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CN101127412B - A coupling output structure for gyrotron traveling wave amplifier - Google Patents

A coupling output structure for gyrotron traveling wave amplifier Download PDF

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CN101127412B
CN101127412B CN2007101219798A CN200710121979A CN101127412B CN 101127412 B CN101127412 B CN 101127412B CN 2007101219798 A CN2007101219798 A CN 2007101219798A CN 200710121979 A CN200710121979 A CN 200710121979A CN 101127412 B CN101127412 B CN 101127412B
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circular waveguide
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tapered circular
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CN101127412A (en
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杜朝海
刘濮鲲
耿志辉
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Abstract

本发明一种回旋行波管放大器耦合输出结构,具有一输入端口;具有一输出端口:输出端口半径大于输入端口半径;在输入端口与输出端口之间级联有第一级渐变圆波导和第N级渐变圆波导。采用两段修正道尔夫——切比雪夫渐变圆波导级联,或者采用两段修正道尔夫——切比雪夫渐变圆波导中间级联一过渡圆波导。该耦合输出结构解决了已有技术的尺寸过大、输入端口反射系数不够低、杂模抑制能力不够强等问题。该耦合输出结构应用于回旋行波管放大器中取得了积极的效果,这对于发展我国应用于的远程雷达,电子信息对抗等方面的高功率微波源具有重要的实际工程意义。

Figure 200710121979

A coupling output structure of a gyrotron traveling wave tube amplifier in the present invention has an input port; an output port: the radius of the output port is greater than the radius of the input port; a first-stage tapered circular waveguide and a second-stage gradient circular waveguide are cascaded between the input port and the output port N-level tapered circular waveguide. Two sections of modified Dorff-Chebyshev tapered circular waveguides are cascaded, or two sections of modified Dorff-Chebyshev tapered circular waveguides are cascaded in the middle to a transitional circular waveguide. The coupled output structure solves the problems of the prior art that the size is too large, the reflection coefficient of the input port is not low enough, the mixed mode suppression ability is not strong enough, and the like. The coupling output structure has been applied to the cyclotron traveling wave tube amplifier and achieved positive results, which has important practical engineering significance for the development of high-power microwave sources used in long-range radar and electronic information countermeasures in my country.

Figure 200710121979

Description

一种回旋行波管放大器耦合输出结构 A Coupling Output Structure of Contronic TWT Amplifier

技术领域technical field

本发明属于微波技术领域,它特别涉及高功率微波器件。The invention belongs to the field of microwave technology, and particularly relates to high-power microwave devices.

背景技术Background technique

我国在远程雷达的发展方面与国外差距很大,主要是没有合适的高功率微波源,而目前国内研制的高功率微波源,其功率远不能满足超远程雷达系统的需求,但是回旋行波管放大器是最有可能满足这种要求的高功率微波源之一。There is a big gap between my country and foreign countries in the development of long-range radar, mainly because there is no suitable high-power microwave source, and the power of the high-power microwave source developed in China is far from meeting the needs of ultra-long-range radar systems. Amplifiers are one of the high power microwave sources most likely to meet this requirement.

回旋行波管放大器的耦合输出结构从根本上讲,就是一个圆波导渐变结构,它的主要作用就是将半径较小的圆波导匹配到半径较大的圆波导上。能够完成这个功能的渐变结构的渐变方法有很多种,直线渐变、指数渐变和切比雪夫渐变等,多种方式。不同的渐变方式,在不同的应用中具有不同的性能。在回旋行波管放大器的应用中,通常采用单段渐变结构。Fundamentally speaking, the coupling output structure of the gyrotron amplifier is a circular waveguide gradient structure, and its main function is to match the circular waveguide with a smaller radius to the circular waveguide with a larger radius. There are many gradient methods for the gradient structure that can accomplish this function, such as linear gradients, exponential gradients, and Chebyshev gradients. Different gradient methods have different performances in different applications. In the application of the gyro-traveling-wave tube amplifier, a single-stage taper structure is usually used.

在附图中,图1A、图1B、图1 C和图1D示出了一种根据现有技术的解决方案设计的回旋行波管放大器耦合输出结构,它采用单段修正道尔夫——切比雪夫渐变圆波导参考文献:[1]H.Flugel,E.Kuhn,“Computer-Aided Analysis and Design of Circular Waveguide Tapers”.IEEE trans.,Microwave Theory and Techniques,vol.36,no.2,Feb.1988,pp 332-336.。为了便于和本发明的实施方案比较,图1A、图1B、图1C和图1D所例出现有技术解决方案与本发明的实施例具有相同的输入端口半径和输出端半径,分别为5.82mm和20mm。In the accompanying drawings, Fig. 1A, Fig. 1B, Fig. 1C and Fig. 1D show a kind of coupling output structure of the gyrotron traveling wave tube amplifier designed according to the solution of the prior art, which adopts a single-segment modified Dolf—— Chebyshev tapered circular waveguide references: [1] H.Flugel, E.Kuhn, "Computer-Aided Analysis and Design of Circular Waveguide Tapers". IEEE trans., Microwave Theory and Techniques, vol.36, no.2, Feb. 1988, pp 332-336. For ease of comparison with embodiments of the present invention, the prior art solutions shown in Fig. 1A, Fig. 1B, Fig. 1C and Fig. 1D have the same input port radius and output port radius as the embodiment of the present invention, which are 5.82mm and 5.82mm respectively. 20mm.

图1A是单段修正道尔夫——切比雪夫渐变圆波导的半径随轴向位置的变化图。图1D、图2D和图3D中的曲线所代表的意义分别是:曲线S11表示耦合输出结构的输入端口1反射系数;曲线S12表示耦合输入波导的工作主模TE11由输入端口1到输出端口2的传输曲线;曲线S121表示工作主模TE11从输入端口耦合到输出端口的第一杂模TM11的传输曲线;曲线S122表示工作主模TE11从输入端口1耦合到输出端口2的第二杂模TE31的传输曲线。图1C、图1D、图2C、图2D、图3C和图3D采用有限元数值计算方法计算得到。Fig. 1A is a diagram of the variation of the radius of a single-segment modified Dolf-Chebyshev tapered circular waveguide with the axial position. The meanings represented by the curves in Fig. 1D, Fig. 2D and Fig. 3D are respectively: Curve S11 represents the reflection coefficient of input port 1 of the coupling output structure; Curve S121 represents the transmission curve of the first miscellaneous mode TM11 of the working main mode TE11 coupled from the input port to the output port; curve S122 represents the second miscellaneous mode TE31 of the working main mode TE11 coupled from the input port 1 to the output port 2 the transmission curve. Fig. 1C, Fig. 1D, Fig. 2C, Fig. 2D, Fig. 3C and Fig. 3D are calculated by finite element numerical calculation method.

