15 Parabolic mirror antenna. Main characteristics. Multi-mirror antennas. Features of the development of mirror antennas

Parabolic mirror antenna. Main characteristics. Multi-mirror antennas. Features of the development of mirror antennas.

15.1. The principle of operation of mirror antennas

Parabolic antennas are one of the most common types of antennas used in modern radio engineering systems for various purposes (radio relay communication systems, radar stations, satellite communication systems and television, radio control systems, etc.). They are applied in various wavelength ranges, from meter to meter. The most common are antennas with mirrors in the form of a paraboloid of rotation, a truncated paraboloid, a parabolic cylinder, and clippings from a parabolic rotation (usually with an oval-shaped outline). Such a wide distribution of these antennas due to the possibility of forming a wide variety of radiation patterns with respect to the simplicity of the design, sufficiently high efficiency, low noise temperature.

A parabolic antenna consists of two elements: a metal mirror with a parabolic profile and an irradiator placed in the focus of the mirror. An antenna diagram with a parabolic mirror is shown in Fig. 15.1.

The principle of operation of the antenna is based on the fact that the sum of the distances from the focus F of the mirror and from the mirror to the aperture is a constant value (FA + AA '= FB + BB' ...). Consequently, if a spherical wave source is located at the focus, then after reflection from a mirror, the wave is converted to a plane one, and the radiating aperture of the antenna is excited in phase.

A parabolic antenna is characterized by geometrical parameters a - aperture radius (aperture), f - focal length and 0 - aperture angle, which are related by

0

a  2 f tg. (15.1)

2

If  0  2 (а2f), a paraboloid is called a long-focus lens, for  0 2 (а2f) - short-focus.

The parabolic profile of the mirror is described in a rectangular coordinate system by the equation

y 2  4 fx, where f is the focal length, in the polar coordinate system the ratio is

2 f

.

1 cos 

From the point of view of the formation of the radiation field and the radiation pattern, the antenna with a mirror in the form of a paraboloid of rotation can be viewed as a phase-excited circular open, the amplitude distribution of the exciting field on which is described by some function A (r, a). The form of this function determines the shape and parameters of the antenna pattern for a given opening size (width of the main lobe; the level of lateral radiation).

The necessary law of the amplitude distribution of the exciting field on the aperture of the antenna, i.e. the form of the function A (r, a), can be implemented by selecting the antenna feed using the appropriate directional diagram of the iometric parameters of the mirror.

15.2. Illuminators of mirror antennas

Based on the principle of operation of a mirror antenna, we can formulate the following fairly obvious requirements for irradiators of these antennas:

1. The irradiator must have a phase center, which is located at the focus of the paraboloid of rotation (for a parabolic cylinder, the irradiator must form a cylindrical wave with a line of phase centers located on the focal line of the parabolic cylinder).

1. The amplitude radiation pattern of the irradiator should be such that almost all the power from the irradiator falls on the mirror. The irradiator should be absent in the direction opposite to the direction of the mirror. In addition, because the amplitude distribution in the aperture of the mirror is created mainly by the irradiator diagram, the form of the amplitude diagram of the irradiator must correspond to the required form of the amplitude field distribution in the aperture of the mirror.
2. The irradiator is in the field, reflected from the mirror, so its dimensions should be as small as possible so that it creates the minimum shading for the field and is mirrored.
3. Because Since the electrical strength and frequency properties of a mirror antenna are mainly limited by the irradiator, these parameters of the irradiator must correspond to those of the entire mirror antenna.

The most common types of mirror antenna feeds are vibrator, slot or waveguide-horn feeds. Consider their design features.

Vibratory irradiators consist of an active resonant half-wave vibrator and a counter reflector in the form of a metal disk or a passive vibrator. The supply of vibrator emitters is carried out from a coaxial feeder or waveguide. Vibrators powered by a coaxial feeder are used as feeds in the decimeter and long wavelength parts of the centimeter wave band, the waveguide powering of the vibrators is used in a shorter wavelength (35 cm) wave range.

In fig. 15.2 the most common designs of vibrator emitters with power from a coaxial feeder with a characteristic impedance of  50 Ω are shown.

