二战雷达研发经验：短波传播理论概览

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《MIT辐射实验室丛书V13 - PROPOGATION OF SHORT RADIO WAVES》是一本深入探讨短波无线电波传播的专业书籍，由美国麻省理工学院辐射实验室的专家团队在二战期间雷达技术研究的基础上编撰，于1947年通过麦克劳希尔出版社发行。该书系列共28本，旨在提供雷达系统工程的全面理解，特别是对于短波段电磁理论的应用和发展。第一部分，章节I "ELEMENTS OF THE PROBLEM" 由John E. Freehafer and Donald Kerr共同撰写。这一章有两个主要目标：首先，它为读者提供了一系列关键定义和概念，帮助他们在后续章节中更好地理解和导航复杂的技术细节。作者避免了过多的专业术语和方法，以便初学者能够快速把握问题的核心，而不是陷入冗长的重复解释。章节开始时，作者提到当前微波领域的工作人员已经重新关注赫兹时代验证麦克斯韦电磁理论的波段。虽然全书不会详述波段演变的历史细节，但会简要概述这一转变中的关键特征，因为它们与当前的研究密切相关。此外，书中讨论的问题有许多与早期研究有着直接的联系，这表明科学和技术的发展并非孤立，而是继承和演进的过程。书中详细介绍了短波无线电波的传播特性，包括其物理原理、传播模式（如直线传播、散射和衍射）、衰减因素（如吸收和散射损耗）、以及如何通过频率选择性来优化信号传输。此外，还可能涵盖了天线设计、频率选择和波束形成等关键技术，这些都是理解短波通信和雷达系统设计的基础。随着技术的不断发展，短波应用扩展到了无线通信、卫星通信、雷达探测等多个领域。在面对现代社会中的无线网络挑战，如多径干扰、信号衰减和频率规划时，这本书提供的理论框架无疑为读者提供了宝贵的指导。《MIT辐射实验室丛书V13 - PROPOGATION OF SHORT RADIO WAVES》不仅是一本关于短波无线电波传播的权威指南，而且是对电磁学历史和现代应用之间联系的深入探讨，是从事相关专业研究或实践者不可或缺的参考资料。

ELEMENTAS OF THE PROBLEM [SEC. 1.5

at that height. Thus, because the separation between the N-profile and

characteristic 1 increases with height, the inclination of the associated ray

labeled 1 in Fig. 1.7b becomes increasingly steep as the ray arises. On

the other hand, the ray that starts downward with the same numerical

value of the inclination angle as ray 1 becomes less steeply inclined, until

at the height at which the characteristic intersects the N-profile the ray

is horizontal and has a turning point.

This ray is labeled 1‘ in Fig. 1.7b.

ModifiedindexN _

Ranger ~

(a)

(/))

FIG. 1.7.—Ray family associated with a linear N-protile.

Note that a single characteristic corresponds to two rays having slopes at

the transmitter that are numerically equal but opposite in sign. In

Fig. 1.7b the rays that start downward are denoted by primes. Line 2 is

the characteristic of the tangent or horizon ray 2’. Line 3 is the char-

acteristic of a ray 3’ that is reflected from the earth’s surface.

It should

be noted that although we have assumed that the index

n is constant and

equal to unity, the rays are curved.

This is as it should be, as the earth

has been assumed to be flat. The region to the right of ray 2’ is not

reached by the ray family and is therefore the shadow or diffraction zone.

Now let us consider the case shown in Fig. 1.8a in which the N-profile

has a surface N inversion and z,, the height of the transmitter, is less than

d, the height at which N assumes ib minimum value. Let characteristic ~

be drawn tangent to the N-profile at its minimum, and let the distance

between characteristic 2 and the vertical reference line

AB drawn through

the point on the N-profile at the transmitter height be denoted by c#2.

