Radar Fundamentals (Part I) – Aircraft 101

 介绍

“RADAR”一词是 RAdio Detection And Ranging 的首字母缩写词。正如最初设想的那样，无线电波用于检测目标的存在并确定其距离或范围。一个多世纪前，人们首次注意到无线电波被物体反射。1903 年，德国利用无线电波的反射来演示海上船只的探测。1922 年，马可尼在英国提出了同样的想法，但没有引起官方的兴趣。这些早期实验使用连续波或 CW 传输，并依靠目标对传输波的反射来指示目标的存在。CW 传输可以检测物体的存在，如果无线电波形成窄波束，还可以提供方位角信息。CW 传输无法提供范围。

距离信息的缺乏是一个严重的限制，但最终通过调制无线电波传输以发出一串短脉冲来克服。脉冲传输和回波返回接收器之间的时间提供了距离的直接测量

目标角度辨别是雷达系统的另一个关键能力。为了让雷达系统检测到目标，天线必须在发射和接收 RF 能量期间指向目标。雷达系统准确确定角度的能力是天线水平波束宽度的函数。如果雷达扫描以真北为参考，则可以相对于真北测量雷达回波的角度。

确定目标速度是雷达系统的一项重要能力，以实现雷达利用多普勒效应。多普勒效应是无线电波的频率从相对于雷达移动的目标反射时发生变化或偏移的现象。为了测量准确的速度，雷达的中央处理器计算发射波频率和反射波频率之间的差异。下图中f o是雷达的发射频率，f t是反射波的频率。

• 对于静止目标，反射信号的频率将等于发射信号的频率

• 对于向雷达移动的目标，反射信号的频率将高于发射信号
• 远离雷达的目标的反射频率将低于发射频率

重要的是要记住，影响多普勒频移的因素不是目标绝对速度，而是目标的径向速度。因此，目标和雷达之间的方位角非常重要。

 

 

基础词汇表

频率

发射信号的频率是射频能量每秒完成一个周期的次数

 

波长

任何射频信号的一个特征是波长。波长是空间中传播的正弦波波峰之间物理距离的量度。大多数雷达信号的波长以厘米或毫米为单位。波长和频率成反比关系：频率越高，波长越短

 

极化

极化是射频波在空间传播时的方向。极化有两种类型：线性和圆极化。极化由雷达天线确定

1. 旅行电磁能有两个组成部分：静电场和磁场。这两个场始终相互垂直并垂直于行进方向。波的极化是根据静电场的方向来定义的。许多雷达天线都是线性极化的，无论是垂直还是水平。下面描述的信号是垂直极化的。
2. 一些雷达使用圆极化来改善雨中的目标检测。圆极化可以是右手或左手方向。对于圆极化，静电场的方向随时间变化并围绕垂直于传播方向的固定平面描绘圆形轨迹。对于右旋圆极化信号，静电矢量似乎顺时针旋转方向。对于左旋圆极化信号，旋转是逆时针的。可以通过将任一手的拇指指向传播方向并将手指卷曲在静电场旋转方向来观察圆极化。
3. 极化对接收器和发射器的影响是相当明显的。如果天线设计用于接收特定极化，则将难以接收具有相反极化的信号。这种情况被定义为交叉极化。交叉极化对电子战的影响可能是巨大的。如果雷达警告接收器天线被极化以接收垂直极化信号，则可能无法检测到使用水平极化雷达信号的威胁系统。此外，如果电子攻击 (EA) 系统上的干扰天线也是垂直极化的，则可能无法检测到能够干扰该系统。下表说明了极化对所选发射和接收天线组合的影响：

雷达地平线

无论雷达系统采用何种扫描方式，地形都会限制雷达视线 (LOS) 和目标检测。雷达视野是飞机探测系统性能的关键区域，由雷达波束上升的距离定义s 距离地球表面足够高，无法检测到低水平的目标，换句话说，这是雷达系统由于地球曲率而可以检测到目标的最大范围。.重要的是要记住，在大气中传播的无线电波是弯曲的或折射的，并且不会以完美的直线传播。然而，折射的程度取决于大气条件，这些条件变化很大并且难以准确量化和预测。由于这些原因，大多数雷达计算都基于无线电波沿直线传播的假设。雷达地平线的概念就是基于这个假设。（在 for距离以下的mula以海里 (nm) 为单位，高度以英尺为单位）

由于 LOS，目标高度在最大雷达探测范围中也起着重要作用

增加雷达视距，常用的方法是增加天线高度。

这条规则有一个例外，它们被称为超视距雷达 (OTH) 雷达。与通过几乎直线直接向目标发送和接收无线电来检测目标的常规雷达不同，地平线雷达必须使用“弯曲”它们的波路径来绕过地球曲率的限制。OTH雷达有两种。他们是：