从图1A可以看到在当前参数条件下,该耦合输出结构长度为195.798mm;图1B是图1A所对应的耦合输出结构的剖面图;图1C是图1B结构对应的驻波比图,其中在16GHz处的驻波比约为1.4,在大于17.5GHz的频率范围内驻波比约为1.1以下;图1D是图1B结构对应的杂模抑制情况,从图中可以看到,杂模抑制曲线S121和S122在高频段17.5GHz以上处于-15dB到-20dB之间。这些都说明根据现有技术的解决方案和基于当前结构参数而设计的耦合输出结构在结构尺寸、驻波比和杂模抑制能力等方面都还不够理想。From Figure 1A, it can be seen that under the current parameter conditions, the length of the coupling output structure is 195.798mm; Figure 1B is a cross-sectional view of the coupling output structure corresponding to Figure 1A; Figure 1C is a standing wave ratio diagram corresponding to the structure of Figure 1B, where The standing wave ratio at 16GHz is about 1.4, and the standing wave ratio is about 1.1 or less in the frequency range greater than 17.5GHz; Figure 1D shows the situation of mixed mode suppression corresponding to the structure of Figure 1B. It can be seen from the figure that the mixed mode suppression The curves S121 and S122 are between -15dB and -20dB above the high frequency band 17.5GHz. These all show that the solutions based on the prior art and the coupling output structure designed based on the current structural parameters are not ideal in terms of structural size, standing wave ratio, and ability to suppress mixed modes.

发明内容Contents of the invention

本发明的目的是解决现有技术的单段修正道尔夫——切比雪夫渐变圆波导结构的尺寸过大、输入端口反射系数不够低、杂模抑制能力不够强等问题,为此,本发明提供一种回旋行波管放大器耦合输出结构。The purpose of the present invention is to solve the problems of the single-segment modified Dolf-Chebyshev tapered circular waveguide structure in the prior art, such as the size is too large, the reflection coefficient of the input port is not low enough, and the mixed mode suppression ability is not strong enough. The invention provides a coupling output structure of a gyrotron traveling wave tube amplifier.

为了实现所述目的,本发明提供的多段级联式回旋行波管放大器耦合输出结构的技术方案如下:In order to achieve the stated purpose, the technical scheme of the coupling output structure of the multi-stage cascaded traveling wave tube amplifier provided by the present invention is as follows:

具有一输入端口;具有一输出端口:输出端口半径大于输入端口半径;在输入端口与输出端口之间级联有第一级渐变圆波导和第N级渐变圆波导。It has an input port; it has an output port: the radius of the output port is greater than the radius of the input port; between the input port and the output port, there are a first-level tapered circular waveguide and an N-level tapered circular waveguide cascaded.

根据本发明的实施例,所述第一级渐变圆波导和第N级渐变圆波导采用修正道尔夫——切比雪夫渐变圆波导。According to an embodiment of the present invention, the first-level tapered circular waveguide and the N-th stage tapered circular waveguide use a modified Dolf-Chebyshev tapered circular waveguide.

根据本发明的实施例,采用二段波导级联,即第一级渐变圆波导与第二级渐变圆波导级联;第一级渐变圆波导的一端为输入端口,第二级渐变圆波导的一端为输出端口。According to the embodiment of the present invention, two-stage waveguide cascading is adopted, that is, the first-stage tapered circular waveguide is cascaded with the second-stage tapered circular waveguide; one end of the first-stage tapered circular waveguide is the input port, and the second-stage tapered circular waveguide One end is an output port.

根据本发明的实施例,所述第一级渐变圆波导和第二级渐变圆波导采用修正道尔夫——切比雪夫渐变圆波导。According to an embodiment of the present invention, the first-stage tapered circular waveguide and the second-stage tapered circular waveguide are modified Dolf-Chebyshev tapered circular waveguides.

根据本发明的实施例,采用三段波导级联,即在第一级渐变圆波导与第三级渐变圆波导之间级联有第二级过渡圆波导;第一级渐变圆波导的一端为输入端口,第三级渐变圆波导的一端为输出端口。According to an embodiment of the present invention, a three-stage waveguide cascade is adopted, that is, a second-stage transitional circular waveguide is cascaded between the first-stage tapered circular waveguide and the third-stage tapered circular waveguide; one end of the first-stage tapered circular waveguide is An input port, and one end of the third-stage tapered circular waveguide is an output port.

根据本发明的实施例,所述第一级渐变圆波导和第三级渐变圆波导采用修正道尔夫——切比雪夫渐变圆波导,第二级过渡圆波导是一段圆柱波导。According to an embodiment of the present invention, the first-stage tapered circular waveguide and the third-stage tapered circular waveguide are modified Dolf-Chebyshev tapered circular waveguides, and the second-stage transitional circular waveguide is a section of cylindrical waveguide.

根据本发明的实施例,所述第一级渐变圆波导的整体半径变化小于第N级渐变圆波导的整体半径变化;第一级渐变圆波导的第一参考杂模抑制度小于第N级渐变圆波导的第一参考杂模抑制度。According to an embodiment of the present invention, the overall radius change of the first-stage tapered circular waveguide is smaller than the overall radius change of the N-stage tapered circular waveguide; the first reference complex mode suppression degree of the first-stage tapered circular waveguide is smaller than that of the N-stage tapered The first reference noise-mode rejection for a circular waveguide.

