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The concept of the phase center of the antenna. Phase radiation pattern

Reducing the level of side lobes of mirror antennas by positioning metal strips in the aperture

Akiki D, Biayneh V., Nassar E., Harmush A,

University of Notre Dame, Tripoli, Lebanon

Introduction

In a world of increasing mobility, there is a growing need for people to connect and access information, regardless of where the information is located or the individual. From these considerations, it is impossible to deny that telecommunications, namely the transmission of signals over distances, is an urgent need. The demands for wireless communication systems to be so perfect and ubiquitous mean that increasingly more efficient systems need to be developed. When improving a system, the main initial step is to improve the antennas, which are the main element of current and future systems wireless communication. At this stage, by improving the quality of the antenna parameters we will understand a decrease in the level of its side lobes of its radiation pattern. Reducing the level of side lobes, naturally, should not affect the main lobe of the diagram. Reducing the side lobe level is desirable because for antennas used as receiving side lobes make the system more vulnerable to extraneous signals. In transmitting antennas, side lobes reduce information security, since the signal may be received by an unwanted receiving party. The main difficulty is that the higher the sidelobe level, the higher the probability of interference in the direction of the sidelobe with the highest level. In addition, increasing the level of side lobes means that signal power is dissipated unnecessarily. Much research has been done (see, for example, ), but the purpose of this article is to review the “strip positioning” method, which has proven to be simple, effective and low cost. Any parabolic antenna

can be developed or even modified using this method (Fig. 1) to reduce interference between antennas.

However, the conductive strips must be very precisely positioned to achieve sidelobe reduction. In this paper, the "strip positioning" method is tested through experiment.

Description of the task

The problem is formulated as follows. For a particular parabolic antenna (Fig. 1), it is necessary to reduce the level of the first side lobe. The antenna radiation pattern is nothing more than the Fourier transform of the antenna aperture excitation function.

In Fig. Figure 2 shows two diagrams of a parabolic antenna - without stripes (solid line) and with stripes (line depicted with *), illustrating the fact that when stripes are used, the level of the first side lobe decreases, however, the level of the main lobe also decreases, and the level also changes the remaining petals. This shows that the position of the stripes is very critical. It is necessary to position the strips in such a way that the width of the main lobe at half power or the antenna gain does not change noticeably. The level of the rear lobe should also not change noticeably. The increase in the level of the remaining petals is not so significant, since the level of these petals is usually much easier to reduce than the level of the first side lobes. However, this increase should be moderate. Let us also remember that Fig. 2 is illustrative.

For the above reasons, when using the "strip positioning" method, the following must be kept in mind: the strips must be metal in order to fully reflect the electric field. In this case, the position of the stripes can be clearly determined. Currently, side lobe level measurements

Rice. 2. Antenna radiation pattern without stripes (solid)

and with stripes (

Rice. 3. Theoretical normalized radiation pattern in dB

two methods are used - theoretical and experimental. Both methods complement each other, but since our evidence is based on a comparison of experimental diagrams of antennas without breakdowns and with stripes, in this case we will use the experimental method.

A. Theoretical method. This method consists of:

Finding the theoretical radiation pattern (RP) of the antenna under test,

Measurements of the side lobes of this pattern.

The pattern can be taken from the technical documentation of the antenna, or can be calculated, for example, using the Ma1!ab program or using any other suitable program using known relationships for the field.

The P2P-23-YHA mirror parabolic antenna was used as the antenna under test. The theoretical value of the DP was obtained using the formula for a circular aperture with uniform excitation:

]ka2E0e іkg Jl (ka 8Іпв)

Measurements and calculations were performed in the E-plane. In Fig. Figure 3 shows the normalized radiation pattern in the polar coordinate system.

B. Experimental method. In the experimental method two antennas must be used:

The receiving antenna under test,

Transmitting antenna.

