of the radiation slot hole is gradually varied distribution along cable axial direction, the distribution of the tilt angle is determined according to the first Chebyshev polynomial;The tilt angle is the included angle between the long axis direction of the radiation slot hole and cable axial direction.By the equal corrugation characteristics of the first Chebyshev polynomial, the tilt angle distribution can be constrained, the sensitive regulation and control of radiation intensity and the low disturbance of characteristic impedance can be considered, and the global uniform controllable of impedance fluctuation is realized.

Description

Technical Field

[0001] This invention relates to the field of leaky coaxial cable technology, and in particular to a leaky coaxial cable with Chebyshev tilt distribution and its preparation method. Background Technology

[0002] Leaky coaxial cables combine signal transmission and radiation capabilities, and are commonly used for wireless coverage in enclosed or semi-enclosed environments such as subway tunnels, highway tunnels, mines, large stadiums, and underground spaces. The periodic slots in the outer conductor of a leaky coaxial cable allow electromagnetic energy transmitted within the cable to gradually leak along the cable's direction into the external space, thus creating continuous coverage.

[0003] Traditional leaky coaxial cables typically employ a periodic slotted structure with equal inclination angles and uniform specifications, resulting in a generally uniform and fixed radiation intensity along the entire cable. However, when application environments present diverse coverage requirements, such as tunnel bifurcation, curved sections, localized blind spots in station halls, or special operating areas in mines, a single radiation intensity is insufficient to meet the coverage needs of different locations. This usually necessitates the addition of repeater equipment, external antennas, or localized blind spot compensation devices, which not only increases system costs and construction complexity but also complicates subsequent maintenance.

[0004] Therefore, how to achieve flexible and controllable adjustment of radiation intensity while ensuring stable characteristic impedance and low standing wave performance of the cable is currently a challenge for leaky cable technology. Summary of the Invention

[0005] Therefore, the technical problem to be solved by this invention is to overcome the insufficient degree of freedom in adjusting the radiation intensity of existing leaky coaxial cables. This invention provides a leaky coaxial cable with a Chebyshev tilt distribution and its manufacturing method. By changing the tilt angle to alter the effective cutting length of the slot for the TEM wave axial surface current, the radiation coupling efficiency of the slot can be controlled. Furthermore, by constraining the tilt distribution with the equiripple characteristics of a first-type Chebyshev polynomial, both sensitive control of radiation intensity and low disturbance of characteristic impedance can be achieved, realizing globally uniform and controllable impedance fluctuations. This solves the industry problem of the inability to simultaneously achieve low standing wave ratios and adjustable radiation.

[0006] To solve the above-mentioned technical problems, the present invention provides a leaky coaxial cable with Chebyshev tilt distribution, comprising: Inner conductor; An insulating layer is formed to cover the inner conductor. A slotted outer conductor is wrapped around the insulating layer. The slotted outer conductor has multiple radial slots arranged at equal intervals along the axial direction, and the slot width of each radial slot is uniform along the entire line. The outer sheath covers the slotted outer conductor; The inclination angle of the radial slot is distributed in a continuous and gradual manner along the cable axis, and the distribution of the inclination angle is determined according to a Chebyshev polynomial of the first kind; the inclination angle is the angle between the major axis of the radial slot and the cable axis.

[0007] In one embodiment of the present invention, the tilt angle of the radial slot is... Axial position Following Chebyshev polynomials in Equal ripple distribution within the interval.

[0008] In one embodiment of the present invention, the tilt angle distribution function is: ; in Based on the tilt angle, This is the maximum tilt angle offset. for Chebyshev polynomial of the first kind, It is of order 3 to 5. Here are the axial position coordinates of the gradient zone. The physical length of the transition zone; the total physical length of the cable is the length of the transition zone. The sum of the lengths of the smooth transition zones at both ends, The value of ensures that the tilt angle oscillates in a controlled manner within a preset range.

[0009] In one embodiment of the present invention, the tilt angle varies from 10° to 45°.