Skywave OTH 雷达 (OTH-B)

OTH-B 雷达通过使用通常在 5-28 Mhz 之间的非常低的频率来克服地球曲率限制，因此它们能够从电离层（大气顶部的电离层）“反弹”（散射）它们的波。

由于这种独特的设计，OTH-B雷达可以探测到数千公里外的飞机，即使这些飞机在非常低的高度飞行。然而，由于 OTH-B 雷达使用的频率非常低，因此它们不仅非常不准确，而且需要非常大的天线，每个天线的高度通常高达 15-20 米，而整个雷达阵列通常在 2-20 米之间。 3公里长。此外，接收和发射阵列需要分开放置，彼此相距约150-200公里。由于尺寸过大，OTH 雷达是大型固定目标

此外，由于OTH-B雷达需要将波从电离层反射回来，并且波反射回来的接近角有限制，因此在雷达前方有一个大的锥形盲区，目标可以'被检测到，这个区域通常称为跳跃区。OTH-B雷达的跳跃区长度通常为800-2700公里，因此OTH雷达仅用于警告目的

表面/地面波雷达 (OTH-SW) 

OTH-SW 雷达通过使用 1.6-3 Mhz（最高可达 20 Mhz）的极低传输频率克服了地球曲率的限制。这些电磁波倾向于围绕边缘或曲线弯曲或“衍射”，它们耦合到导电海洋表面形成“地波”。它们可以在地平线上弯曲，并会跟随地球的曲率。尽管有常见的“地波”雷达名称，但 OTH-SW 只能在海岸线上使用，因为它们需要海洋的导电特性。

与 OTH-B 雷达类似，OTH-SW 雷达也需要大型天线才能运行，其精度也非常有限。然而，OTH-SW 雷达没有像 OTH-B 雷达一样的跳跃区域限制，它们的发射和接收子阵列可以彼此非常靠近地放置，只有 1-2 km艺术。另一方面，OTH-SW 雷达的射程比 OTH-B 雷达短得多，而 OTH-B 雷达可以探测到最远 5500 公里以外的目标，而 OTH-SW 雷达通常在 300-350 公里以外达到顶峰。

传播

无线电能的传播特性深受地球表面和大气条件的影响。对雷达性能的任何分析都必须考虑与“真实世界”环境中的射频辐射相关的传播现象。最重要的传播现象包括折射、反常传播（管道）和衰减。

折射

在真空中，无线电波沿直线传播。然而，在地球大气层中传播的无线电波并不沿直线传播。地球的大气层会弯曲或折射无线电波。无线电波大气折射的影响之一是雷达的视线 (LOS) 增加。这种雷达 LOS 的增加有效地扩展了雷达系统的范围。

射频波在大气中的折射是由传播速度随高度的变化引起的。折射率 (n) 用于描述这种速度变化，由以下等式定义

术语折射率 (N) 用于预测折射对 RF 波传播的影响。折射率是折射率的“放大”表达式，雷达设计人员使用它来计算折射对实际雷达系统的影响。在正常的雷达工作频率下，可以使用以下公式计算含有水蒸气的空气的折射率

随着高度的增加，气压计IC压力和水蒸气含量迅速下降。同时，绝对温度以标准自减率缓慢下降。使用上面的等式，可以看出大气的折射率随着高度的增加而降低。这种折射率的降低意味着无线电波的速度随着高度的增加而增加。结果是无线电波向下弯曲或折射。无线电波折射主要影响低天线仰角的地面雷达系统，尤其是在地平线或附近。一般来说，由于折射，雷达系统相对于光学和红外系统的雷达视野增加了大约 10-15%

对于大多数雷达应用，折射不是仰角超过 5 度的因素。

异常传播 

当大气的折射率因温度梯度、压力或水蒸气含量的变化而改变时，就会发生非标准或异常传播。这些参数可以产生范围广泛的非标准传播条件。

有3种类型的异常传播

次折射： 当大气条件导致雷达波束弯曲小于标准大气或向上弯曲时，就会发生这种情况。当大气相对于标准大气不稳定时，就会发生这种情况。次折射导致雷达超过通常在标准大气条件下观察到的目标，并导致雷达的雷达视界范围缩小。除了低估回波高度之外，这种现象还倾向于减少最低仰角切割中的地面杂波。发生亚折射的典型情况是倒 V 形测深，其特征是干绝热或超绝热温度递减率和恒定或随高度增加的水分供应。近地表空气通常是干燥的。这种情况在沙漠地区和山脉的背风面很常见，

