雷达导航原理与应用——MIT辐射实验室丛书

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"MIT辐射实验室丛书 V2-RADAR AIDS TO NAVIGATION" 本书是《雷达系统工程》丛书中的一卷，出自二战后美国麻省理工学院辐射实验室的专家之手，旨在分享他们在雷达研发领域的专业知识和经验。这套丛书中包含了28本专著，涵盖了雷达技术的各个方面，对当时及后来的雷达发展产生了深远影响。在本卷《雷达导航辅助》中，作者们首先介绍了雷达的基本原理。他们以一种易于理解的方式解释了雷达的工作机制，以便读者能够更好地理解和应用到不同类型的雷达系统中，包括空基雷达、陆基雷达和舰载雷达。 "雷达工作原理"这一章节由J.S. Hall撰写，他阐述了雷达的基本思想：通过发射电磁波并接收从物体反射回来的回波来探测目标。这个概念借鉴了人类和动物（如蝙蝠）利用声音回声导航的自然现象。例如，盲人可以通过脚步声或手杖的敲击声的回音感知周围环境，避开障碍物。同样，蝙蝠在完全黑暗中飞行时，依赖超声波回声定位来避免碰撞。 101节深入讨论了这个基本理念。雷达系统通过发射无线电波，这些波遇到物体后会被反射回来。雷达设备接收到这些回波后，根据回波的时间差和频率变化计算出目标的距离、速度和方向。这种技术使得在各种环境下，无论是在空中、地面还是海面上，都能实现远距离的目标探测和定位。通过这部分内容，读者可以了解到雷达在导航中的核心作用，它不仅帮助飞机、船只等交通工具在能见度低的条件下安全行驶，还在军事、气象预报、航空交通控制等多个领域发挥了至关重要的作用。此外，该书还可能探讨了雷达信号处理、天线设计、干扰与反干扰策略等高级话题，为读者提供了全面的雷达技术知识。《MIT辐射实验室丛书 V2-RADAR AIDS TO NAVIGATION》是一部珍贵的历史资料，它记录了雷达技术早期的发展，同时也是现代雷达工程的重要参考文献。对于希望深入了解雷达系统及其在导航中应用的人来说，这是一本不可多得的读物。

PRINCIPLES OF RADAR

[SEC.

1.3

fraction of the time. In some applications the value of P, is limited

by the averoge power capabilities of the transmitter tube, particularly

when long pulses or high repetition rates are used in conjunction with high

pulse power. A pulse power of 1 megawatt, or 1000 kw, can be main-

tained for periods of 1 psec 400 times per sec.

The minimum discernible signal Sti can be defined roughly as the

smallest signal power which a receiver-indicator system is able to detect

and amplify in such a way that the observer can distinguish visually

between it and random power fluctuations on the face of the indicator

tube. Such fluctuations first appear as small spots along the sweep and

are commonly described as “noise.”

This term stems from the fact that

this phenomenon was first observed as a hissing roar in radio receivers. A

good observer-receiver combination will sometimes detect a signal whose

strength is a millionth of a millionth of 1 watt, or 10–12 watts. Since

there is very little difference in complexity or cost between good and poor

receivers, an effo@ should always be made to use the best receiver

available. A competent observer is an equally good investment.

It is of interest to note that the power radiated by the antenna may

exceed by a billion billion times that returned to it by a barely detectable

signal.

The antenna gain G of a transmitting system represents the increase

in power in a particular direction which results when the radar energy is

focused by the antenna as compared with the energy which would have

been transmitted in that direction if the antenna radiated equally in all

directions. An object which radiates equally in all directions—the sun,

for example-is called an “isotropic” radiator. The energy from a small

light source can be directed into a parallel beam by placing this source at

the focus of a parabolic mirror.

When a short rod (called a dipole) or a horn is placed at the focus

of a searchlight type of reflector, which has an area A, and is fed by

electromagnetic energy of wavelength A, the gain is given by the expres-

sion G = KA/A2, where K is a factor which depends upon the type of

antenna. Its value is about 5 for an antenna using a dipole or horn

feed with a parabolic reflector.

A horn feed consists simply of a piece

of rectangular waveguide whose flared open end faces the paraboloid and

is placed at its focus. If the aperture of the reflector were 3 ft and the

wavelength were 3.25 cm (X-band) the gain would be close to 3100.

We have seen that the resulting beamwidth would be 7.3/D or 2.4°

between half-power points. If the aperture were doubled, the beam-

width would be halved and the gain quadrupled.

