RCS计算方法简单介绍

RCS计算方法

RCＳ得计算方法内容提要·目标ＲCＳ精确解法·矩量法·高频区目标ＲCＳ近似计算方法–几何光学法–物理光学法–几何绕射理论–物理绕射理论E + k E = 0H + k H = 0 目标RCS 精确解法· 波动方程２ 2 2 2 · 边界条件 n ⋅ (Ｅ１ E 2 ) = 0 ｎ ⋅ (H １ H 2 ） = 0ｎ ⊕ (Ｄ1 D 2 ） = 〉 sｎ ⊕ （B 1 B 2 ) = ０ · 限制 · 求解上述方程必须要使物体表面与某一个可分离得坐标系相吻合，也即有严格级数解可以利用时,波动方程才能有严格得解析解。

· 但只有少数几种形体能满足这种要求.n + 1=n 1 ( 1) ( 2 )(b n a n )目标RCS 精确解法· 球得后向散射雷达散射截面⎛ =2 n 2ˆ ˆ ˆˆ ˆ ˆ· 控制方程– Str ａtton —Ch ｕ积分方程E s = +s ［i ⎤∝ （ｎ ⋅ Ｈ）⎭ +(n ⋅ E ） ⋅ (n ⊕ E ) ⎭ ]ｄs Ｈ s = +s ［i ⎤∝ (n ⋅ E )⎭ +（n ⋅ H ） ⋅ (n ⊕ H ） ⎭ ]ｄs·求解思路–将积分方程写成带有积分算符得符号方程;–将待求函数表示为某一组选用得基函数得线性组合并代入符号方程；–用一组选定得权函数对所得得方程取矩量，得到一个矩阵方程或代数方程组;–求解代数方程组。

·特点––––ﻮ精度较高在目标外部轮廓取样时,间隙不得超过波长得1/5左右.当目标尺寸与波长相比很大时,取样数量十分庞大主要用于低频区与谐振区得散射问题。

高频区目标RＣS近似计算方法·依据–大多数探测雷达得波长都远远小于飞行器得特征尺寸.–在高频区复杂目标得散射场可瞧作各个散射源产生得散射场得综合。

·方法––––几何光学法物理光学法几何绕射理论物理绕射理论几何光学法·概念–当电磁波波长与目标尺寸相比很小时,可以近似地用几何光学得观点来研究物体上电磁波得散射现象。

雷达截面积（RCS）的基础知识

雷达截面积（RCS）的基础知识雷达截面积(Radar Cross Section, RCS)是目标在雷达接收方向上反射雷达信号能力的度量，一个目标的RCS等于单位立体角目标在雷达接收天线方向上反射的功率(每单独立体角)与人射到目标处的功率密度(每平方米)之比。

目标的RCS取决于目标结构(形状和材料)、雷达工作频率、雷达极化方式和雷达观测角。

通常情况下，平面目标具有较强的镜反射回波，而赋形、涂覆雷达吸波材料和采用非金属材料等隐身技术则可以大大降低目标雷达截面积。

目标雷达截面积的一些特性可用一些简单的模型来描述。

根据雷达波长与目标尺寸的相对关系，可分三个区域来描述目标雷达截面积。

瑞利区。

在此区域，目标尺寸远小于信号波长，目标雷达截面积与雷达观测角度关系不大，与雷达工作频率的4次方成正比。

谐振区。

在此区域，波长与目标尺寸相当。

目标雷达截面积随着频率变化而变化，变化范围可达10dB；同时由于目标形状的不连续性，目标雷达截面积随雷达观测角的变化而变化。

光学区。

在此区域，目标尺寸大于信号波长，下限值通常比瑞利区目标尺寸的上限值高一个数量级。

简单形状目标的雷达截面积可以接近它们的光截面，目标或雷达的移动会造成视线角的变化，将导致目标雷达截面积发生变化。

简单金属形状的雷达截面积可以通过公式估算，但对于像飞机这样非常复杂的目标，其表面与RCS之间没有牢固的关系，它会随照射雷达的方向而显着变化。

复杂目标会包含镜面反射、边缘绕射、尖顶绕射、爬行波绕射、行波绕射和非细长体因电磁突变引起的绕射。

当电磁波垂直射入局部光滑目标表面时，在其后向方向上产生很强的散射回波，这种散射称为镜面反射，它是强散射源。

当电磁波入射到目标边缘棱线时，散射回波主要来自于目标边缘对入射电磁波的绕射，它与反射不同之处在于一束入射波可以在边缘上产生无数条绕射线，是重要的散射源。

对于无隐身措施的常规飞机，它的散射场包括反射和绕射场，主要是镜面反射和边缘绕射起作用。

(完整版)雷达截面积(RCS)

雷达有效探测距离和RCS的四次方根呈正比关系。

例如，探测距离缩短一半，RCS就需要减少为原来的1/16比如某型雷达对3平米RCS战斗机目标的探测距离是200公里那么对0。

065平米RCS探测距离为76。

7公里四次方率是个理想公式，是仅有很低白噪声干扰情况下使用功率门限过滤时的探测距离。

实际上在战场ECM环境下四次方率用于描述对RCS〈0.1M^2的目标不是很合适，探测距离随目标RCS减小而缩短的速度比理论上要快。

四次方关系是由基本雷达距离公式得出的，是雷达制定距离性能的重要参照之一。

局限性是仅考虑了雷达机内平均噪声电平,实际使用中要加入具体的修正,以及虚警率等必须注意的问题。

专用的连续波发射器可以用到占空比100%，因为发射器不考虑接收,不需要作1/2时间收,1/2时间发.机载雷达用的准连续波实际是高脉冲重复频率波型，占空比只能接近50％，如狂风ADV用的AI24，其远距探测即使用高占空比的准连续波。