超折射：当大气条件导致雷达波束比在标准大气中更向地球表面弯曲，但弯曲程度不足以击中地面时，就会发生这种情况。这可能有助于显着增加雷达视野。大气折射率随高度迅速下降时形成的超折射效应。当温度随海拔高度升高而水蒸气含量随海拔高度降低时，就会发生这种情况。温度随海拔升高而升高称为逆温。当温暖干燥的空气流过较冷的表面时，通常会发生这种情况；日伊斯兰国如果较冷的表面是水，则最有效——由于混合，大气的下层被冷却和润湿。随着海风的发展，凉爽潮湿的空气在温暖干燥的大陆气团下向内陆移动，也可能发生这种情况。在帮助扩展雷达视野的同时，超折射效应会导致高估雷达测量的高度。发生超折射时，会在比标准更高的仰角观察降水目标。此外，它可以导致检测到更多的范围折叠回波，因为当超折射使雷达波束弯曲时，它可以传播很长的距离并从目标反射超出雷达的明确范围。超折射的另一个不利影响涉及雷达在扩展范围内检测非降水目标的能力。地面杂波是一种高反射回波模式，通常由靠近雷达的地形特征和其他物体产生，在超折射条件下会扩大。当雷达波束弯曲到足以靠近地面行进或沿着地面反弹很长距离时，将在更大范围内检测并显示地表特征。雷达的用途被削弱了，因为通常很难区分地面回波和降水目标。

 

管道：是一种独特的超折射形式。要生产管道，温度反转必须非常明显。超折射管道就像波导一样捕获无线电波。这会引导雷达信号并减少衰减。为了使无线电波在管道内传播，雷达信号相对于管道的角度应小于 1 度。被管道捕获的无线电波利用折射率的降低，比正常传播得更远。这可以极大地扩展雷达系统的视野。管道内雷达范围的扩展会导致管道外雷达覆盖范围的减少。由于波导而减少的雷达覆盖区域称为雷达孔。由于雷达孔，波导引起的雷达范围扩大可能会导致沿其他传播路径的雷达覆盖范围减少。这些漏洞会严重降低预警雷达系统的有效性。例如，雷达系统利用在地面形成的管道来扩展低空雷达范围。通常会检测到刚好在管道上方飞行的空中目标，但由于管道的存在，这些目标可能会被遗漏。水蒸气含量是产生风管的重要因素。因此，大多数管道是在水面上和温暖的气候下形成的。通常会检测到刚好在管道上方飞行的空中目标，但由于管道的存在，这些目标可能会被遗漏。水蒸气含量是产生风管的重要因素。因此，大多数管道是在水面上和温暖的气候下形成的。通常会检测到刚好在管道上方飞行的空中目标，但由于管道的存在，这些目标可能会被遗漏。水蒸气含量是产生风管的重要因素。因此，大多数管道是在水面上和温暖的气候下形成的。 

衰减

当穿过大气层时，一部分无线电波能量撞击氧气和水蒸气并被吸收为热量。大气气体引起的衰减损耗基于无线电波的频率。在低于 1 GHz 的频率下，大气衰减的影响是微不足道。在 10 GHz 以上，大气衰减急剧增加。这种显着的信号损失会影响在毫米波段工作的雷达的最大探测范围。无线电衰减会随着高度的增加而降低。空对空雷达经历的衰减将取决于目标的高度和目标的距离。对于地面雷达，衰减将随着天线仰角的增加而降低。

 

多径效应：

对于地基雷达，雷达波束的下部通常会从地面反射并干扰接收信号。

这种干扰可以是建设性的（当它增加接收信号的幅度时）或破坏性的（当它降低接收信号的幅度时）。人们可以认为这是天生的“主动取消”

相互作用是破坏性的还是建设性的将取决于相位差。相位差会受到距离/目标高度/天线高度/入射角/频率的影响

 

 

 

表面反射对接收信号的影响程度取决于称为反射系数的因素。系数越高，反射的幅度就越大。因此，它会对雷达产生更大的影响。一般来说，平坦的地表和平坦的海面反射系数高，而波涛汹涌的海面，尤其是波涛汹涌的地面，反射系数会很低。因此，多径效应对舰船雷达的影响远大于对地面雷达的影响

多径效应的相互作用会导致雷达覆盖破裂成多个小波瓣，不像广告视频中常见的气泡覆盖。在波瓣的峰值处，检测范围可以高达正常自由空间值的两倍。相比之下，在零点处，检测范围可以低至零。 

 

低频雷达受多径效应的影响更大，因为它们的波瓣和零点之间的距离很远，导致盲区

脉冲宽度

脉冲宽度 (PW) 也称为脉冲持续时间 (PD)，是发射器发出 RF 能量的时间。脉冲宽度以微秒为单位测量。它对距离分辨能力有影响，即是指雷达根据距离区分两个目标的准确程度。距离分辨率最多是脉冲在等于脉冲宽度的时间内传播的距离的二分之一。这种限制是自然强加的