[0010] In one embodiment of the present invention, a smooth transition area is further included between the gradient area of ​​the tilt angle and the ungrooved areas at both ends of the cable, wherein the tilt angle of the radial slot in the smooth transition area is linearly distributed from the starting boundary of the ungrooved area to the gradient area.

[0011] In one embodiment of the present invention, the insulating layer is physically foamed polyethylene, and the equivalent dielectric constant of the insulating layer is 1.2 to 1.3.

[0012] In one embodiment of the present invention, the radiating slot is a rectangular slot or an elliptical slot.

[0013] In one embodiment of the present invention, the diameter of the inner conductor, the outer diameter of the insulation layer, and the equivalent dielectric constant of the insulation layer are matched to ensure that the basic characteristic impedance of the leaky coaxial cable meets the design requirement of 50±5Ω; the slotted outer conductor is formed of smooth copper strip.

[0014] This invention also provides a method for preparing a leaky coaxial cable with a Chebyshev tilt distribution, comprising: S1: Co-extrude and coat a foamed insulating layer on the outside of the inner conductor, controlling the concentricity deviation of the insulating layer to be less than 0.05 mm and the outer diameter tolerance to be ±0.05 mm; S2: Radial slots are processed on the copper strip according to a preset first type of Chebyshev polynomial tilt angle distribution, so that the tilt angle of each of the radial slots changes continuously and gradually along the axial direction, resulting in a slotted outer conductor. S3: An outer sheath is extruded over the slotted outer conductor to form the finished cable; In step S2, laser engraving or mechanical stamping is used. When using laser engraving, firstly, smooth copper strips are longitudinally wrapped and welded to form a solid outer conductor. Then, a five-axis linkage laser engraving system is used to process radial slots one by one on the surface of the cylindrical outer conductor after cabling, according to a preset Chebyshev gradient function. The tilt angle is continuously and gradually changed by adjusting the scanning path angle of the laser galvanometer in real time. The five-axis linkage laser engraving system is used in conjunction with a synchronous negative pressure adsorption device. At the instant the laser cuts through the slotted outer conductor, high-pressure airflow combined with negative pressure suction is used to extract the cut copper foil fragments online in real time. When mechanical stamping is used, before the smooth copper strip is longitudinally wrapped and welded, a CNC punch press is used to punch out radial slots with gradually changing tilt angles on the smooth copper strip. The tilt angle is continuously and gradually changed along the axial direction by servo control of the mold rotation angle. After stamping, the slotted copper strip is longitudinally wrapped and welded to form a slotted outer conductor.

[0015] In one embodiment of the present invention, when using laser engraving, an ultraviolet or green pulsed laser is used, supplemented by nitrogen or argon gas protection; or a picosecond pulsed laser or a femtosecond pulsed laser is used. When using laser engraving, the edge tolerance of a single radial groove is controlled within ±0.05mm, and the radial groove is staggered from the longitudinal welding seam of the copper strip by no less than 5mm. A real-time height sensor is used to dynamically maintain a constant laser focus on the surface of the cylindrical cable to improve the grooving quality of the cylindrical surface.

[0016] The technical solution of the present invention has the following advantages over the prior art: This invention discloses a leaky coaxial cable with a Chebyshev tilt angle distribution and its manufacturing method. The tilt angle of the slots is continuously and gradually varied along the cable axis, hole by hole. The tilt angle distribution is constrained by the equiripple characteristics of a Chebyshev polynomial of the first kind, achieving controlled gradual variation of radiation intensity while maintaining stable characteristic impedance. This invention can achieve low voltage standing wave ratio and uniform coverage in the 800MHz~3.0GHz frequency band, and is suitable for wireless coverage in enclosed spaces such as tunnels, mines, and large stadiums.

[0017] This invention features adjustable radiation. Compared to ordinary constant-inclination leaky cables, this invention increases the degree of freedom in adjusting radiation while maintaining the same low standing wave level.

[0018] This invention features low standing wave characteristics. The equiripple characteristics of the Chebyshev polynomial ensure that the amplitude of tilt angle changes and the resulting impedance fluctuations are controlled throughout, without local abrupt changes, thus achieving low standing wave performance in leaky cables.