E=[P＊G*RCS*L*T］/(4*pi^3＊R^4)]E:接收能量P：发射机功率G:雷达天线增益RCS：目标雷达截面积L:信号波长T：目标被照射时间R:到目标的距离相控阵指的是雷达的天线形式，以相位或频率扫描的电扫描天线代替传统的机械扫描天线。

连续波、单脉冲等则代表雷达的工作体制，代表雷达以何种方式工作，和天线形式无直接联系。

占空比一般由雷达类型决定，收发共用同一天线的脉冲雷达占空比在50%以下，收、发天线分置的连续波雷达占空比就是100％。

战斗机雷达和大部分搜索雷达为收发共用的脉冲工作方式,不论采用机械扫描天线还是无、有源天线，占空比均小于50%,大的接近50%，小的只有千分之几.美国F—22隐身战斗机进驻日本冲绳，隐身轰炸机B—2也可驻扎关岛.对隐身飞机作战问题的热烈讨论，带热了一个词——飞机雷达截面积。

雷达截面积是一个人为的参数,牵涉因素很多，而且因为它关系到飞机作战效能，因此所有国家都不会公开自己飞机的精确数值，或发表一些模糊的误导宣传值，所以人们从报刊或正式文献上看到的数据差别很大。

RCS 计算平板或圆球的手算公式

RADAR CROSS SECTION (RCS)Radar cross section is the measure of a target's ability to reflect radar signals in the direction of the radar receiver, i.e. it is a measure of the ratio of backscatter power per steradian (unit solid angle) in the direction of the radar (from the target)to the power density that is intercepted by the target.The RCS of a target can be viewed as a comparison of the strength of the reflected signal from a target to the reflected signal from a perfectly smooth sphere of cross sectional area of 1 m as shown in Figure 1 .2The conceptual definition of RCS includes the fact that not all of the radiated energy falls on the target. A target’s RCS (F ) is most easily visualized as the product of three factors:F = Projected cross section x Reflectivity x Directivity .RCS(F ) is used in Section 4-4 for an equation representing power reradiated from the target.Reflectivity: The percent of intercepted power reradiated (scattered) by the target.Directivity: The ratio of the power scattered back in the radar's direction to the power that would have been backscattered had the scattering been uniform in all directions (i.e. isotropically).Figures 2 and 3 show that RCS does not equal geometric area. For a sphere, the RCS, F = B r ,2where r is the radius of the sphere.The RCS of a sphere is independent of frequency if operating at sufficiently high frequencies where 8<<Range, and 8<< radius (r). Experimentally,radar return reflected from a target is compared to the radar return reflected from a sphere which has a frontal or projected area of one square meter (i.e.diameter of about 44 in). Using the spherical shape aids in field or laboratory measurements since orientation or positioning of the sphere will not affect radar reflection intensity measurements as a flat plate would. If calibrated, other sources (cylinder, flat plate, or corner reflector, etc.) could be used for comparative measurements.To reduce drag during tests, towed spheres of 6", 14" or 22" diameter may be used instead of the larger 44" sphere, and thereference size is 0.018, 0.099 or 0.245 m respectively instead of 1 m. When smaller sized spheres are used for tests you 2 2may be operating at or near where 8-radius. If the results are then scaled to a 1 m reference, there may be some 2perturbations due to creeping waves. See the discussion at the end of this section for further details.In Figure 4, RCS patterns are shown asobjects are rotated about their vertical axes(the arrows indicate the direction of theradar reflections).The sphere is essentially the same in alldirections.The flat plate has almost no RCS exceptwhen aligned directly toward the radar.The corner reflector has an RCS almost ashigh as the flat plate but over a wider angle,i.e., over ±60E, the return from a cornerreflector is analogous to that of a flat platealways being perpendicular to yourcollocated transmitter and receiver.Targets such as ships and aircraft oftenhave many effective corners. Corners are sometimes used as calibration targets or as decoys, i.e. corner reflectors.An aircraft target is very complex. It has a great many reflecting elements and shapes. The RCS of real aircraft must be measured. It varies significantly depending upon the direction of the illuminating radar.P r 'PtGtGr82F(4B)3R4R2 BT 'PtGtFPjGj4BP r 'PtGtGr82F(4B)3R4'PjGjGr82(4B R)288S J. Typical Aircraft RCSFigure 5 shows a typical RCS plot of a jet aircraft. The plot is anazimuth cut made at zero degrees elevation (on the aircrafthorizon). Within the normal radar range of 3-18 GHz, the radarreturn of an aircraft in a given direction will vary by a few dB asfrequency and polarization vary (the RCS may change by a factorof 2-5). It does not vary as much as the flat plate.As shown in Figure 5, the RCS is highest at the aircraft beam dueto the large physical area observed by the radar and perpendicularaspect (increasing reflectivity). The next highest RCS area is thenose/tail area, largely because of reflections off the engines orpropellers. Most self-protection jammers cover a field of view of+/- 60 degrees about the aircraft nose and tail, thus the high RCSon the beam does not have coverage. Beam coverage isfrequently not provided due to inadequate power available tocover all aircraft quadrants, and the side of an aircraft istheoretically exposed to a threat 30% of the time over the averageof all scenarios.Typical radar cross sections are as follows: Missile 0.5 sq m; Tactical Jet 5 to 100 sq m; Bomber 10 to 1000 sq m; and ships 3,000 to 1,000,000 sq m. RCS can also be expressed in decibels referenced to a square meter (dBsm) which equals 10 log (RCS in m).2Again, Figure 5 shows that these values can vary dramatically. The strongest return depicted in the example is 100 m in2 the beam, and the weakest is slightly more than 1 m in the 135E/225E positions. These RCS values can be very misleading2because other factors may affect the results. For example, phase differences, polarization, surface imperfections, and material type all greatly affect the results. In the above typical bomber example, the measured RCS may be much greater than 1000 square meters in certain circumstances (90E, 270E).SIGNIFICANCE OF THE REDUCTION OF RCSIf each of the range or power equations that have an RCS (F) term is evaluated for the significance of decreasing RCS, Figure 6 results. Therefore, an RCS reduction can increase aircraft survivability. The equations used in Figure 6 are as follows:Range (radar detection): From the 2-way range equation in Section 4-4: Therefore, R%F or F% R41/4Range (radar burn-through): The crossover equation in Section 4-8 has:Therefore, R%F or F% RBT BT21/2Power (jammer): Equating the received signal return (P) in the two way range equation to the received jammer signal (P)r r in the one way range equation, the following relationship results:Therefore, P%F or F% P Note: jammer transmission line loss is combined with the jammer antenna gain to obtain G.j j t-.46-.97-1.55-2.2-3.0-4.0-5.2-7.0-10.0-400.10.20.30.40.50.60.70.80.91.0dB REDUCTION OF RANGEdB REDUCTION OF RANGE10 Log ( P 'j / P j )(DETECTION )(BURN-THROUGH)(JAMMER)j / P jFigure 6. Reduction of RCS Affects Radar Detection, Burn-through, and Jammer PowerExample of Effects of RCS Reduction - As shown in Figure 6, if the RCS of an aircraft is reduced to 0.75 (75%) of its original value, then (1) the jammer power required to achieve the same effectiveness would be 0.75 (75%) of the original value (or -1.25 dB). Likewise, (2) If Jammer power is held constant, then burn-through range is 0.87 (87%) of its original value (-1.25 dB), and (3) the detection range of the radar for the smaller RCS target (jamming not considered) is 0.93 (93%)of its original value (-1.25 dB).OPTICAL / MIE / RAYLEIGH REGIONSFigure 7 shows the different regions applicable for computing the RCS of a sphere. The optical region (“far field”counterpart) rules apply when 2B r/8 > 10. In this region, the RCS of a sphere is independent of frequency. Here, the RCS of a sphere, F = B r . The RCS equation breaks down primarily due to creeping waves in the area where 8-2B r. This area 2is known as the Mie or resonance region. If we were using a 6" diameter sphere, this frequency would be 0.6 GHz. (Any frequency ten times higher, or above 6 GHz, would give expected results). The largest positive perturbation (point A)occurs at exactly 0.6 GHz where the RCS would be 4 times higher than the RCS computed using the optical region formula.Just slightly above 0.6 GHz a minimum occurs (point B) and the actual RCS would be 0.26 times the value calculated by using the optical region formula. If we used a one meter diameter sphere, the perturbations would occur at 95 MHz, so any frequency above 950 MHz (-1 GHz) would give predicted results.CREEPING WAVESThe initial RCS assumptions presume that we are operating in the optical region (8<<Range and 8<<radius). There is a region where specular reflected (mirrored) waves combine with back scattered creeping waves both constructively and destructively as shown in Figure 8. Creeping waves are tangential to a smooth surface and follow the "shadow" region of the body. They occur when the circumference of the sphere - 8 and typically add about 1 m to the RCS at certain 2frequencies.。