脉冲重复间隔/时间（PRI/PRT）

脉冲重复时间是一个发射脉冲开始与下一个脉冲之间经过的时间；脉冲重复率的倒数。

脉冲重复频率 (PRF)

脉冲重复频率 (PRF) 是特定时间单位内重复信号的脉冲数，通常以每秒脉冲数来衡量，是 e以赫兹 (Hz) 表示。PRF 和 PRI 相关，因为 PRI 是 PRF 的倒数。重要的是要注意雷达的工作频率与脉冲重复频率不同，即使两者都是以 Hz 为单位测量的，它们是脉冲雷达信号的完全不同的特性。雷达通过测量脉冲发射和目标返回接收之间经过的时间来计算到目标的距离。对于明确的距离测量，对于雷达发射的每个脉冲，从目标接收到的脉冲不应超过一个。因此，雷达所需的最大距离决定了雷达的最大重复频率。

错开

雷达可以采用多种自适应措施来降低其对ECM的敏感性；使欺骗性干扰器的工作更加困难的一个因素是交错脉冲序列的结合。PRF 交错是通过确保没有相邻的 PRI 相等来实现的。生成的不同 PRI 的数量称为交错的“位置”。双位置交错将有两个 PRI 值，例如 300 微秒和 500 微秒，如图所示

雷达的 PRF 是所有脉冲序列的总和，因此如果 RWR 在 PRF 上运行，则交错模式中固有的额外识别将无用。这个问题是通过测量 PRI 而不是 PRF 来克服的，这样 RWR 测量基本 PRI 的次数等于交错级别的数量。

PFI抖动

PRI 抖动可视为随机交错。这也是一种对抗欺骗性干扰器的技术。PRI 抖动没有 PRI 值的重复模式，只要满足最大范围条件，连续脉冲之间的时间允许在一系列设置间隔内以完全随机的方式变化，理论上，这允许无限数量的 PRI要生成的模式。

雷达探测范围

在讨论飞机和现代航空电子设备时，尤其是 F-22 等隐形飞机、ALQ-99 等现代干扰机或 S-300/400 等现代地对空导弹系统时，许多爱好者错误地认为雷达探测、跟踪是二元的质量（要么他们假设雷达将始终检测到飞机，要么飞机完全不可见）。但是，这种假设是不准确的。无论涉及什么系统，雷达检测都是一种数量特征，受雷达峰值功率、脉冲等因素的影响重复频率，目标的雷达截面，雷达增益等。雷达探测距离可以通过上式估算。

雷达截面 

雷达横截面与目标的面积不同，尽管通常使用平方米单位来测量雷达横截面（另一个可用于测量 RCS 的单位是 dBsm ）。雷达横截面是衡量目标能力的指标向雷达接收器的方向反射雷达信号。换句话说，它是雷达（从目标）方向上每球面度（单位立体角）的反向散射功率与目标截获的功率密度之比的度量。RCS的概念定义包括事实上，并不是所有的辐射能量都落在目标上。

• 投影横截面：
  几何横截面是指目标呈现给雷达的区域，或其投影面积。该区域将根据目标呈现给雷达的角度或方向而变化。换句话说，如果目标直接飞向雷达并被正面观察，则目标可能会呈现给雷达的最小投影区域。从侧面、顶部或底部看会呈现出更大的投影区域。
• 反射率：
  .雷达功率不一定从飞机的所有部分反射出来，一些部件产生比其他部件更强的雷达反射。此外，一些雷达功率通常会被目标吸收。这种吸收对于涂有称为雷达吸收材料 (RAM) 的特殊物质的飞机或使用称为雷达吸收结构 (RAS) 的内部反射器捕获入射雷达波的飞机来说尤其如此。反射率是指被反射的截获功率的分数目标，无论方向如何
• 方向性：
  雷达能量反射不均匀，具体取决于目标的形状，雷达波会比其他方向更多地反射到某个方向。反射到雷达的功率称为反向散射功率。方向性定义为在雷达方向上反向散射的功率与在该方向上散射的功率之比，如果散射实际上在所有方向上都是均匀的

简单金属形状的雷达截面可以通过下表中的公式估算（变量 λ 表示雷达的波长，假设其小于形状的尺寸。）

与球体或圆柱体不同，飞机是一个非常复杂的目标。它有很多反射元素和形状。对于此类目标，目标表面和 RCS 之间没有固定关系。因此，必须测量飞机雷达横截面，因为它会根据照明雷达的方向发生显着变化。