[0019] This invention provides a dual-track process route of laser engraving and mechanical stamping, which is stable and suitable for mass production.

[0020] This invention employs a synchronous negative pressure adsorption laser engraving process, which completely solves the industry pain point of copper foil residue contaminating the insulation layer, and significantly improves product yield and reliability. Attached Figure Description

[0021] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

[0022] Figure 1 This is a schematic diagram showing the gradual distribution of the tilt angle along the axial direction of the leaky coaxial cable of the present invention.

[0023] Figure 2 This is a schematic diagram of the cross-sectional structure of the coaxial cable with gradually changing tilt angle according to the present invention.

[0024] Figure 3 This is a diagram of the third-order Chebyshev equal-wave gradient curve along the axial direction of the tilt angle of the present invention.

[0025] Explanation of reference numerals on the accompanying drawings: 1. Inner conductor; 2. Insulation layer; 3. External conductor; 4. Radial slots; 5. Outer protective sleeve. Detailed Implementation

[0026] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0027] In this invention, when directions (up, down, left, right, front, and back) are described, it is only for the convenience of describing the technical solution of this invention, and does not indicate or imply that the technical features referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, it should not be construed as a limitation of this invention.

[0028] In this invention, "several" means one or more, "multiple" means two or more, "greater than," "less than," "exceeding," etc., are understood to exclude the stated number; "above," "below," "within," etc., are understood to include the stated number. In the description of this invention, the terms "first" and "second" are used only to distinguish technical features and should not be construed as indicating or implying relative importance, or implicitly indicating the number of indicated technical features, or implicitly indicating the order of the indicated technical features.

[0029] In this invention, unless otherwise explicitly defined, the terms "setting," "installing," and "connecting" should be interpreted broadly. For example, they can refer to a direct connection or an indirect connection through an intermediate medium; a fixed connection, a detachable connection, or an integrally formed connection; a mechanical connection, an electrical connection, or a connection capable of mutual communication; or the internal connection of two components or the interaction between two components. Those skilled in the art can reasonably determine the specific meaning of the above terms in this invention based on the specific content of the technical solution.

[0030] Example 1 Reference Figure 1 , Figure 2 As shown, this embodiment provides a leaky coaxial cable with a Chebyshev tilt distribution, comprising: Inner conductor 1; Insulating layer 2 covers the outer surface of the inner conductor 1; The slotted outer conductor 3 is covered by the insulating layer 2. The slotted outer conductor 3 is provided with a plurality of radial slots 4 arranged at equal intervals along the axial direction. The slot width of each radial slot 4 is uniform along the entire line. The outer sheath 5 covers the slotted outer conductor 3; The tilt angle of the radial slot 4 is distributed in a continuous and gradual manner along the cable axis, and the distribution of the tilt angle is determined according to the first kind of Chebyshev polynomial; the tilt angle is the angle between the major axis of the radial slot 4 and the cable axis.

[0031] Specifically, refer to Figure 3 As shown, the tilt angle of the radial slot 4 Axial position Following Chebyshev polynomials in Equal ripple distribution within the interval.

[0032] Specifically, the tilt angle distribution function is: ; in Based on the tilt angle, This is the maximum tilt angle offset. for Chebyshev polynomial of the first kind, It is of order 3 to 5. Here are the axial position coordinates of the gradient zone. The physical length of the transition zone; the total physical length of the cable is the length of the transition zone. The sum of the lengths of the smoothly connected regions at both ends, the Chebyshev polynomial It is a dimensionless normalized coordinate system, and its domain is... For each radial slot 4, corresponding to the entire length of the gradient region, the tilt angle is taken as the axial position of the center of the radial slot 4 (4). The function of place The value, The value of ensures that the tilt angle oscillates in a controlled manner within a preset range.

[0033] In one embodiment, the tilt angle varies from 10° to 45°.

[0034] In one embodiment, a smooth transition area is also included between the gradient area of ​​the tilt angle and the ungrooved areas at both ends of the cable, wherein the tilt angle of the radial slot 4 in the smooth transition area is linearly distributed from the starting boundary of the ungrooved area to the gradient area.

