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外文翻译关于雷达3000字

来源:免费论文网 | 时间:2016-12-05 11:29:57 | 移动端:外文翻译关于雷达3000字

篇一:现代雷达技术外文翻译

一种亚太赫兹真实孔径成像雷达

摘要

对于频率在100MHz到10THz之间的电磁波,由于缺乏高功率源和由水蒸气产生的强电磁吸收,只有极少数的雷达系统和其他系统会在这个频段内工作。出于这个原因,它有时被称为太赫兹间隙。功率源的技术正在改善,从而有利于雷达系统在这个新的前沿电磁波谱的操作。在靠近毫米波/亚毫米波过渡这个频谱区域的下端,相对于更高的频率,该频段的器件更加容易获得,大气衰减也更适中。一个具有长达数百米的成像面的真实孔径雷达已经研制成功,它利用组件可以产生大约50mW的功率。它可以发送一个垂直方向的扇形波束扫描视场中的方位,并在两个垂直方向上接收,此时具有相同位移位置的扇形波束形成干涉,由此可以产生三维图像的表面形貌(排列,方位和高度)。本文介绍了该原型系统的设计,并提出了初步成果,扩展了之前的工作。

关键词:成像雷达,太赫兹,干涉,真实波束成像

一、简介

在太赫兹和亚太赫兹频率(0.14-1太赫兹)工作的有源成像系统已经被开发用于各种场合,主要用于隐藏的武器的检测和生物医学成像等非常狭窄的用途。造成这种范围限制是由于水蒸气对这个频段电磁能量的强吸收以及大多数源只能提供相对较低的功率。虽然已经开发出有合理输出功率的亚太赫兹系统,但是它们或者没有被应用与实验室和研究环境之外,或者不能持续输出,这是多普勒测速雷达的一个关键参数。继续研究亚太赫兹系统和传输将使许多长景的应用现在就开始变得可行,例如成像雷达,宽带通信和遥感。

成像雷达,包括合成孔径雷达(SAR)可以使用其中多个接收器位移在空间和时间的干涉,得到差分相位图算出表面高度估计来提供附加维度。但是也有极少数著名论证性干涉雷达的工作频率高于100GHz(可能同时有这方面的研究)。一个亚太赫兹干涉雷达将提供一个平台,以研究各种可利用短波长的优势产生高分辨率地形图,并且研究和验证后向散射雷达,地形连贯性和亚太赫兹传播理论模型的应用。

这项研究的目标是设计和建造一个概念验证亚太赫兹干涉成像雷达的各种应用。其中灵敏度是一个设计因素,使此平台可以用来探索频谱的这一部分。经证明干涉概念工程的措施可以采取优化系统,以执行涉及尺寸,重量和功率约束(例如无人平台),包括高级天线技术,单片微波集成电路(MMIC)和专用集成电路(ASIC)的特定应用。

二、系统设计

为了达到使用较低成本的组件达到开发验证一个概念体系的目标,一个如图1所示的雷达系统被设计和试制出来。该雷达的主要操作参数在表1。一个微型计算机用于控制雷达,包括波形和扫描参数,并显示结果。所有的数模转换器(DAC)和模数转换器(ADC)电路都使用商业现货(COTS)的电路板。该数模转换器的主频可达2.8GHz,因此理论上可以产生峰值频率1.4GHz,具有几MHz到

1.4 GHz的带宽和有14位分辨率的波形。

表一 操作参数

图一 系统框图。在灰色框的模块叠加的是连接各个接收机。

A、射频域模拟

由数模转换器所产生的中频模拟波形经由常规超外差混频,通过滤波以去除图像频率和不希望的混频分量来变换到一个更高的中频(IF)。高速数模转换器对于这种设计更为有利,这样可以产生更好的窄带信号,以降低频率对带通滤波器的截止频率锐度的要求。上变频后面是一系列乘法放大器链,以获得射频(RF)输出。