示例：作为方位角函数的 Mig-29 的模拟雷达横截面。

示例 2：作为方位角函数的 C-29 货机的雷达横截面

示例 3：作为方位角函数的 AV-8B Harrier 的雷达截面

示例 4：使用和不使用 RAM 的 F-15 Eagle 的雷达横截面

示例 5：使用和不使用 RAM 的 AH-64 Apache 的雷达横截面

示例 6：基于飞机配置的雷达散射特性变化

军用陆基和海基车辆的 RCS 通常比军用飞机大，因为后者出于空气动力学原因通常更圆，而地面、海基车辆通常由扁平装甲板和许多支架、天线等组成。

示例：驱逐舰在 10 Ghz 的雷达横截面

飞机可以设计成将 99% 以上的信号能量从雷达方向散射出去，并吸收其余 99% 的信号能量，从而使它们的 RCS 低得多。

示例：作为方位角函数的隐形飞机的模拟雷达横截面。

 

• 在阅读“RCS as a function of aspect”图表时，重要的是要记住，如果方位角发生变化，较大的 RCS 值并不总是会导致更高的检测距离。原因可以 在这里找到

球体的一个独特特征是它的雷达横截面不受其雷达波束方向的影响，这与其他形状（例如圆柱体或平板）不同。因此，飞机的 RCS 通常被比作一个特定大小的球体。

 

复杂物体（例如飞机）的总雷达反射由几种不同类型的反射构成：

• 镜面反射率：  th这是光学区域中最重要的反射形式（当结构尺寸 > 10 倍波长时），表面就像入射雷达脉冲的镜子。大部分入射雷达能量根据镜面反射定律反射（反射角等于入射角）。这种反射可以通过整形显着减少
• 行波/表面波返回： 飞机机体上的入射雷达波撞击会在表面产生行波电流，该电流沿着路径传播到表面边界，例如前缘、表面不连续……等，这样的表面边界可能会导致向后行波或使波向多个方向散射。这种反射可以通过雷达吸波材料，雷达吸波结构，减少表面间隙或边缘对齐（使其波瓣出现在低优先级区域）来减少
• 衍射：撞击非常尖锐的表面或边缘的波被散射，而不是遵循壮观的反射定律。
• 爬波返回： th这是行波的一种形式，它在沿物体表面行进时不面对表面不连续且不被障碍物反射，因此它能够绕过物体并返回到雷达。与正常行波不同，爬行波沿着入射波阴影的表面传播（因为它必须绕过物体）。结果，爬行波的振幅将随着传播的距离而减小，因为它无法从阴影区域的入射波中获取能量。蠕波主要围绕弯曲或圆形物体传播。因此，隐身战斗机和隐身巡航导弹不使用管状机身。然而，蠕变波返回比镜面反射弱得多。

每种类型的回报将占对象总 RCS 值的百分比取决于对象位于哪个区域。术语区域将很快解释。

当物体的周长至少比入射雷达波的波长长 10 倍时，高频区域（或光学区域）适用. 在这种情况下，镜面反射机制主导雷达反射（反射角等于入射角），就像台球碰撞一样。对发射雷达的反射——通过倾斜表面减少，使它们很少垂直于雷达，并通过内部整形、雷达吸收材料 (RAM) 或频率的组合抑制来自发动机进气口和天线腔等重入结构的反射选择性表面。在这种情况下，“表面波”机制对 RCS 的贡献很小，但仍然存在。如果波长相对于表面较小，则这些波很弱，当雷达信号处于掠角时，它们的重叠将产生最大的反向散射。当这些电流遇到不连续点时，例如表面的末端，它们突然变化并发出“边缘波”。来自不同边缘的波由于它们的相位而产生建设性或破坏性的相互作用。结果是它们可以加强镜面反射方向的反射并产生“旁瓣”——镜面反射周围的回波扇，随着角度偏离镜面反射方向而迅速起伏并减弱。光学区域的表面波反射通常非常小。

Mie region or also known as the  resonance region :         applies when   object circumference*0.1 ≤ radar wavelength ≤ object circumference*1       in this region the surface wave can also swing around a structure’s back side, becoming “creeping waves” that shed energy incrementally and contribute to backscatter when they swing back toward the threat radar. This creeping wave can interferes constructively or destructively with the specular backscatter to produce a  variation in the object’s RCS. Creeping wave doesn’t follow mirror like reflection rule, thus the common angular shape of stealth aircraft doesn’t help deflect them away from the threat radar.

那么为什么隐身在低频时效果较差呢？随着雷达雷达波长的增加，镜面反射强度降低，但波瓣宽度变宽（雷达也有同样的现象，如果孔径大小不变，频率降低会增加雷达波束宽度）。因为镜面反射波瓣变宽，整形变得不那么有效，因为它更难将雷达波从源头偏转（重要的是要注意，虽然这种波瓣变宽现象使整形效果不佳，但它也降低了强度反射，因为能量将分布在更宽的体积上）

Specular reflections from flat surfaces decrease with the square of the wavelength but widen proportionally: at 1/10th the surface length(approaching Mie region) they are around 6 deg. wide.