The pattern of the antenna under test is determined by rotating it and fixing the field level with the required accuracy. To improve accuracy, it is preferable to perform readings in decibels.

B. Adjusting the level of side lobes. By definition, the first side petals are those closest to the main petal. To fix their position, it is necessary to measure the angle in degrees or radians between the direction of the main radiation and the direction of the maximum radiation of the first left or right lobe. The directions of the left and right side lobes should be the same due to the symmetry of the pattern, but in an experimental pattern this may not be the case. Next, you also need to determine the width of the side lobes. It can be defined as the difference between the pattern zeros to the left and right of the side lobe. Here one should also expect symmetry, but only theoretically. In Fig. Figure 5 shows experimental data on determining the side lobe parameters.

As a result of a series of measurements, the position of the strips for the P2P-23-YXA antenna was determined, which are determined by the distance (1.20-1.36)^ from the axis of symmetry of the antenna to the strip.

After determining the side lobe parameters, the position of the stripes is determined. The corresponding calculations are performed for both theoretical and experimental patterns using the same method, described below and illustrated in Fig. 6.

Constant d - the distance from the axis of symmetry of the parabolic antenna to the strip located on the surface of the aperture of the parabolic mirror, is determined by the following relationship:

„d<Ф = ъ,

where d is the experimentally measured distance from the point of symmetry on the surface of the mirror to the strip (Fig. 5); 0 - the angle between the direction of the main radiation and the direction of the maximum of the side lobe found experimentally.

The range of C values is found by the relationship: c! = O/dv

for values of 0 corresponding to the beginning and end of the side lobe (corresponding to the zeros of the pattern).

After determining the range C, this range is divided into a number of values, from which the optimal value is experimentally selected

Rice. 4. Experimental setup

Rice. 5. Experimental determination of side lobe parameters Fig. 6. Strip positioning method

results

Several positions of the strips were tested. When moving the strips away from the main lobe, but within the found range C, the results improved. In Fig. Figure 7 shows two patterns without stripes and with stripes, demonstrating a clear decrease in the level of side lobes.

In table Table 1 shows comparative parameters of the pattern in terms of the level of the side lobes, directivity and width of the main lobe.

Conclusion

Reduction in the level of side lobes when using stripes - by 23 dB (the level of side lobes of an antenna without stripes -

12.43 dB). The width of the main petal remains almost unchanged. The method discussed is very flexible, since it can be applied to any antenna.

However, a certain difficulty is the influence of multipath distortions associated with the influence of the earth and surrounding objects on the pattern, which leads to a change in the level of the side lobes up to 22 dB.

The method discussed is simple, inexpensive and can be completed in a short time. In the following we will try to add additional stripes in different positions and examine the absorption stripes. In addition, work will be carried out on the theoretical analysis of the problem using the method of geometric diffraction theory.

Far field radiation pattern of the antenna P2F- 23-NXA linear magnitude - polar plot

Rice. 7. DN antenna P2F-23-NXA without stripes and with stripes

Antenna comparison parameters

Side lobe level

Theoretical pattern (program Ma11a) pattern according to technical documentation 18 dB 15 dB

Measured pattern without stripes 12.43 dB

Measured pattern with stripes With multipath Without multipath

Main lobe width in degrees D D, dB

Theoretical DN (program Ma^ab) 16,161.45 22.07

DN for technical documentation 16,161.45 22.07

Measured pattern without stripes 14,210.475 23.23

Measured pattern with stripes 14,210.475 23.23

Literature

1. Balanis. C Antenna Theory. 3rd Ed. Wiley 2005.

2. IEEE standard test procedures for antennas IEEE Std. 149 - 1965.

3. http://www.thefreedictionary.com/lobe

4. Searle AD., Humphrey AT. Low sidelobe reflector antenna design. Antennas and Propagation, Tenth International Conference on (Conf. Publ. No. 436) Volume 1, 14-17 April 1997 Page(s):17 - 20 vol.1. Retrieved on January 26, 2008 from IEEE databases.

