Junhong Wang, Yunjie Geng, Chong Zhang, Xingying Huo
{"title":"周期性漏波结构的辐射特性及其在漏波天线设计中的应用","authors":"Junhong Wang, Yunjie Geng, Chong Zhang, Xingying Huo","doi":"10.1109/APMC.2015.7411769","DOIUrl":null,"url":null,"abstract":"For a leaky waveguide with periodic slots cut in the wall, the guided wavelength can be expressed as: λ<sub>g</sub> = λ<sub>0</sub>/√(ε<sub>g</sub>). (1) Here, ε<sub>g</sub> is an equivalent dielectric constant of the leaky waveguide, and is expressed by ε<sub>g</sub> = ε<sub>r</sub> - (λ<sub>0</sub>/λ<sub>c</sub>')<sup>2</sup>, (2) where εr is the dielectric constant of the material filled in the waveguide, and it equals 1 when no dielectric is filled; λ<sub>0</sub> is the wavelength in free space, and λ<sub>c</sub>' is the cut off wavelength of the fundamental mode in the leaky waveguide. λ<sub>c</sub>' is actually different from that in closed waveguide, but the difference is not significant. The propagation constant of the leaky waveguide is then expressed by β = k0 √(ε<sub>g</sub>), (3) where k<sub>0</sub> is the wave number in free space. As we know, periodic structures can excite a lot of spatial harmonics, and some of them can leak away from the structures. The radiation condition and the beam angle of the mth harmonic are -1 <; √ ε<sub>g</sub> + m λ<sub>0</sub> / P <; 1, (4) φ<sub>m</sub> = cos<sup>-1</sup> (√(ε<sub>g</sub>) + mλ<sub>0</sub> / P), (5) where P is the period of the slots cut in the waveguide wall. From the analysis we find that the radiation beam directions of the spatial harmonics of leaky waveguide are determined by both the equivalent dielectric constant ε<sub>g</sub> and the period of the slots P, so either changing of ε<sub>g</sub> or changing of P will lead to changing of radiation beam angle. Based on these theory and formulas, the transmission and radiation characteristics of spatial harmonics of the leaky waveguide are studied first, and the relationships between the radiation field and structure parameters are studied as well. It can be found that for a leaky waveguide, both the harmonics with negative order (m <; 0) and positive order (m ≥ 0) can generate leaky waves. This is different from that of the leaky coaxial cable, in which only the harmonics with negative order (m <; 0) can generate leaky wave. An approach based on numerical method for analyzing the propagation constant of leaky waveguide is also given, and the relationship between the propagation constant and waveguide parameters is analyzed. The radiation property of the spatial harmonics of periodic leaky wave structures is then used in the design of antennas with beam-formed radiation patterns, for low power consumption wireless communication application. The basic principle of the design is to superpose the radiations from the -1th order spatial harmonics of a number of leaky wave structures with different slot periods in a weighting way, and the weighting factors are determined by the desired radiation pattern. Since different periodic structures generate radiation beams in different directions, and different weighting factors lead to different radiation strengths, so by properly selecting the periodic structures and weighting factors, the desired radiation pattern can be formed. But for realistic application, these leaky structures with different slot periods should be mapped into one structure that can be fabricated. So the functions describing different periodic slot structures are also superposed together in a weighting way, and the combination slot structural function for the realistic leaky wave antenna is finally obtained. The weighting factors used in the radiation field superposition and the weighting factors used in the structural function superposition are two different sets of weighting functions, and they should be mapped into each other, the key is to find the relationship between the radiation field and the structure parameters. While the weighting factors for structural function superposition is found, we obtain the final antenna structure. Using this method, two kinds of new leaky wave antennas with beam-formed radiation patterns are designed based on rectangular waveguide and SIW structures.","PeriodicalId":269888,"journal":{"name":"2015 Asia-Pacific Microwave Conference (APMC)","volume":"102 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":"{\"title\":\"Radiation characteristic of the periodic leaky wave structure and its application to leaky wave antenna design\",\"authors\":\"Junhong Wang, Yunjie Geng, Chong Zhang, Xingying Huo\",\"doi\":\"10.1109/APMC.2015.7411769\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For a leaky