At lower frequency, the effect of traveling wave and diffraction is also more pronoun. For flat surfaces, traveling waves grow with the square of wavelength and their angle of peak backscatter rises with the square root of wavelength: (at 1/10th the surface length, it is over 15 deg). As the power of surface wave grow, the power of creeping wave return also grow. Tip diffractions and edge waves from facets viewed diagonally also grow with the square of wavelength. The end result is that the net value of stealth aircraft’s RCS often increases in Mie region. Maximum RCS is often reached when the wavelength reaches the circumference of the structure

Example: Simulated  radar cross-section of a B-2 aircraft and AGM-86 missiles  as a function of aspect angle ( at 10 Ghz and 1 Ghz respectively )

Example: anechoic chamber measurement of a metallic F-117 model at the frequency range from 0.1-2 GHz

There is a common misconception that any low-frequency radar can render stealth aircraft useless regardless of their transmitting power or aperture size (Ex:  Tikhomirov NIIP L-band transmitter on the leading edge of Flanker series are often cited by enthusiasts as a counter  stealth system) , that is wrong however. While it is true that stealth aircraft will often have higher RCS in Mie region. It is important to remember that given equal radar aperture area,  lower frequency radars will have much wider beam compared to high-frequency radars, thus, the concentration of energy is much lower making them more vulnerable to jamming, lower gain also result in lower accuracy. Moreover, as mentioned earlier lower frequency also resulted in wider reflection beamwidth, hence weaker reflection. As a result, most low-frequency radars have much bigger transmitting antenna compared  high-mid frequency  radar (to get narrow beamwidth) ,it is also the reason that  fighters fire control radar still work in X-band, because a L-band, VHF band radars of similar size would be too inaccurate for any purpose others than early warning.

So, is there any way for  modern stealth aircraft to reduce their return even in Mie region?. The answer is YES

To begin with, the negative effect of traveling wave and diffraction can be reduced by: aligning discontinuities to direct traveling waves towards angles of unavoidable specular return, such as the wing leading edge, thus limit their impact at other angles.

Example: serrated edges are used in place where there is current discontinuity such as weapon bay door so that traveling wave return reflected toward less important angle

Another common method to reduce the effect of surface wave is designing airframe facets with non-perpendicular corners and so radars view them along their diagonals, at low angles and across from the facets’ smallest angles, limits the area of edge-wave emission. Surface wave diffraction can also be reduced by blending facets. The first stealth aircraft, the F-117, was designed with a computer program that could only predict reflections from flat surfaces, necessitating a fully faceted shape, but all later stealth aircraft such as B-2 , F-35 , F-22, X-47 use blended facets. Shapes composed of blended facets are not only more aerodynamic but also allow currents to smoothly transition at their edges, reducing surface-wave scattering. Therefore, blended bodies have the potential for a lower RCS than fully faceted structures,  especially at low-frequency regime. And blending the curves around an aircraft in a precise mathematical manner can reduce RCS around the azimuth plane by an order of magnitude. The penalty is often a slight widening of the specular return at the curves, but in directions at which threat radars are less likely to be positioned. This was one of the great discoveries of the second generation of stealth technology.

Example: Air frame of first generation stealth aircraft such as F-117 are fully facet. Whereas second and third generation of stealth aircraft such as F-35, B-2, X-47 uses blended facet design where needed.

It is, however, important to remember that, even though a blended body shape can benefit stealth characteristics because they reduce surface scattering compared to sharp facet design. A full circular (tube) body is extremely bad for stealth application, the reason is that the surface wave doesn’t get scatter but will travel a full circle around the object and come back to the source (also known as creeping wave return).

While it is possible to reduce the number of sharp edges with blended edge design, it is not possible to get rid of them all, for example an aircraft will always have wing and inlet edges. Thus, there are the need for  trailing edge and leading edge treatment. As mentioned earlier,  the edge diffraction is  more pronoun at lower frequency
  To reduce the effect of edge diffraction, the wing and inlet leading edge  can be made to be a soft electromagnetic surface, this is done by using lightweight material such as glass fiber honeycomb loaded with carbon in a concentration increasing from tip to base. 

Alternatively, a tapered resistive sheet can be sticked or painted on the edge to achieve the same result. Additionally the edge can be made from bulk absorber to improve the result. Similar to the previous example, the resistivity of the sheet will reduce from the maximum at the front tip of the edge to near zero at the rear. The resistivity of the sheet can be increased by adding holes and reduce by adding metal particles in it. 