5. Schrank H. Low sidelobe reflector antennas. Antennas and Propagation Society Newsletter, IEEE Volume 27, Issue 2, April 1985 Page(s):5 - 16. Retrieved on January 26, 2008 from IEEE databases.

6. Satoh T. shizuo Endo, Matsunaka N., Betsudan Si, Katagi T, Ebisui T. Sidelobe level reduction by improvement of strut shape. Antennas and Propagation, IEEE Transactions on Volume 32, Issue 7, Jul 1984 Page(s):698 - 705. Retrieved on January 26, 2008 from IEEE databases.

7. D. C Jenn and W. V. T. Rusch. "Low sidelobe reflector design using resistive surfaces," in IEEE Antennas Propagat., Soc./URSI Int. Symp. Dig., vol. I, May

1990, p. 152. Retrieved on January 26, 2008 from IEEE databases.

8. D. C Jenn and W. V. T. Rusch. "Low sidelobe reflector synthesis and design using resistive surfaces," IEEE Trans. Antennas Propagat., vol. 39, p. 1372, Sept.

1991. Retrieved on January 26, 2008 from IEEE databases.

9. Monk A.D., and Cjamlcoals P.J.B. Adaptive null formation with a reconfigurable reflector antenna, IEEE Proc. H, 1995, 142, (3), pp. 220-224. Retrieved on January 26, 2008 from IEEE databases.

10. Lam P., Shung-Wu Lee, Lang K, Chang D. Sidelobe reduction of a parabolic reflector with auxiliary reflectors. Antennas and Propagation, IEEE Transactions on. Volume 35, Issue 12, Dec 1987 Page(s):1367-1374. Retrieved on January 26, 2008 from IEEE databases.

Level of side lobes of the radiation pattern

Side lobe level (SLL) antenna radiation pattern (DP) - the relative (normalized to the maximum RP) level of antenna radiation in the direction of the side lobes. Typically, UBL is expressed in decibels.

An example of an antenna radiation pattern and parameters: width, directivity, UBL, backward radiation suppression coefficient

The pattern of a real (finite size) antenna is an oscillating function in which the direction of the main (maximum) radiation and the main lobe of the pattern corresponding to this direction are identified, as well as the directions of other local maximums of the pattern and the corresponding so-called side lobes of the pattern.

Usually, UBL is understood as the relative level of the largest side lobe of the pattern. For directional antennas, as a rule, the largest side lobe is the first (adjacent to the main) side lobe.

Also used average lateral radiation level(the pattern is averaged in the sector of lateral radiation angles), normalized to the maximum pattern.

As a rule, to assess the level of radiation in the “backward” direction (in the direction opposite to the main lobe of the pattern), a separate parameter is used, and this radiation is not taken into account when estimating the UBL.

Reasons for the decline in UBL

In the receiving mode, an antenna with a low UBL is “more noise-resistant”, since it better selects the desired signal space against the background of noise and interference, the sources of which are located in the directions of the side lobes
An antenna with a low UBL provides the system with greater electromagnetic compatibility with other radio electronics and high-frequency devices
An antenna with a low UBL provides the system with greater stealth
In the antenna of the automatic target tracking system, erroneous tracking by side lobes is possible
A decrease in the UBL (at a fixed width of the main lobe of the pattern) leads to an increase in the level of radiation in the direction of the main lobe of the pattern (to an increase in the directivity): antenna radiation in a direction other than the main one is a waste of energy. However, as a rule, with fixed dimensions of the antenna, a decrease in the UBL leads to a decrease in the coefficient of performance, an expansion of the main lobe of the pattern and a decrease in the efficiency.

The price to pay for a lower UBL is the expansion of the main lobe of the radiation pattern (with fixed antenna dimensions), as well as, as a rule, a more complex design of the distribution system and lower efficiency (in phased array).

