14 Horn antennas. Features of construction. Criteria for the selection of geometric parameters. Analysis of the pattern. Coefficient of directional

Horn antennas. Features of construction. Criteria for the selection of geometric parameters. Analysis of the pattern. Coefficient of directional horn antenna.

A generalized model of a horn antenna is shown in Fig. 14.1. but)

Based on the model shown in fig. 14.1., You can consider the following options for aperture emitters:

-

E-sector horn, with a P  a and b P  b;

-

H-sector horn, with a P  a and b P  b;

-

pyramidal peaked horn, with a Р  a and b Р  b.

We note the following patterns in the behavior of a poly group.  The type of wave in the horn is the same as in the waveguide exciting the horn.  Unlike a waveguide, the surface of equal phases in a horn is not a plane,

and the surface of a cylinder with a center at the vertex O for a sectorial horn and the surface of a spheroid for a pyramidal horn.  The phase velocity of the wave in the horn is variable. It is more in the mouth of the horn and approaches the speed of light.  In the horn, unlike the waveguide, there is no critical wavelength. This is because the infinite horn can always find a section that

will be sufficient to propagate any type of wave.

 Local surface resistance WS in the mouth of the horn is approximately equal to the characteristic impedance of free space W0.

The radiating surface of a horn is the surface of its opening. Particular attention is paid to the amplitude-phase distribution of the field in the aperture of the horn antenna. The amplitude distribution of the field on the aperture coincides with the field distribution in the cross section of the waveguide for the main type of wave. In the plane E, a uniform amplitude field distribution is observed, in the plane H - a cosine

 y

E y  E 0 cos      ,  a p  E y H x , W0 where E0 is the electric field strength in the middle of the aperture;  (x, y) is the phase error in the opening of the horn, resulting from the non-plane phase front in the pile. The wave front in the process of its movement in the horn is converted from flat vtsilindricheskuyu (vectorial) or spherical (in pyramidal horns). Let us analyze in more detail the nature of the phase error in the sectorial horn, the longitudinal section of which is shown in Fig. 14.2.

Fig.14.2 - Longitudinal section of the H-sector horn

An arc of a circle KML centered at the top of the horn O is a line of equal phases. At an arbitrary point M having the x coordinate, the field phase lags behind the phase in the middle of the aperture (point O) by an angle



2 2 22 2 x 2  2

 (x) = OM  R H   R H  x  R N  R H    1  2   1  1  .

  R 

 H 



 x 2  1 2 Laying out  1   in a Taylor series and limiting with x << R N first two д R H 2

members get

 x 2

 (x) .

 R N

The phase distribution has a quadratic character in the plane in which the opening of the horn is made. The maximum phase error (maximum phase shift relative to the center of the aperture) is determined by the ratio

b 2

E  p

- in the E-plane:  , (14.1)

max 4 R 2

H  a p

- in the H-plane:  max , (14.2)

4 R where R is the length of the horn (see fig. 2.1). The maximum phase error attained at the corners of the pyramidal ruler is determined by the ratio

 a 2 b 2 

 pp

 max   .



4 R R



If the maximum phase errors in the mouth of the horn does not exceed the permissible

E  H 3

max , max , 24 then the coefficient of the directional action (LPC) of the horn antenna for a given length will be maximum. Horn horns, the dimensions of which correspond to the maximum values ​​of KND, are called "optimal". Their sizes are related to the length of the horn by the following ratios:

b p 2 R E , (14.3)

2

a p 2 R H . (14.4)

3 We now turn to the study of the directivity pattern of a sectorial horn. Taking into account (14.1), (14.2) in the wide-area horn

2

x  i  x 2

H

E y  E 0 cos e  R ; (14.5)

a

P

W S  W 0 . The directivity factor is calculated as follows. In plane H:

, 0) (f																  () fx								  cos 2 2 0E b aa P								a xP	 iexp		R2 P 2x	   exp ikx sin dx				
							0E bP			 22 RH					       4 Ri exp H												 a 1 t				        ) (i) () (2sin 121 2 S uC uC u								) (2S u		(14.6)
     4 Ri exp H																			   a 1 P							        i) () (2sin 43 2 C uC u											 ) (3S u	   ) (4S u
Where	1u			2 1				 HP R a					HR				  1Pa					     2sin							,
	2u			2 1					 HP R a					HR				  1 Pa					        2sin,
	3u			2 1					 HP R a					HR				  1 Pa					        2sin,
	4u			2 1					 HP R a					HR				  1 Pa					     2sin							.