本发明的积极效果:本发明的多段级联式回旋行波管放大器耦合输出结构解决了现有技术解决方案的单段修正道尔夫——切比雪夫渐变圆波导结构[1]的尺寸过大、输入端口反射系数不够低、杂模抑制能力不够强等问题。在本发明实施例所述耦合输出结构工作频带靠近其输入端口的截止频率15.1GHz,其特点是工作频带内驻波比较低,杂模抑制能力高,结构紧凑,内壁光滑。将该耦合输出结构与现有技术在相同结构参数的下设计的单段修正道尔夫——切比雪夫渐变圆波导结构相比,它具有更好的传输性能,它具有更加紧凑的结构、更低的驻波比和更好的杂模抑制能力,而且较好地满足回旋行波管放大器的整管组装要求。Positive effects of the present invention: the coupling output structure of multi-stage cascaded cyclotron traveling wave tube amplifiers of the present invention solves the single-stage modified Dolf-Chebyshev tapered circular waveguide structure [1] of the prior art solution. Large, the input port reflection coefficient is not low enough, the mixed mode suppression ability is not strong enough and so on. In the embodiment of the present invention, the coupling output structure has a working frequency band close to the cut-off frequency of its input port of 15.1 GHz, which is characterized by relatively low standing wave in the working frequency band, high ability to suppress mixed modes, compact structure, and smooth inner wall. Compared with the single-segment modified Dolf-Chebyshev tapered circular waveguide structure designed under the same structural parameters in the prior art, the coupling output structure has better transmission performance, and it has a more compact structure, Lower VSWR and better ability to suppress mixed modes, and better meet the assembly requirements of the whole tube of the gyro-traveling-wave tube amplifier.

本发明应用于回旋行波管放大器这种高功率微波源,在雷达目标成像、雷达反低空飞行目标、导弹防御和电子对抗等国防领域,以及深空探测、遥感、气象和导航等民用领域都有很好的应用前景。The present invention is applied to the high-power microwave source of the cyclotron traveling wave tube amplifier, and is used in national defense fields such as radar target imaging, radar anti-low flying target, missile defense and electronic countermeasures, as well as civil fields such as deep space detection, remote sensing, meteorology and navigation. It has a good application prospect.

附图说明Description of drawings

图1A是现有技术的回旋行波管放大器耦合输出结构的半径随轴向位置的变化;Fig. 1A is the variation of the radius of the coupled output structure of the gyrotron traveling wave tube amplifier with the axial position in the prior art;

图1B是图1A结构所对应结构的剖面图;Fig. 1B is a sectional view of the structure corresponding to the structure of Fig. 1A;

图1C是图1A结构所对应的驻波比;Fig. 1C is the standing wave ratio corresponding to the structure of Fig. 1A;

图1D是图1A结构所对应的杂模抑制情况;Fig. 1D is the situation of heterogeneous mode suppression corresponding to the structure of Fig. 1A;

图2A是本发明实施例1的半径随轴向位置的变化;Fig. 2A is the variation of the radius with the axial position in Embodiment 1 of the present invention;

图2B是图2A实施方案所对应结构的剖面图;Fig. 2B is a sectional view of the structure corresponding to the embodiment of Fig. 2A;

图2C是图2A实施方案所对应的驻波比;Fig. 2C is the standing wave ratio corresponding to the embodiment of Fig. 2A;

图2D是图2A实施方案所对应的杂模抑制情况;Fig. 2D is the situation of heterogeneous mode suppression corresponding to the embodiment of Fig. 2A;

图3A是根据本发明的实施例2的半径随轴向位置的变化;Fig. 3 A is the variation of the radius with the axial position according to Embodiment 2 of the present invention;

图3B是图3A实施方案所对应结构的剖面图;Fig. 3B is a sectional view of the structure corresponding to the embodiment of Fig. 3A;

图3C是图3A实施方案所对应的驻波比;Fig. 3 C is the standing wave ratio corresponding to the embodiment of Fig. 3A;

图3D是图3A实施方案所对应的杂模抑制情况;Fig. 3D is the situation of heterogeneous mode suppression corresponding to the embodiment of Fig. 3A;

具体实施方案specific implementation plan

为了帮助更好地理解本发明,下面将参考附图举例描述本发明的具体实施方案,以下将结合附图具体阐述多段级联式回旋行波管放大器耦合输出结构。In order to help a better understanding of the present invention, the specific implementation of the present invention will be described below with reference to the accompanying drawings, and the coupling output structure of multi-stage cascaded gyrotron amplifiers will be described in detail below with reference to the accompanying drawings.

回旋行波管放大器在毫米波段具有的高功率和宽带宽能力,使其成为高功率微波源中倍受关注的一种相干辐射源,在雷达和通信系统中已经得到广泛的应用。回旋行波管放大器的主互作用段采用的波导半径不符合电子注热负荷需求或收集极电压限制,因此,需要用一段渐变波导来连接互作用段和输出窗,也即耦合输出结构。回旋行波管放大器的耦合输出结构能够将工作于靠近截止频率的主互作用波导中的高能微波耦合到外部的微波功率传输系统。与此同时,耦合输出结构必须要有低的驻波比和高的杂模抑制能力。The high-power and wide-bandwidth capabilities of the cyclotron traveling-wave tube amplifier in the millimeter wave band make it a coherent radiation source that has attracted much attention among high-power microwave sources, and has been widely used in radar and communication systems. The waveguide radius used in the main interaction section of the gyrotron TWT amplifier does not meet the electron heat injection load requirements or the collector voltage limit. Therefore, a tapered waveguide needs to be used to connect the interaction section and the output window, that is, the coupling output structure. The coupling output structure of the gyrotron amplifier can couple the high-energy microwave in the main interaction waveguide working near the cutoff frequency to the external microwave power transmission system. At the same time, the coupled output structure must have a low standing wave ratio and high rejection of heterogeneous modes.

回旋行波管放大器的工作特性对其耦合输出结构的设计提出以下两点限制:其一,结构上,高功率回旋行波管放大器的工作频率通常靠近其主互作用波导的截止频率,主互作用波导半径相对较小;为了传输较高的功率,要求外部传输波导具有相对较大的半径。因此,耦合输出结构的输出端圆波导半径通常比输入半径大2~3倍以上。耦合输出结构的长度应该尽可能短,以减小对回旋管整管体积和工作磁场的要求。耦合输出结构的内壁要光滑,以防止打火。要保证耦合输出结构的输出和输入口的波导半径的变化梯度应该尽可能低,以免输出波导和外部系统连接时传输性能改变。The working characteristics of the gyrotron TWT amplifier put forward the following two restrictions on the design of its coupling output structure: First, structurally, the operating frequency of the high-power gyrotron TWT amplifier is usually close to the cut-off frequency of its main interaction waveguide, and the main interaction waveguide The active waveguide has a relatively small radius; in order to transmit higher powers, the outer transmission waveguide is required to have a relatively large radius. Therefore, the radius of the circular waveguide at the output end of the coupled output structure is usually 2 to 3 times larger than the input radius. The length of the coupling output structure should be as short as possible to reduce the requirements on the volume of the gyrotron and the working magnetic field. The inner wall of the coupling output structure should be smooth to prevent sparking. It is necessary to ensure that the change gradient of the waveguide radius between the output of the coupling output structure and the input port should be as low as possible, so as to prevent the transmission performance from changing when the output waveguide is connected to an external system.

