雷达与波长,他们之间不得不说的关系!

中二故事会2021-06-07 14:14:45

  • 雷达散射截面积

Simulated radar cross section of a stealth aircraft as a function of aspect angle.

An unique characteristic of a sphere is that it’s radar cross section is not affected by it’s orientation to the radar beam unlike others shapes such as cylinder or plate. As a result aircraft’s RCS are often be compared to a sphere of a certain size. 

2πa/λ>10

Another unique characteristic of sphere is that if 2πa/λ >10 (with a is the sphere radius, λ is radar operating wavelength) then the RCS(σ) of the sphere approaches its geometric projected area πa², this is called theoptical region where the sphere RCS does not change along with the radar’s operating  frequency as long as initial condition is met.

1<2πa/λ<10

When 1<2πa/λ<10, it is called Mie region, in this region a creeping wave travels around the sphere and back towards the receiver where it interferes constructively or destructively with the specular backscatter to produce a  variation in the sphere’s RCS , the sphere RCS could varied between 0.26 to 4 times the value calculated in optical region.

2πa/λ < 1

When 2πa/λ < 1, it is called Rayleigh Region, in this region the sphere’s RCS is inversely proportional to the 4th power of the wavelength (exponentially smaller than values calculated in optical and Mie region).

Fluctuation of RCS in Mie region and Rayleigh region happened not only to simple body like a sphere but also to complex bodies like aircraft, however it happened in a much more complex manner that will be explained below:

To start with, the total radar reflection of a complex body such as aircraft made from several different kinds of reflections:

Specular return: this is the most significant form of reflection in optical region (when structure size >10 times wavelength), surface acts like a mirror for the incident radar pulse. 

Most of the incident radar energy is reflected  according to the law of specular reflection (the angle of reflection is equal to the angle of incidence). This kind of reflection can be reduced significantly by shaping.

Traveling/Surface wave return: an incident radar wave strike on the aircraft body can generate a traveling current on surface that propagates along a path to surface boundaries such as leading edge, surface discontinuous …such surface boundaries can either cause a backward traveling wave or make the wave scattered in many directions .

This kind of reflection can be reduced by radar absorbing material, radar absorbing structure, reduce surface gap or edges alignment (so that their lobes occur in low priority region )

Diffraction: wave striking a very sharp surface or edge are scattered instead of following law of spectacular reflection.

Creeping wave return: this is a form of traveling wave that doesn’t face surface  discontinuous and not reflected by obstacle when traveling along object surface , thus it is able to travel around object and come back at the radar. 

Unlike normal traveling wave, creeping wave traveled along surface shadowed from incidence wave (because it has to go around the object). As a result, the amplitude of creeping wave will reduce the further it has to travel because it can’t feed energy from the  incident wave in shadow region. 

Creeping wave mostly traveled around a curved or circular object. Hence, stealth fighters and stealth cruise missiles do not use tube fuselage. Nevertheless, creeping wave return are often much weaker than spectacular return.


A high-frequency regime (or optical region) applies when the structure is at least 10 times longer than the incident radar wave. 

In this regime, specular mechanisms dominate the radar, (the angle of reflection equals the angle of incidence), like billiard balls colliding.

Reflection towards the emitting radar is reduced by angling surfaces so that they are rarely perpendicular to radars and suppressing the reflections from re-entrant structures such as engine intakes and antenna cavities with combinations of internal shaping, radar absorbent material (RAM) or frequency selective surfaces. 

In this regime, “surface wave” mechanisms are small contributors to RCS, but are still present. If the wavelength is small relative to the surface, these waves are weak and their overlap will generate maximum backscatter when the radar signal is at grazing angles. 

When these currents encounter discontinuities, such as the end of a surface, they abruptly change and emit “edge waves.” 

The waves from different edges interact constructively or destructively due to their phases. The result is they strengthen the reflection in the specular direction and create “sidelobes” – a fan of returns around the specular reflection which undulate rapidly and weaken as the angle deviates from the specular direction. 

The currents can also swing around to a structure’s back side, becoming “creeping waves” that shed energy incrementally and contribute to backscatter when they swing back toward the radar. Surface wave reflections are generally very small in the optical region.