Ways to reduce UBL

The main way to reduce the UBL when designing an antenna is to choose a smoother (declining towards the edges of the antenna) spatial distribution of the current amplitude. A measure of this “smoothness” is the surface utilization factor (SUF) of the antenna.

Reducing the level of individual side lobes is also possible by introducing emitters with a specially selected amplitude and phase of the exciting current - compensation emitters in the phased array, as well as by smoothly changing the length of the wall of the radiating aperture (in aperture antennas).

An uneven (different from linear law) spatial distribution of the current phase across the antenna (“phase errors”) leads to an increase in the UBL.

UBL reduction goals

In the receiving mode, an antenna with a low UBL is “more noise-resistant”, since it better selects the desired signal space against the background of noise and interference, the sources of which are located in the directions of the side lobes
An antenna with a low UBL provides the system with greater electromagnetic compatibility with other radio electronics and high-frequency devices
An antenna with a low UBL provides the system with greater stealth
In the antenna of the automatic target tracking system, erroneous tracking by side lobes is possible
A decrease in the UBL (at a fixed width of the main lobe of the pattern) leads to an increase in the level of radiation in the direction of the main lobe of the pattern (to an increase in the directivity): antenna radiation in a direction other than the main one is a waste of energy. However, as a rule, with fixed antenna dimensions, a decrease in the UBL leads to a decrease in the coefficient of performance, an expansion of the main lobe of the pattern and a decrease in the efficiency.

Ways to reduce UBL

Since the antenna pattern in the far zone and the amplitude-phase distribution (APD) of currents along the antenna are interconnected by the Fourier transform, the UBL as a secondary parameter of the pattern is determined by the APD law. The main way To reduce the UBL when designing an antenna is to select a smoother (falling towards the edges of the antenna) spatial distribution of the current amplitude. A measure of this “smoothness” is the surface utilization factor (SUF) of the antenna.

Markov G. T., Sazonov D. M. Antennas. - M.: Energy, 1975. - P. 528.

Voskresensky D. I. Microwave devices and antennas. Design of phased antenna arrays.. - M.: Radio engineering, 2012.

Ensuring a sufficiently low level of side lobes in the pattern, as noted earlier, is one of the most important requirements for modern antennas.

When analyzing linear systems of continuously located emitters, the dependence of the level of side lobes on the AR law in the system was noticed.

In principle, it is possible to select an AR law in the system in which there are no side lobes in the pattern.

Indeed, let there be an in-phase lattice of two isotropic

emitters located at a distance d= - from each other (Fig. 4.36).

We will consider the excitation amplitudes of the emitters to be identical (uniform AR). In accordance with formula (4.73) DN of a two-element lattice

When 0 changes from ± - the value of sin0 changes from 0 to ±1, and the value of D0) - from 2 to 0. The DN has only one (main) lobe (Fig. 4.36). There are no side petals.

Consider a linear lattice consisting of two elements, each of which represents the lattice discussed above. We still consider the new array to be in phase, the distance between the elements X

d = -(Fig. 4.37, A).

Rice. 4.36. In-phase array of two isotropic emitters

Rice. 4.37.

The AR law in a lattice takes the form 1; 2; 1 (Fig. 4.37, b).

In accordance with the multiplication rule, the array pattern has no side lobes (Fig. 4.37, V):

The next step is an in-phase linear system consisting of two

previous ones, displaced in a straight line by a distance - (Fig. 4.38, A). We get a four-element lattice with AR 1; 3; 3; 1 (Fig. 4.38, b). The pattern of this array also does not have side lobes (Fig. 4.38, c).

Continuing according to the planned algorithm to increase the number of emitters in the system, for the pattern of a common-mode array consisting of eight elements, we obtain the formula

Rice. 4.38.

AR in such a lattice will be written accordingly in the following form: 1; 7; 21; 35; 35; 21; 7; 1. The written numbers are coefficients in the series expansion of Newton’s binomial (1 + x) 7, therefore the corresponding AR is called binomial.

