13 Antennas with circular polarization of the radiation field: cylindrical, conical, flat spiral . Principles of construction. characteristics.

13.1. Spiral antenna description

Spiral antennas can be divided into groups according to the design features:

• - elliptical;
• - cylindrical;
• - conical;
• - flat;
• - made on a conformal surface (for example, on a hemisphere);
• - combined structures;
• - antennas made of a conductor with a constant cross section (wire structure) or width (strip structure);
• - antennas made of a conductor with varying cross-section (wire structure) or width (strip structure).

The geometry of the elliptical spiral antennas is determined by the dimensions of the spiral-forming cylinder with a cross-section in the form of an ellipse, for which the ratio of semi-axes can be set within (1 ... 0). If the ratio of semi-axes of an ellipse is one, then the spiral antenna formed on the basis of a cylinder with a circular cross section is called a cylindrical spiral antenna (CSA). If the ratio of the semiaxes of the ellipse is zero, then such a flat structure is a Z-antenna. In other cases, the structure made on a cylinder with an elliptical cross section is an elliptical spiral antenna (ESA).

By the number of emitters used, spiral antennas are divided into groups:

- single;

- multiple;

- antenna arrays.

The main advantages of spiral antennas are:  the possibility of creating a radiation field with a polarization from linear to circular;  the ability to provide the required radiation characteristics and input

antenna characteristics due to the change of geometric parameters of the spiral;  simplicity and reliability of the design;  relatively small overall dimensions of the antenna;  on the basis of cylindrical, conical, hemispherical spiral antennas can be

combined structures (spherocylindrical, cylindroconic, etc.) are made;  it is possible to ensure a relatively low level of lateral back radiation (less than –15 ... –10 dB in the working frequency range) without using large screens;  the possibility of a good match with a sleep band in a wide frequency band.

13.2. Field structure with circular polarization

Spiral antennas form a radiation field with elliptical (or circular) polarization. In contrast to the field of a linearly polarized wave (Fig. 13.1, a), for which the electric field vector intensity is located in



some plane ZOY (E Z ), in the case of a field with rotating polarization with



electromagnetic wave propagation along the OY axis, the vector E rotates around this axis with a certain angular frequency  (Fig. 13.1, b). If, when observed from input



of the spiral antenna terminals, the vector E rotates clockwise, the field is considered to be right-handed, otherwise it is left-handed.

OB

One		of	major		characteristics				fields			radiation,		describing			him
polarization structure					is the ellipticity coefficient,										defined as
an attitude	small			Oa	and	big		OB			semi-axes		ellipse			polarization
(see fig. 13.1, b)
					CE 		Oa			,

which can take values ​​from 0 to 1.

The most common is the case of an elliptically polarized wave (Fig. 13.2), which can be considered as the result of a superposition of two orthogonal linearly polarized waves of the same frequency and shifted in phase by. Another variant of wave representation with elliptical polarization is the result of the superposition of two field-circular polarizations of the same frequency, but opposite to the direction of rotation.

Thus, in accordance with the electromagnetic wave model presented in Fig. 13.2, the polarization structure of the field depends on the relationship between the two linear

 

components E X and E Z of the wave propagating along the axis OY.

 

The linearly polarized components of the field E X and E Z are described by the expressions:

E X  E mx cost;

 E mz cost  ,





where  is the phase shift between E X and E Z , E mx , E mz are the amplitudes of the intensity

 E

fields of linearly polarized waves into which a vector is expanded (Fig. 13.2).

According to the accepted model, the field of elliptical polarization can be described using the ellipse equation [1]

E 2 EE E 2

XXZ Z 2

 2 cos  sin . (13.1)

E 2 EE E 2

mx mxmz mz

In the case when  0, the radiation field of the antenna has a purely linear polarization, which according to (13.1) is determined by the relation

E mx

E X  E Z. E mz

2n1

If  (n  0, 1, 2, 3, ...), then the field acquires an elliptical polarization

2

E X 2 E Z 2

2  2 1,

E mx E mz in this case the semi-axes of the ellipse OA and OB coincide with the coordinate axes OX and OZ, which corresponds to fig. 13.1, b.

In the case when the amplitudes E  E  E the antenna radiation field will have

mx mz m

circular polarization.



