Academic Journal of Science and Technology ISSN: 2771-3032 | Vol. 2, No. 1, 2022 22 A Design of an Equalized Gaussian Beam Antenna Applied in A Coal Mine Environment Tianyuan Chen*, Lingfei Cheng, Ankang Liu College of Physics and Electronic Information, Henan University of Science and Technology, Henan, China * Corresponding author: Chen Tianyuan (Email: 786557005@qq.com) Abstract: The environment of confined spaces such as tunnels and coal mines is complex and changeable. When the wireless signal propagates in it, it will be affected by the reflection and diffraction of the shaft wall, which puts forward higher requirements for the radiation beam of the coal mine antenna. In this paper, the corrugated horn antenna model is selected to design a coal mine antenna whose radiation pattern is almost equal to the Gaussian beam. Starting from the expression of Gaussian beam, combined with the radiation field formula of the horn antenna, the effects of slot depth, slot spacing, slot width and horn opening angle on the radiation beam are analyzed. The axial slot corrugated conical horn antenna designed in this paper has a gain greater than 13dBi in the frequency band, the side lobe level is less than -25dB, and the VSWR is less than 1.25 in the designed full frequency band. By comparing the pattern of the horn antenna and the pattern of the Gaussian beam, the results show that the axially grooved corrugated conical horn designed in this paper basically coincides with the Gaussian beam under ideal conditions, and the E and H planes are the Gaussian with a -10dB taper angle of 35°. The beams are basically the same. The equalized Gaussian beam antenna designed in this paper has important guiding significance for the antenna design in coal mine detection and exploration. Keywords: Mine, Gaussian beam, Antenna, Wireless communication system. 1. Introduction Coal is one of the important energy sources in China, and coal mining in China is mainly underground. In mine tunnels, wireless communication is an important means of communication to ensure production operation and personnel safety. [1-2] Underground tunnel environment is complex and harsh, the space is small, resulting in radio waves in the restricted space presents complex propagation characteristics, and the ground radio wave propagation characteristics are very different, resulting in the ground mature wireless communication system is difficult to smoothly transplant to the underground.[3-5] As the source end of the wireless communication system, the performance of the antenna has an important impact on the coverage effect of electromagnetic waves in mine tunnels. The special environment of coal mine shaft, with serious multipath undulation, large wireless fading, and electromagnetic waves propagating in the restricted space on all sides, existing wireless communication is hardly applicable to underground communication. In order to solve the problem of restricted radiation beam in restricted space, scholars at home and abroad have conducted a lot of experiments and researches on this issue. The literature [6] shows that the signal attenuation rate of horizontally polarized antenna is smaller at the sidewall than at the top arm using geometric optical model simulation. The research team from China University of Mining and Technology discussed the effects of waveguide structure [7], dielectric wall electrical parameters, carrier frequency and wave propagation distance in the literature, and gave the optimal beam index for mining antennas. The literature [8] combines geometrical-optical theory and numerical method to give the calculation formula for the attenuation of electromagnetic transmission in the restricted space of electromagnetic wave coal mine. The Perceptive Mine Research Center of China University of Mining and Technology uses a model based on dielectric waveguide theory to derive the coupling efficiency and direction function of the antenna in the roadway. And the effect of the antenna location in the coal mine shaft on the radiation field distribution is simulated and analyzed with a horizontally polarized half-wave dipole as an example. [9] According to the geometry characteristics of the tunnel, Prof. Zhang Zhijun [10~12] believes that the mining antenna should have the characteristics of high gain and bi-directional radiation; Prof. Wang Junhong's [13] team uses ideal Gaussian beam as the simulation of transmitting antenna beam and studies the influence of parameters such as flap width, beam pointing, polarization mode and antenna position on the radio wave coverage in the tunnel. Most scholars do not give a better antenna solution [14~17] for the various problems that exist, so there is an urgent need for an antenna whose radiation beam can be better applied to the communication in the coal mine shaft. This paper starts from the expression of radiation field of horn antenna and gives the theoretical model applicable to radiation beam in coal mine environment. On this basis, the corrugated horn antenna with high overlap with Gaussian beam is designed, and the main flap is obvious in the working band, and the sub-flap level is less than -25dB in both E-plane and H-plane, with excellent in-band matching characteristics. 