微带天线rcs计算

微带天线rcs计算微带天线RCS(RadarCrossSection)计算是用来描述微带天线RCS性能和发射特性用的一种计算方法。

它可以用来测量微带天线接收到的飞机雷达信号强度，为分析飞行器在雷达可见度方面的安全性提供可靠的参考数据，并且可以应用于改善微带天线结构的设计，使其在雷达信号强度方面更加适宜。

RCS计算一般涉及微带天线的构造特性、雷达定位参数、天线参数和射频耦合特性等，以粒子双折射法为核心的计算方法常被使用，其基本原理是使用偏振和方向计算射频定位信号。

二、计算方法1.造特性首先，微带天线RCS计算要结合天线的构造特性进行，一般要使用素子，用素子间连接结构和素子极化等方法组合在一起到实现所需条件。

2.达定位参数其次，雷达定位参数是微带天线RCS计算的重要参数之一，如接收机位置、方位角、频率等，以此来确定微带天线的接收定位能力。

3.线参数另外，天线参数也是微带天线RCS计算的重要参数，主要包括天线的振幅增益、噪声指数、相位等参数。

4.频耦合特性最后，射频耦合特性是微带天线RCS计算的最重要参数，这包括接收机位置、方向角、频率等内容。

三、计算结果分析1.点数和路径长度首先，使用粒子双折射法计算微带天线RCS时，首先要确定节点的数量和路径的长度。

一般情况下，节点数越多，路径越长，则计算精度就越高，结果也更可靠。

2.数模拟其次，使用粒子双折射法计算微带天线RCS时，需要进行参数模拟，以模拟发射特性、接收特性以及方向特性等。

3.算结果最后，经过参数模拟之后，可以获得微带天线RCS计算的结果，根据所获得的结果，可以对飞行器在雷达可见度方面的安全性进行准确的分析，也能应用于改善微带天线结构的设计，使其在雷达信号强度方面更加适宜。