通常,简单的连续波调频(FMCW)系统利用耦合器将发射给信道的信号频率与接收信号混合后传输给接收机。如图1中所描绘的设计,但是,在信号被分离到较低的频率是因为两个主要原因:1)耦合频率在100GHz以上的信号要么损失很大要么非常昂贵,2)低频中电缆可以用来代替波导,它允许接收机灵活的以试验通过基线干涉仪在不同的距离来隔离。如图中方框图,所述耦合信号驱动发射天线通过一个附加的乘法器放大器链旨在最大限度地输出功率,而不是分裂耦合的信号,并将其引导到接收机。实用组件技术的发展改变了耦合器的传统取向。该系统利用了在接收器的次谐波混频器,使得来自发射器的参考振荡器信号只需要被发送频率的一半。FMCW系统有效地应用展宽处理和下变频为单边带信号。因此,接收混频器的输出是用于短距离应用的极窄带信号,尽管发射波形带宽很宽,但是输出信号可以低通滤波(因为合适用于短程信号频率是几kHz到约100MHz)和数字化标准模数转换。

B、数字域

发射波形由一个工作在中频的高速数模转换器生成。这样可以严格控制波形,有能力在改变波形参数的同时保持线性度,并从通带中消除直流分量。对于此演示系统,波形是用数模转换器评估板兼容的数字码型发生器来编程的,然而,下一代的系统将驱动采用FPGA的数模转换器。

一旦模数转换器接受到信号就会进行数字化处理,处理发生在一个FPGA模块或使用由图2中的粉块所指示的微型计算机的软件。处理开始使用均衡器降低两个干涉接收信道之间的幅度和相位失配。校准程序确定均衡器下限的参数。接下来进行频谱分析,先进行2k至8k的实FFT变换,从时域测量转换到频域。这之后是扫描由它产生多普勒测量的扫描配置来确定指定的驻留时间进行相干积分。最后,产生的复杂的二维图像被存储到存储器中。在此阶段,可以处理来自两个接收机的图像,以减少斑点噪声连同其他滤波措施来改善相位展开过程。标准干涉处理被应用于创建地形场,也就是说,通过给定的雷达状态和基线几何形状,和进一步的图像处理,生成最终显示的相位差。如果该应用程序被用来创建一个高分辨率地形地图,可以将数据覆盖到现有较低分辨率的地形数据,例如,数字地形高程数据库(DTED)数据。

图二 通过位于点A和B两个接收器计算一个点表面高度形成几何形状

C、干涉

有两个位移接收机,由于不同的视角产生的两个图像具有稍微不同的相位(即,稍微不同的范围的图像)。将一个图像与第二个图像的复共轭相乘将得到相位差。这个相位必须被打开删除不连续的π和-π(即去掉在相位中2π的非单值性)。图二表示出了通过位于相距S的点A和点B的两个接收机来估计几何物体中一个表面点的高度Xs。鉴于S是通常比XS小得多,近似可以用ZS作为该图像样品的垂直高度。所以可以得出

其中R0是平均雷达范围延迟坐标,然后被合理估计出平均值RA、RA′、RB和RB′。垂直基线角由θp限定。因此,一个反演算法由下式给出

最后两个偏移项取决于任意选择的基准平面高度和已知的两个接收机的相位偏移。

D、测试和演示

在整合中和之后,系统测试是开发的重要组成部分。图3显示了两种方案的RF前端安装在设备上。从后面可以看到,将K波段信号与RF输出相乘的收发器以及顶部接收器(通道A)和次谐波混频器。前视图显示间隔的两个接收器的发射角相关,所有这些都使用聚苯乙烯交联树脂镜头聚焦。在组件的侧面是手动调整的仰角支架,下面是扫描方位转台。为了测试的目的建造了两个三面角反射器,

篇二:雷达的发展论文中英文对照资料外文翻译文献

中英文对照资料外文翻译文献

英文原文:

The development of radar The basic concept of radar formed in the early 20th century. But it was not until, before and after the second world war LeiDaCai get rapid development. As early as the beginning of the 20th century, European and American scientists already know that electromagnetic waves are reflected by the object. In 1922, Italy g. Marconi radio waves may detect objects of papers published. U.S. navy lab found in double base continuous wave radar can be found in it by ship. In 1925, the United States can start work on ranging radar pulse modulation, and first use it to measure the height of the