So why is stealth less effective at low frequency? 

As the radar wavelength of radar grows,  the intensity of specular reflections is reduced but its lobes width are widen (the same phenomenon also happened to radar, if aperture size remained the same, the reduction in frequency will increase radar beamwidth). 

Because the specular reflection lobes are widen, shaping become less effective because it will be harder to deflect radar wave aways from the source (it is important to note that, while this lobe widening phenomenon making shaping less effective, it also reduce the intensity of the reflection because the energy will be distributed over a wider volume)

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). 

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 when wavelength approaching Mie region related to aircraft size. Thus, low-frequency radars are often regarded as a counter to stealth technology

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 )

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. 

At high relative frequencies, surface waves can also be suppressed with RAM. 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: Airframe 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).

Regarding the issue of stealth and low frequency, there are 3 common misconceptions. 

The first common misconceptionis that any low-frequency radar can render stealth 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 (their accuracy can be estimated by radar gain equation that will be provided later).

Modern stealth aircraft also use various methods to reduce their return even in Mie region , simulation done by MBDA  shown that even though their radar operating within low-frequency range from UHF to F band, their AWACs still struggle to detect stealth aircraft from their frontal aspect.

The second 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 increasing in frequency. 

As surface-wave effects grow, their phases can interfere constructively or destructively with specular reflections. This phenomenon is illustrated in the simple form with a sphere(as mentioned earlier). 

As wavelength grows relative to the circumference, the creeping wave circling the sphere grows continuously, but its phase interference with the specular return varies. 

This causes the sphere’s RCS to undulate, with successively higher peaks corresponding to phase matches between the specular return and the strengthening creeping wave. 

This phenomenon is known as Mie scattering (also known as the resonance region) and this regime where the wavelength is between one and 1/10th the size of the structure. Maximum RCS is often reached when the wavelength reaches the approximate size of the structure. 

Once the wavelength grows past this point (when wavelength get bigger than target size), 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

Example : Frontal  su-27 RCS as a function of frequencies

The third common misconception is about the quarter wavelength rule, it is popular among enthusiasts to think that the RAM (radar absorbing material ) must be at least as thick as 1/4 the operating frequency of the radar to have any absorbing characteristic. That is wrong however. 

While RAM absorbing capabilities often reduce at low frequency, they do not disappear completely. For example: MnZn ferrite RAM with thickness of merely 3 mm can have absorbing rating of -5dB (or absorbing by 68%) at 2 GHz (wavelength of 2 Ghz wave is about 15 cm  long)

Reduce radar detection range
减少雷达检测距离

One easy to see benefit of RCS reduction is the deduce in enemy detection range, thus giving pilots  more times to react to the threat or getting into weapon engagement zone.

Example: radar detection range between conventional and stealth aircraft.


常规飞机和隐身飞机之间的雷达探测距离对比

Improve jamming effectiveness
提升干扰效果

It is a common misconception that stealth technology is short live and as radar get more powerful, soon, they will be able to out range weapon engagement envelop, thus renders all money spend on RCS reduction a waste. 

This impression is inaccurate because any technology that can increase a radar peak power or gain will also benefit a jammers in the same ways. And stealth have a synergy relationship with jamming.

Another common opinion is that the gap in RCS can easily be close by using a more powerful jammer. This is also inaccurate because RCS directly proportional to the power required to jam a radar at a certain distance.

Which mean when RCS is reduced to 1/100th the original value, the required jamming power is also reduced to 1/100th the original value to achieve the same effect. 

In others words, if a stealth aircraft need a 10 kW jammer, a conventional asset will need  jammer with power of 10Mw or more.

If the jamming power is keeping the same then burn-through range is reduced by 10 times, which mean stealth assets (RCS=0.001m2) can get 10 times closer the threat compared to conventional aircraft (RCS=0.1m2). 

In other words, even if adversary radar can see through jamming of conventional assets from 400 km aways, a stealth asset can still get within 40 km of such radar using exactly same jamming system.