[0035] Furthermore, the length of the initial smooth transition zone is preferably 3 to 10 times the center-to-center distance of the radial slots 4, and the inclination angle linearly transitions from the initial boundary to the inclination angle value at the beginning of the gradient zone. The inclination angle of the final smooth transition zone linearly transitions from the corresponding inclination angle value at the end of the gradient zone to the final boundary. For example, if the inclination angle at the beginning of the gradient zone is 10°, then the smooth transition zone can be provided with a spacing of 5 radial slots 4, so that the inclination angle of the radial slots 4 gradually changes from 2°, 4°, 6°, 8°, 10° to 10° from the side near the ungrooved area.

[0036] The length of the smooth transition zone at the end can be adjusted according to the angle span of the end to reduce reflection. By setting a smooth transition zone, abrupt changes in tilt angle between the ungrooved area and the gradient area can be avoided, reducing local reflections introduced by structural discontinuities. This transition method has a simple structure, controllable processing, and is suitable for engineering implementation.

[0037] In one embodiment, the insulating layer 2 is physically foamed polyethylene, and the equivalent dielectric constant of the insulating layer 2 is 1.2 to 1.3.

[0038] It should be noted that the first kind of Chebyshev polynomials in Within the interval, it exhibits equiripple characteristics: the absolute values ​​of all extrema are equal. This ensures that the amplitude of tilt angle changes and the resulting impedance fluctuations are controlled throughout, without local abrupt changes, providing a physical basis for low standing waves. The key to determining standing wave performance lies in whether the impedance gradient is gentle and whether there are local abrupt changes, rather than the mathematical form of the angle curve itself. The Chebyshev distribution provides a deterministic, reproducible, smooth gradient function that can achieve the desired radiation modulation effect with minimal ripple cost within a given tilt angle range. It should be noted that, due to the nonlinear relationship between tilt angle and radiation efficiency, the equiripple distribution of the tilt angle is not equivalent to the equiripple distribution of radiation intensity. The tilt angle is an important design parameter affecting the radiation coupling coefficient of the radiation slot 4; by controlling the tilt angle distribution through Chebyshev polynomials, the distribution of radiation intensity along the line can be controlled.

[0039] Furthermore, in long-distance periodic structures, even if the impedance disturbance of a single radiating slot 4 is extremely small, the reflections from thousands of radiating slots 4 may still coherently superimpose at a specific frequency, forming a structural return loss reflection peak. This embodiment utilizes the equiripple characteristics of Chebyshev polynomials (the higher the order, the better) to ensure that the impedance fluctuation amplitude is uniformly controllable across the entire length, and its spatial spectrum is determined by the order n and the amplitude. This ensures that strong reflection peaks are avoided at specific frequencies.

[0040] The tilt angle exhibits long-period fluctuations along the entire length. By macroscopically modulating the radiation intensity of hundreds or even thousands of radiation slots along the entire line, the uniformity of long-distance coverage can be optimized by adjusting the distribution of radiation coupling intensity along the line.

[0041] This embodiment preferably uses a third-order Chebyshev polynomial because it achieves a balance between controllable tilt angle change rate, impedance stability, and fabrication difficulty; the higher the order, the greater the fabrication difficulty. First-order and second-order polynomials are suitable for low-cost scenarios with low performance requirements, while fourth-order and fifth-order polynomials are suitable for special scenarios with extremely high requirements for coverage uniformity and are very difficult to fabricate.

[0042] Based on periodic transmission line theory, the first-order Bragg resonance condition , Let be the phase constant of the electromagnetic wave propagating along the axial direction of the leaky coaxial cable. The axial distance between the centers of two adjacent radial slots 4 is P = 40 mm in this embodiment, and the equivalent dielectric constant of the insulating layer 2 is... =1.25, yielding a first-order Bragg resonant frequency f≈3.35GHz, which exceeds the upper limit of the 800MHz~3.0GHz operating frequency band. It should be noted that the slow-wave effect caused by the slotting in the outer conductor 3 will cause the equivalent dielectric constant to be slightly higher than the baseline value, potentially resulting in a slight downward shift in the actual Bragg frequency. By rationally designing the parameters of the radiating slot 4, it can be ensured that the Bragg frequency remains outside the target frequency band with sufficient margin, effectively suppressing its influence.