111 Similarly in the plane E: kb P 

sin sin 

 R H iR H   2 

f  (,) E 0 b exp  C (v)  C (v)  i  S (v) S (v) kb , (14.7)

P 2 12 12

22 4aP

 P 

sin 2

1  a P R H  ;

where v  

 1 2 R H  a P

 

1  a R 

v 2   P  H   .



2 Ra

 HP 

The normalized radiation patterns (NF) of the horn antenna in the common-mode opening proposal (with phase errors not exceeding the allowable values) can be calculated using the formulas:

b p 

sin sin 

1 cos   

- in the E-plane: f 

; (14.8)

E 

2 b p sin 



Ap 

cos sin 

1cos   

- in the H-plane: f 

, (14.9) 2 2a p 2

H 

1 sin 





The width of the main beam of the horn antenna pattern in the E and N planes (2 E and 2 H ) is determined by the level of half power by the formulas:

0.5 0.5

E 

H-sector horn: 2 0.5 0.88 [rad]; (14.10)

b

H 

2 0.5 1.4 [rad]; (14.11)

a

p

E 

E-sector horn: 2 0.5 0.93 [rad]; (14.12)

b p

H 

2 0.5 1.18 [rad]; (14.13)

a

E 

pyramid horn: 2 0.5 0.93 [too happy]; (14.14)

b p

H 

2 0.5 1.4 [rad]. (14.15)

a

p

The coefficient of the directed action of the H-sector horn D H is determined by the formula [3] 4bR

P h 2

     2 , (14.16)

D H  CuCv SuSv

a P

x 2  x 2 

Cx d; t dt are Fresnel integrals; 0 2  0 2 

where   cos t tSx   sin

1  a R H  1  a R H 

 P 

 ; v   P   .

u 









2 Ra 2 Ra

 H P 

 H P 

In fig. 14.3 the graphs of KND D N dependence on

aP

the relative size of the aperture of the H-sector horn for various lengths of the horn



R H.

The coefficient of directional action of the E-sector horn D E is determined by the formula [3]

64aR    b  b   

P E 2P 2P

D E   C     S   . (14.17)



b P 2R E 2R E 

 

The coefficient of directional action of the pyramidal horn D, taking into account (14.16, 14.17), is determined by the following formula [3]

 2

D  D E D H. (14.18) 32a P b P

The coefficient of the directed action (KND) of the optimal horn antenna is calculated by the formula: 4S

D								2		,				(14.19)
Where	S 	abr		- geometric aperture area;									-	utilization rate
surfaces that			determined by amplitude						A		ifphasic			ф	field distribution in
antenna aperture:					fa   	.

For optimal sectorial horns,  a  0.81 takes into account the cosine

the nature of the amplitude distribution of the field in the H-plane;  f  0.8 - non-phase

opening in one of the planes under the condition  max  n.

Therefore, for sectorial horn antennas  0.81 0.8  0.64.

For optimal pyramidal horns under the same conditions,  а  ф 2  0.52 (non-phase opening in both planes was taken into account).

Horn antennas are used in practice as independent directional antennas, and as irradiators of mirror and lens antennas, as well as emitters of the PHAR. Horn antennas are especially widely used in laboratory installations when measuring the radiation pattern and gain of other antennas. The advantage of remote antennas is the simplicity of their design and good band properties. Practically, the working frequency band of a horn antenna is limited by the waveguide supplying it and is about 100%.

The lack of horn antennas is the need to choose too long the length of the horn for receiving highly directional radiation. As follows from formulas (14.3), (14.4), the optimal length of a horn is proportional to the square of the sizes of the aperture a P and b P , and

the width of the radiation pattern is inversely proportional to a P and b P to the first power. Therefore, to narrow the radiation pattern of a horn antenna n times its aperture size should be increased n times, and the length of a horn n times 2 times.

This circumstance imposes restrictions on the width of the horn antenna pattern. So, with a horn length approximately equal to the size of one of its opening sides, the width of the radiation pattern is about 2025. When narrowing the width of the radiation pattern to 10, the length of the horn is approximately 4 ... 5 times the size of the larger side of its opening.

There are various ways to reduce the length of a horn. The essence of these methods is to compensate or reduce the phase error in the opening of the horn. One of the most commonly used in practice ways to reduce the length of a horn is to install a lens opening that eliminates phase errors (Fig. 14.4, a).

In this case, the length of a horn is chosen from the conditions of good matching of the waveguide supplying the horn with free space and is approximately equal to (1 ... 0.5) its opening width.

In fig. 14.4, b shows another way of aligning the phase front in the aperture of a horn by equalizing the length of the path traveled by the wave from the top of the horn to various points in the opening. To obtain an in-phase common field, the ABC curve, which forms the wall of a bent horn, must have the shape of a parabola.