四、结论微带天线RCS计算是用来表示微带天线RCS性能和发射特性用的一种计算方法，在提高微带天线结构的可见度、准确性方面有着重要的应用价值。

主要的计算方法是使用粒子双折射法，其原理是借助偏振和方向计算射频定位信号。

RCS计算方法11

RCS的计算方法内容提要·目标RCS精确解法·矩量法·高频区目标RCS近似计算方法–几何光学法–物理光学法–几何绕射理论–物理绕射理论E + k E = 0 H + k H = 0 目标RCS 精确解法· 波动方程2 22 2· 边界条件 n ⋅ (E 1 E 2 ) = 0 n ⋅ (H 1 H 2 ) = 0n ⊕ (D 1 D 2 ) = 〉 sn ⊕ (B 1 B 2 ) = 0· 限制· 求解上述方程必须要使物体表面与某一个可分离的坐标系相吻合，也即有严格级数解可以利用时，波动方程才能有严格的解析解。

· 但只有少数几种形体能满足这种要求。

n + 1=n 1 ( 1) ( 2 )(b n a n ) 目标RCS 精确解法· 球的后向散射雷达散射截面⎛ = 2n 2ˆ ˆ ˆ ˆ ˆ ˆ矩量法· 控制方程– Stratton-Chu 积分方程E s = +s [i ⎤∝ (n ⋅ H )⎭ +(n ⋅E ) ⋅ (n ⊕ E ) ⎭ ]ds H s = +s[i ⎤∝ (n ⋅ E )⎭ +(n ⋅ H ) ⋅ (n ⊕ H ) ⎭ ]ds矩量法·求解思路–将积分方程写成带有积分算符的符号方程;–将待求函数表示为某一组选用的基函数的线性组合并代入符号方程;–用一组选定的权函数对所得的方程取矩量，得到一个矩阵方程或代数方程组;–求解代数方程组。

·特点––––精度较高在目标外部轮廓取样时，间隙不得超过波长的1/5左右。

当目标尺寸与波长相比很大时，取样数量十分庞大主要用于低频区和谐振区的散射问题。

高频区目标RCS近似计算方法·依据–大多数探测雷达的波长都远远小于飞行器的特征尺寸。

–在高频区复杂目标的散射场可看作各个散射源产生的散射场的综合。

·方法––––几何光学法物理光学法几何绕射理论物理绕射理论几何光学法·概念–当电磁波波长与目标尺寸相比很小时，可以近似地用几何光学的观点来研究物体上电磁波的散射现象。

对空打击面积专业名词

对空打击面积专业名词空打击面积（RCS），即雷达截面积（Radar Cross Section），是一个重要的概念，用于描述目标物体对于雷达回波的散射截面。

本文将从简到繁、由浅入深地介绍空打击面积，包括定义、计算方法、影响因素以及相关应用。

我将分享我的观点和理解，帮助你全面、深入地理解这一主题。

一、定义空打击面积是指目标物体对于雷达波束的接收截面，也可理解为目标物体在雷达系统中的"反射面积"。

它是一个量化目标物体在雷达系统中的能量反射情况的参数，通常用单位面积（平方米）表示。

二、计算方法空打击面积的计算是通过模拟或实测目标物体对于不同频率和波段的雷达波束的散射特性来完成的。

计算方法多种多样，其中常用的方法有几何光学法、物理光学法和计算机仿真法。

这些方法根据目标物体的形状、材料和雷达波束的特征等因素来计算空打击面积。

三、影响因素目标物体的形状、尺寸、材料和姿态是影响空打击面积的重要因素。

一般来说，对于雷达系统来讲，目标物体的尺寸越大，形状越复杂，材料越吸波，姿态越容易使得雷达波束反射消散，其空打击面积就越小；反之，目标物体的空打击面积就越大。

频率和波长也是决定空打击面积大小的因素之一。

四、相关应用空打击面积的概念广泛应用于军事、航空航天、雷达系统等领域。

在军事领域，空打击面积的减小是隐形战机设计的目标之一，通过优化飞机的形状和材料，可以尽可能降低战机的雷达可探测范围，提高战机的隐身性能。

在航空航天领域，空打击面积对于飞机的性能和安全至关重要，研究和控制空打击面积可以提高飞机的隐身性能、减小雷达侦测范围和整体结构的防护。

在雷达系统领域，了解目标物体的空打击面积有助于改进雷达系统的设计，提高雷达的敌我识别能力和目标探测精度。

个人观点和理解空打击面积作为衡量目标物体在雷达系统中的散射特性的重要参数，对于军事和航空航天领域具有重要意义。

随着科技不断发展，人们对于隐形技术和隐身性能的需求越来越高，对空打击面积的研究和控制也变得愈发重要。

角反射器rcs计算公式

角反射器rcs计算公式
角反射器rcs的计算公式如下:
Rc = √(R2 - r2)
其中,Rc是角反射器的rcs(radius of closing range),R是距离目标的最大距离,r是目标距离角反射器的距离。