[0043] Specifically, the radiation slot 4 is a rectangular slot or an elliptical slot.

[0044] Specifically, the diameter of the inner conductor 1, the outer diameter of the insulation layer 2, and the equivalent dielectric constant of the insulation layer 2 are matched to ensure that the basic characteristic impedance of the leaky coaxial cable meets the design requirement of 50±5Ω; the slotted outer conductor 3 is formed of smooth copper strip.

[0045] It should be noted that the radiative coupling efficiency of the leaky coaxial cable is directly related to the angle at which the radiating slot 4 cuts the surface current flow lines of the outer conductor 3. Generally, radiative coupling increases when the angle between the radiating slot 4 and the surface current increases, and decreases when the angle decreases. The specific degree of influence is related to factors such as the size of the radiating slot 4 and the operating frequency. In this embodiment, by changing the tilt angle, the cutting angle of the radiating slot 4 to the surface current is adjusted at different axial positions, thereby controlling the radiation intensity of each radiating slot 4.

[0046] Within a given tilt angle range, the relative change in impedance is small, and the impedance fluctuation amplitude is uniform and controllable throughout the entire length, which is beneficial for maintaining a low reflection level. Therefore, a gradual change in tilt angle can achieve flexible control of radiation intensity without significantly worsening the standing wave ratio.

[0047] Example 2 This embodiment provides a method for preparing a leaky coaxial cable with a Chebyshev tilt distribution as described in Embodiment 1, comprising: S1: A foamed insulating layer 2 is co-extruded and coated on the inner conductor 1, and the concentricity deviation of the insulating layer 2 is controlled to be less than 0.05 mm, and the outer diameter tolerance is ±0.05 mm. S2: Radial slots 4 are processed on the copper strip according to the preset first type of Chebyshev polynomial tilt angle distribution, so that the tilt angle of each of the radial slots 4 changes continuously and gradually along the axial direction to obtain the slotted outer conductor 3. S3: An outer sheath 5 is extruded over the slotted outer conductor 3 to form the finished cable.

[0048] In step S2, the radial slot 4 can be adopted in one of the following two ways: Method 1 is laser engraving, which is suitable for precision machining.

[0049] When using laser engraving, a smooth copper strip is first longitudinally wrapped and welded to form a solid outer conductor 3. Then, a five-axis linkage laser engraving system is used to process radial slots 4 one by one on the surface of the cylindrical outer conductor 3 after cabling, according to a preset Chebyshev gradient function. The tilt angle is continuously and gradually changed by adjusting the scanning path angle of the laser galvanometer in real time. The tilt angle of the radial slot 4 is continuously and gradually changed by adjusting the scanning path angle of the laser galvanometer in real time. By adopting a route of cabling first and then slotting, deformation of the radial slot 4 caused by subsequent copper strip forming is avoided.

[0050] Furthermore, the five-axis linkage laser engraving system can be used in conjunction with a synchronous negative pressure adsorption device. At the instant the laser cuts through the slotted outer conductor 3, high-pressure airflow combined with negative pressure suction is used to extract the cut copper foil fragments online in real time. By setting up the synchronous negative pressure adsorption device, copper foil fragments can be completely prevented from falling into the foamed insulation layer 2, eliminating the problems of local impedance abrupt changes and VSWR deterioration caused by metal residue, significantly improving product yield and reliability.

[0051] When using laser engraving, an ultraviolet or green pulsed laser is employed, supplemented with nitrogen or argon gas protection; alternatively, a picosecond or femtosecond pulsed laser can be used. The femtosecond laser pulse width is much shorter than the thermal diffusion time of copper, meaning the heat is carried away by vaporized material before being conducted to the insulating layer 2. Combined with coaxial gas curtain-assisted cooling, this effectively prevents thermal damage to the insulating layer 2. The reduced edge processing quality caused by the increased laser incident angle at both ends of the radial slot 4 on the cylindrical surface can be mitigated by adjusting the laser power in segments or by using dynamic focus compensation.