其二,传输性能上,耦合输出结构必须要有较低的驻波比,以避免反射波影响主互作用回路正常工作;还要求高能微波在耦合输出结构中传输的模式稳定度高,输出圆波导必须要有较好的杂模抑制能力。这两点限制对回旋行波管放大器耦合输出结构的设计提出很大的挑战。Second, in terms of transmission performance, the coupling output structure must have a low standing wave ratio to avoid reflected waves affecting the normal operation of the main interaction loop; it is also required that the high-energy microwave transmission mode in the coupling output structure has high stability and the output circle The waveguide must have a good ability to suppress mixed modes. These two limitations pose a great challenge to the design of the coupling output structure of the gyro TWT amplifier.

修正道尔夫——切比雪夫渐变圆波导在波导渐变中已经被广泛地采用,与其他的渐变方式(如线性渐变、指数渐变等)相比,具有输入输出端口波导半径变化梯度为零,内壁光滑等优点,杂模抑制能力强等优点[1]。但是,通常情况下的修正道尔夫——切比雪夫渐变圆波导工作频带范围都远离端口的截止频率。而在回旋行波管放大器的应用中,需要耦合输出结构的工作频带靠近其输入端口的截止频率。在这种情况下,若采用单段修正道尔夫——切比雪夫渐变圆波导作为回旋行波管放大器耦合输出结构就会出现尺寸结构不够紧凑、反射不够低、杂模抑制能力不够强等问题。因此采用单段修正道尔夫——切比雪夫渐变圆波导的耦合输出结构也就不能很好满足实际的需求,而本发明提出的多段级联式回旋行波放大器耦合输出结构能够得到更紧凑的尺寸结构、更小的反射系数和更好的杂模抑制能力。Modified Dolf-Chebyshev tapered circular waveguide has been widely used in waveguide tapering. Compared with other tapering methods (such as linear tapering, exponential tapering, etc.), the change gradient of waveguide radius with input and output ports is zero. It has the advantages of smooth inner wall and strong suppression ability of mixed modes [1]. However, the working frequency range of the modified Dolf-Chebyshev tapered circular waveguide is usually far away from the cut-off frequency of the port. However, in the application of the gyrotron traveling wave tube amplifier, the working frequency band of the coupled output structure needs to be close to the cutoff frequency of its input port. In this case, if a single-segment modified Dolf-Chebyshev tapered circular waveguide is used as the coupling output structure of the convoluted traveling wave tube amplifier, the size and structure will not be compact enough, the reflection will not be low enough, and the ability to suppress mixed modes will not be strong enough. question. Therefore, the coupling output structure of the single-section modified Dolf-Chebyshev tapered circular waveguide cannot meet the actual needs well, and the coupling output structure of the multi-section cascaded convolution traveling wave amplifier proposed by the present invention can be more compact Smaller size structure, smaller reflection coefficient and better ability to suppress miscellaneous modes.

图1A、图1B、图1C和图1D示出了一种现有技术方案,它采用单段修正道尔夫——切比雪夫渐变圆波导。为了更加准确地说明本发明设计方案的性能的优越性,特别设计和计算了与本发明具有相同结构参数的单段修正道尔夫——切比雪夫渐变圆波导作为参考。将这个参考设计方案的半径变化图1A、结构图1B、驻波比图1C和杂模抑制情况图1D与本发明的两个实施例进行对比,更容易分辨出其中的不同点和本发明性能的优越性。Figures 1A, 1B, 1C and 1D show a prior art solution using a single segment modified Dolf-Chebyshev tapered circular waveguide. In order to more accurately illustrate the performance superiority of the design scheme of the present invention, a single-segment modified Dolf-Chebyshev tapered circular waveguide with the same structural parameters as the present invention is specially designed and calculated as a reference. Comparing the radius change Fig. 1A, structure Fig. 1B, standing wave ratio Fig. 1C and heterogeneous mode suppression Fig. 1D of this reference design scheme with the two embodiments of the present invention, it is easier to distinguish the differences and the performance of the present invention superiority.

相关理论[1]表明修正道尔夫——切比雪夫渐变圆波导的三个设计参数,可以有由以下方程描述:The relevant theory [1] shows that the three design parameters of the modified Dolf-Chebyshev tapered circular waveguide can be described by the following equations:

WW maxmax (( dBdB )) == -- 2020 loglog 1010 [[ 22 xx mm xx nno xx mm 22 -- xx nno 22 lnln (( aa 22 aa 11 )) ·· θθ sinhsinh (( θθ )) (( 0.217230.21723 )) ]]

aa (( θθ )) == aa 11 expexp {{ lnln (( aa 22 aa 11 )) ∫∫ -- θθ θθ II 00 (( θθ 11 -- (( ξξ // θθ )) 22 )) 22 sinhsinh θθ dξdξ }}

zz (( θθ )) == 22 kk 00 xx mm 22 -- xx nno 22 ∫∫ -- θθ θθ aa 22 (( ξξ )) dξdξ

其中,a、z分别是渐变波导半径和长度;Wmax是设计过程中的第一参考杂模抑制度。I0是第一类零阶修正贝塞尔函数。a1、a2分别是输入波导和输出波导的半径。k0是工作频带中心频率的自由空间波数。xn、xm分别是工作主模和第一参考杂模所对应的贝塞儿函数导数的根。需要说明的是,第一参考杂模抑制度Wmax只是一个参考值,用于确定积分边界θ。以下将详细地叙述设计参数、设计过程和取得的性能。Among them, a and z are the radius and length of the tapered waveguide respectively; W max is the first reference mixed-mode suppression degree in the design process. I 0 is the zero-order modified Bessel function of the first kind. a 1 and a 2 are the radii of the input and output waveguides, respectively. k0 is the free-space wavenumber at the center frequency of the operating frequency band. x n and x m are the roots of the Bessel function derivatives corresponding to the working principal mode and the first reference miscellaneous mode respectively. It should be noted that the first reference noise-mode suppression degree W max is only a reference value for determining the integral boundary θ. The design parameters, design process and achieved performance will be described in detail below.