In the case in which the phase shift is 0 , the axis of the ellipse OA and OB, shown on

2 fig. 13.1, b, will not coincide with the coordinate axes.

13.2. Design performance of helical antennas

A cylindrical spiral antenna (Fig. 13.3) is a spiral 1 made of wire, one end of which is free and the other is connected at point 3 with the inner conductor of the coaxial line 4, the outer conductor of which is attached to the metallic shield 2 antenna.

one

2

1 - helix; 2 - screen;

3

3 - connection point of the power line; 4 - coax. Fig. 13.3 - Cylindrical spiral antenna:

The main advantages of spiral antennas are:

 the possibility of creating a polar emission by polarizing the linear pre-circular one;

 the ability to provide the required radiation characteristics and antenna input characteristics by changing the geometrical parameters of the spiral (overall circumference, angle of turns, number of turns, number of spiral conductors, approach excitation mode (in-phase, quadrature), compression of cylindrical spiral ellipse);

 simplicity and reliability of the design;

 small transverse dimensions of the antenna;

 based on cylindrical, conical, hemispherical spiral antennas, combined structures (spherocylindrical, cylindroconical, etc.) can be made;

 the possibility of providing a relatively low level of side and rear radiation (less than –15… –10 dB in the working frequency range) without using large screens;

 the possibility of good coordination with the feeder in the wide frequency band.

13.3. The radiation field of a single-way cylindrical spiral antenna

Consider the characteristics of the radiation field of a single-pass cylindrical spiral antenna. Its simplified model is presented in Fig. 13.4, a, b, where the following notation is entered: a

- the radius of the helix; d is the step of winding the turns of the helix (dipole length); n is the number of turns;

(fig. 13.4, b) - the length of the turn between points “1” and “2” in fig. 13.4, a;

d

 arcsin is the angle of inclination of the helix relative to the XОZ plane.

L

a) b)

The polarization structure of the antenna field and the radiation mode depend on the ratio of the geometric parameters a, d and wavelength. In practice, spiral antennas are used for dual operation:

1) non-directional radiation mode;

2) the mode of axial radiation.

In the case of the mode of non-directional radiation, the length of the spiral turn is less than the wavelength . The antenna can be represented as a system of axial annular frames and dipoles with a length equal to d  . CSA operates in the small frame mode, so the total



the field created by the antenna has a maximum value when  (see Fig. 13.5, a). With

2

small in comparison with  transverse dimensions of the antenna, the number of turns n does not affect the shape of the radiation pattern (DN) and the polarization structure of the field. Therefore, just consider the field of two elements: a dipole and one turn of a spiral. So for the dipole we can write the ratio

30Ilkd  j kr 60Il d  jkr

E d  j sin e  j sin e, (13.2)

rr

where I l is the tokan amplitude of the input terminals of the dipole; r - distance points 2

observations; k .



λ

2a  λ 2a 

π

a) b) Fig. 13.5 - Mode of non-directional radiation (a) and mode of axial radiation (b)

For a frame emitter, the effective frame length is lр  kS, where S is the area

framework. Therefore, from (13.2) we obtain the relation for the polar frame E p in the form

120I  2 S

d  jkr

E p  j 2 sin e, (13.3)

 r

where I d is the current at the effective length of the frame.



The resulting field consists of two orthogonal components of E d (the dipole field



long d) and E p (frame field with a perimeter of 2a). In the event that the field components are



shifted in phase by, and the currents on the frame and dipole of the same amplitude (I d = I l ), then

2

coefficient of ellipticity is equal to

d d

E d

K E 

. (13.4)

2Sl dr

E p

So from (13.4) it follows that if the condition d  lp were satisfied, then the radiation field in the XOZ plane would have circular polarization, but in practice the pitch of the helix d turns out to be much smaller than the current frame length (d  lp), therefore the field is characterized by a linearly polarized .