Example : burn-through distance of F-35, F-18E with same jamming assets, same threat radar (image not to scale)


F-35/F-18E有相同干扰设备,雷达烧穿距离对比

Burn-through Range is the radar to target range where the target return signal can  first be distinguished from the Jamming signal (rendering jamming ineffective).


或许你认为现在雷达越来越强大,探测距离越来越远,雷达峰值功率也越来越容易更高,天线增益也可越来越高,所以千方百计减少RCS也是白搭,浪费钱财,总会被检测到的。

或许你也会认为现在干扰机也越来越强大,RCS大小造成的差距在减小,RCS大小不同的飞机都可以靠干扰机来弥补。与其花钱千方百计的减少RCS还不如花钱让干扰机更强大。

其实上面的想法是不可靠的,低的雷达散射界面积(RCS)除了可以大幅减少雷达的探测距离,其隐身效果与干扰也有着协同的关系。

任何可以增加雷达峰值功率或天线增益的技术也将以相同的方式使干扰机受益。

RCS与将雷达阻塞在一定距离所需的干扰功率成正比。这意味着当RCS减小到原来的1/100时,所需的干扰功率降低到原来的1/100便可达到相同的效果。换句话说,如果一架隐形飞机需要一个10千瓦的干扰机,一个传统的飞机将需要10兆瓦或更多功率的干扰机才可实现被发现距离相同。

如果干扰能力保持不变,烧穿距离将减少10倍,也就是说隐形飞机(RCS = 0.001m2)与传统飞机(RCS = 0.1m2)相比,可以获得10倍的威胁。意味着使对方雷达可以从400公里的距离看到传统飞机的干扰,可让雷达要到40公里范围内才可看到隐身飞机。

所以,千方百计降低RCS的隐身钱不白花!


什么是“烧穿距离”?

“烧穿距离”是指使对方电子干扰失效的距离。烧穿距离以内,干扰对雷达无效。烧穿距离与平台的雷达截面积的平方根成比例,而雷达探测距与平台的雷达截面积的四次方根成比例。所以,平台雷达截面积降低了以后,烧穿距离比雷达探测距下降得更快。


后续:波长与雷达的关系


点击图片放大可看清

频率与波长的关系

首先,与雷达波长”不得不说的关系就是频率,这也是大家都知道的一个关系:波长越长,频率越低;波长越短,频率越高;波长与频率的乘积是固定值光速。

天线孔径和增益与波长的关系

我们知道天线的孔径大小和增益都会受到波长的制约,且看公式:

其中,G表示天线增益,Ae表示天线有效孔径。从上图公式可以直观的看出,在天线有效孔径大小相同的情况下,较短波长,可以获得较大的天线增益,成平方的反比关系;而要获得同样的天线增益值,天线有效孔径与波长的平方成正比关系,也就是波长越短,需要的天线有效孔径越小,所以想小型化需要利用更高的频率。

例如,同样都想达到40dB的天线增益,X波段需要的有效孔径不到1m2,而UHF波段的雷达需要数百平方米的天线孔径。所以,我们常见的机载火控雷达通常是X波段,而UHF反隐身雷达总是具有很大的块头。

雷达发射功率与波长的关系

由于波长对天线孔径尺寸的影响,也会间接影响到雷达的发射功率,因为雷达的发射功率会在很大程度上受到电压梯度和散热要求的限制。因此,毫不奇怪的是米波雷达可以发射数兆瓦的平均功率,而毫米波雷达仅可达到数百瓦。当然,雷达功率并不是说能多大就需要做到多大,而是综合考虑探测距离、重量、成本等因素。甚至是发射功率也可以自适应控制,在探测到目标后便减少到仅需的功率用以跟踪目标。

雷达波束宽度与波长的关系


从上述公式可以看出,获得较窄的波束宽度,需要较短的波长和较大的天线尺寸,这与天线增益的公式是对应的,因为窄的波束会带来高的增益。

空间拓展损耗与波长的关系

其中自由空间的损耗单位是dB,常数32.45是在距离单位是km和频率单位是MHz情况下计算出来的。波长越短,频率越高,空间拓展损耗越大。除了发射功率,空间拓展损耗大也是毫米波相比于米波雷达作用距离较近的一个原因。