Fig.15.2 - Vibrator irradiators with coaxial cable supply

In designs on fig. 15.2, a, b use a disk reflector, in a design of fig. 15.2, in - the passive vibrator. For symmetric excitation of a symmetric vibrator, if we assign a symmetric coaxial line, we use balancing devices in the form of a quarter wave beaker (in Fig. 15.2, a, c) or a balancing gap (Fig. 15.2, b). Asterisks draw. 15.2 shows the position of the phase center of the irradiator, which is located between the vibrator and the reflector.

The directivity of the vibrator with a counter reflector can be approximately

calculated as a diagram of a single vibrator			) 1 (F 	by multiplier
lattices:
FBL		   cossin1 kbF,		(15.2)
where b is the distance from the vibrator to the counter reflector.

The directivity pattern of a dual-vibrator irradiator can be calculated by the formulas:

- in the E plane



cos  2 sin 

f E ()  1 q 2 2q cos (kd cos );

cos 

- in the H plane

f H ()  1q 2 2q cos (kd cos), (15.3)

where  is the angle that determines the direction to the observation point (the angle  is calculated from the axis of the feed); d is the distance between the active and passive vibrators;

R 2  X 2

12 12

- the ratio of the amplitudes of the currents in the passive and active vibrators;

q  22

R X

22 22

Xx

12 22

arctg arctg - the ratio of the phases of the currents in the passive and active

RR

12 22

vibrators; R12, X12 - leaving mutual resistance of the vibrators; R22, X22 - components of the self-resistance of a passive vibrator.

In fig. 15.3 shows the design of vibrator irradiators with power from a rectangular waveguide. Vibrators are mounted on a thin metal plate that is perpendicular to the direction of the electric field and therefore is not excited by it.

The length of the vibrators and the distance between them are selected in such a way that the subsequent (in the direction from the mirror) vibrator is a reflector with respect to the previous one. This ensures the formation of unidirectional radiation of the vibrators to the mirror. In a four-vibrator emitter, it is possible to obtain a more symmetrical pattern with respect to the oscillator. Vibratory irradiators have a fairly wide radiation pattern. The optimum angle of aperture of the mirror 2  for such irradiators is about 140-160.

The advantage of vibrator irradiators is the slight shading created by the power supply system of these irradiators.

The disadvantage of the vibrator irradiators is their narrowband, associated with the resonant properties of the vibrators, as well as the relatively high level of radiation in the directions opposite to the directions on the mirror.

In the centimeter wavelength range, a two-slot feed is widely used, the design of which is shown in Fig. 15.4.

A two-slot feed represents a rectangular waveguide, which ends with a rectangular resonator with two symmetrically located half-wave slots in its wide wall. The distance d between the slits is chosen



equal approximately. The distance from the slots to the side walls of the resonator is selected

2 of the conditions of good coordination with the supply waveguide. For the same slots, a narrowing of the waveguide along a narrow wall is used. To set up the irradiator, assemble a screw in the wide wall of the resonator. Duplex feed is obtained

compact and shade the mirror a little. Its radiation pattern is close to axisymmetric and, as a first approximation, can be approximated by the cos function in

planes H and

cos



kd

sin





in the plane of E.

2

The disadvantage of a double-slot feed is the limitations on the relatively small transmitting power associated with the low dielectric strength of the slits, and the narrow band of the feed due to the narrow-band gap radiators.

Wave-horn irradiators represent either the open end of a waveguide, or a small horn fed by a waveguide. Waveguides (horns) of both rectangular and circular cross sections are used. The latter are more preferable, since their radiation pattern is more symmetrical about the waveguide axis. On the other hand, rectangular distributor irradiators make it possible to obtain different widths of the radiation pattern in perpendicular planes and, therefore, also irradiators are preferable for specular antennas with an oblong opening.

Horn irradiators have quite significant opportunities for regulating the width of the irradiator diagram, as well as the shape of this diagram within the angle of the mirror opening. For this purpose, in addition to the selection of the size of the horn, impedance structures are used, made in the form of a set of annular grooves on the inner walls of the horn. By selecting the parameters of these grooves, it is possible to obtain a more uniform irradiation of the mirror while maintaining a low power level of the irradiator passing by the mirror. Dielectric lenses are also used to extend the interrupter diagram.

Horn irradiators are structurally simple, have good banding properties, transmit considerable power and therefore are most widely used for back-to-back antennas. Their main disadvantage is the relatively large shading of the aperture of the mirror both by the horn itself, and by the fastening system that supports it and by the feeding waveguide.