 

This allows the surface current to transition slowly rather than abruptly as well as be absorbed and thus reduce the edge diffraction as well as surface wave

On the other hand, creeping wave return will be reduced by trailing edge treatment , a thin high resistance strip is often applied on the trailing edge to absorb the energy of the surface wave

As mentioned earlier, the resistive strip/tape must have a width at least half the wavelength of the lowest frequency of interest to be effective, so it is plausible to estimate the lowest frequency where the edge treatment can remain effective. 

For example: the inlet edge strip/tape treatment of F-35 has width between 22- 25.4 cm, which would indicate the lowest frequency where the treatment can still be effective is around 0.5-0.7 GHz

 

Rayleigh Region applies when the circumference of the object is smaller than the radar wavelength. A common misconception is that the lower the operating frequency of the radar ( longer wavelength ), the better it would perform again stealth assets. That is wrong, however. It is important to remember that aircraft RCS does not necessarily grow linearly with increase in frequency. Once the radar wavelength grows past the target’s circumference, the specifics of target geometry cease to be important and only its general shape affects reflection. The radar wave is longer than the structure and pushes current from one side of it to the other as the field alternates, causing it to act like a dipole and emit electromagnetic waves in almost all directions. This phenomenon is known as Rayleigh scattering. At this point, the RCS for aircraft  will then decrease with the fourth power of the wavelength and can get exponentially smaller as the frequency reduce.

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One thing we must remember is that, aircraft are object with very complex shape with many components of different size, thus, even in one specific  wavelength, we often found that some parts of the aircraft could be in Rayleigh region, some in Mie region and the rest in optical region. 

It is interesting to note that the polarization of radar also have an impact on their capabilities against stealth aircraft:

Against wing-fuselage blended stealth aircraft, their vertical polarized RCS (written as VV) is higher than the horizontal polarized RCS (written as HH) in most cases, while the RCS curve for the flying-wing stealth aircraft is just the opposite. For both stealth design, the RCS levels of horizontal and vertical polarized both decrease as the frequency increase, but the horizontal polarized RCS has a faster downward trend. The surface distribution has little influence on horizontally polarized RCS characteristics. On the contrary, it has a significant impact on Vertically polarized RCS characteristics, and the amplitude of the vertical polarized RCS increases with the spanwise cross-section thickness.

• Radar detection range and RCS 

 

 

 Decibel ( dB )

Radar Gain (directivity)

Most radiators emit stronger radiation in one direction than in another As a transmitting antenna, gain describes how well the antenna converts input power into radio waves headed in a specified direction. In layman term: Gain describe how narrow the radar beam is, high gain radars create narrow beam width, low gain radars create wide beam width. Narrow radar 's beam width benefits radar resolution and detection range while wide radar beam benefit sector scanning time. The relationship between radar gain and operating frequency , radar aperture is illustrated in the table below.

 

• Radar Beamwidth  and  Elevation-Azimuth Resolution  

As stated earlier , radar beam width play a vital role in their angular accuracy characteristics because as long as targets stay within the radar beam, there will be reflection , the problem is if several targets fly close enough that their angular separation is smaller than the radar beamwidth, all the return  echoes will be  blended into one return , and radar will only display a single target on screen . To display two distinct radar returns of 2 target close to each other, radar beam needs to be able to pass between them without causing a return. Elevation-azimuth resolution is the ability of a radar to display two targets flying at approximately the same range with a certain angular separation, such as two fighters flying line-abreast tactical formation. The elevation-azimuth resolution capability is usually expressed in nautical miles and corresponds to the minimum angular separation required between two targets for separate display.

Angular resolution in nautical miles ( 1.852 km ) can be estimated by equation below

It important to remember that a radar vertical beamwidth is not necessary the same as it’s horizontal beamwidth. Hence, the azimuth and elevation resolution may be different.

• Range Resolution

Range resolution is the ability of a radar to separate two targets that are close together in range and are at approximately the same azimuth. The range resolution capability is determined by pulse width.A radar pulse in free space occupies a physical distance equal to the pulse width multiplied by the speed of light, which is about 984 feet per microsecond. If two targets are closer together than one-half of this physical distance, the radar cannot resolve the returns in range, and only one target will be displayed.

The range resolution of the radar is usually expressed in feet and can be computed using the equation below. It is the minimum separation required between two targets in order for the radar to display them separately on the radar scope so smaller value for range resolution is desirable

As explained earlier, the longer the pulse, the worse the resolution would be. Range resolution is proportional to pulse width and inverse proportional to bandwidth

Shorter pulse will improve range resolution but will also reduce the power of the transmitted radar wave, thus reduce radar detection range.

To improve radar detection range and range resolution at the same time, a technique called pulse compression was invented.