这个公式基于两个假设:
1. 角反射器的中心点是相对平衡的,即当用户向角反射器发射电磁波时,反射器中心点也会产生相同的反射。

2. 角反射器接收到的所有电磁波都满足能量守恒定律,即每个电磁波都会将部分能量反射回去,并且能量总量保持不变。

利用这些假设,我们可以推导出这个公式。

具体来说,假设角反射器中心点位于距离用户为R的距离处,距离角反射器为r的电磁波会被反射回来。

那么,在用户和角反射器之间没有其他障碍物的情况下,反射器接收到的所有电磁波都满足能量守恒定律。

因此,R2表示角反射器中心点到目标点的距离,r2表示目标点到角反射器中心点的距离。

然后,我们可以将这两个距离平方并相除,得到rcs的平方根。

最后,将这个平方根带回到原公式中,即可得到角反射器rcs的计算公式。

需要注意的是,这个公式仅适用于电磁波能量小于等于目标点的反射损耗。

如果电磁波能量大于目标点的能量,则电磁波会在目标点发生反射,但能量会被损失掉。

在这种情况下,我们需要使用其他更精确的公式来计算角反射器的rcs。

活动板类角反射器的RCS计算

第３８卷第３期
２０１５年６月
长春理工大学学报（自然科学版）
ＪｏｕｎａｒｌｏｆＣｈａｎｇｃｈｕｎＵｎｉｖｅｒｓｉｔｙｏｆＳｃｉｅｎｃｅａｎｄＴｅｃｈｎｏｌｏｇｙ（ＮａｔｕｒａｌＳｃｉｅｎｃｅＥｄｉｔｉｏｎ）
ｅｎａｎｄｔｈｅｐｈｙｓｉｃａｌｏｐｔｉｃａｌｉｎｔｅｇｒａｌｅｑｕａｔｉｏｎｆｏｒｍｕｌｔｉｐｌｅ — — ｂｏｕｎｃｅｉｓｄｅｄｕｃｅｄ．ＴｈｅｒｅｓｕｌｔｓｏｆｔｒｉｈｅｄｒａｌｃｏｍｅｒｒｅｌｆｅｃｔｏｒｓｗｉｔｈｍｏｖａｂｌｅｓｉｄｅｐｌａｔｅｓａｎｄｔｏｐｐｌａｔｅａｒｅｇａｉｎｅｄａｎｄＲＣＳｉｎｗｅｌｌａｃｃｏｒｄａｎｃｅｗｉｈｔｔｈｅｍｅａｓｕｒｅｍｅｎｔｓ．Ａｆｔｅｒｔｈｅｃｏｍ— ｐａｒｉｓｏｎｓｏｆｔｈｅｓｅｔＷＯｋｉｎｄｓｏｆｒｅｌｆｅｃｔｏｒｓｗｉｔｈａｃｏｍｍｏｎｏｎｅ，ｓｏｍｅｖａｌｕａｂｌｅｃｏｎｃｌｕｓｉｏｎｓｒｅａｄｒａｗｎ．
Ｖｏ１＿３８Ｎｏ．３
Ｊｕｎ．２０１５

RCS计算方法

航空宇航学院RCS的计算方法内容提要·目标RCS精确解法·矩量法·高频区目标RCS近似计算方法–几何光学法–物理光学法–几何绕射理论–物理绕射理论E + k E = 0 H + k H = 0目标RCS 精确解法· 波动方程2 2 2 2· 边界条件n ⋅ (E 1 E 2 ) = 0 n ⋅ (H 1 H 2 ) = 0 n ⊕ (D 1 D 2 ) = 〉 s n ⊕ (B 1 B 2 ) = 0· 限制· 求解上述方程必须要使物体表面与某一个可分离的坐标系相吻合，也即有严格级数解可以利用时，波动方程才能有严格的解析解。

· 但只有少数几种形体能满足这种要求。

n + 1=n 1( 1) ( 2 )(b n a n )目标RCS 精确解法· 球的后向散射雷达散射截面⎛ = 2n2ˆ ˆ ˆˆ ˆ ˆ·控制方程– Stratton-Chu积分方程E s = +s[i⎤∝ (n ⋅ H )⎭ +(n ⋅ E ) ⋅ (n ⊕ E )⎭ ]dsH s = +s[i⎤∝ (n ⋅ E )⎭ +(n ⋅ H ) ⋅ (n ⊕ H )⎭ ]ds· 求解思路– 将积分方程写成带有积分算符的符号方程;– 将待求函数表示为某一组选用的基函数的线性组合并代入符号方程;– 用一组选定的权函数对所得的方程取矩量，得到一个矩阵方程或代数方程组; – 求解代数方程组。

· 特点– – – –精度较高在目标外部轮廓取样时，间隙不得超过波长的1/5左右。

当目标尺寸与波长相比很大时，取样数量十分庞大主要用于低频区和谐振区的散射问题。

高频区目标RCS近似计算方法·依据–大多数探测雷达的波长都远远小于飞行器的特征尺寸。

–在高频区复杂目标的散射场可看作各个散射源产生的散射场的综合。

·方法––––几何光学法物理光学法几何绕射理论物理绕射理论几何光学法·概念–当电磁波波长与目标尺寸相比很小时，可以近似地用几何光学的观点来研究物体上电磁波的散射现象。

RCS计算方法

RCS的计算方法内容提要·目标RCS精确解法·矩量法·高频区目标RCS近似计算方法–几何光学法–物理光学法–几何绕射理论–物理绕射理论E + k E = 0 H + k H = 0 目标RCS 精确解法· 波动方程2 22 2· 边界条件 n ⋅ (E 1 E 2 ) = 0 n ⋅ (H 1 H 2 ) = 0n ⊕ (D 1 D 2 ) = 〉 sn ⊕ (B 1 B 2 ) = 0· 限制· 求解上述方程必须要使物体表面与某一个可分离的坐标系相吻合,也即有严格级数解可以利用时,波动方程才能有严格的解析解。