在现有技术与本发明的两个具体实施方式中,举例中采用输入端口1的半径取5.82mm,输出端口2的半径取20mm,输出端口的半径是输入端口半径的3.44倍。根据计算可以得到,选择输出端口半径与输入端口半径之比为1,或者大到5倍,即半径之比为1倍到5倍之间都能够得到很好的性能。In the two specific implementations of the prior art and the present invention, the radius of the input port 1 is 5.82 mm, the radius of the output port 2 is 20 mm, and the radius of the output port is 3.44 times the radius of the input port. According to the calculation, it can be obtained that the ratio of the radius of the output port to the radius of the input port is 1, or as large as 5 times, that is, the ratio of the radius is 1 to 5 times, and good performance can be obtained.

为了说明本发明的多段级联式回旋行波管放大器耦合输出结构与现有的单段修正道尔夫——切比雪夫渐变圆波导的结构和性能上的优越性,在以下的叙述中将采用对比的方法,将本发明的实施例1,如图2A、图2B、图2C和图2D所示,实施例2,如图3A、图3B、图3C和图3D所示,与现有技术如图1A、图1B、图1C和图1D所示,进行对比阐述。In order to illustrate the superiority in the structure and performance of the multi-stage cascaded gyro-traveling wave tube amplifier coupling output structure of the present invention and the existing single-stage modified Dolf-Chebyshev tapered circular waveguide, the following description will Adopt the method of comparison, with embodiment 1 of the present invention, as shown in Figure 2A, Figure 2B, Figure 2C and Figure 2D, embodiment 2, as shown in Figure 3A, Figure 3B, Figure 3C and Figure 3D, and existing The techniques are shown in Figure 1A, Figure 1B, Figure 1C and Figure 1D for comparative illustration.

请参阅图1A、图1B、图1C和图1D,示出了采用现有技术单段修正道尔夫——切比雪夫渐变圆波导结构设计的回旋行波管放大器耦合输出结构的详细情况。设计参数:输入端口1半径5.82mm,输出端口2半径20mm,第一参考杂模抑制度Wmax为-60dB,整体长度为195.798mm。图1A示出了有解决方案(单段修正道尔夫——切比雪夫渐变圆波导结构)的半径随轴向位置的变化。图1B示出了图1A对应结构的剖面图。图1C示出了图1B结构对应的驻波比,其中在16GHz处的驻波比约为1.4,在大于17.5GHz的频率范围内约为1.1以下。图1D是图1B结构对应的杂模抑制情况,从图中可以看到,曲线S121和S122在高频段(17.5GHz以上)处于-15dB到-20dB之间;曲线S11表示耦合输出结构的输入端口1反射系数,曲线S12表示耦合输入波导的工作主模TE11由输入端口1到输出端口2的传输曲线。图1A、图1C和图1D说明基于已有解决方案的单段修正道尔夫——切比雪夫渐变圆波导结构具有结构尺寸大、输入端口1反射系数不够低、杂模抑制能力不够强等问题。Please refer to Fig. 1A, Fig. 1B, Fig. 1C and Fig. 1D, which show the details of the coupled output structure of the convoluted TWT amplifier using the prior art single-segment modified Dolf-Chebyshev tapered circular waveguide structure design. Design parameters: the radius of input port 1 is 5.82mm, the radius of output port 2 is 20mm, the first reference mixed mode suppression degree W max is -60dB, and the overall length is 195.798mm. Figure 1A shows the variation of radius with axial position for a solution (single-segment modified Dolf-Chebyshev tapered circular waveguide structure). Figure 1B shows a cross-sectional view of the structure corresponding to Figure 1A. FIG. 1C shows the standing wave ratio corresponding to the structure of FIG. 1B , wherein the standing wave ratio is about 1.4 at 16 GHz, and is about 1.1 or less in the frequency range greater than 17.5 GHz. Figure 1D is the mixed mode suppression corresponding to the structure of Figure 1B. It can be seen from the figure that the curves S121 and S122 are between -15dB and -20dB in the high frequency band (above 17.5GHz); the curve S11 represents the input port of the coupling output structure 1 reflection coefficient, the curve S12 represents the transmission curve of the working main mode TE11 coupled into the waveguide from the input port 1 to the output port 2. Figure 1A, Figure 1C and Figure 1D illustrate that the single-segment modified Dolf-Chebyshev tapered circular waveguide structure based on the existing solutions has the advantages of large structure size, insufficient reflection coefficient of input port 1, and insufficient suppression of mixed modes, etc. question.

实施例1:请参阅图2A、图2B、图2C和图2D,采用两段修正道尔夫——切比雪夫渐变圆波导级联而成设计的回旋行波管放大器耦合输出结构的详细情况。请参阅图2A,示出了实施例1的半径随轴向距离的变化。在图2B中,耦合输出结构采用二段波导级联,即第一级渐变圆波导3与第二级渐变圆波导4级联;第一级渐变圆波导3的一端为输入端口1,第二级渐变圆波导4的一端为输出端口2。第一级渐变圆波波导3和第二级渐变圆波导4都是修正道尔夫——切比雪夫渐变圆波导。该实施例的设计参数为:输入端口1半径5.82mm,输出端口2半径20mm,整体长度为174.487mm。其中,第一级渐变圆波导3输入半径5.82mm,输出半径7.5mm,长度54.27mm,设计时Wmax为-75dB;第二级渐变波导4的输入半径7.5mm,输出半径20mm,长度130.317mm,设计时Wmax为-35dB。Embodiment 1: Please refer to Fig. 2A, Fig. 2B, Fig. 2C and Fig. 2D, the details of the coupling output structure of the convoluted traveling wave tube amplifier designed by cascading two sections of modified Dolf-Chebyshev tapered circular waveguides . Please refer to FIG. 2A , which shows the variation of the radius with the axial distance in Embodiment 1. Referring to FIG. In Figure 2B, the coupling output structure adopts two-stage waveguide cascading, that is, the first-stage tapered circular waveguide 3 is cascaded with the second-stage tapered circular waveguide 4; one end of the first-stage tapered circular waveguide 3 is the input port 1, and the second stage tapered circular waveguide One end of the tapered circular waveguide 4 is the output port 2 . Both the first-stage tapered circular waveguide 3 and the second-stage tapered circular waveguide 4 are modified Dolf-Chebyshev tapered circular waveguides. The design parameters of this embodiment are: the radius of the input port 1 is 5.82 mm, the radius of the output port 2 is 20 mm, and the overall length is 174.487 mm. Among them, the input radius of the first-stage tapered circular waveguide 3 is 5.82mm, the output radius is 7.5mm, and the length is 54.27mm, and the W max is -75dB during design; the input radius of the second-stage tapered waveguide 4 is 7.5mm, the output radius is 20mm, and the length is 130.317mm , W max is -35dB during design.