Then any ray whose initial angle of inclination is less than a, has a char-

acteristic that lies between characteristic 2 and line

All. Characteristic 1

is a case in point. As the distance between characteristic 1 and the

N-profile decreases with increasing height, the inclination of the associated

ray 1 of Fig. 1.8b decreases with height. At the height at which the

SEC. 1.5]

THE MODIFIED INDEX 17

characteristic intersects the N-profile the ray has zero inclination and

hence has a turning point. As the separation between the characteristic

and N-profile increases as the height decreases below that of the turning

point, the ray becomes more and more steeply inclined as it turns toward

the surface. At the surface the ray turns once more and begins another

“hop.”

Thus the ray proceeds by a series of hops and is confined to a

layer near the surface. It is easy to see that this same behavior char-

acterizes all rays for which a < aP and that energy is trapped in the layer

of air below height

d. It is convenient to refer to such a layer as a duct.

ModifiedindexN—

Ranger _

(a)

(b)

FIG. 1ii. —Modified index profile and ray pattern for a simple surface duct.

Rays whose initial inclinations are greater than a, have characteristics

that lie to the left of line 2, as, for example, characteristic 3. As char-

acteristic 3 does not intersect the N-profile, the msociated ray 3 has no

turning point. As the ray rises from the transmitter its inclination at first

decreases and reaches a minimum but not zero value at height

d. From

there on the inclination increases monotonically. The ray 3 therefore

penetrates the duct. Thus we see that ray 2 whose initial inclination

angle is aP, the so-called angle of

penetration, divides the family of rays

into two groups: those which are trapped and those which penetrate the

N-inversion.

It should be noted that in the case of the refraction represented by

Fig. 1.8 there is theoretically no region that is not reached by the ray

family. There is therefore no shadow region such as is found in Fig. 17

and no horizon ray. Instead a region of relatively high energy density

near the surface penetrates what is normally the diffraction region and

gives rise to abnormally high signal strengths. This is the qualitative

explanation of the action of surface ducts.

The two examples just discussed serve to illustrate the general prin-

ciples of qualitative ray tracing.

These same principles may be used to

appraise the refraction produced by other types of N-profiles. Thus, for

ELEMENTS OF THE PROBLEM

[SEC. 15

example, it is readily seen that an “overhanging” elevated inversion such

as is shown in profile

E of Fig. 1”6 gives rise to a surface duct. On the

other hand the elevated inversion of profile

F of the same figure produces

an elevated duct whose geometrical boundaries extend from the top of the

inversion to the height at which the tangent to the minimum intersects

the N-profile. Finally it is easy to see that profile G gives rise to both a

surface and an elevated duct.

Although ray tracing yields a convenient qualitative picture of the

trapping phenomenon, it leads to error in two respects: (1) It gives no hint

of the way in which frequency enters into the effect, and (2) it suggests

that appreciable effects can be obtained only when the receiver and trans-

mitter are in the duct.

FIG.1.9.—The rays associated with a single mode of propagation in a waveguide

Let us consider the frequency dependency first. The physical situation

in the presence of a duct is in many ways analogous to that in a waveguide.

In both cases the field may be resolved into a sum of elementary waves or

modes; but whereas in the case of a guide all of the modes are completely

confined to the guide, in the case of a duct all of the modes to some extent

penetrate the top of the duct. Those modes for which this penetration or

leakage is small may be represented by rays that proceed by a series of

hops just as in the case of the guide.

To pursue this analogy further let

us consider a waveguide filled with material of constant index N. Fig-

ure 1”9 shows the mode whose rays are inclined at angle B to the sides of

the guide. Let

r be the coordinate measured along the axis of the guide

and z be the coordinate perpendicular to the axis.

Then the phase change

due to a displacement

da along a ray inclined at angle ~ is

(8)

where x is the wavelength in vacuo.

Because the phase is the sum of a

part that depends only on

r and a part that depends only on z, it is possible

to separate the mode into waves traveling in the

r and z directions and to

consider the two parts separately.

The waves that travel in the z direc-

tion bounce back and forth between the surfaces of the guide and interfere

with each other. In order that this interference be not chaotic and the

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二战雷达研发经验：短波传播理论概览

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