Director and log-periodic dipole antennas

3.1. Director vibrator antennas

Directorial antennas (antennas of the “wave channel” type) are widely used on meter and decimeter waves as directional axial radiation antennas. The antenna consists of one active and several passive vibrators. Passive is called a vibrator , to which, instead of a generator, a resistance is connected to the input points for settings. The current in the passive vibrator is induced by the field emitted by the active vibrator . In a particular case, the value may be zero.

Let us first consider the properties of simpler radiating systems, consisting of one active and one passive vibrator, the tuning resistance of which is purely reactive: (Fig. 10).

Figure 10. Explanations for the consideration of the properties of simple radiating systems

We use the Kirchhoff equations to analyze this system.

, .

The first equation for this situation remains unchanged; in the second equation, the absence of a generator in a passive vibrator should be taken into account and resistance settings as a result

(2)

where – own resistance of the passive vibrator, depending on its diameter and length; – mutual resistance, depending on the geometry of the entire system.

We represent the ratio of currents in the form Then

Of interest are the cases when those. the passive vibrator in relation to the active vibrator served as a reflector or director . It is impossible to strictly achieve these conditions simultaneously for q and Ψ in the case of a passive vibrator. However, with the arm length of the active vibrator and a passive vibrator can be set to a mode close to the reflector mode if . A mode close to the director mode is achieved when the condition the value can be adjusted both with the help of the tuning resistance and by changing the length of the passive vibrator, i.e. adjusting the value while the resistance set equal to zero, i.e. short-circuit the input points of the passive vibrator . In the ranges of meter and decimeter waves, the second method is usually used. For a passive vibrator to work as a reflector, its total length must be somewhat greater than 0.5λ. To work as a director, the length of the passive vibrator must be somewhat less than 0.5λ .

The radiation directivity can be increased by using several passive vibrators at the same time. Usually, only one passive vibrator performs the function of a reflector (Fig. 11), since if additional passive vibrators are installed, they will be excited very weakly. Sometimes, to reduce the level of radiation in the rear half-space, additional reflectors are used, located above and below the main reflector. The number of directors can be quite large, since each previous director directs energy towards the next one (hence the name “wave channel”), thereby creating favorable conditions for the excitation of directors.

Figure 11. Antenna wave channel

With proper antenna tuning, the current induced in the reflector should lead in phase the current in the active vibrator. The currents in the directors must lag behind in phase, and the more the director is farther from the active element. In this case, the radiation maximum is directed along the antenna axis (toward the directors) .

For a given antenna geometry , i.e. with known vibrator lengths and distances between them, the amplitudes and phases of the currents in all vibrators necessary to calculate the RP can be found by solving a system of N Kirchhoff equations , where N is the total number of vibrators, including one active vibrator, reflector and directors. Since the amplitude distribution in the director antenna differs from uniform, the calculation of the RP after finding the currents should be carried out according to the general formula. In this case, the shape of the DP of one element can be approximately calculated by the length corresponding to the active vibrator.

A much more difficult task is the problem of synthesizing a director antenna, i.e. finding the number of vibrators and their location to implement the given electrical characteristics of the antenna , for example, KND. A general method for solving the problem of synthesizing such antennas does not yet exist. Usually, numerical optimization methods implemented on a computer are used.

Currently, a large number of different designs of VHF director antennas have been developed . The distance between the active vibrator and the reflector is taken equal to The first director is separated from the active vibrator by The same distance is chosen between the directors . Sometimes, to expand the operating frequency range, the first director is installed at a short distance from an active vibrator. The length of the active vibrator is selected from the condition of compensation of the reactive component of the input resistance (taking into account the induced resistances). The lengths of the reflector and directors differ from the length of the active vibrator by about 5…10% in the direction of elongation and shortening, respectively . In order to reduce the side lobes, the lengths of the directors are reduced as they move away from the active vibrator. The director antenna can also be printed.

A loop vibrator is usually used as an active vibrator . This is explained by the fact that due to the influence of passive vibrators, the input impedance of the active vibrator in the director antenna decreases. When using a conventional half-wave active vibrator, its input impedance as part of the antenna is reduced to 20 … 30 Ohm, which makes it difficult to match the antenna with the supply line. The inherent input impedance of the loop vibrator (about 300 ohms) is 4 times greater than that of a conventional balanced vibrator , so even under the influence of neighboring passive vibrators, it remains sufficient for matching . In addition, this vibrator can be mounted at the point of zero potential directly to a metal rod (see Fig. 11). Passive vibrators are also attached (usually welded) at the midpoint to this rod, which is very convenient in terms of design. Antenna power is usually carried out over a coaxial cable using baluns .