Consider the mode of axial radiation (see. Fig. 13.5, b), in which the length of the spiral helix is ​​chosen close to the wavelength. When this occurs, in-phase or close to neplozlozhenie fields of coils in the axial direction. DN in this case approaches the DN of the line of emitters excited in the traveling wave mode when the condition

L . Thus, in the traveling wave mode, which coincides with the axial radiation mode, a field of circular polarization is created. In this case, the resulting amplitude DN F  will be defined as for the array of emitters excited in the traveling wave mode F ()  f () f () f, (13.5)

el resh

where f resh () is a grating multiplier consisting of n frame radiators

(fig. 13.4, a);  - screen multiplier; f el () - DN of the spiral turn, which can

f screen 

define by

f el () cos. (13.6)

To determine f resh (), it is necessary to analyze the phase difference of currents between

turns "1" and "2"  1  2 (see. Fig. 13.4, a). For  1 2 we can write

 1  2 k f L,

2 2c

where k ; v f - phase velocity of a wave in a turn; c is the speed of light in the free ф  ф  v ф

space. With this in mind

2c

 L. (13.7)

12

 v f

In order for the radiation from all n turns to form in the axial direction, the phase increment on the turn must be 2, therefore the condition

 2 l d 2kd, (13.8)

12



where l is the perimeter of the frame, which should be close to the wavelength, kd is the phase shift on the dipole (see fig. 13.4, a). Comparing (13.7) and (13.8) we get

vf L

.

c l d

Knowing that  1  2 kl d for f resh () we can write



sin n kd coskl d 



2 

f res () . (13.9)

1 

sin kd coskl d 



2 

The antenna under study is located above the screen, so you can use the method of mirror images. In accordance with this method, when determining the field created by an antenna, it is believed that it is placed over an ideally conducting surface with dimensions much greater than the wavelength. The secondary currents induced on the surface of a flat screen are excluded from consideration by introducing a dummy radiator, which is a mirror image of a real antenna. The mirror radiator is located on the continuation of the normal, connecting the axis of symmetry of the real antenna with a conducting screen. At any point in the half-space (where the antenna under study is located), the mirror radiator creates exactly the same field as the real antenna.

With this in mind, when calculating the antenna antenna pattern, it is necessary to take into account the influence of the screen using the screen multiplier.

106

screen  cos  k n d sin  

f , (13.10)  2 

n d

where is the distance from the screen to the center of the array of coaxial frame emitters (see fig.

213.4, a). Then, the resulting amplitude DN of the antenna across the field, taking into account (13.5), (13.6) and (13.9), (13.10), will be determined by the expression: F () f el () f resh () f ecr. (13.11)

For an approximate calculation of the characteristics of spiral antennas, you can use the empirical formulas:

- DN width at half power level 52 



hail; (December 13)

Lnd



- directional coefficient (KND) in the direction of the axis of the spiral

 2 

L  d

D 10lg   15n   , dB; (13.13)

 



- input resistance

L

Rx 140  , Ohm. (13.14)

13.4. Features of the design performance of spiral antennas

The design of a single-elliptical spiral antenna (Fig. 13.6) should contain: a) a supporting frame; b) spiral conductor; c) reflecting screen; d) microwave connector; e) antenna fixing elements on the supporting structure; e) a radio transparent protective cap to protect the antenna from mechanical

damage (fiberglass, fiberglass or polystyrene).

The supporting frame must be made of a dielectric material with a low dielectric constant and losses, which reduces its effect on the characteristics of the radiation antenna. The outer contour of the frame must match the outer contour of the spiral antenna. The frame structure is selected from the options:

- cruciform, formed by two dielectric plates located at a right angle relative to each other.

- solid frame, made in the form of a cylinder or a truncated cone.

The spiral conductor is made of copper wire with a diameter in cross section of 1 ... 2 mm or copper tape with a width of 3 ... 5 mm. Spiral conductor must be laid along the frame in accordance with the specified spiral profile.

The screen is round or square in shape and is a solid metal surface. The screen should provide a reduction in the back radiation of the antenna. The overall screen size should be at least (1 ... 3). The screen was located at the base of the frame perpendicular to the axis of the spiral. The center of the frame is aligned with the center of the screen.

A hole is made on the screen in which the microwave connector is installed, which is fixed on the screen with screw connections. The base of the spiral conductor is connected to the center conductor of the connector.

See also

• 6. Symmetrical vibrator. The radiation field of the Hertz dipole and symmetrical vibrator. Directional pattern