根据上述设计参数,第一级渐变圆波导3的整体半径变化小于第二级渐变圆波导4的整体半径变化,即第一级渐变圆波导3的整体半径变化较小,只有1.68mm,第二级渐变圆波导4的整体半径变化较大,为12.5mm。经过计算,第一级渐变圆波导3的整体半径变化取值0.8mm,或则到2mm,第二级渐变圆波导4的整体半径变化取值13.38mm,或者小到12.18mm,这样的取值范围内设计,都可以得到很好的传输性能。第一级渐变圆波导3的第一参考杂模抑制度比第二级渐变圆波导4的第一参考杂模抑制度小30dB。经过计算,第一级渐变圆波导3的第一参考杂模抑制度比第二级渐变圆波导4的第一参考杂模抑制度小20dB,或者小40dB,这样的取值范围内设计,都可以得到很好的传输性能。According to the above design parameters, the overall radius change of the first-stage tapered circular waveguide 3 is smaller than the overall radius change of the second-stage tapered circular waveguide 4, that is, the overall radius change of the first-stage tapered circular waveguide 3 is small, only 1.68mm, and the second The overall radius of the gradually tapered circular waveguide 4 varies greatly, which is 12.5 mm. After calculation, the overall radius change of the first-stage tapered circular waveguide 3 is 0.8 mm, or 2 mm, and the overall radius change of the second-stage tapered circular waveguide 4 is 13.38 mm, or as small as 12.18 mm. Design within the range can get good transmission performance. The first reference mixed-mode suppression degree of the first-stage tapered circular waveguide 3 is 30 dB smaller than the first reference mixed-mode suppression degree of the second-stage tapered circular waveguide 4 . After calculation, the first reference mixed-mode suppression degree of the first-stage tapered circular waveguide 3 is 20dB or 40dB lower than the first reference mixed-mode suppression degree of the second-stage tapered circular waveguide 4. Designs within such a value range are all Good transmission performance can be obtained.

与已有解决方案在相同的结构参数即输入端口1和输出端口2的半径下的结构相比较,即与图1B相比较,可以发现本实施例的整体长度更短,结构更加紧凑。Compared with the structure of the existing solution under the same structural parameters, that is, the radii of the input port 1 and the output port 2 , that is, compared with FIG. 1B , it can be found that the overall length of this embodiment is shorter and the structure is more compact.

请参阅图2C,示出了该方案的驻波比。具体情况是:驻波比小于1.15的频带范围是16GHz~18.5GHz;驻波比小于1.05的频带范围是16.37GHz~18.5GHz;驻波比小于1.03的工作频带为16.50GHz~18.45GHz,且带内驻波比曲线很平坦。工作频带的中心频率17.25GHz为输入端的工作模式的截止频率15.1GHz的1.14倍。与现有技术方案在相同的结构参数即输入端口1和输出端口2的半径下的结构的驻波比相比较,即与图1C相比较,实施例1的在整个工作频带内具有更低的驻波比,即实施例1比现有技术方案具有更低的反射,更好的传输性能。请参阅图2D,示出了本发明实施例1的杂模抑制情况。在整个15.5GHz~18.5GHz的频带范围内第一杂模TM11,如曲线S121所示被抑制在-28.5dB以下;第二杂模TE31,如曲线S122所示被抑制在-33.5dB以下。对比现有技术的方案如图1C可以看出本实施例杂模抑制能力更好。曲线S11表示耦合输出结构的输入端口1反射系数,曲线S12表示耦合输入波导的工作主模TE11由输入端口1到输出端口2的传输曲线。通过对本发明实施例1的阐述和与现有技术方案的系统比较,可以看出本发明实施例1比现有技术方案具有更加紧凑的结构、更低的驻波比和更好的模式抑制能力。Please refer to Figure 2C, which shows the VSWR of this scheme. The specific situation is: the frequency band with standing wave ratio less than 1.15 is 16GHz to 18.5GHz; the frequency band with standing wave ratio less than 1.05 is 16.37GHz to 18.5GHz; The ISWR curve is very flat. The center frequency of 17.25 GHz of the operating frequency band is 1.14 times the cutoff frequency of 15.1 GHz of the operating mode of the input end. Compared with the standing wave ratio of the structure under the same structural parameters, that is, the radius of the input port 1 and the output port 2, that is, compared with Fig. 1C, the embodiment 1 has a lower Standing wave ratio, that is, embodiment 1 has lower reflection and better transmission performance than the prior art solution. Please refer to FIG. 2D , which shows the suppression of mixed modes in Embodiment 1 of the present invention. In the entire frequency range of 15.5GHz-18.5GHz, the first miscellaneous mode TM11 is suppressed below -28.5dB as shown by the curve S121; the second miscellaneous mode TE31 is suppressed below -33.5dB as shown by the curve S122. Comparing the solution of the prior art as shown in FIG. 1C , it can be seen that the mixed mode suppression capability of this embodiment is better. The curve S11 represents the reflection coefficient of the input port 1 of the coupling-out structure, and the curve S12 represents the transmission curve of the working main mode TE11 coupled into the waveguide from the input port 1 to the output port 2 . Through the elaboration of Embodiment 1 of the present invention and the system comparison with the prior art solution, it can be seen that the embodiment 1 of the present invention has a more compact structure, lower standing wave ratio and better mode suppression ability than the prior art solution .

