Main lobe width and side lobe level
The width of the DN (main lobe) determines the degree of concentration of the radiated electromagnetic energy. DN width is the angle between two directions within the main lobe, in which the amplitude of the electromagnetic field strength is 0.707 from the maximum value (or 0.5 from the maximum value in terms of power density). The width of the DN is designated as follows:
2i is the width of the BP in terms of power at the level of 0.5;
2i - the width of the DN in tension at the level of 0.707.
The index E or H denotes the width of the DN in the corresponding plane: 2i, 2i. A power level of 0.5 corresponds to a field strength level of 0.707 or a - 3 dB level on a logarithmic scale:
Experimentally, the BP width can be conveniently determined from a graph, for example, as shown in Figure 11.
Figure 11
The level of the side lobes of the antenna pattern determines the degree of spurious radiation of the antenna of the electromagnetic field. It affects the quality of electromagnetic compatibility with nearby radio electronic systems.
The relative level of the side lobe is the ratio of the amplitude of the field strength in the direction of the maximum of the first side lobe to the amplitude of the field strength in the direction of the maximum of the main lobe (Figure 12):
Figure 12
This level is expressed in absolute units, or in decibels:
Directional and transmitting antenna gain
Directional action factor (directivity factor) quantitatively characterizes the directional properties of a real antenna in comparison with a reference non-directional (isotropic) antenna with a DP in the form of a sphere:
KND is a number showing how many times the power flux density P (u, q) of the real (directional) antenna is greater than the power flux density P (u, q) of the reference (non-directional) antenna for the same direction and at the same distance, provided that the radiation powers of the antennas are the same:
Taking into account (25), you can get:
Antenna gain (GF) is a parameter that takes into account not only the focusing properties of the antenna, but also its ability to convert one type of energy into another.
NS is a number showing how many times the power flux density P (u, c) of the real (directional) antenna is greater than the power flux density of the PE (u, c) reference (non-directional) antenna for the same direction and at the same distance, provided that that the powers supplied to the antennas are the same.
The gain can be expressed in terms of the KND:
where is the antenna efficiency. In practice, they use - the antenna gain in the direction of maximum radiation.
Phase directional diagram. Antenna phase center concept
Phase pattern is the dependence of the phase of the electromagnetic field emitted by the antenna on the angular coordinates.
Since in the far zone of the antenna the field vectors E and H are in-phase, then the phase pattern is equally related to the electric and magnetic components of the EMF emitted by the antenna. The phase DP is denoted as follows: W = W (u, q) at r = const.
If W (u, q) = const at r = const, then this means that the antenna forms a phase wave front in the form of a sphere. The center of this sphere, in which the origin of the coordinate system is located, is called the phase center of the antenna (FCA). It should be noted that not all antennas have a phase center.
For antennas with a phase center and a multi-lobed amplitude pattern with clear zeros between them, the phase of the field in adjacent lobes differs by p (180 °). The relationship between the amplitude and phase radiation patterns of the same antenna is illustrated in Fig. 13.
Figure 13 - Amplitude and phase pattern
The direction of propagation of the EMW and the position of its phase front at each point in space are mutually perpendicular.
Ideally, the beam directed by the antenna towards the satellite should be in the form of a sharp pencil. Unfortunately, because the wavelength is small compared to the antenna aperture (diameter), the fixed focal point is not really accurate. This causes slight divergence of the main beam and some unwanted pickup of off-axis signals. The resulting polar diagram consists of a narrow beam called main petal and a series of side lobes of lesser amplitude.
Typical radiation pattern of a parabolic
reflector in polar coordinate system
Because polar diagrams are often difficult to interpret, a rectangular representation is preferred. The normalized theoretical signal characteristic for a uniformly irradiated antenna with a diameter of 65 cm at a frequency of 11 GHz is shown in the figure:
In fact, the factors listed above will contribute to the introduction of irregularities in this characteristic, but the general picture of the shown dependence will remain unchanged.
Background noise enters the antenna system mainly through the side lobes, so it is important that they are as small as possible in relation to the amplitude of the main lobe. A uniformly irradiated antenna theoretically creates the first and largest of these side lobes at about -17.6 dB below the maximum main lobe.