· 但只有少数几种形体能满足这种要求。

n + 1=n 1 ( 1) ( 2 )(b n a n ) 目标RCS 精确解法· 球的后向散射雷达散射截面⎛ = 2n 2ˆ ˆ ˆ ˆ ˆ ˆ矩量法· 控制方程– Stratton-Chu 积分方程E s = +s [i ⎤∝ (n ⋅ H )⎭ +(n ⋅E ) ⋅ (n ⊕ E ) ⎭ ]ds H s = +s[i ⎤∝ (n ⋅ E )⎭ +(n ⋅ H ) ⋅ (n ⊕ H ) ⎭ ]ds矩量法·求解思路–将积分方程写成带有积分算符的符号方程;–将待求函数表示为某一组选用的基函数的线性组合并代入符号方程;–用一组选定的权函数对所得的方程取矩量,得到一个矩阵方程或代数方程组;–求解代数方程组。

·特点––––精度较高在目标外部轮廓取样时,间隙不得超过波长的1/5左右。

当目标尺寸与波长相比很大时,取样数量十分庞大主要用于低频区与谐振区的散射问题。

高频区目标RCS近似计算方法·依据–大多数探测雷达的波长都远远小于飞行器的特征尺寸。

–在高频区复杂目标的散射场可瞧作各个散射源产生的散射场的综合。

·方法––––几何光学法物理光学法几何绕射理论物理绕射理论几何光学法·概念–当电磁波波长与目标尺寸相比很小时,可以近似地用几何光学的观点来研究物体上电磁波的散射现象。

RCS 计算平板或圆球的手算公式

RADAR CROSS SECTION (RCS)Radar cross section is the measure of a target's ability to reflect radar signals in the direction of the radar receiver, i.e. it is a measure of the ratio of backscatter power per steradian (unit solid angle) in the direction of the radar (from the target)to the power density that is intercepted by the target.The RCS of a target can be viewed as a comparison of the strength of the reflected signal from a target to the reflected signal from a perfectly smooth sphere of cross sectional area of 1 m as shown in Figure 1 .2The conceptual definition of RCS includes the fact that not all of the radiated energy falls on the target. A target’s RCS (F ) is most easily visualized as the product of three factors:F = Projected cross section x Reflectivity x Directivity .RCS(F ) is used in Section 4-4 for an equation representing power reradiated from the target.Reflectivity: The percent of intercepted power reradiated (scattered) by the target.Directivity: The ratio of the power scattered back in the radar's direction to the power that would have been backscattered had the scattering been uniform in all directions (i.e. isotropically).Figures 2 and 3 show that RCS does not equal geometric area. For a sphere, the RCS, F = B r ,2where r is the radius of the sphere.The RCS of a sphere is independent of frequency if operating at sufficiently high frequencies where 8<<Range, and 8<< radius (r). Experimentally,radar return reflected from a target is compared to the radar return reflected from a sphere which has a frontal or projected area of one square meter (i.e.diameter of about 44 in). Using the spherical shape aids in field or laboratory measurements since orientation or positioning of the sphere will not affect radar reflection intensity measurements as a flat plate would. If calibrated, other sources (cylinder, flat plate, or corner reflector, etc.) could be used for comparative measurements.To reduce drag during tests, towed spheres of 6", 14" or 22" diameter may be used instead of the larger 44" sphere, and thereference size is 0.018, 0.099 or 0.245 m respectively instead of 1 m. When smaller sized spheres are used for tests you 2 2may be operating at or near where 8-radius. If the results are then scaled to a 1 m reference, there may be some 2perturbations due to creeping waves. See the discussion at the end of this section for further details.In Figure 4, RCS patterns are shown asobjects are rotated about their vertical axes(the arrows indicate the direction of theradar reflections).The sphere is essentially the same in alldirections.The flat plate has almost no RCS exceptwhen aligned directly toward the radar.The corner reflector has an RCS almost ashigh as the flat plate but over a wider angle,i.e., over ±60E, the return from a cornerreflector is analogous to that of a flat platealways being perpendicular to yourcollocated transmitter and receiver.Targets such as ships and aircraft oftenhave many effective corners. Corners are sometimes used as calibration targets or as decoys, i.e. corner reflectors.An aircraft target is very complex. It has a great many reflecting elements and shapes. The RCS of real aircraft must be measured. It varies significantly depending upon the direction of the illuminating radar.P r 'PtGtGr82F(4B)3R4R2 BT 'PtGtFPjGj4BP r 'PtGtGr82F(4B)3R4'PjGjGr82(4B R)288S J. Typical Aircraft RCSFigure 5 shows a typical RCS plot of a jet aircraft. The plot is anazimuth cut made at zero degrees elevation (on the aircrafthorizon). Within the normal radar range of 3-18 GHz, the radarreturn of an aircraft in a given direction will vary by a few dB asfrequency and polarization vary (the RCS may change by a factorof 2-5). It does not vary as much as the flat plate.As shown in Figure 5, the RCS is highest at the aircraft beam dueto the large physical area observed