The effective cross-sectional area of the target u is a quantity which

measures the ability of a target to reflect radar signals and is a factor which

the radar set designer must consider in order to make his radar capable of

SFic.1.3]

DESIGN CONSIDERATIONS 17

detecting targetiof aknowncross sectional a given range. The value

ofu depends on the aspect, shape, size, and composition of the target.

Forcomplex targets like ships and airplanes, udoes not change rapidly

with the wavelength of the incident energy when microwaves are used.

It is customary to define the effective scattering cross section of a target

as the cross section of a reflecting sphere which would give an echo of the

same strength at the same range. Such a sphere would reflect energy

isotropically.

Flat surfaces can give an intense directional reflection, as the wind-

shield of an automobile does when it flashes in the sunlight. A complex

target like an airplane maybe said to reradiate the incident radar energy

ss a complex pattern of lobes. This pattern is analogous to a sequence

of flashes tha~ would come from different parts of an aircraft if it were

maneuvering in the sunlight. Consequently, the intensity of an airplane

signal fluctuates considerably as the position of these lobes changes with

respect to the radar from one scan to the next.

Characteristic changes

in signal strength produced by the roll of a ship, the bobbing of a buoy,

or the undulation of waves can often be identified readily by an experi-

enced observer. Land signals are usually steadier, but are still subject to

variations caused by movements of foliage or tall objects in the wind.

Atmospheric changes do not usually cause such rapid variations in signal

strength. The value of u changes so quickly with the aspect of a moving

target that it is often possible to pick up a target, momentarily, above

the radar horizon, at a range twice that at which it would be continuously

visible.

The dependence of u on the shape and size of surface vessels is given

in Sec. 10.1. It varies from about 70 ft ~ for a 40-ft cabin cruiser to

80,000 ft~ for a large freighter. The head-on aspect of a small Navy

aircraft, SNC, was found to have an equivalent cross section of only

70 ft?, less than 10 per cent of the value (800 ftz) for a four-engine

airplane,

Metallic surfaces reflect more energy than nonconducting surfaces

and give larger effective cross sections for objects of the same size.

ordinary paint does not markedly change the value of a.

The relationship among the above factors can be very simply derived

in the following manner. The area of the surface of a sphere of radius

R is 4mR2, If an isotropic radiator with peak power P, were at its center,

the power falling on a unit area of the inside of this surface would be

P, --L

&R%

If an antenna of gain G replaced this isotropic radiator and if the

maximum energy were directed toward this unit area, the power falling

on it would be

PRINCIPLES QF RADAR

p . pt -.&.

When we substitute the effective cross section o

[sm. 1.3

(1)

for this unit area we

find that the target, now considered as a source, will radiate power in

the direction of the antenna equal to P, $.

If A is the area of this

antenna, then the fraction —

Gv A

&R2

of this reradiated power, or Pt ————

&R2 &R2’

will be intercepted and fed to the receiver. If the minimum signal power

which can be distinguished from noise on the indicator is S~, the maxi-

mum range of the radar is such that this received signal is equal to Sti,

GuA

or Smb=Pt —.

l&rZR~

If we now substitute the expression G = KA/h2 for the gain and

solve for R~, we have

(2)

where C = K/l&rz. Since, for an average antenna, K is about 5, C = ~.

This “range equation”

shows that the maximum range of a given

radar on a target of cross section u could theoretically be doubled by:

(1) increasing the peak transmitter power or the observer-receiver sen-

sitivityy by a factor of 16; (2) increasing the area of the antenna dish

fourfold; or (3) reducing the wavelength by a factor of 4.

This equation taken by itself does not give a complete picture of the

problem of radar design. The quantity S~h is affected by such factors

as repetition rate, scanning speed, and pulse length, each of which in

turn affects the observability of a given signal on the indicator. Tech-

nical limitations and the relationships among the factors involved have

not yet been touched upon. These matters, together with considerations

which influence the choice of wavelength, will now be discussed briefly.

Repetition Rate.—It is possible to decrease Sti by increasing the

repetition rate because this would effectively put more pulses on the

target during a single scan and make the signal on the indicator sweep

more easily distinguishable from random noise.

It has been found exper-

imentally that if the repetition rate is changed by a factor n, S’* is

changed by a factor of n% and the range is changed by a factor of n}i.

If the repetition rate were doubled (n = 2), S- would be reduced by @

and the range would be increased by only 9 per cent.

The time interval between successive pulses must be long enough to

allow each pulse to reach the target and to return before the following

pulse is transmitted. The repetition rate must, therefore, not exceed a

SEC.1.3]

DESIGN CONSIDERATIONS

value compatible with the maximum range of the set. The average

power of the transmitter tube depends directly on how often it is required

to send out pulses. Its power capabilities often limit the repetition rate.