[0052] When using laser engraving, the edge tolerance of a single radial groove hole 4 is controlled within ±0.05mm, and the radial groove hole 4 is staggered from the longitudinal welding seam of the copper strip by no less than 5mm. A real-time height sensor is used to dynamically maintain a constant laser focus on the surface of the cylindrical cable to improve the grooving quality of the cylindrical surface.

[0053] Method two is mechanical stamping, suitable for industrial mass production. When using mechanical stamping, before longitudinally wrapping and welding the smooth copper strip, a CNC punch press is used to punch radial slots 4 with gradually changing inclination angles on the smooth copper strip. The inclination angle is continuously and gradually changed along the axial direction by servo-controlled mold rotation. After stamping, the slotted copper strip is longitudinally wrapped and welded to form the slotted outer conductor 3. This method is highly efficient and suitable for large-scale production.

[0054] S3: Extrusion of outer sheath 5. The outer sheath 5 material is extruded over the slotted outer conductor 3 to form the outer sheath 5. During the extrusion process, a shaping mold and supporting fixtures can be used to ensure the stability of the shape of the radiation slot 4.

[0055] Example 3 This embodiment provides a leaky coaxial cable with a Chebyshev tilt distribution. In this embodiment, the inner conductor 1 is an annealed oxygen-free copper tube with a diameter of 1.8 mm; the insulation layer 2 is physically foamed polyethylene, and the equivalent relative permittivity of the insulation layer 2 is... The outer diameter of the insulation layer 2 is 4.5 mm, and the concentricity deviation is less than 0.03 mm. The slotted outer conductor 3 is formed of a smooth copper strip with a thickness of 0.12 mm. Rectangular radial slots 4 are provided on the slotted outer conductor 3. The slot width of the radial slots 4 is uniformly 3.0 mm, the slot length is 10 mm, and the axial distance between the centers of two adjacent radial slots 4 is 1.25. The outer sheath 5 is 40mm thick; the outer sheath 5 is made of flame-retardant, low-smoke, halogen-free polyolefin with a thickness of 1.5mm.

[0056] In this embodiment, the tilt angle of the radial slot 4 is continuously and gradually distributed along the cable axis, and the tilt angle is the angle between the major axis of the radial slot 4 and the cable axis. The tilt angle distribution function is: ; in, Located in the axial position The radial slot hole 4 is tilted at an angle. It is a third-order Chebyshev polynomial of the first kind. Here are the axial position coordinates of the gradient region, in meters, representing the physical length of the gradient region. The value is 100m. The minimum and maximum values ​​of the tilt angle are respectively: ; The total physical length of the cable is the sum of the length of the transition zone and the length of the smooth connection zone at both ends.

[0057] The smooth connection zone is located between the gradually changing tilt angle zone and the ungrooved areas at both ends of the cable. The length of the initial smooth connection zone is preferably 3 to 10 times the center-to-center distance of the radial slots 4, and the tilt angle of the radial slots 4 linearly transitions from 0° to 10°; the length of the terminal smooth connection zone is determined according to the terminal angle span, and the tilt angle of the radial slots 4 linearly transitions from 45° to 0°.

[0058] Based on periodic transmission line theory, the first-order Bragg resonance condition is: ; in, Let be the phase constant of the electromagnetic wave propagating along the axial direction of the leaky coaxial cable. It is the axial distance between the centers of two adjacent radial slots 4. Represented as: ; in, For frequency, The equivalent relative permittivity of insulating layer 2 is given by [the value of the permittivity]. Let P be the speed of light in a vacuum. When P = 40 mm and εr = 1.25, the first-order Bragg resonant frequency is obtained as: ; Therefore, when P=40mm and εr=1.25, the calculated first-order Bragg resonant frequency is approximately 3.35GHz, which exceeds the upper limit of the 800MHz~3.0GHz operating frequency band. Thus, this embodiment can reduce the risk of Bragg reflection peaks generated by the periodic slot structure within the target operating frequency band, and its impact is effectively suppressed.