The above types of feeds are used in mirror antennas with a mirror in the form of a paraboloid of rotation. For mirror antennas in the form of parabolic cylinders, linear feeds with a length equal to the length of the generator mirror are required. Waveguide-slot and vibrator grids of emitters, as well as sectorial horns can be used as linear feeds. Quite often, a segmented parabolic feed is used as a linear feed (Figure 15.4).

Fig.15.4 - Segmental parabolic feed

It consists of two parallel metal plates located at a distance equal to the size of one of the walls of the waveguide. On the one hand, the plates form a flat opening, on the other hand, a reflector of a parabolic profile is located between the plates. The focus of the parabola, located in the flat aperture, is an open end of a rectangular waveguide. After reflection from the parabolic profile in the opening of the irradiator, a phase field is formed.

119

15.3. Directional characteristics of mirror antennas.

Mirror Antenna Pattern

The main radiation characteristic of the antenna is its radiation pattern, which is completely determined by the distribution of the field excited in the plane of the aperture by the radiator.

In the future we will assume that the phase front of the field of the irradiator is spherical, and therefore, in the plane of the antenna aperture there will be a flat front, which corresponds to the phase excitation.

In the case of common-mode excitation of the antenna aperture in the form of a paraboloid of rotation, its radiation pattern is calculated by the following expression:

j k sin  ( cos sin )

F (, )  (1  cos ) f (, ) ed  d , (15.4)

S where f () is the function describing the amplitude distribution of the field in the aperture; S is the geometric area of ​​the aperture; k = 2 is the wave number;   - spherical coordinates of the observation point, while  is measured from the normal to the aperture.

For further integration in formula (15.4), it is convenient to switch from the Cartesian coordinates   to the polar coordinates r and :  r cos , r sin , then dd = rdrd, and formula (15.4) is written as

2 a

F (, )  (1 cos) f (r, ) expjkr sin cos () rdrd, (15.5)



00

where a is the radius of the aperture. If introduce variables: 2  a

u  sin , r H  r / a,



then we get the next expression for the DN

2 1

F (u, )  a (1 cos) f (r,) expjur cos () r dr d. (15.6)

HH HH

2 

00

Here f (r H , ) is the normalized distribution of the field amplitude in the aperture-amplitude. The integral in formula (15.6) depends on the form of the function f (r H ,), which is an approximating function for the polar emission of a given feed. Taking into account formula (15.6) and a given type of amplitude function f (r H , ), we investigate the main parameters of the DN of the common-mode aperture. Consider the following cases. If the antenna has a uniform amplitude distribution, then f (r H , ) 1, and the integration in (15.6) gives the following expression

 2a 

J 1  sin  2  

F (u)  2a (1 cos ), (15.7)

2a sin 

  2a 

where J 1  sin  is the first-order Bessel function.  

The absence in (15.7) of the dependence on  indicates the axial symmetry of the DN of a circular aperture, i.e. the DN is “needle-like”. The normalized days of power will be determined by the following ratio

2

 2a 

J 1  sin 

2 

 

F (u)

. (15.8)

2a

2 sin 



It is often necessary, before calculating the DN, to make an approximate estimate of some important parameters of the DN, such as the width of the DN at half power level — 2 E 0.5 (in the E plane, with  = 0) and 2 H 0.5 (in the H plane, with ), The angular position of the first zero of the DN 0 in the plane E and in the plane H; level of the first side lobe in dB field strength, determined by the окbok value

E

side, dB side , d B 20lg

.

E max

Then, for the distribution f (r H , ) we will have the following values ​​of the specified parameters:

EH 

2 2 58.9 degrees,

0.5 0.5

2a

EH 

  69.8,

00 2a

k 17 dB. In this case, the surface utilization ratio (KPI) of the aperture is the largest and equitin. Let the amplitude distribution, which can be described by the following function, occur in the aperture: f (r H ,) (1  r H 2 ) n , (15.9) where n = 1,2,3 ... Substituting ( 15.9) in formula (15.6), we obtain

1 22 n

F (u)  2a (1 cos ) (1 r) J (ur) d r, (15.10)

H 0 HH 0



where J 0 (ur H ) is the zero-order Bessel function. The DND parameters will have the following values:

- with n = 1:

EH 

2 2 84.2 degrees;

0.5 0.5

2a

EH 

 0  0  arcsin (93,4);

2a k 24.6 dB;

- with n = 2:

EH 

2 2 84.2 degrees;

0.5 0.5

2a

EH 

 0  0  arcsin (116.3);

2a k 30.6 dB;

- with n = 3:

EH 

2 2 94.5 degrees;

0.5 0.5

2a

EH 

 0  0  arcsin (138,7);

2a

- with n = 4:

EH 

2 2103.7 degrees;

0.5 0.5

2a

EH 

 0  0  arcsin (159.9).