ionosphere. The early 30 s, Europe and the United States some countries began to develop detection radar pulse modulation of the plane. In 1936, the United States developed the role is about 40 kilometers distance, resolution of 457 meters, pulse radar detection of aircraft. In 1938, the UK has been deployed on the nearby French native coast a chain of early warning radar observation of enemy planes. During the second world war, due to operational needs, the development of radar technology is very fast. In terms of using spectrum, the pre-war devices and technology can only achieve tens of megahertz. Early in the war, Germany first developed into large power three, four tube, to increase the frequency to 500 MHZ and above. This not only improved the precision of radar search and guide the plane, but also improves the performance of anti-aircraft gun control radar, the anti-aircraft gun has a higher hit ratio. Work in 1939, the British invented in the 3000 MHZ power, ground and airplanes equipped with use of the magnetron microwave radar, the allied forces in the air combat and air - sea operations. Later in the war, the United States to further increase the frequency of magnetron to 10 gigahertz, realize the airborne radar miniaturization and to improve the accuracy of measurement. In terms of fire control, the development of precision automatic tracking radar SCR - 584, the anti-aircraft gun shooting from the early war thousands of rounds of shot down a plane, up to dozens of hit a plane.

Late 40 s moving target display technology, which is beneficial to the ground clutter and sex of discovery targets in clutter background. High performance of the moving target indication radar coherent signal must launch, so power is developed, such as, the forward wave tube device. Appeared high speed jet 50 s, 60 s appeared in the low altitude penetration aircraft and, long-range missiles and military satellite, promoted the rapid increase of radar performance. 60 ~ 70 s, computers, and large scale digital

integrated circuit is applied to the radar, the radar performance is greatly improved, while reducing the volume and the weight, improve the In LeiDaXin system, new technology, has been more widely adopted the s and tracking moving target display, single pulse Angle measuring and pulse compression technology, etc.; In the '60 s appeared; In the 70 s solid phased array radar and pulse doppler radar.

In China, the radar technology grew out from the early 50 s. China's development of the radar has equipped the army. China has developed into anti-aircraft two coordinates, and three coordinates alert to - air missile guidance radar, guidance radar, long-range missiles, the initial period of range measurement radar and reentry period of range measurement and recycling. Developed by China's large radar observations are also used in China and other countries to launch satellites. In civil, ocean-going ships sailing navigation and collision avoidance radar, the airport control of radar as well as weather radar have been production and application. China's development of airborne synthetic aperture radar have been able to obtain large clear map of surveying and mapping. China's development of a new generation of radar have been using a computer or microprocessor, and the application of medium and large scale integrated circuit of the digital information processing technology, frequency has been extended to millimeter wave band.

Radar, is due to Britain and Germany during World War II war, England need a detecting air metal objects radar (Technology) can help search for German aircraft in air defense battle. During World War II, radar has been ground to air, air-to-ground bombing (search), air-to-air (interception) radar fire control, IFF function.

After World War II, the development of the single pulse angle tracking radar, pulse Doppler signal processing, synthetic aperture and pulse compression with high resolution, IFF combined system, combined with

computer automatic fire control system, terrain avoidance and terrain following, passive or active phased array, frequency agility, multi-target detection and tracking new radar system.

Later, with the progress of microelectronics and other fields of science, the development of radar technology, its connotation and the research contents are constantly expanding. At present, means of detecting radar have formerly only radar a detector to the development of the infrared light, ultraviolet light, laser and other optical detection means integration cooperation.

Modern radar and ability of function makes the battlefield commander in various search and tracking of target scanning mode, and the interference error of automatic correction, and most of the control function is completed in the internal.

Automatic target recognition can enable weapon system to maximize the role of integrated radar system, airborne early warning aircraft and JSTARS this is battlefield identification friend or foe ability in fact has become the future battlefield information control center.

Radar, is due to Britain and Germany during World War II war, England need a detecting air metal objects radar (Technology) can help search for German aircraft in air defense battle. During World War II, radar has been ground to air, air-to-ground bombing (search), air-to-air (interception) radar fire control, IFF function.

After World War II, the development of the single pulse angle tracking radar, pulse Doppler signal processing, synthetic aperture and pulse compression with high resolution, IFF combined system, combined with computer automatic fire control system, terrain avoidance and terrain following, passive or active phased array, frequency agility, multi-target detection and tracking new radar system.

Later, with the progress of microelectronics and other fields of science, the

development of radar technology, its connotation and the research contents are constantly expanding. At present, means of detecting radar have formerly only radar a detector to the development of the infrared light, ultraviolet light, laser and other optical detection means integration cooperation.