2. Design Principle The corrugated horn has outstanding advantages over the traditional light wall horn. Its directional diagram of each radiation plane has an almost complete equalization effect, and it has approximately coincident phase centers in the E plane and the H plane. Although the processing of corrugated horn is complicated, it is widely used in high-precision single pulse tracking, reflective surface antenna and other equipment due to its good electrical performance. The corrugated horn is made by embedding a corrugated groove in the conventional 23 light wall horn, which regulates the radiation field by suppressing the harmful electric field bypassing and deeply proportioning the content of each operating mode. As a result, good electrical performance with low subflap, low cross- polarization, wide frequency band and high aperture utilization can be achieved. The designed horn form is a corrugated horn with axial slotting. It has been widely used because of its relatively simple design. Analysis of the radiation field of the corrugated conical horn is very complicated, so the field of the corrugated circular waveguide aperture is analyzed. The mixed mode of Hmn mode and Emn mode can be transmitted within the circular waveguide. By designing the slot depth d, slot width w, and tooth thickness t of the corrugated slot inside the waveguide, the operating modes are fully mixed and matched to transmit to the aperture surface to form the required field. Figure 1. Corrugated circular waveguide As shown in Figure 1, a polar coordinate system (ρ, φ) is established in the circular waveguide cross-section, and when the circular waveguide forms an equilibrium mixed-mode HE11 mode through the corrugated slot, then there is a circular waveguide caliber field distribution of the form         ρ 0 0 c φ 1 0 c E =-jA J k ρ cos mφ E = jA J k ρ sin mφ   (1) in the formula 2 2 2 c=k k  ,  0 cJ k  is the first type of Bessel function A1 is each normalization constant. Also transforming equation (1) into the right angle coordinate system, we have.  xs 1 0 c c ys γ E = jA J k ρ k E = 0  (2) From (2), it can be learned that the aperture field is independent of the φ direction and is a circularly symmetric field. Far-field integration of the aperture field can be obtained as a function of the radiation direction of the waveguide radiator. The principle of the corrugated horn is similar to that of the corrugated waveguide, both of which use the slot spacing and slot depth to change the working mode to form an equilibrium mixed mode, which is finally integrated on the aperture surface. The Gaussian beam can be approximated as a conical beam of a horn antenna, and there is no sub-flap or cross- polarization in any direction, which can be used for point-to- point communication in restricted spaces such as coal mines. The Gaussian beam is composed of an electric dipole along the x-axis placed at the complex space position (0, 0, jb) and a magnetic dipole along the y-axis placed at the complex space position (0, 0, -jb), after deducing that it produces a radiation field of      jkr kbcosθe E r,θ ,φ A e 1 cosθ cosφθ sinφφ kr        (3) where (r, θ, φ), is the spherical coordinate system in which the Gaussian beam is located, and A is a constant. From equation (3), the Gaussian beam can be varied by changing the coordinates of its position b placed in complex space to change the level AdB at a given angle θ. The relationship is   1 cosθ 20 lg A 2 b= 20k 1 cosθ lg e        (4) 2.1. Antenna Design and Simulation As shown in Figure 2, the design structure of corrugated cone horn is generally divided into four segments, namely, radius transformation segment, mode transformation segment, transition segment and radiation segment. Firstly, the functions and design principles of each segment are introduced; among them, the mode transformation segment is used to