实施例2:请参阅图3A、图3B、图3C和图3D,图中示出了采用两段修正道尔夫——切比雪夫渐变圆波导中间加载一段均匀圆波导级联而成设计的回旋行波管放大器耦合输出结构的详细情况。请参阅图3A,示出了本发明实施例2的半径随轴向距离的变化。在图3B中,耦合输出结构采用三段波导级联,即在第一级渐变圆波导5与第三级渐变圆波导7之间级联有;第一级渐变圆波导5的一端为输入端口1,第三级渐变圆波导7的一端为输出端口2。第一级渐变圆波导5和第三级渐变圆波导7都是修正道尔夫——切比雪夫渐变圆波导;第二级过渡圆波导6是一段圆柱波导,介于第一级渐变圆波导5和第三级渐变圆波导7之间。该实施例的设计参数为:输入端口1半径5.82mm,输出端口2半径20mm,整体长度为180.397mm。其中,第一级渐变圆波导5输入半径5.82mm,输出半径7mm,长度47.923mm,设计时Wmax为-75dB;第二级过渡圆波导6是一段长度为17mm半径为7mm均匀圆波导;第三级渐变圆波导7是其输入半径7mm,输出半径20mm,长度115.474mm,设计时Wmax为-32dB。Embodiment 2: Please refer to Fig. 3A, Fig. 3B, Fig. 3C and Fig. 3D, which shows the design of two sections of modified Dolf - Chebyshev tapered circular waveguide loaded with a section of uniform circular waveguide cascaded in the middle. Details of the coupling output structure of the gyrotron traveling wave tube amplifier. Please refer to FIG. 3A , which shows the variation of the radius with the axial distance in Embodiment 2 of the present invention. In FIG. 3B, the coupling output structure adopts three-stage waveguide cascading, that is, there is a cascade connection between the first-stage tapered circular waveguide 5 and the third-stage tapered circular waveguide 7; one end of the first-stage tapered circular waveguide 5 is an input port 1. One end of the third-stage tapered circular waveguide 7 is the output port 2 . The first-stage tapered circular waveguide 5 and the third-stage tapered circular waveguide 7 are both modified Dolf-Chebyshev tapered circular waveguides; the second-stage transitional circular waveguide 6 is a section of cylindrical waveguide between the first-stage tapered circular waveguide 5 and the third grade tapered circular waveguide 7. The design parameters of this embodiment are: the radius of the input port 1 is 5.82 mm, the radius of the output port 2 is 20 mm, and the overall length is 180.397 mm. Among them, the first-stage tapered circular waveguide 5 has an input radius of 5.82mm, an output radius of 7mm, and a length of 47.923mm, and the W max is -75dB during design; the second-stage transition circular waveguide 6 is a uniform circular waveguide with a length of 17mm and a radius of 7mm; The three-stage tapered circular waveguide 7 has an input radius of 7mm, an output radius of 20mm, a length of 115.474mm, and a W max of -32dB during design.

根据上述设计参数,第一级渐变圆波导5的整体半径变化小于第二级渐变圆波导7的整体半径变化,即第一级渐变圆波导5的整体半径变化较小,只有1.18mm,第三级渐变圆波导7的整体半径变化较大,为13mm;。经过计算,第一级渐变圆波导5的整体半径变化取值0.8mm,或则到2mm,第二级渐变圆波导7的整体半径变化取值13.38mm,或者到12.18mm,这样的取值范围内设计,都可以得到很好的传输性能。第一级渐变圆波导5的第一参考杂模抑制度比第三级渐变圆波导7的第一参考杂模抑制度小33dB。经过计算,第一级渐变圆波导5的第一参考杂模抑制度比第二级渐变圆波导7的第一参考杂模抑制度小20dB,或者小40dB,这样的取值范围内设计,都可以得到很好的传输性能。According to the above design parameters, the overall radius change of the first-stage tapered circular waveguide 5 is smaller than the overall radius change of the second-stage tapered circular waveguide 7, that is, the overall radius change of the first-stage tapered circular waveguide 5 is small, only 1.18 mm, and the third The overall radius of the graded tapered circular waveguide 7 varies greatly, which is 13mm; After calculation, the overall radius change of the first-stage tapered circular waveguide 5 is 0.8mm, or to 2mm, and the overall radius change of the second-stage tapered circular waveguide 7 is 13.38mm, or to 12.18mm, such a value range Internal design can get good transmission performance. The first reference mixed-mode suppression degree of the first-stage tapered circular waveguide 5 is 33 dB smaller than the first reference mixed-mode suppression degree of the third-stage tapered circular waveguide 7 . After calculation, the first reference mixed-mode suppression degree of the first-stage tapered circular waveguide 5 is 20dB or 40dB lower than the first reference mixed-mode suppression degree of the second-stage tapered circular waveguide 7. Designs within such a value range are all Good transmission performance can be obtained.

与现有技术方案在相同的结构参数即输入端口1和输出端口2的半径的结构相比较,即与图1B相比较,可以看出实施例2的整体长度更短,结构更加紧凑。Compared with the structure of the existing technical solution with the same structural parameters, that is, the radius of the input port 1 and the output port 2, that is, compared with FIG. 1B, it can be seen that the overall length of embodiment 2 is shorter and the structure is more compact.

请参阅图3C,示出了该实施例的驻波比。具体情况是:驻波比小于1.1的频带范围是15.8GHz~18.5GHz;驻波比小于1.05的频带范围是16.44GHz~18.5GHz。与现有技术方案在相同的结构参数即输入端口1和输出端口2的半径的结构的驻波比相比较,即与图1C相比较,可以看出实施例2的在整个工作频带内具有更低的驻波比,即实施例2比现有技术方案具有更低的反射,更好的传输性能。请参阅图3D,示出了该方案的杂模抑制情况。请参阅图3D,示出了该方案的杂模抑制情况。在整个15.5GHz~18.5GHz的频带范围内第一杂模TM11(曲线S121)被抑制在-25dB以下;第二杂模TE31(曲线S121)被抑制在-32dB以下。曲线S11表示耦合输出结构的输入端口1反射系数,曲线S12表示耦合输入波导的工作主模TE11由输入端口1到输出端口2的传输曲线。对比现有技术方案图1C可以看出实施例2杂模抑制能力更好。通过对本发明实施例2的阐述和与现有技术方案的系统比较,可以看出本发明实施例2比现有技术方案具有更加紧凑的结构、更低的驻波比和更好的模式抑制能力。Referring to Figure 3C, the standing wave ratio of this embodiment is shown. The specific situation is: the frequency range of the VSWR less than 1.1 is 15.8GHz-18.5GHz; the frequency range of the VSWR less than 1.05 is 16.44GHz-18.5GHz. Compared with the standing wave ratio of the structure with the same structural parameters, that is, the radius of the input port 1 and the output port 2, compared with the prior art solution, that is, compared with FIG. 1C, it can be seen that the embodiment 2 has a better Low standing wave ratio, that is, embodiment 2 has lower reflection and better transmission performance than the prior art solution. Please refer to Fig. 3D, which shows the mixed mode suppression of this scheme. Please refer to Fig. 3D, which shows the mixed mode suppression of this scheme. The first miscellaneous mode TM11 (curve S121 ) is suppressed below -25dB in the entire frequency range of 15.5GHz-18.5GHz; the second miscellaneous mode TE31 (curve S121 ) is suppressed below -32dB. The curve S11 represents the reflection coefficient of the input port 1 of the coupling-out structure, and the curve S12 represents the transmission curve of the working main mode TE11 coupled into the waveguide from the input port 1 to the output port 2 . Comparing Fig. 1C of the prior art solution, it can be seen that Embodiment 2 has a better capability of suppressing complex modes. Through the elaboration of Embodiment 2 of the present invention and the system comparison with the prior art solution, it can be seen that the embodiment 2 of the present invention has a more compact structure, lower standing wave ratio and better mode suppression ability than the prior art solution .