Modern radar and ability of function makes the battlefield commander in various search and tracking of target scanning mode, and the interference error of automatic correction, and most of the control function is completed in the internal.

Automatic target recognition can enable weapon system to maximize the role of integrated radar system, airborne early warning aircraft and JSTARS this is battlefield identification friend or foe ability in fact has become the future battlefield information control center.

Radar and the role of the eyes and ears similar, of course, it is no longer a masterpiece of nature, at the same time, it is the information carrier of radio waves. In fact, whether visible light or radio waves, in essence is the same thing, is the electromagnetic wave propagation in a vacuum, the speed is the speed of light C, the difference is their different frequency and wavelength. The principle is that the transmitter radar equipment to electromagnetic energy into space in one direction through the antenna, electromagnetic wave reflection in this direction of objects encountered; radar antenna to receive the reflected wave, and sent to the receiving equipment for processing, extract some information about the object (target object to the range, range rate or radial velocity, range, etc.).

Measurement of the distance is a measure of the actual transmitted pulse and the echo pulse time difference between, because the electromagnetic waves travel at the speed of light, accurate distance which can be converted into the target.

Measurement of target azimuth is sharp beam position measurement using

篇三:外文翻译---相控阵和雷达技术的突破

毕业设计(论文)

外文文献翻译

翻译(1)题目

翻译(2)题目

学 院 相控阵和雷达技术的突破 发射KU-波段的相控阵天线在FSS通信系统中的应用 电子信息学院

专 业

英文译文1:

相控阵和雷达技术的突破

【摘要】 许多人认为雷达是一个成熟的领域,不会发生任何新的变化,这种看法存在很久了,没有比这个看法更错误的了。当我1950年参与到雷达领域的时候,我也有过同样的看法,例如,我认为麻省理工学院的雷达丛书已经是包罗万象了,不需要增加任何新的内容。然而我是多么的错啊,从那时起雷达技术领域中已经发生了许多令人眼花缭乱的发展,雷达一直受益于Moore s定律和许多新的技术上的成果,例如,MMIC GaAs T/R组件和相控阵组件。现在雷达技术发展得更快了,在这篇文章里,我将给出某些最近突破的例子。

【关键词】 雷达;有源相控阵;MMIC;MEMS;T/R组件;相控阵;AESA;电扫;GaAs;GaN;SiC;CMOS;数字波束形成;自适应阵列;旁瓣对消器;超宽带天线;金属材料;电子管;真空电子器件;回旋管;磁控管;速调管;行波管;微波功率组件;MPM;功率放大组件;SBX;GBR—P

0:SEA-BASED X-波段雷达

24层楼高的SEA-BASED X-波段相控阵雷达是一个世界奇迹。

1:GaAs MMIC T/R模块(单片微波集成电路)

在过去的十年成功和广泛的应用了MMIC和AESA(有源电子扫描阵) 2:低成本 ¥19K AESA

谁说AESA是非常昂贵的,在DARPA(Defense Advanced Research Projects Agency美国国防部先进研究项目局)的低资金¥19K资助下使35GHZ相控阵成为可能。DARPA已经资助发展了¥10 X-band,10’smW,单T/R芯片模块。

3:低成本的MEMS(微机电系统)相控阵

即使我们只有一个低损耗的移相器,那么就能够用在一个模块上安装很多的移相而MEMS提供了这个可能。MEMS开关已经提高了3个数量级的可靠性,在2003年10月报道,开关寿命已经达到6000亿.这还有降低损耗的需要,通过4位移相器用RADANT透镜在1维空间扫描的天线损耗是1.25dB.2维扫描需要2个镜头,所以2维的RADANT阵列扫描对于2路的损耗就是5Db,但是正在取得进展。

4:GaN(氮化镓,属第三代半导体材料),SIC(碳化硅)

宽禁带的GaN和SIC MMIC 芯片,使,在T/R模块电源上提高1-2个数量级,成为可能。这项技术将有可能在未来通过升级现有的AESA替换GaAs T/R 组件或SIC T/R与GaN模块,提高10倍电源。这个提供了10倍的改善在搜索整个或者78%轨道范围中。

5:SiGe

SiGe具有使用Si为基质的优势,对集成电路产业的技术,其丰富的资源,可以借鉴。它以较低的成本提供了较高的性能潜能。SiGe 在微波输出功率和噪声系数与GaAs竞争中没有优势。它提供了低成本和在单芯片上整合多种功能的能力。在一个芯片上可以增加微波功率放大器和低噪声的数字接收机也可以是增加A/D和数字电路。