If present in a linear discrete system P emitters, the binomial AR is determined by the coefficients in the expansion of the Newton binomial (1 + x) n ~ 1, and the DN of the system is the expression

As we see from expression (4.93), the pattern has no side lobes.

Thus, by using a binomial AR in an in-phase discrete system, it is possible to achieve complete elimination of side lobes. However, this is achieved at the cost of a significant expansion (compared to a uniform AR) of the main lobe and a decrease in the efficiency of the system. In addition, difficulties arise in practically ensuring in-phase excitation of emitters and sufficiently accurate binomial AR in the system.

A system with binomial AR is very sensitive to changes in AFR. Small distortions in the ADF law cause the appearance of side lobes in the pattern.

For these reasons, binomial AR is practically not used in antennas.

AR, which produces the so-called optimal DP, turns out to be more practical and expedient. By optimal we mean such a DN, in which, for a given width of the main lobe, the level of the side lobes is minimal, or for a given level of the side lobes, the width of the main lobe is minimal. The AR corresponding to the optimal AP can also be called optimal.

For a discrete in-phase system of isotropic emitters, located

laid at a distance A> - from each other, optimal is

Dolph - Chebyshevsky AR. However, in a number of cases (with a certain number of emitters and a certain level of side lobes) this AR is characterized by sharp “bursts” at the edges of the system (Fig. 4.39, A) and difficult to implement. In these cases, they move to the so-called quasi-optimal AR with a smooth decay to the edges of the system (Fig. 4.39, b).

Rice. 4.39. Amplitude distributions: A- Dolph - Chebyshevskoe;

b - quasi-optimal

With a quasi-optimal AR, compared to the optimal level, the level of the side lobes increases slightly. However, implementing a quasi-optimal AR is much simpler.

The problem of finding an optimal and, accordingly, quasi-optimal AR has also been solved for systems of continuously located emitters. For such systems, the quasi-optimal AR is, for example, the Taylor distribution.

The level of the back and side lobes of the voltage radiation pattern γυ is defined as the ratio of the EMF at the antenna terminals during reception - from the side of the maximum of the back or side lobe to the EMF from the side of the maximum of the main lobe. When an antenna has several back and side lobes of different sizes, the level of the largest lobe is usually indicated. The level of the back and side lobes can also be determined by power (γ P) by squaring the level of the back and side lobes by voltage. In the radiation pattern shown in Fig. 16, the back and side lobes have the same level, equal to 0.13 (13%) in EMF or 0.017 (1.7%) in power. Back and side lobes of directional receivers television antennas are usually in the range of 0.1....25 (voltage).

In the literature, when describing the directional properties of receiving television antennas, the level of the back and side lobes is often indicated, equal to the arithmetic mean of the levels of the lobes at the middle and extreme frequencies of the television channel. Let us assume that the level of the lobes (according to the EMF) of the antenna pattern of the 3rd channel (f = 76 ... 84 MHz) is: at frequencies 75 MHz - 0.18; 80 MHz - 0.1; 84 MHz - 0.23. The average level of the petals will be equal to (0.18+0.1+0.23)/3, i.e. 0.17. The noise immunity of an antenna can be characterized by the average level of the lobes only if in the frequency band of the television channel there are no sharp “spikes” in the level of the lobes that significantly exceed the average level.

An important note must be made regarding the noise immunity of a vertically polarized antenna. Let us turn to the radiation pattern shown in Fig. 16. In this diagram, typical of horizontally polarized antennas in the horizontal plane, the main lobe is separated from the back and side lobes by the directions of zero reception. Vertical polarization antennas (for example, “wave channel” antennas with vertical vibrators) do not have zero reception directions in the horizontal plane. Therefore, the back and side lobes in this case are not clearly defined and noise immunity is defined in practice as the ratio of the signal level received from the forward direction to the signal level received from the rear direction.