waveguide with periodic slots cut in the wall, the guided wavelength can be expressed as: λ<sub>g</sub> = λ<sub>0</sub>/√(ε<sub>g</sub>). (1) Here, ε<sub>g</sub> is an equivalent dielectric constant of the leaky waveguide, and is expressed by ε<sub>g</sub> = ε<sub>r</sub> - (λ<sub>0</sub>/λ<sub>c</sub>')<sup>2</sup>, (2) where εr is the dielectric constant of the material filled in the waveguide, and it equals 1 when no dielectric is filled; λ<sub>0</sub> is the wavelength in free space, and λ<sub>c</sub>' is the cut off wavelength of the fundamental mode in the leaky waveguide. λ<sub>c</sub>' is actually different from that in closed waveguide, but the difference is not significant. The propagation constant of the leaky waveguide is then expressed by β = k0 √(ε<sub>g</sub>), (3) where k<sub>0</sub> is the wave number in free space. As we know, periodic structures can excite a lot of spatial harmonics, and some of them can leak away from the structures. The radiation condition and the beam angle of the mth harmonic are -1 <; √ ε<sub>g</sub> + m λ<sub>0</sub> / P <; 1, (4) φ<sub>m</sub> = cos<sup>-1</sup> (√(ε<sub>g</sub>) + mλ<sub>0</sub> / P), (5) where P is the period of the slots cut in the waveguide wall. From the analysis we find that the radiation beam directions of the spatial harmonics of leaky waveguide are determined by both the equivalent dielectric constant ε<sub>g</sub> and the period of the slots P, so either changing of ε<sub>g</sub> or changing of P will lead to changing of radiation beam angle. Based on these theory and formulas, the transmission and radiation characteristics of spatial harmonics of the leaky waveguide are studied first, and the relationships between the radiation field and structure parameters are studied as well. It can be found that for a leaky waveguide, both the harmonics with negative order (m <; 0) and positive order (m ≥ 0) can generate leaky waves. This is different from that of the leaky coaxial cable, in which only the harmonics with negative order (m <; 0) can generate leaky wave. An approach based on numerical method for analyzing the propagation constant of leaky waveguide is also given, and the relationship between the propagation constant and waveguide parameters is analyzed. The radiation property of the spatial harmonics of periodic leaky wave structures is then used in the design of antennas with beam-formed radiation patterns, for low power consumption wireless communication application. The basic principle of the design is to superpose the radiations from the -1th order spatial harmonics of a number of leaky wave structures with different slot periods in a weighting way, and the weighting factors are determined by the desired radiation pattern. Since different periodic structures generate radiation beams in different directions, and different weighting factors lead to different radiation strengths, so by properly selecting the periodic structures and weighting factors, the desired radiation pattern can be formed. But for realistic application, these leaky structures with different slot periods should be mapped into one structure that can be fabricated. So the functions describing different periodic slot structures are also superposed together in a weighting way, and the combination slot structural function for the realistic leaky wave antenna is finally obtained. The weighting factors used in the radiation field superposition and the weighting factors used in the structural function superposition are two different sets of weighting functions, and they should be mapped into each other, the key is to find the relationship between the radiation field and the structure parameters. While the weighting factors for structural function superposition is found, we obtain the final antenna structure. Using this method, two kinds of new leaky wave antennas with beam-formed radiation patterns are designed based on rectangular waveguide and SIW structures.\",\"PeriodicalId\":269888,\"journal\":{\"name\":\"2015 Asia-Pacific Microwave Conference (APMC)\",\"volume\":\"102 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"9\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2015 Asia-Pacific Microwave Conference (APMC)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/APMC.2015.7411769\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2015 Asia-Pacific Microwave Conference (APMC)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/APMC.2015.7411769","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 9
摘要