The disadvantage of the antenna is its limited operating range . When the wavelength changes, the main lobe expands, the level of the side lobes increases, the radiation in the opposite direction increases, and the coordination of the antenna with the feeder is disturbed. The antenna can be used in the frequency band of approximately 5…15% of the fundamental frequency . Directorial antennas are widely used as receiving television antennas and in radar. From a single director antenna, it is usually not possible to obtain a pattern with a width of less than 15 … 20 °. To increase the directivity of the radiation, the antennas are combined into in-phase arrays (Fig. 12, a).

A) b)

Figure 12. In-phase array (a) and director antenna with reflector (b)

Another way to improve the efficiency of such antennas with a relatively small number of vibrators is to build on their basis antennas of reverse radiation . To do this, the antenna is equipped with a flat reflector, which is located near the last director (Fig. 12, b). The maximum radiation of the antenna is obtained in the direction opposite to the direction of the maximum RP of the director antenna . According to the principle of operation, return radiation antennas are somewhat reminiscent of parabolic ones, but differ from them in a much simpler form of reflector . For large flat screens the parameters of the antenna deteriorate, which is explained by the appearance of out-of-phase excited regions at the edges of the reflector due to the large path difference from the active vibrator to the central and extreme points of the reflector. In connection with this, the edges of the reflector are given a stepped shape (see Fig. 12, b, dashed line). Return antennas can be built on the basis of other axial radiation antennas, for example, dielectric rod antennas or helical radiators.

It should be borne in mind that the main advantage of return radiation antennas – a decrease in longitudinal dimensions – is achieved due to a significant increase in transverse dimensions .

3.2. Log-periodic dipole antennas

Log-periodic antennas (LPA) belong to the class of ultra-wideband antennas that retain both the shape of the pattern and the value of the input impedance when changing the frequency . There are a large number of different modifications of LPA. Consider a variant of the vibrator LPA shown in Fig. 14. The antenna consists of linear vibrators connected to a two-wire line. Excitation is carried out using a coaxial line, which is laid inside one of the wires of a two-wire line, shaped like a tube . Such a transition from a coaxial to a two-wire line does not require a balun. The lengths of the vibrators satisfy the relation where – the period of the structure, regardless of the number n (n=1,2,…). The lines connecting the ends of the vibrators form an angle

Figure 14. Log-periodic antenna

According to the principle of operation, such an LPA resembles a director antenna . It resonates at the frequency fo , i.e. that vibrator is most intensively excited, the arm length of which is close to a quarter of the wavelength ( ), since the input resistance of this vibrator can be considered active. Other vibrators are excited much weaker, since their input resistance is large due to the large reactive component . The active region of the antenna, which forms the radiated field, usually includes three to five vibrators, including the resonant one and those adjacent to it on both sides . The phase relations of currents in the vibrators of the active region are determined by the length of the vibrators, mutual influence and their serial connection to different conductors of the supply line. In this case, it turns out that the currents in shorter vibrators lag behind, and in longer ones they are ahead in phase of the current in the resonant vibrator . Accordingly, shorter vibrators operate in the director mode, while longer ones act as a reflector. The radiation maximum is directed towards the top of the antenna .

If the frequency of the generator decreases and becomes equal to then the next, longer vibrator will start to resonate, respectively, the active area will move towards longer vibrators. On the contrary, as the frequency increases, the active region will shift towards the top of the antenna. At all frequencies

(5)

where n is the number of the vibrator; – resonant frequency of the n -th vibrator, the properties of the antenna remain unchanged. In the intervals between resonant frequencies, the properties of the antenna change, but only slightly. Taking the logarithm of (5), we obtain . On a logarithmic scale, resonant frequencies repeat at intervals equal to , which determined the name of the antenna of this class .

From the foregoing, it is clear that the width of the operating frequency band of the LPA on the lower side is limited by the allowable dimensions of the longest vibrators and on the upper side – the possible accuracy of the vibrators near the power points Practically can be obtained in about ten times the wavelength range almost unchanged DN. In the same range of KBV in the feeder (with proper selection ) does not fall below 0.6…0.7 . It should be taken into account that due to the movement of the active region along the length of the antenna, the position of the phase center of the antenna also changes with frequency . The latter circumstance does not matter, for example, when receiving television programs, but it is important when using LPA as a feed for parabolic antennas, as well as when working with broadband signals. The calculation of currents in LPA vibrators requires taking into account their mutual influence not only in free space, but also in the supply line wires.