2a With an increase in n and the degree of decay of the amplitude of the field at the edge of the aperture of the mirror, the instrumentation aperture decreases as shown in the table 15.1.

Table 15.1 - The dependence of the antenna KIP on n

n	one	0.56	0.44	0.36
Instrumentation	0.75	2	3	four

However, in practice, they strive to increase the antenna KND by increasing the field amplitude at the edges of the aperture, at least up to –10 dB relative to the maximum field at the center of the mirror aperture. Such falling distributions are located on a pedestal with an amplitude equal to .

In this case

f (r H , ) 1 (1) r H 2 . (15.11) Let us analyze the parameters of the DN for the distribution (15.11). In this case, the DN F (u) and instrumentation  for a circular aperture are defined as:

J 1 (u) J 2 (u)

F (u)  (1 cos)  2 (1) 2 , (15.12)

  uu   3 (1) 2

. (15.13)

4 1 (1)

The parameters of the DN will be presented in the form of table 15.2.

Table 15.2 - Numerical Parameters DN

	2E, H 0.5, hail	2E, H 0, hail	DB
0.1	67.4 (a)	178 (a)	–24,3
0.2	66.4 (a)	170 (a)	–23
0.3	64.8 (a)	163.8 (a)	–22
0.4	63.6 (a)	158 (a)	–21,5
0.5	62.8 (a)	152.2 (a)	–20,5
0.6	61.4 (a)	150 (a)	–19.9
0.7	60.2 (a)	147.8 (a)	–19.36
0.8	59.8 (a)	144.2 (a)	–18,8
0.9	59 (a)	142  (a)	–18,0
1.0	58.5 (a)	139.6  (a)	–17,6

In practice, it is rarely possible to obtain an amplitude distribution with circular symmetry. Usually, the field jumps at the edges of the aperture in the E and H planes are different. Tak distribution of amplitudes, changing according to the law

f (r H , ) 1 r H 2 cos 2 , (15.14) is created by the field of a linearly polarized feed.

Coefficient of directional action of the mirror antenna and its dependence on the geometric dimensions of the antenna.

Let us analyze the effect of the focal length on the density distribution of surface currents J e on the inside of the mirror, the directivity gain and the gain G of the mirror antenna. In Fig. 16.16 shows examples of the distribution of currents flowing over the surface of the mirror in the case of a short-focus (Fig. 16.16, a) and long-focus (Fig.16.16, b) mirror. A vibrator with a disk counter reflector was chosen as the irradiator of the mirror antenna. The current distribution is constructed in accordance with the formula (16.33).

Как видно, в короткофокусном зеркале линии поверхностного тока существенно искривлены. Кроме того, имеются точки P (полюса), в окрестности которых ток меняет направление.Положение полюсов на зеркале определяется направлениями нулевых значений диаграммы направленности облучателя. Для длиннофокусных зеркал линии тока искривлены меньше, причемчем больше фокусное расстояние, тем меньше искривление линий тока.

Рис.15.5 — Распределение токов J e на поверхности параболическогозеркала: а – зеркалокороткофокусное; б – зеркало длиннофокусное.

Искривление линий тока в зеркальной антенне является вредным явлением, т.к. приводит к появлению кроссполяризационной составляющей в ее поле излучения. В самом

eee

деле, раскладывая вектор тока J e на координатные составляющие J , J , J , нетрудно

x yz

понять, что поле основной поляризации в направлении оси антенны создается только J y e

составляющей тока. Хотя J z e составляющая тока и излучает поле основной поляризации, однако уровень этого излучения заметен лишь в области боковых лепестков. Составляющая же тока J x e излучает поле паразитной поляризации. Так как направление J x e в соседних квадратах зеркала противоположно, то в главных плоскостях ZOX и ZOY поле, излучаемое током J x e , равно нулю.Максимального значения кроссполяризационная составляющая достигаетвдиагональных плоскостях.