In practice, exposure is rarely uniform. The irradiation distribution accuracy depends on the type of illuminator installed. This brings us to the concept of effective area or efficiency of an antenna system. In other words, most of the signal strength is collected from the center of the mirror and decreases towards the outer edges of the antenna. Therefore, a weak aperture of the antenna reflector can serve as protection against background noise.
Incomplete (insufficient) mirror irradiation reduces the level of the first side lobe to less than -20 dB, thus reducing the effect of background noise. At first glance, this solution seems ideal, but it leads to some undesirable consequences - a decrease in the antenna gain and a corresponding increase in the beam (main lobe) width. The main characteristic of the antenna radiation pattern is its half-power width, which is calculated as the width of the main lobe of the pattern at the level of -3 dB. The equations that are used to calculate the beamwidth at any given main lobe level are complex and time consuming to perform. However, parameters such as -3dB main lobe width, first side-lobe amplitude and first zero position (notch), depending on the specified irradiation method, can be easily calculated using the expressions in the table below. The cosine distribution is close to the mean, and if the method of received exposure is unknown, it can be used as a first approximation when calculating the -3 dB beamwidth.
Reducing the level of side lobes of reflector antennas by positioning metal strips in the aperture
Akiki D, Biayneh V., Nassar E., Kharmush A,
University of Notre Dame, Tripoli, Lebanon
Introduction
In a world of increasing mobility, there is a growing need for people to communicate and access information, regardless of where the information is located or the individual. From these considerations, it cannot be denied that telecommunications, namely the transmission of signals over a distance, is an absolute must. The requirements for wireless communication systems for their perfection and ubiquity lead to the fact that more and more efficient systems need to be developed. When improving the system, the main starting step is to improve the antennas, which are the main building blocks of current and future wireless communication systems. At this stage, by improving the quality of the antenna parameters, we mean a decrease in the level of its side lobes of its directional pattern. A decrease in the level of side lobes, of course, should not affect the main lobe of the diagram. Lowering the side lobe level is desirable because for antennas used as receive antennas, the side lobes make the system more vulnerable to unwanted signals. In transmitting antennas, side lobes reduce the security of information, since the signal can be received by an unwanted receiving side. The main difficulty is that the higher the level of the side lobes, the higher the probability of interference in the direction of the side lobe with the highest level. In addition, an increase in the sidelobe level means that signal power is wasted unnecessarily. A lot of research has been done (see, for example), but the purpose of this article is to consider the "strip positioning" method, which has proven to be simple, effective and low cost. Any parabolic antenna
can be designed or even modified using this method (Fig. 1) to reduce interference between antennas.
However, the conductive strips must be very precisely positioned in order to achieve a reduction in the level of the side lobes. In this article, the "strip positioning" method is tested by experiment.
Description of the task
The problem is formulated as follows. For a particular parabolic antenna (Fig. 1), it is required to lower the level of the first side-lobe. Antenna radiation pattern is nothing more than the Fourier transform of the excitation function of the antenna aperture.
In fig. 2 shows two diagrams of a parabolic antenna - without stripes (solid line) and with stripes (the line shown by *), illustrating the fact that when using strips, the level of the first side lobe decreases, however, the level of the main lobe also decreases, and the level also changes the rest of the petals. This shows that the position of the stripes is very critical. It is necessary to position the strips so that the half-power main lobe width or antenna gain does not change appreciably. The level of the back 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 lower 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 stated reasons, when using the "strip positioning" method, the following must be borne in mind: the strips must be metallic in order to fully reflect the electric field. In this case, the position of the stripes can be clearly identified. Currently to measure the level of side lobes
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 antenna diagrams without breakages and with stripes, in this case we will use the experimental method.
A. Theoretical method. This method consists of:
Finding the theoretical radiation pattern (DP) of the antenna under test,
Measurements of the side lobes of this DN.
The antenna 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 field relationships.