Due to the fact that only a few vibrators are involved in the radiation at a given frequency, the RP turns out to be quite wide (Fig. 15), and in the E-plane (the plane in which the vibrators are located) it turns out narrower than in the H-plane (the plane where the vibrators are located). perpendicular to the axes of the vibrators) .

Increase with the same narrows the RP, as the number of vibrators entering the active region increases. Angle reduction with the same also narrows the RP, since this increases the distance between adjacent vibrators, i.e. the active area expands. What has been said is true only up to some critical values .

Figure 15. Directional pattern of the LPA

If the wires of the line supplying the LPA are placed at an angle to each other, then a spatial LPA will be obtained (Fig. 16). The radiation pattern of such an antenna in the H-plane is much narrower than that of a flat LPA, due to the influence of the multiplier of the system formed by the diversity in the H-plane of the active regions of each of the canvases.

Figure 16. Spatial LPA

In the E-plane, the pattern of the RP remains practically the same. Feeder wires in this design produce spurious polarized radiation, but this is usually low. In the VHF range, log-periodic antennas are used as broadband feeds for parabolic and lens antennas, as well as receiving television antennas .

4. Antennas of rotating polarization and surface waves

4.1. Turnstile emitter

In the simplest version, the turnstile emitter consists of two symmetrical electric vibrators located perpendicular to each other (Fig. 17). The excitation of the vibrators is carried out by currents of equal amplitude, but shifted in phase by 90 °.

At point A, which lies on the z -axis (Fig. 17), the vectors of the electric field emitted by the vibrators are orthogonal to each other, have different amplitudes and are shifted in phase by 90°, which ensures circular polarization of the resulting field at this point .

When the observation point deviates from the axis, the phase relationships between the field components are preserved, but the amplitude relationships are violated. So, at point B, which lies in the y0z plane (see Fig. 17), the amplitude of the field component created by the vibrator oriented along the y axis decreases, as a result, the field has an elliptical polarization . At points located in the x0y plane, the polarization is linear , since both vibrators create at these points only one spatial component of the electric field, which lies in the x0y plane, and at points on the axis of each of the vibrators (points C, D, E and F in Figure 17) the field is created only by radiation from another vibrator. The radiation pattern in this plane has a circular shape.

Figure 17. The principle of operation of the turnstile emitter

A feature of the turnstile emitter is the dependence of the phase of the emitted field on the angular coordinates of the observation point . To prove this, it suffices to consider the fields at points C and D ) and compare them with each other: they are equal in amplitude, but differ in phase by . Therefore, turnstile antennas do not have a phase center.

The radiation of the antenna into the lower half-space is usually eliminated by a screen spaced from the plane of the vibrators by 0.25λ. The power supply to each vibrator is usually carried out by a coaxial cable using a balancing device, which is conveniently attached to the screen . The inputs of balancing devices are interconnected. The phase shift can be implemented by including in the power path of one of the vibrators an additional line segment with a length where is the wavelength in the line.

Turnstile antennas are sometimes used in the construction of television transmitting antennas with horizontal polarization . Radiation along the z -axis in such antennas is suppressed by using several turnstile emitters parallel to each other and offset along the z -axis by 0.5λ .

4.2. Spiral Antennas

Spiral antennas are widely used in the ranges of centimeter, decimeter and less often meter waves . Consider first the cylindrical helical antenna shown in Fig. 18. The antenna consists of a helical wire connected to the inner conductor of the exciting coaxial cable. The outer wire (braid) of the cable is attached to a metal disk (shield) , which prevents the current flowing along the inner surface of the cable from penetrating its outer surface. In addition, the disk acts as a reflector , reducing the antenna’s radiation into the rear half-space.

Figure 18. Cylindrical helical antenna

To ensure the axial radiation mode, the diameter of the spiral D is chosen so that the length of the turn l is approximately equal to the wavelength of the current in the spiral (while D = ). Theoretical studies show that in an infinite spiral, under the condition the mode of a traveling current wave with phase velocity is set where c is the speed of light. As the wavelength λ shortens, the phase velocity increases, approaching the speed of light, as the wave lengthens decreases. In a spiral of finite length, reflection from the end takes place, but it is small (the reflection coefficient does not exceed 0.2). In addition, higher types of waves occur at the beginning and end of the antenna. Usually, in the first approximation, reflection and higher types of waves are neglected and it is assumed that the current amplitude is constant along the length of the antenna.