by the radar and perpendicularaspect (increasing reflectivity). The next highest RCS area is thenose/tail area, largely because of reflections off the engines orpropellers. Most self-protection jammers cover a field of view of+/- 60 degrees about the aircraft nose and tail, thus the high RCSon the beam does not have coverage. Beam coverage isfrequently not provided due to inadequate power available tocover all aircraft quadrants, and the side of an aircraft istheoretically exposed to a threat 30% of the time over the averageof all scenarios.Typical radar cross sections are as follows: Missile 0.5 sq m; Tactical Jet 5 to 100 sq m; Bomber 10 to 1000 sq m; and ships 3,000 to 1,000,000 sq m. RCS can also be expressed in decibels referenced to a square meter (dBsm) which equals 10 log (RCS in m).2Again, Figure 5 shows that these values can vary dramatically. The strongest return depicted in the example is 100 m in2 the beam, and the weakest is slightly more than 1 m in the 135E/225E positions. These RCS values can be very misleading2because other factors may affect the results. For example, phase differences, polarization, surface imperfections, and material type all greatly affect the results. In the above typical bomber example, the measured RCS may be much greater than 1000 square meters in certain circumstances (90E, 270E).SIGNIFICANCE OF THE REDUCTION OF RCSIf each of the range or power equations that have an RCS (F) term is evaluated for the significance of decreasing RCS, Figure 6 results. Therefore, an RCS reduction can increase aircraft survivability. The equations used in Figure 6 are as follows:Range (radar detection): From the 2-way range equation in Section 4-4: Therefore, R%F or F% R41/4Range (radar burn-through): The crossover equation in Section 4-8 has:Therefore, R%F or F% RBT BT21/2Power (jammer): Equating the received signal return (P) in the two way range equation to the received jammer signal (P)r r in the one way range equation, the following relationship results:Therefore, P%F or F% P Note: jammer transmission line loss is combined with the jammer antenna gain to obtain G.j j t-.46-.97-1.55-2.2-3.0-4.0-5.2-7.0-10.0-400.10.20.30.40.50.60.70.80.91.0dB REDUCTION OF RANGEdB REDUCTION OF RANGE10 Log ( P 'j / P j )(DETECTION )(BURN-THROUGH)(JAMMER)j / P jFigure 6. Reduction of RCS Affects Radar Detection, Burn-through, and Jammer PowerExample of Effects of RCS Reduction - As shown in Figure 6, if the RCS of an aircraft is reduced to 0.75 (75%) of its original value, then (1) the jammer power required to achieve the same effectiveness would be 0.75 (75%) of the original value (or -1.25 dB). Likewise, (2) If Jammer power is held constant, then burn-through range is 0.87 (87%) of its original value (-1.25 dB), and (3) the detection range of the radar for the smaller RCS target (jamming not considered) is 0.93 (93%)of its original value (-1.25 dB).OPTICAL / MIE / RAYLEIGH REGIONSFigure 7 shows the different regions applicable for computing the RCS of a sphere. The optical region (“far field”counterpart) rules apply when 2B r/8 > 10. In this region, the RCS of a sphere is independent of frequency. Here, the RCS of a sphere, F = B r . The RCS equation breaks down primarily due to creeping waves in the area where 8-2B r. This area 2is known as the Mie or resonance region. If we were using a 6" diameter sphere, this frequency would be 0.6 GHz. (Any frequency ten times higher, or above 6 GHz, would give expected results). The largest positive perturbation (point A)occurs at exactly 0.6 GHz where the RCS would be 4 times higher than the RCS computed using the optical region formula.Just slightly above 0.6 GHz a minimum occurs (point B) and the actual RCS would be 0.26 times the value calculated by using the optical region formula. If we used a one meter diameter sphere, the perturbations would occur at 95 MHz, so any frequency above 950 MHz (-1 GHz) would give predicted results.CREEPING WAVESThe initial RCS assumptions presume that we are operating in the optical region (8<<Range and 8<<radius). There is a region where specular reflected (mirrored) waves combine with back scattered creeping waves both constructively and destructively as shown in Figure 8. Creeping waves are tangential to a smooth surface and follow the "shadow" region of the body. They occur when the circumference of the sphere - 8 and typically add about 1 m to the RCS at certain 2frequencies.。