Наличие на зеркале полюсов приводит, кроме возрастания кроссполяризационной составляющей, к ослаблению поля излучения основной поляризации, т.к. за полюсами составляющаятока оказывается противофазной по сравнению с этой же составляющей между полюсами.

Таким образом, приведенные результаты показывают, что в короткофокусных зеркальных антеннах возникают дополнительные потери в коэффициенте усиления, связанные с рассеяниемчасти мощности на кроссполяризационное излучение и ослаблением

поля основной поляризации из-за наличия противофазных составляющих тока J y e . AT

длиннофокусных антенная эти явления проявляются менее заметно. По этой причине на практике чаще используются длиннофокусные зеркальные антенны. Если же габаритные ограничениявынуждают использовать короткофокусные зеркала, то для ослабления неприятных явлений в таких зеркалах делают вырезы вредных зон, расположенных вокруг полюсов.

Вычисление коэффициента направленного действия антенны производитсяпо формуле

D    4 

2 , (15.15)

F 1 ()d F 2 () cos d



2

 

где F1() и F2() — нормированные диаграммы направленности по мощности антенны в горизонтальной ивертикальной плоскостях, соответственно.

Коэффициентусиления G апертурной антенны определяетсяпо формуле

4

G  2 S a  (15.16)

 где  — коэффициентполезного действия антенны.

Основными источниками потерь в длиннофокусной зеркальной антенне являются потери на рассеивание части мощности облучателя мимо зеркала. Обозначая через P , P соответственнополную мощность излучения облучателя и мощность излучения

Σобл Σзер

облучателя, попадаемую на зеркало, и учитывая, что поток мощности пропорционален квадрату амплитудной диаграммы направленности, получаем

o 2

F обл , sin dd

 2

P Σзер

o 0

  , (15.17)

P 2

Σобл 2

F обл ,sin dd



00

где 2 (,) — двумерная диаграмманаправленности облучателя.

E обл

Если диаграмма направленности облучателя симметрична относительно оси антенны и можетбыть аппроксимирована функцией вида: 2 cos n ,0/2

Eл ,  , (15.18)

 0, /2  где n — любое положительное число, то после подстановки (15.18) в (15.17), получаем

2n1

1cos  0 . (15.19)

График зависимости  от  0 , рассчитанный по формуле (15.19) при n=1, представлен на рис.15.6. Качественная зависимость  от  0 остается неизменной и при других формах диаграммынаправленности облучателя.

Коэффициент использования поверхности раскрыва зеркальной антенны  полностью определяется характером амплитудного распределения поля в раскрыве зеркала. С увеличением  0 увеличивается спадание амплитудного распределения к краям зеркала и

поэтому  уменьшается с увеличением  0 . In fig. 15.6 показана характерная качественная

зависимость  от  0 для зеркальных антенн. Там же приведен график зависимости g 

от  0 . Параметр g называется эффективность зеркальной антенны и связан с ее коэффициентомусиления соотношением:

4

G  2 S a g . (15.20)

 Как следует из рис.15.6 существует оптимальный угол раскрыва  , при котором

0 опт

эффективность, а, следовательно, коэффициентусиления зеркальной антенны максимальны. Эффективность зеркальной антенны зависит только от диаграммы направленности

2 

облучателяиугла раскрыва зеркала 0 :

2

 2 2  0

ctg 0 F обл ,tg  dd



2

00 2

. (15.21)

 2  F 2 ,sin dd

обл



00

График зависимости g от  0 для частного случая диаграммы облучателя,

диаграммы направленности облучателявида (15.18)

Для наиболее употреб***яемых на практике облучателей параметр аппроксимации n в выражении (15.18) лежит в интервале n=1...2. При этом оптимальный угол раскрыва лежит в интервале 0 опт 5565. Оптимальное фокусное расстояние fт выражается через т и

диаметр раскрыва 2R 0 :



R 0 опт

fт  o ctg

2 2 . (15.22) Уровень ослабления поля на краю зеркала при f fт составляет 7,5 8,0 дБ по сравнению с полем в центре раскрыва зеркала.Максимальная эффективность в соответствии с рис. 15.7 достигает величины

g max 0,82. На практике затенение облучателя и системы крепления, кроссполяризационные потери и ряд других эффектов приводят к уменьшению эффективности до значений

g 0.40.6.