Gain. The more directional the antenna, i.e., the smaller the opening angle of the main lobe and the lower the level of the rear and side lobes of the radiation pattern, the greater the EMF at the antenna terminals.

Let's imagine that a symmetrical half-wave vibrator is placed at a certain point in the electromagnetic field, oriented towards maximum reception, that is, located so that its longitudinal axis is perpendicular to the direction of arrival of the radio wave. A certain voltage Ui develops at a matched load connected to the vibrator, depending on the field strength at the receiving point. Let's put it next! at the same point in the field, instead of a half-wave vibrator, an antenna with greater directivity oriented towards maximum reception, for example, an antenna of the “wave channel” type, the directional pattern of which is shown in Fig. 16. We will assume that this antenna has the same load as the half-wave vibrator, and is also matched with it. Since the “wave channel” antenna is more directional than a half-wave vibrator, the voltage across its load U2 will be greater. The voltage ratio U 2 /’Ui is the voltage gain Ki of a four-element antenna or, as it is otherwise called, the “field”.

Thus, the voltage or “field” gain of an antenna can be defined as the ratio of the voltage developed by the antenna at a matched load to the voltage developed at the same load by a half-wave vibrator matched to it. Both antennas are considered to be located at the same point in the electromagnetic field and oriented towards maximum reception. The concept of power gain Kp is also often used, which is equal to the square of the voltage gain (K P = Ki 2).

In determining the gain, two points must be emphasized. Firstly, in order for antennas of different designs to be compared with each other, each of them is compared with the same antenna - a half-wave vibrator, which is considered a reference antenna. Secondly, to obtain in practice a gain in voltage or power, determined by the gain, it is necessary to orient the antenna towards the maximum of the received signal, i.e. so that the maximum of the main lobe of the radiation pattern is oriented towards the arrival of the radio wave. The gain depends on the type and design of the antenna. Let us turn to an antenna of the “wave channel” type for clarification. The gain of this antenna increases with the number of directors. The four-element antenna (reflector, active vibrator and two directors) has a voltage gain of 2; seven-element (reflector, active vibrator and five directors) - 2.7. This means that if instead of half-wave

vibrator use a four-element antenna), then the voltage at the input of the television receiver will increase by 2 times (power by 4 times), and a seven-element antenna by 2.7 times (power by 7.3 times).

The value of the antenna gain is indicated in the literature either in relation to a half-wave vibrator, or in relation to the so-called isotropic emitter. An isotropic radiator is an imaginary antenna that completely lacks directional properties, and the spatial radiation pattern has the corresponding shape of a -sphere. Isotropic emitters do not exist in nature, and such an emitter is simply a convenient standard with which the directional properties of various antennas can be compared. The calculated voltage gain of the half-wave vibrator relative to the isotropic emitter is 1.28 (2.15 dB). Therefore, if the voltage gain of any antenna relative to an isotropic emitter is known, then divide it by 1.28. we obtain the gain of this antenna relative to the half-wave vibrator. When the gain relative to an isotropic driver is specified in decibels, then to determine the gain relative to a half-wave vibrator, subtract 2.15 dB. For example, the voltage gain of the antenna relative to an isotropic emitter is 2.5 (8 dB). Then the gain of the same antenna relative to the half-wave vibrator will be 2.5/1.28, i.e. 1.95^ and in decibels 8-2.15 = 5.85 dB.

Naturally, the real gain in signal level at the TV input, given by one or another antenna, does not depend on which reference antenna - half-wave vibrator or isotropic emitter - the gain is specified in relation to. In this book, gain values are given in relation to a half-wave vibrator.

In the literature, the directional properties of antennas are often assessed by the directivity coefficient, which represents the gain in signal power in the load, provided that the antenna has no losses. The directional coefficient is related to the power gain Kr by the relation

If you measure the voltage at the receiver input, you can use the same formula to determine the field strength at the receiving location.

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