基于伴随方程和自动微分的rcs表面敏感度计算

基于伴随方程和自动微分的rcs表面敏感度计算让我们来深入了解一下关于基于伴随方程和自动微分的rcs表面敏感度计算。

这个主题涉及到雷达散射战术中非常重要的内容，对于理解和优化雷达系统性能有着重要意义。

1. 什么是伴随方程和自动微分？在介绍rcs表面敏感度计算之前，我们需要先了解伴随方程和自动微分这两个概念。

伴随方程是偏微分方程理论的一个重要概念，它通常用来描述一个系统的敏感度分析。

而自动微分则是一种数值计算方法，用来计算函数的导数。

这两个概念在雷达散射领域中有着广泛的应用，可以帮助我们计算rcs表面的敏感度。

2. rcs表面敏感度计算的原理基于伴随方程和自动微分的方法可以帮助我们更准确地计算rcs表面的敏感度。

通过建立散射场的数学模型，并使用伴随方程和自动微分方法，我们可以得到rcs表面对参数变化的敏感度。

这对于优化雷达系统的设计和性能具有非常重要的意义。

3. rcs表面敏感度计算的应用rcs表面敏感度计算在实际应用中有着广泛的应用。

在雷达系统的设计和优化中，我们需要考虑不同参数对系统性能的影响，而rcs表面敏感度计算可以帮助我们更好地理解这些影响。

在目标识别和跟踪中，rcs表面敏感度计算也可以帮助我们更准确地分析目标的特性和动态变化。

4. 个人观点和总结在我看来，基于伴随方程和自动微分的rcs表面敏感度计算是雷达散射领域中的一项非常重要的技术。

它不仅可以帮助我们更深入地理解雷达系统的性能，还可以为系统的设计和优化提供重要参考。

希望未来能够有更多的研究和应用，进一步推动这一领域的发展。

总结回顾：在本文中，我们深入探讨了基于伴随方程和自动微分的rcs 表面敏感度计算。

首先介绍了伴随方程和自动微分的基本概念，然后详细解释了rcs表面敏感度计算的原理和应用。

个人观点认为这项技术对雷达系统的性能优化至关重要。

希望通过本文的介绍，读者能对这一主题有更全面、深入的理解。

通过以上内容，希望本文能够帮助你更好地理解并掌握基于伴随方程和自动微分的rcs表面敏感度计算。

RCS-978比率差动校验计算方法

南瑞继电保护RCS-978变压器保护比率差动校验方法说明，RCS-978保护可以自动算出各侧额定电流和平衡系数。

改变系统定值的时候，各区保护定值都要确定一下，要不运行灯不亮。

1,设定系统参数设定完毕后，可以查看差动计算定值单如下:序号定值名称数值序号定值名称数值01 I侧平衡系数0. 999 07 ∏I侧额定电流 1.48002 II侧平衡系数0. 999 08 IV侧额定电流 1.48003 III侧平衡系数 2. 657 09 零差I侧平衡系数 1.00004 IV侧平衡系数 2. 657 10 零差II侧平衡系数 2. 00005 I侧额定电流 3. 935 11 零差公共侧平衡系数 2.00006 II侧额定电流 3. 935 12差动启动电流：Iset=0.3Ie，比率制动系数K=0. 5稳态比率差动的动作特制动电流0. 6.有用公式：Id>O. 2Ir+Icdqd Ir<=0. 5Ie 公式 1 Ir=l∕2 ( Il ∣+ ∑2∣+ ∑3∣+∙∙∙+ Im ) 公式2Id= Il + l2+l3+∙∙∙ + Im公式3其中，Ie为变压器额定电流，∏到Im为变压器各侧电流，Icdqd为稳态比率差动启动电流，Id为差动电流，Ir为制动电流，2.差动各侧电流相位差的补偿Yo 侧:I∖=(I A-I O)U B=(I B-I O)Uc=(Ic-Io)上式中，1全为矢量.单加入A相电流时,310=la单加入B相电流时,3Io=Ib单加入C相电流时,3Io=Ic△侧：I%(I A-I C)∕.3I'B=(I B-I A)∕.3Uc= (IC-I B)∕V∕3上式中，I全为矢量.3逻辑校验3.1,各侧差动启动电流的校验单加入高压侧A相电流为例：设h=Ix'(估计是面板显示数据)则：Ir=l/2Ix' Id=Ix,带入公式1得：Ix,>O. 2*l∕2Ix,+Icdqd所以：lcdqd<O. 91x,再有相位补偿：Ix（加入值）=3∕2Ix）（3/2是怎么过来的？？？）所以：1x（加入值）=1.5Tcdqd∕0. 9由定值得：lcdqd=O. 31e=0. 3*3. 935=1. 1805则:Ix=l. 5*1. 1805/0. 9=1. 9675结论,在加入值在大于1. 9675时差动应动作。

RCS计算方法

航空宇航学院
几何绕射理论
• 绕射场是沿绕射射线传播的，绕射射线所形成的圆锥面称为Keller锥。
– 当入射线与边缘垂直时，圆锥面退化为与边缘垂直的平面圆盘。
• 在高频区时绕射和反射一样是一种局部现象。
– 也就是说绕射只取决于散射体绕射点邻域内的物理特性和几何特性，这可以称之为局部原理。
• 离开绕射点后的绕射线仍遵循几何光学的定律，即在绕射射线管中能量是守恒的。
入射波
照射区
阴影区
场强为零
航空宇航学院
远场近似
• 如果目标表面上任一点到观察点Ｐ的距离Ｒ远远大于目标的尺寸，则格林函数的梯度可简化为
ˆ ∇ψ ≅ iksψ
其中
ห้องสมุดไป่ตู้e ψ= 4π R
ikR
航空宇航学院
切平面近似
• Stratton-Chu积分方程右端包含有总场，为使方程简化成定积分问题，应将方程中右端的总场用入射场来表示。 • 为了将入射场与散射场联系起来，假设目标表面上的任一点及其附近表面曲率半径比波长大得多，根据平面波在无穷大平面上电磁边界条件，对于理想导体表面，入射场与散射场的关系为
航空宇航学院
几何绕射理论计算过程
• 首先必须找出这样的边缘单元，它们在局部的 Keller锥上的一条母线贯穿远区场的观察点。 • 设想在整个目标的边缘上可建立起多个小Keller 锥，在计算中只需包含那些朝向观察点方向的 Keller锥的边缘，而忽略所有的其它边缘。 • 将到达观察点的所有射线的散射场进行叠加。
ˆ ˆ n × E = n × (E i + E s ) = 0 ˆ ˆ ˆ n × H = 2n × H s
航空宇航学院

RCS计算方法简单介绍

RCS计算方法

雷达截面积（RCS）的基础知识

(完整版)雷达截面积(RCS)

RCS 计算平板或圆球的手算公式

微带天线rcs计算

RCS计算方法11

对空打击面积 专业名词

角反射器rcs计算公式

活动板类角反射器的RCS计算

RCS计算方法

RCS计算方法

RCS 计算平板或圆球的手算公式

基于伴随方程和自动微分的rcs表面敏感度计算

RCS-978比率差动校验计算方法

RCS计算方法

对空打击面积专业名词