Because the range is improved and moving target indication (see

Sec. 7.9) is more satisfactory, it is usually desirable, within the limitations

mentioned in the previous paragraph, to make the repetition rate as high

as possible. There is a very wide range in the repetition rates used with

different radars; some operate at 60 and others at 4000 pulses per sec.

Scanning Losses.—Another consideration that enters into the value of

k’~bis that of scanning losses. 1 The range of a radar system when its

antenna is continuously scanning is not so great as it is when this antenna

is continuously pointed in the general direction of the target.

This latter

condition is called ‘‘ searchlighting. ”

The detectability of a weak signal (expressed as S~,m)is affected by

the rate of scan for much the same reason that it is affected by the changes

in the repetition rate. An experimental comparison between conditions

of scanning and searchlighting has shown that

Smi. is proportional to

(8/t)~, where t is the time in seconds during which pulses are striking

the target on each scan. This relationship holds only for values of t less

than 8 sec. If, for instance, the antenna rotates at 6 rpm, it scans 36° per

sec. If the beam is 6° wide, pulses effectively strike the target for + sec

per scan.

Sti is then (48) )$ times as large as its value under search-

lighting conditions and the loss in range is equal to (48)% = 1.62. In

other words, the range under searchlighting conditions is 1.62 times

greater for a given target than if the antenna were rotating at 6 rpm.

Thus it is evident that the ratio of beamwidth to scan rate governs the

amount of scanning loss. To avoid excessive losses, a radar producing

a narrow beam should be made to scan slowly.

Pulse Length.-Another factor which affects the range of a system is

the pulse length. The random background-noise power of a receiving

system, PE, is directly proportional to its bandwidth and inversely pro-

portional to the pulse length. Since S~ is proportional to

P., it is also

inversely proportional to the pulse length. If the pulse length were

doubled, the range would be increased by a factor of 2~~,or 19 per cent.

The limitations imposed by lengthening the pulse are: (1) the loss in

minimum range detection and in range resolution; (2) an increase in the

signal return from clouds and ground clutter compared with the return

from sharply defined targets; (3) considerations of permissible average

transmitted power. In order to maintain the same average power as the

pulse is lengthened, it is customary to reduce the repetition rate. The

disadvantages in doing this have been previously outlined.

1A completediscussionof scanninglossesis given in

Radar System En@”nseri~,

Vol.

1,RadiationLaboratoryS&es.

PRINCIPLES OF RADAR [SEC.1.3

A pulse length of 1 or 2 psec has been found to be a good compromise

when reasonable range resolution and extreme ranges are required. A

pulse length of+ or+ psec has been used to advantage in shipborne radar

systems where range resolution and minimum range are more important

than the detection of targets at great distances. Radar systems which

can transmit either short or long pulses have proven satisfactory.

A useful summary of these factors affecting the minimum observable

signal is given by the equation

is.=—

[

angle of scan in 8 sec 94

(PyF) ~’ beamwidth

(3)

The proportionality factor of 90 is an empirical constant that fits experi-

mental data so that the approximate useful range of several representa-

tive systems can be calculated from Eq. (2) when the above expression

is used for S~~.

Choice of Wavelength.—We have seen from previous discussion that

the directivity of the radar beam is increased as shorter wavelengths

are used. Thk increase in antenna gain results in improved range per-

formance and gives greater angular resolution for a given dish size.

There are, however, several reasons why it is not always profitable to go

the whole way and to use the shortest available wavelength-1.25 cm.

In the first place, the transmitter power available at 1.25 cm is

roughly 25 per cent of that for 3.2-cm waves and only 5 per cent of that

for 10-cm waves.

The atmospheric attenuation, which is so pronounced

at 1.25 cm, becomes less and less objectionable as longer wavelengths

are used. The use of shorter wavelengths makes the mechanical toler-

ances of the antenna correspondingly more rigorous, because it is desir-

able to preserve the parabolic figure of the dish to one-eighth of the

wavelength. If the radar is to be used primarily for scanning, a narrow

beam would allow fewer pulses to hit the target than would a wide beam.

The same arguments regarding the effect on range as a result of changing

the number of pulses hitting the target apply here also. At least five

pulses per scan are required for satisfactory operation with beacons

(Sec. 19) and a minimum of 10 pulses per scan when MTI (Sec. 7.9)

is used. Further considerations regarding the choice of wavelength

appear in Sec. 7.1.

We see from the above discussion that although the range of a radar

system depends primarily on only half a dozen factors, these factors

are by no means independent of one another and must be weighed in

such a way that the set can best carry out the job for which it was

primarily designed.

A typical airborne radar designed for navigation is described in Sec.

6.3. One of the most powerful land-based radars ever used for the detec-

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