• Pulse compression 

Pulse compression comes from the need to have large enough pulse without sacrifice range resolution. The basic principles of pulse compression are simple. Instead of transmitting a square pulse with the same characteristic from start to finish, radar instead transmits very long pulses that can be divided into several sub pulses after matched filtering.Thus, radar range resolution would then depend on the length of the sub pulses rather than total pulse length. Pulse compression can be either phase or frequency coded. One side benefit of code compression is that it makes radar much more resistance to jamming.

One of the first form of pulse compression is chirp compression (also known as linear frequency modulated pulse) where the frequency of pulse either increase or decrease with time.

Because chirps compression is predictable for ECM and often require very wide bandwidth, another form of pulse compression called binary phase coded compression were invented. In phase coded compression, the phase is used to distinguish sub pulses instead of the frequency.

It is important to remember that chirp and binary phase coded pulse compression are only the two most basics forms of pulse compression, modern radar use various different kind of pulse compression such as Pseudo random noise sequences, Polyphase, Quadriphase, Costas code, Welti codes, Huffman code

Comparison between phase coded vs frequency coded pulse compression:

• Radar Resolution Cell

A radar’s pulse width, horizontal beamwidth, and vertical beamwidth form a three dimensional resolution cell. A resolution cell is the smallest volume of airspace in which a radar cannot determine the presence of more than one target. The resolution cell of a radar is a measure of how well the radar can resolve targets in range, azimuth, and altitude. The horizontal and vertical dimensions of a resolution cell vary with range. The closer to the radar, the smaller the resolution cell will be. The physical dimension of resolution cell can be easily calculated using equation given for range and angular resolution given above.

• Radar gain and radar detection range

Duty Cycle

Duty cycle is the fraction of the time that a system is in an “active” state. Duty cycle is the proportion of time during which a component, device, or system is operated. If a transmitter operates for 1 microsecond, and is shut off for 99 microseconds, then is run for 1 microsecond again, and so on. The transmitter runs for one out of 100 microseconds, or 1/100 of the time, and its duty cycle is therefore 1/100, or 1 percent. The duty cycle is used to calculate both the peak power and average power of a radar system.

Peak  Power 

The energy content of a continuous-wave radar transmission may be easily figured because the transmitter operates continuously. However, pulsed radar transmitters are switched on and off to provide range timing information with each pulse. The amount of energy in this waveform is important because the maximum range is directly related to transmitter output power. The more energy the radar system transmits, the greater the target detection range will be. Peak power is the amplitude, or power, of an individual radar pulse.

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Average Power

Average power is the power distributed over the pulse recurrence time. The energy transmitted by average power can be computed by multiplying average power by PRT. Since the energy in a set of pulses determines detection range, average power or energy provides a better measure of the detection range of a radar than does peak power. Average
power can be increased by increasing the PRF, by increasing the pulse width, or by increasing peak power.

 

Minimum Detectable Signal ( P-min )

Radar send out pulses and analyze reflection to detect and track targets. The reflection signal power is competing with some interfering signal in order to be detected or recognized. Interfering signal sources may be ground or sea returns, meteorological clutter returns, atmospheric reflections, jamming, or more likely, random noise generated within the receiving circuitry. The latter source is always present to some degrees, while the other sources are variable and can be zero. Therefore, the internal noise power is normally used for determining the maximum range of the radar system.The maximum range performance is determined by a very small signal to noise ratio when the signal begins to fade and become indistinguishable from the noise.

Rest Time

Rest time is the time between the end of one transmitted pulse and the beginning of the next. It represents the total time that the radar is not transmitting. Rest time is measured in microseconds

Recovery Time (RT)

A radar is not only a transmitter but also a receiver.Recovery time is the time immediately following transmission time during which the receiver is unable to process returning radar energy. RT is determined by the amount of isolation between the transmitter and receiver and the efficiency of the duplexer. A part of the high power transmitter output spills over into the receiver and saturates this system. The time required for the receiver to recover from this condition is RT

Listening time (LT)

Listening time is the time the receiver can process target returns often express in microseconds. Listening time is measured from the end of the recovery time to the beginning of the next pulse, or PRT- (PW + RT).

The relationship between recovery time, rest time and listening time is illustrated in the diagram below

 

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• 蒋浩, 昂海松 “F-35战斗机气动隐身特性分析”, 南京航空航天大学航天工程学院, 南京 210016
• （STEPHEN TRIMBLE Flight Global 2010）于 2016 年 3 月 20 日访问 < https://www./news/articles/eurofighter-boasts-typhoon-reign-over-f-35-345265/ >
• 低频反隐形技术的物理和进展（2016 年 8 月 25 日访问）《航空周刊与太空技术》，丹尼尔·卡茨

 

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