Consider the radiation of one coil of an antenna with a length , considering it flat for simplicity . In the traveling wave mode, the current distribution along the coil is described by the expression where – current amplitude; magnitude – the coordinate of the point on the coil, counted along the circle. On fig. 19 shows the current distribution for time points . As can be seen, at each moment the radiation of the coil is equivalent to the radiation of two bent in-phase excited vibrators, creating a maximum of radiation along the axis of the coil with polarization parallel to the straight line 1-1′ (see Fig. 19).

The position of these vibrators in time changes continuously with a circular frequency, as a result, radiation with a rotating polarization is created along the axis .

Figure 19. Current distribution for time points

The multi-turn design of the helical antenna leads to radiation amplification along the antenna axis . Let us define more precisely the requirements for the length of the coil l, taking into account that the actual coil due to the winding pitch S does not lie in the same plane. The development of one turn of the spiral is shown in fig. 18, b. The phase shift between the fields of two adjacent turns at a point on the antenna axis is the sum of the phase incursion of the traveling wave of current along the turn of the helix and phase difference due to the winding step Resultant phase shift . To ensure the maximum directivity factor , it is known that this shift is close to where N is the number of turns. However, since the value of Ψ is large (close to 2π) in the helix in the axial radiation mode , it is possible to ensure the maximum directivity factor only under the condition that From here we get

(6)

When condition (6) is satisfied and N is large , the polarization of the field on the helix axis is close to circular . More optimal conditions for circular polarization are obtained at a slightly lower value which can be found from the condition Under this condition, the fields of the coil elements, separated by a quarter of its length and forming radiation with mutually perpendicular polarization, are shifted in phase exactly by When the observation point deviates from the axis, the polarization becomes elliptical.

Since with the shortening of λ the ratio increases (and vice versa), condition (6) and, therefore, the directional properties are practically preserved in a relatively wide frequency band , from (0.7…0.8)λ 0 to 1.2λ 0 , where λ 0 is the calculated wavelength. The radiation pattern of a helical antenna can be calculated based on the formula

Value

To achieve maximum bandwidth, the winding angle is chosen equal to 12…15 o . The radius of the screen (solid or lattice) is usually taken equal to (0.5 … 0.8) L , where L is the length of the spiral (see Fig. 18, a). The width of the DN of a cylindrical helical antenna at half power is usually not less than 20 … 25 ° . To improve the directional properties, helical antennas are connected into arrays.

Although theoretical consideration shows that a helical antenna, like a turnstile radiator, does not have a phase center in the strict sense, within the main lobe of the pattern, it can be assumed that the surface of equal phases deviates little from a spherical one, the center of which is located in the geometric center of the antenna. Knowing the phase center is important, for example, when using helical antennas as feeds for parabolic antennas.

Conical helical antennas (Fig. 20) have better band properties than cylindrical helical antennas. The axial radiation of such antennas is formed not by the entire antenna, but only by the active region, i.e. turns, the length of which is close to λ . As the frequency changes, the active region moves along the axis of the antenna .

Figure 20. Conical helical antenna

Flat spiral antennas are widely used , including antennas in the form of an Archimedean spiral (Fig. 21, a). A two-way helical antenna can be printed and excited either by a two-wire line or by a coaxial cable laid along one of the arms (an idle cable is laid along the other arm to maintain symmetry, Fig. 21, b).

Figure 21. Double helical antenna

The antenna can be considered as a two-wire line coiled into a spiral, and in the initial part of the antenna, the currents in adjacent turns are in antiphase and, accordingly, do not radiate . With distance from the power points, the phase shift between currents in adjacent turns decreases due to the path difference.

Indeed, elements 1 and 2, located on both sides of a circle of radius r 0 at different approaches of the spiral, have a path difference equal to half the length of this circle, i.e. Taking into account antiphase excitation, the phase difference of elements 1 and 2 will be At magnitude those. adjacent turns are excited in phase in the traveling wave mode . These turns form a radiation field with circular polarization in the direction of the antenna axis , which is preserved in a wide frequency band. The lower frequency is determined by the outer diameter of the helix, and the upper frequency is determined by the accuracy of the antenna near the feed points.

The radiation pattern consists of two wide lobes oriented normally to the helix plane . It is also possible to obtain one-sided radiation from the helix by placing a screen behind it (usually at a distance where – wavelength at the middle frequency of the range), however, the presence of a screen narrows the operating frequency band.

The described types of helical antennas, in addition to independent use, are used, as already noted, as feeds for mirror antennas, elements of various arrays , including phased antenna arrays.

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