对于壁面有周期性狭缝的漏波导,其波导波长可表示为:λg = λ0/√(εg)。(1)式中,εg为漏波导的等效介电常数,表示为εg = εr - (λ0/λc′)2,(2)式中,εr为波导中填充材料的介电常数,当不填充介质时εr = 1;λ0为自由空间波长,λc′为漏波导中基模的截止波长。λc′实际上与闭合波导中的λc′不同,但差异不显著。漏波导的传播常数表示为β = k0√(εg),(3),其中k0为自由空间中的波数。正如我们所知,周期结构可以激发大量的空间谐波,其中一些可以从结构中泄漏出来。第m次谐波的辐射条件和波束角为-1 g + mλ0 / P m = cos-1(√(εg) + mλ0 / P),(5)其中P为波导壁上切割槽的周期。分析发现,泄漏波导空间谐波的射束方向由等效介电常数εg和缝隙周期P共同决定,因此,改变εg或改变P都会导致射束角的变化。基于这些理论和公式,首先研究了泄漏波导空间谐波的传输和辐射特性,以及辐射场与结构参数之间的关系。可以发现,对于漏波导,负次谐波(m <;0)和正阶(m≥0)会产生漏波。这与漏同轴电缆不同,漏同轴电缆中只有负次谐波(m <;0)会产生漏波。给出了一种基于数值方法分析泄漏波导传播常数的方法,并分析了传播常数与波导参数的关系。周期性漏波结构的空间谐波的辐射特性随后被用于设计具有波束形成辐射方向图的天线,用于低功耗无线通信应用。该设计的基本原理是将多个不同槽期漏波结构的-1阶空间谐波的辐射以加权方式叠加,加权因子由期望的辐射方向图确定。由于不同的周期结构会产生不同方向的辐射光束,不同的权重因子导致不同的辐射强度,因此通过合理选择周期结构和权重因子,可以形成所需的辐射方向图。但在实际应用中,这些具有不同槽期的漏水结构应该被映射成一个可以制造的结构。将描述不同周期缝隙结构的函数以加权方式叠加在一起,最终得到实际漏波天线的组合缝隙结构函数。辐射场叠加中的权重因子与结构函数叠加中的权重因子是两组不同的权重函数,二者应相互映射,关键是要找到辐射场与结构参数之间的关系。同时找出结构函数叠加的权重因子,得到最终的天线结构。利用该方法,设计了两种基于矩形波导和SIW结构的新型波束形辐射天线。
Radiation characteristic of the periodic leaky wave structure and its application to leaky wave antenna design
For a leaky waveguide with periodic slots cut in the wall, the guided wavelength can be expressed as: λg = λ0/√(εg). (1) Here, εg is an equivalent dielectric constant of the leaky waveguide, and is expressed by εg = εr - (λ0/λc')2, (2) where εr is the dielectric constant of the material filled in the waveguide, and it equals 1 when no dielectric is filled; λ0 is the wavelength in free space, and λc' is the cut off wavelength of the fundamental mode in the leaky waveguide. λc' is actually different from that in closed waveguide, but the difference is not significant. The propagation constant of the leaky waveguide is then expressed by β = k0 √(εg), (3) where k0 is the wave number in free space. As we know, periodic structures can excite a lot of spatial harmonics, and some of them can leak away from the structures. The radiation condition and the beam angle of the mth harmonic are -1 <; √ εg + m λ0 / P <; 1, (4) φm = cos-1 (√(εg) + mλ0 / P), (5) where P is the period of the slots cut in the waveguide wall. From the analysis we find that the radiation beam directions of the spatial harmonics of leaky waveguide are determined by both the equivalent dielectric constant εg and the period of the slots P, so either changing of εg or changing of P will lead to changing of radiation beam angle. Based on these theory and formulas, the transmission and radiation characteristics of spatial harmonics of the leaky waveguide are studied first, and the relationships between the radiation field and structure parameters are studied as well. It can be found that for a leaky waveguide, both the harmonics with negative order (m <; 0) and positive order (m ≥ 0) can generate leaky waves. This is different from that of the leaky coaxial cable, in which only the harmonics with negative order (m <; 0) can generate leaky wave. An approach based on numerical method for analyzing the propagation constant of leaky waveguide is also given, and the relationship between the propagation constant and waveguide parameters is analyzed. The radiation property of the spatial harmonics of periodic leaky wave structures is then used in the design of antennas with beam-formed radiation patterns, for low power consumption wireless communication application. The basic principle of the design is to superpose the radiations from the -1th order spatial harmonics of a number of leaky wave structures with different slot periods in a weighting way, and the weighting factors are determined by the desired radiation pattern. Since different periodic structures generate radiation beams in different directions, and different weighting factors lead to different radiation strengths, so by properly selecting the periodic structures and weighting factors, the desired radiation pattern can be formed. But for realistic application, these leaky structures with different slot periods should be mapped into one structure that can be fabricated. So the functions describing different periodic slot structures are also superposed together in a weighting way, and the combination slot structural function for the realistic leaky wave antenna is finally obtained. The weighting factors used in the radiation field superposition and the weighting factors used in the structural function superposition are two different sets of weighting functions, and they should be mapped into each other, the key is to find the relationship between the radiation field and the structure parameters. While the weighting factors for structural function superposition is found, we obtain the final antenna structure. Using this method, two kinds of new leaky wave antennas with beam-formed radiation patterns are designed based on rectangular waveguide and SIW structures.