[0059] Comparative Example This comparative example provides a coaxial cable with equal inclination angle leakage. In this comparative example, the inner conductor 1 is an annealed oxygen-free copper tube with a diameter of 1.8 mm; the insulation layer 2 is physically foamed polyethylene, and the equivalent relative permittivity of the insulation layer 2 is... The outer diameter of the insulation layer 2 is 4.5 mm, and the concentricity deviation is less than 0.03 mm. The slotted outer conductor 3 is formed of a smooth copper strip with a thickness of 0.12 mm. Rectangular radial slots 4 are provided on the slotted outer conductor 3. The slot width of the radial slots 4 is uniformly 3.0 mm, the slot length is 10 mm, and the axial distance between the centers of two adjacent radial slots 4 is 40 mm. The outer sheath 5 is made of flame-retardant, low-smoke, halogen-free polyolefin with a thickness of 1.5 mm.

[0060] The difference between this comparative example and Example 3 is that this comparative example does not use Chebyshev polynomials to determine the tilt angle distribution of the radial slot holes 4, nor does it form a gradually changing tilt angle zone that changes continuously hole by hole along the cable axis. Instead, each radial slot hole 4 is arranged with an equal tilt angle.

[0061] The voltage standing wave ratio (VSWR) results of this comparative example and Example 3 at communication frequencies of 900MHz and 2.6GHz are shown in Table 1 below.

[0062] Table 1: Voltage Standing Wave Ratio Results

[0063] As shown in the table above, compared with ordinary constant-angle leaky coaxial cable, Example 3 exhibits a lower voltage standing wave ratio (VSWR) at both 900MHz and 2.6GHz. This example uses Chebyshev polynomial control to continuously and gradually change the tilt angle of the radiation slot 4 along the axial direction, ensuring that the amplitude of tilt angle change and the resulting impedance fluctuation are controlled at every point. This allows for adjustable radiation intensity while reducing the risk of local reflections.

[0064] According to the theory of leakage coaxial cable radiation, the tilt angle adjusts the radiation coupling efficiency by changing the angle at which the slot cuts the surface current lines. Chebyshev polynomials are used in... The equiripple distribution within the interval exhibits controlled oscillations within a tilt angle range of 10° to 45°, with the amplitude of tilt angle variations and the resulting impedance fluctuations being strictly controlled throughout. The superposition and interference of radiation fields from multiple slots optimizes long-distance coverage uniformity. Tilt angle variations have minimal impact on characteristic impedance and do not introduce significant local reflections. The first-order Bragg center frequency is located approximately 3.35 GHz, higher than the upper limit of the operating frequency band, effectively suppressing its influence.

[0065] Finally, it should be noted that the above specific embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to examples, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A leaky coaxial cable with a Chebyshev tilt angle distribution, characterized in that, include: Inner conductor (1); An insulating layer (2) covers the inner conductor (1); The slotted outer conductor (3) is covered outside the insulating layer (2). The slotted outer conductor (3) is provided with a plurality of radial slots (4) arranged at equal intervals along the axial direction. The slot width of each radial slot (4) is uniform along the entire line. The outer sheath (5) covers the slotted outer conductor (3); The tilt angle of the radial slot (4) is distributed in a continuous and gradual manner along the cable axis, and the distribution of the tilt angle is determined according to the first type of Chebyshev polynomial; the tilt angle is the angle between the long axis direction of the radial slot (4) and the cable axis.

2. The leaky coaxial cable with Chebyshev tilt distribution according to claim 1, characterized in that, The tilt angle of the radial slot (4) Axial position Following Chebyshev polynomials in Equal ripple distribution within the interval.