generate HE11 mode and adjust the mode ratio of EH12 and HE11 to eliminate cross-polarization. Transition section and radiation section to achieve tensor transformation, change the radiation direction map of the cone cutting. The radius conversion section is used to achieve impedance matching with the first three sections of the structure, reduce return loss and achieve better impedance matching. Figure 2. General structure of corrugated horn The design of the transform section can be a linear model or a curved model, and the linear section length L1 can be determined by parametric scanning to achieve impedance matching. The mode transformation section can be determined by the desired frequency band, the slot depth is generally transformed by λ/4~λ/2, and the number of open slots is generally 4 slots per wavelength. The slot depth of the final transition section and radiation section is about λ/4, and the tensor angle is determined by the required design cone cutting index. In order to prevent the transmission of higher modes, the input radius R of the circular waveguide is taken to be λ λ R 3.41 2.62   (5) However, since the structure of symmetric structure will not transmit the mode of asymmetric structure, the circular waveguide cannot produce the mode with m > 1 and the optimal transmission radius of HE11 mode is λ r= 1.843 (6) The radius conversion section and the mode conversion 24 section are combined into one, which is a stepped axial corrugated slot structure. As shown in Fig. 4(c), where: d1 is the corrugated horn length; d2 is the length of the moment circle conversion section; R is the outer diameter of the horn aperture; R0 is the inner diameter of the horn aperture; r1 is the outer diameter of the circular waveguide aperture; r2 is the inner diameter of the circular waveguide aperture; dt is the circular waveguide wall thickness; w is the width of the corrugated slot; t is the thickness of the corrugated slot teeth; A to D are the slot depths of each section of the corrugated slot, respectively; a is the wide edge of the rectangular waveguide; b is the rectangular waveguide narrow edge. The slot pitch is generally taken as λ/10~λ/5. And the tooth thickness should be as much as possible under general circumstances, but the smaller the tooth thickness is, the more difficult it is to process and the bigger the error is. So the tooth thickness is generally 0.1-0.3 times the slot spacing. The slot depth is used to adjust the mode content ratio and suppress the harmful current, so the slot depth at the aperture is about equal to λ/4. And the slot depth at the horn neck is about equal to λ/2, which is used for mode transformation and adjustment. Finally, the radiation radius R0 of the horn antenna, which is used to adjust the width of the directional map. Since the actual engineering will not feed directly to the circular waveguide, a moment-circle conversion section is added, as shown in Figure 3. The rectangular waveguide is designed to excite a mode similar to the main mode of the circular waveguide. The long side of the rectangular waveguide in this mode is generally between λ/2 and λ, and the wide side is generally λ/4.4 to λ/2.2. Figure 3. Schematic diagram of the structure of the rectangular-circle conversion section 2.1.1. Simulation of Corrugated Cone Horn The design target gain of the Gaussian-like beam antenna applied to coal mine environment is >13dBi, -10dB cone clipping angle: 34°~36°, VSWR<1.5 in bandwidth; according to the above design requirements, the feed source is simulated and analyzed in HFSS software. The corrugated cone horn model and outer dimensions are shown in Figure 4. (a) Corrugated horn outer dimensions (b) Corrugated horn inner dimensions and conversion section dimensions Figure 4. Corrugated horn model Table 1. Parameter of the simulation Parameters Meaning d1 Corrugated horn length d2 Length of moment circle conversion R Outside diameter of horn caliber R0 Inner diameter of horn bore r1 Outer diameter of circular waveguide r2 Inner diameter of circular waveguide dt Circular waveguide wall thickness w Corrugated groove width t Corrugated groove tooth thickness A~D Depth of each section of corrugated a Rectangular waveguide broadside b Rectangular waveguide with narrow In order to obtain the expected gain index and achieve a usable Gaussian-like beam, the minimum caliber 2R0 of the horn can be calculated for the caliber field is 45.52 mm (assuming 100% utilization of the horn caliber). The design range of calculated aperture and slot width is  2 2 r 4 w+t 22.76mm 9.32mm