6:CMOS(Complementary Metal Oxide Semiconductor互补金属氧化物半导体)

目前CMOS主要用在微波频率,它也使用在Si基材,这个技术还广泛使用在计算

机产业。它拥有低成本的保证,低功耗的T/R模块接收组件。像SiGe它有允许许多功能集成在一块芯片上的优势,甚至超过SiGe.一块芯片上可以有射频,中频基带,微处理器,内存。可调谐滤波器和A/D转换系统在SOC(系统集成芯片)上。它可由GaAs或者GaN结合制作出微波功率放大器和低噪声的数字接收机。利用GaN有足够强大到不受限制的优势。

7:数字波束形成(DBF)

DBF是被应用在微波AESAs雷达,我们看到它被用的越来越广泛;和模拟波束形成有许多明显的优势。对于目前正在实施的大型阵列是指数组的水平,但最终还是会在元素级别上进行。这样做消除了模拟硬件相结合,模拟下变频和所有与他们相关的错误。反过来这将导致超低副瓣。这将允许多种光束指向不同方向的实现,它将能够在同一时刻用天线的不同部分实行不同的应用程序。它允许在降低3dB发射功率的情况能够搜索。现在,随着摩尔定律规律的不断前进,由于增加信号处理所需的成本远远小于减少3dB发射功率的获得成本。DBF能够减少搜索占用的空间(1/2),并且搜索精度能达到40%。DBF也将允许更好的自适应阵列进程。事实上,一个完全的自适应阵列与没有它的计算和瞬间处罚是一样可以实现的。这可以实现自调谐-自调谐阵列处理。这个涉及到干扰器是否干扰了数字定位,然后指向这些干扰器束(这些光束是有效地特征波束),并利用这些作为主瓣。我们拥有10个干扰器,现在必须转换为11*11的矩阵,而不是1000*1000的矩阵和瞬间时间减少100倍。传统的自适应完全阵列,不能确定干扰器的位置,我们可以很容易的确定,不至于使我们被蒙蔽。此方法等效于确定主要成分的方法。

8:超带宽阵列

由于有超带宽的阵列,可以使一个天线在不同的地带有各种不同的应用。 9:电子管的进展(TUBE ADVANCEMENTS)

电子管取得了重大的进展;其中有一些是因为有强大的可用的软件,允许电子管的设计不需要实验和纠错。

10:致谢

我想谢谢Raymond Hale 和 John DeFalco,还有Raytheon 公司提供的GaN,SiC,SiGe和CMOS。

英文原文1:

Phased-Array and Radar Breakthroughs

Dr.Eli Brookner Raytheon Comp

(M/S 3—1—162 528 Boston Post Rd.,Sudbury,MA 01776 Te1.:978—440—4007;ELI_BROOKNER@RAYTHEON.COM)

【Abstract】 Many think that radar is a mature field,nothing new to happen,it having been around a long time. Nothing can be further from the truth.When I entered the field in the 50`s I thought the same thing.The MIT Radiation

Lab.Series was the definitive volume and there was to be nothing more.How wrong 1

was.Since then many amazing new developments have taken place,radar having benefiting from Moore`s law and the incorporation of new technology developments such as MMIC GaAs T/R modules and electronically steered phased array.Things are moving even faster now. In this paper I shall give examples of some of the recent breakthroughs.The topics to be covered are indicated in Fig.1.

【Key words】 Radar,active—phased arrays;MMIC;MEMS;T/R module;phased array;AESA;electronic scanning;GaAs;GaN;SiC;SiGe;CMOS;digital beam forming;adaptive arrays;sidelobe canceler;Ultra—Wideband Antenna;metal materials;tube;Vacuum Electron Device;gyroklystron;gyrotwystron;magnetron;klystron;traveling wave tube; T;microwave power modules;MPM;power amplifier module(PAM);SBX;GBR—P

0 SEA—BASED X—BAND RADAR

The Sea Based X—Band(SBX)24 story high phased array radar shown is a new wonder of the world.