经计算以上两个实施例设计方案的输入端口1圆波导半径5.82mm所对应的最低模式截止频率约为15.1GHz,因此将本发明的实施例1和实施例2与现有技术方案相比较,即将图2C、图3C和图1C相比较,可以发现:本发明在靠近截止频率的工作频带16GHz~18.5GHz内驻波比更低,即传输性能更好。The lowest mode cut-off frequency corresponding to the input port 1 circular waveguide radius of 5.82 mm is calculated to be about 15.1 GHz in the design schemes of the above two embodiments. Therefore, comparing Embodiment 1 and Embodiment 2 of the present invention with the prior art solutions, Comparing Fig. 2C, Fig. 3C and Fig. 1C, it can be found that the present invention has a lower standing wave ratio in the working frequency band 16GHz-18.5GHz close to the cutoff frequency, that is, better transmission performance.

以上所述,仅为本发明中的具体实施方式,但本发明的保护范围并不局限于此,任何熟悉该技术的人在本发明所揭露的技术范围内,可理解想到的变换或替换,都应涵盖在本发明的包含范围之内,因此,本发明的保护范围应该以权利要求书的保护范围为准。The above is only a specific implementation mode in the present invention, but the scope of protection of the present invention is not limited thereto. Anyone familiar with the technology can understand the conceivable transformation or replacement within the technical scope disclosed in the present invention. All should be covered within the scope of the present invention, therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims (5)

1.一种回旋行波管放大器耦合输出结构,其特征在于,该结构用于连接回旋行波管放大器的互作用段和输出窗,是将回旋行波管放大器的互作用段中的高能微波耦合到外部的微波功率传输系统,其中:1. A coupling output structure of a gyro-traveling-wave tube amplifier, characterized in that the structure is used to connect the interaction section and the output window of the gyro-traveling-wave tube amplifier, and the high-energy microwave in the interaction section of the gyro-traveling-wave tube amplifier coupled to an external microwave power delivery system where: 具有一输入端口;具有一输出端口:Has an input port; has an output port: 输出端口半径大于输入端口半径;The output port radius is greater than the input port radius; 在输入端口与输出端口之间级联有第一级圆波导至第N级圆波导;其中第一级圆波导和第N级圆波导为第一级渐变圆波导和第N级渐变圆波导;Between the input port and the output port, a first-level circular waveguide to an N-th-level circular waveguide are cascaded; wherein the first-level circular waveguide and the N-level circular waveguide are the first-level tapered circular waveguide and the N-level tapered circular waveguide; 第一级渐变圆波导和第N级渐变圆波导采用修正道尔夫——切比雪夫渐变圆波导,N等于2或3。The first-stage tapered circular waveguide and the N-stage tapered circular waveguide adopt a modified Dolf-Chebyshev tapered circular waveguide, and N is equal to 2 or 3. 2.根据权利要求1所述回旋行波管放大器耦合输出结构,其特征在于,采用二段波导级联,即第一级渐变圆波导与第二级渐变圆波导级联;第一级渐变圆波导的一端为输入端口,第二级渐变圆波导的一端为输出端口。2. According to the coupling output structure of the gyrotron traveling wave tube amplifier according to claim 1, it is characterized in that a two-stage waveguide cascade connection is adopted, that is, the first stage tapered circular waveguide is cascaded with the second stage tapered circular waveguide; the first stage tapered circular waveguide is cascaded; One end of the waveguide is an input port, and one end of the second-stage tapered circular waveguide is an output port. 3.根据权利要求1所述回旋行波管放大器耦合输出结构,其特征在于,采用三段波导级联,即在第一级渐变圆波导与第三级渐变圆波导之间级联的第二级圆波导为第二级过渡圆波导;第一级渐变圆波导的一端为输入端口,第三级渐变圆波导的一端为输出端口。3. According to the coupling output structure of the gyrotron traveling wave tube amplifier according to claim 1, it is characterized in that three-stage waveguide cascading is adopted, that is, the second stage cascaded between the first stage tapered circular waveguide and the third stage tapered circular waveguide The one-stage circular waveguide is the second-stage transitional circular waveguide; one end of the first-stage tapered circular waveguide is an input port, and one end of the third-stage tapered circular waveguide is an output port. 4.根据权利要求3所述回旋行波管放大器耦合输出结构,其特征在于,所述第一级渐变圆波导和第三级渐变圆波导采用修正道尔夫——切比雪夫渐变圆波导,第二级过渡圆波导是一段圆柱波导。4. According to the coupling output structure of the cyclotron traveling wave tube amplifier according to claim 3, it is characterized in that, the first-stage tapered circular waveguide and the third-stage tapered circular waveguide adopt a modified Dolf-Chebyshev tapered circular waveguide, The second-stage transition circular waveguide is a section of cylindrical waveguide. 5.根据权利要求1所述回旋行波管放大器耦合输出结构,其特征在于,第一级渐变圆波导的整体半径变化小于第N级渐变圆波导的整体半径变化;第一级渐变圆波导的第一参考杂模抑制度小于第N级渐变圆波导的第一参考杂模抑制度。5. according to claim 1 described gyrotron traveling wave tube amplifier coupling output structure, it is characterized in that, the overall radius change of the first stage tapered circular waveguide is smaller than the overall radius change of the Nth stage tapered circular waveguide; the first stage tapered circular waveguide The first reference heterogeneous mode suppression degree is smaller than the first reference heterogeneous mode suppression degree of the Nth grade tapered circular waveguide.
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