3. A leaky coaxial cable with Chebyshev tilt distribution according to claim 2, characterized in that, The tilt angle distribution function is: ； in Based on the tilt angle, This is the maximum tilt angle offset. for Chebyshev polynomial of the first kind, It is of order 3 to 5. Here are the axial position coordinates of the gradient zone. The physical length of the transition zone; the total physical length of the cable is the length of the transition zone. The sum of the lengths of the smooth transition zones at both ends, The value of ensures that the tilt angle oscillates in a controlled manner within a preset range.

4. A leaky coaxial cable with Chebyshev tilt distribution according to claim 2 or 3, characterized in that, The tilt angle varies from 10° to 45°.

5. A leaky coaxial cable with Chebyshev tilt distribution according to claim 1, characterized in that, It also includes a smooth transition area between the gradient area of ​​the tilt angle and the ungrooved areas at both ends of the cable, wherein the tilt angle of the radial slot (4) in the smooth transition area is linearly distributed from the starting boundary of the ungrooved area to the gradient area.

6. A leaky coaxial cable with Chebyshev tilt distribution according to claim 1, characterized in that, The insulating layer (2) is physically foamed polyethylene, and the equivalent dielectric constant of the insulating layer (2) is 1.2 to 1.

3.

7. A leaky coaxial cable with Chebyshev tilt distribution according to claim 1, characterized in that, The radiation slot (4) is a rectangular slot or an elliptical slot.

8. A leaky coaxial cable with Chebyshev tilt distribution according to claim 1, characterized in that, The diameter of the inner conductor (1), the outer diameter of the insulation layer (2), and the equivalent dielectric constant of the insulation layer (2) are matched to each other so that the basic characteristic impedance of the leaky coaxial cable meets the design requirement of 50±5Ω; the slotted outer conductor (3) is formed by smooth copper strip.

9. A method for preparing a leaky coaxial cable with a Chebyshev tilt distribution as described in any one of claims 1-8, characterized in that, include: S1: Co-extrude and coat a foamed insulating layer (2) on the outer side of the inner conductor (1), and control the concentricity deviation of the insulating layer (2) to be less than 0.05 mm and the outer diameter tolerance to be ±0.05 mm; S2: Radial slots (4) are processed on the copper strip according to the preset first type Chebyshev polynomial tilt angle distribution, so that the tilt angle of each of the radial slots (4) changes continuously and gradually along the axial direction to obtain the slotted outer conductor (3). S3: Extruding an outer sheath (5) around the slotted outer conductor (3) to form a finished cable; In step S2, laser engraving or mechanical stamping is used. When using laser engraving, firstly, smooth copper strips are wrapped longitudinally and welded to form a solid outer conductor (3). Then, a five-axis linkage laser engraving system is used to process radial slots (4) on the surface of the cylindrical outer conductor (3) after cabling according to a preset Chebyshev gradient function. The tilt angle is continuously and gradually changed by adjusting the scanning path angle of the laser galvanometer in real time. The five-axis linkage laser engraving system is used in conjunction with a synchronous negative pressure adsorption device. At the instant when the laser cuts through the slotted outer conductor (3), the cut copper foil fragments are extracted online in real time using high-pressure airflow and negative pressure attraction. When mechanical stamping is used, before the smooth copper strip is longitudinally wrapped and welded, a CNC punch press is used to punch out radial slots with gradually changing tilt angles on the smooth copper strip (4), and the tilt angle is continuously gradually changed along the axial direction by servo control of the mold rotation angle. After stamping is completed, the slotted copper strip is longitudinally wrapped and welded to form a slotted outer conductor (3).

10. The method for preparing a leaky coaxial cable with a Chebyshev tilt distribution according to claim 9, characterized in that, When using laser engraving, an ultraviolet or green pulsed laser is used, supplemented with nitrogen or argon gas protection; or a picosecond pulsed laser or a femtosecond pulsed laser is used. When using laser engraving, the edge tolerance of a single radiating slot (4) is controlled within ±0.05mm, and the radiating slot (4) is staggered from the longitudinal welding seam of the copper strip by no less than 5mm. A real-time height sensor is used to dynamically maintain the laser focus on the cylindrical cable surface to improve the grooving quality of the cylindrical surface.

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