1 GaAs MMIC T/R MODULES

The last decade has seen the successful and extensive application of Monolithic Microwave Integrated Circuits(MMICS)to active electronically steered arrays (AESAs). 2 LOW COST,$19K,AESA

Who said AESAs have to be expensive.On DARPA funding the feasibility of a low cost,$19 K.35 GHz array was demonstrated ;see Figs.6 and 7.DARPA has also funded the development of a $10 X-band.10`smW ,single chip T/R module.

3 LOW COST MEMS PHASED ARRAYS

If only we had a low loss phase shifter.Then we could go back to the passive architecture electronic scanned phased array with one module feeding many

phase shifters,like 10.This could potentially reduce the cost of an electronically scanned phased array by a factor of nearly ~ 10. Micro-ElctroMechanical systems (MEMS)offer this promise.MEMS switches have improved their reliability by 3 orders of magnitude over what was reported Oct.2003 in to a life of 600 billion switches.There is still need for improvement in the loss. The loss through a 4 bit phase shifter used in a 1-D scanned RADANT space-fed lens antenna is ~1.25 dB.Two lenses are needed for 2D scan so that the 2-way loss for a 2D scanned RADANT array would be ~5dB.but progress is being made.

4 GaN,SIC

Wide bandgapGaN and SiC MMIC chips offer the potential of one to two orders increase in T/R module power;see Fig.8.This technology would make it possible in the future to upgrade an existing AESA by replacing the GaAs T/R modules with GaN or SiC T/R modules having 10 times the et.3his provides either a 10 times improvement in search volume or a 78% increase in track range.

5 SiGe

SiGe has the advantage of using Si as a substrate,the technology of the integrated circuit industry and whose extensive resources can draw upon.It offers the potential of higher performance at low with GaAs with respect to

cost.SiGe does not compete microwave output power or noise figure.It offers low cost and the ability to integrate many functions on a single chip.On one chip in addition to microwave power amplifiers and low noise figure receiv-

er it can have A/Ds and digital circuitry.Fig.9 shows a moekup of an AESA radar using SiGe T/R modules having a 1 W peak output power.

6 CMOS

CMOS now operates at microwave frequencies.It too uses a Si subtrate and is the technology widely used in the computer industry.It holds the promise of low cost and low power for the receiver parts of T/R modules.Like SiGe it has the advantage of allowing the integration of many functions on a single chip,even more so than SiGe.One chip can have RF,IF,baseband,microprocessor,memory,tuneable filters and A/Ds—a system on a chip(SOC).It can be combined with GaAs or GaN for the microwave power amplifier and low noise figure receiver.Using GaN has the advantage of being robust enough so that a limiter may not be needed.

7 DIGITAL BEAM FORMING(DBF)

DBF is here for microwave AESAs radars.We see it being used more and more; It provides many significant advantages over analog beam forming. For large arrays it is presently being implemented at the sub—array level but eventually it will be done at the element leve1.Doing so eliminates the analog combining hard.. ware,analog down-converting and all the errors associated with them.This in turn will lead to ultra—low side— lobes.It will allow the implementation of multiple beams pointing in different directions.It will enable the adaptive use of different parts of the antenna for different applications at the same time.It permits search with about a 3 dB reduction in transmit power .Now with the continual advance of Moore`s law.the increased cost due to the increased signal processing needed will be far less than the gain from the 3 dB reduction of transmitter power. DBF can also reduce the search occupancy(by about a factor of two)and the search angle accuracy by about 40%.DBF will also permit better adaptive array processing.In fact the equivalence of a fully adaptive array without its computation and transient penalties can be achieved.This can be accomplished with Adaptive—Adaptive Array processing .This involves no more than locating digitally where the jammers are,then pointing beam at these jammers(these beams are effectivelyeigenbeams)and using these beams as sidelobecancelers for the main beam; With 10 jammers we now have to invert an 11×11 matrix instead of a 1000×1000 matrix and the transient time is reduced by a factor of 100;In a classical fully adaptive array one does not make use of the location of the jammers which we can easily determine rather than putting on our blindfolders; This method is equivalent to the method of Principal Components .

8 ULTRA WIDEBAND ARRAYS

Ultra wideband arrays are here.These will allow the use of one antenna for many different applications at different bands.

9 TUBE ADVANCEMENTS

Tubes are making major advances. Some of these are because of the powerful software that permits the design of availability of tubes without the need for trial and error.


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