大气损耗与波长的关系

大气损耗是指电磁波和大气中的水蒸气和氧气分子共振情况下产生的衰减,在10GHz以下一般忽略不计,但是随着更高频率的使用,其影响就不可忽略了,大气损耗与雷达频率(波长)的关系如下图:

从上图可以看出虽然有很大衰减, 但还是存在一些窗口可以利用,例如汽车雷达常用的24GHz/77GHz频段,另外还有35GHz以及94GHz频段附近的毫米波雷达。从上图还可以看出大气中的云和雨也会对电磁波产生较大影响。


那么,不同的雷达“波长”会对雷达系统产生哪些影响,雷达具备哪些特性?

波段划分

我们常说的S波段、X波段的波段划分方法源于二战时期,由历史演变而来,很不规范。后来,又有了规范的A/B/C...的划分方法。雷达波段代表的是发射的电磁波波长(频率)范围,一般情况下,长波(低频)的波段远程性能好,易获得大功率发射机和巨大尺寸的天线;短波长(高频)的波段一般能获得精确的距离和位置,但作用范围短。


P波段(A/B/C)

频率在1GHz频率以下,由于通信和电视等占用频道,频谱拥挤,一般雷达较少采用,只有少数大型的地面预警雷达和天波超视距雷达采用这一频段。使用这些较低的频率,更容易获得大功率的雷达发射功率,电磁波的空间拓展损耗也远低于使用较高频率;

但是,较低的频率需要具有非常大的物理尺寸的天线,限制了角度的分辨性能,并且带宽资源有限也限制了距离分辨力。目前,这些频段正在复苏,这是因为隐身技术在极低的频率下并不具有期望的隐身效果,因此具有反隐身的作用。另外,超宽带(UWB)雷达的新技术也在使用该波段。

L波段(D)

该频段经常传输具有高功率,宽带宽和脉冲内调制的脉冲,是远程地对空警戒雷达的首选;另外,空中交通管制(ATM)远程监控雷达工作在这一频段;这个频段对于远程探测卫星和洲际弹道导弹也是具有吸引力的。

我国的SLC-7雷达就是工作在L波段,采用多项最新雷达技术,作用距离远、测量精度高、抗干扰能力强,并兼具目标类型分辨和敌我识别能力。该雷达采用两维相扫、方位机扫体制,全数字有源相控阵体制,具备对常规空气动力目标,隐身飞机、巡航导弹、空地导弹以及临近空间等目标的探测能力。可为远程防空反导作战提供预警、目标指示、跟踪制导。还可对付目标无人机、火炮和火箭弹目标等。

S波段(E/F)

该频段的雷达系统需要比在较低频率范围内要高得多的发射功率,来达到大的作用距离,是远程探测和三坐标(距离/方位/俯仰)精确测量的折中,例如美军“宙斯盾”的AN/SPY-1系列舰载雷达等。另外,也可用于空中交通管制的机场监视雷达以及机载报警和控制系统。

C波段(G)

在该频带中有许多手持战场监视、导弹控制和地面监视雷达系统,具有中短距离。 天线的尺寸提供了极好的精度和分辨率,但是恶劣天气条件的影响将会非常大。虽然该波段兼具S和X波段的特性,但是一般优先选用S或者X。

X波段(I/J)

在该频带,所使用的波长和天线尺寸之间的关系明显优于较低的频带,这是军事应用中一个相对受欢迎的雷达频段,对于机动及轻量要求高而对作用距离的要求不高时是非常有意义的,例如AN/APG-77/81等机载雷达。

由于其可用带宽较宽,天线尺寸较小,因此该频段对于军事电子情报和基于合成孔径雷达(SAR)的空间或机载成像雷达也是很受欢迎的。

雷达对频段的选择依据主要有:作用距离的需求、天线尺寸的限制、多维信息的分辨性能、传输衰减情况、可用的带宽资源、工艺和成本、当然还要重点考虑雷达的用途和使用场景等等。这些依据中有些是相关的,有些是相互制约的,雷达波段的选择是经过各项因素利弊权衡后的择优结果。

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