A P2P-23-YKHA reflector parabolic antenna was used as a test antenna. The theoretical value of the DP was obtained using the formula for a round aperture with uniform excitation:
] ka2E0e іkg Jl (ka 8Ipv)
Measurements and calculations were performed in the E-plane. In fig. 3 shows the normalized polar pattern.
B. Experimental method. In the experimental method, two antennas should be used:
Receiving antenna under test,
Transmitting antenna.
The antenna pattern of the antenna under test is determined by rotating it and fixing the field level with the required accuracy. For improved accuracy, it is preferable to read in decibels.
B. Adjusts the level of the side lobes. By definition, the first side lobes are those closest to the main lobe. 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 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 this may not be the case in the experimental pattern. Next, you also need to determine the width of the side petals. It can be defined as the difference between the DN zeros to the left and right of the side lobe. Symmetry should also be expected here, but only in theory. In fig. 5 shows the experimental data for determining the parameters of the side lobe.
As a result of a series of measurements, the position of the strips for the P2P-23-NKhA 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 parameters of the side lobe, the position of the stripes is determined. The corresponding calculations are performed for both theoretical and experimental DP 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 mirror surface 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 values for C is found by the ratio: s! = O / dv
for values 0 corresponding to the beginning and end of the side lobe (corresponding to zeros of the pattern).
After determining the C range, this range is divided into a number of values, from which the optimal value is selected experimentally
Rice. 4. Experimental setup
Rice. 5. Experimental determination of the parameters of the side lobes. Fig. 6. Strip positioning method
results
Several positions of the strips have been tested. When moving the stripes away from the main lobe, but within the found C range, the results improved. In fig. 7 shows two BPs without stripes and with stripes, showing a clear decrease in the level of side lobes.
Table 1 shows the comparative parameters of the antenna pattern in terms of the level of side lobes, directivity and width of the main lobe.
Conclusion
Reduction of the side lobe level when using strips - by 23 dB (the level of the side lobes of the antenna without stripes -
12.43 dB). In this case, the width of the main lobe remains almost unchanged. This method is very flexible as it can be applied to any antenna.
However, a certain difficulty is the influence of multipath distortions associated with the influence of the ground and surrounding objects on the pattern, which leads to a change in the level of the side lobes up to 22 dB.
This method is simple, inexpensive, and can be completed in a short time. In what follows, we will try to add additional stripes at different positions and explore absorption stripes. In addition, work will be performed on the theoretical analysis of the problem using the method of the geometric theory of diffraction.
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 Comparative Parameters
Side lobe level
Theoretical DN (program Ma11ab) DN according to technical documentation 18 dB 15 dB
Measured AP without stripes 12.43 dB
Measured DN with stripes With multipath Without multipath
Main lobe width in degrees D D, dB
Theoretical DN (Ma ^ ab program) 16 161.45 22.07
DN according to technical documentation 16 161.45 22.07
Measured DN without stripes 14 210.475 23.23
Measured MD 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, Sep.
1991. Retrieved on January 26, 2008 from IEEE databases.
9. Monk AD., And Cjamlcoals PJ.B. Adaptive null formation with a reconfig-urable 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.
The antenna, regardless of its design, has the property of reversibility (it can work both for reception and for radiation). Often in microwave links, the same antenna can be connected to both the receiver and transmitter at the same time. This allows the signal to be emitted and received in the same direction at different frequencies.
Almost all parameters of the receiving antenna correspond to the parameters of the transmitting antenna, but sometimes they have a slightly different physical meaning.
Despite the fact that the receiving and transmitting antennas have the principle of duality, in terms of design, they can differ significantly. This is due to the fact that the transmitting antenna must pass significant powers through itself to transmit the electromagnetic signal over long (maximum possible) distances. If the antenna works for reception, then it interacts with fields of very low intensity. The type of the current-transmitting structure of the antenna often determines its final dimensions.
Perhaps the main characteristic of any antenna is the directional pattern. Many auxiliary parameters and such important energy characteristics as gain and directivity follow from it.
Directional pattern
The directional pattern (DP) is the dependence of the field strength created by the antenna at a sufficiently large distance from the observation angles in space. In volume, the directional antenna diagram may look like the one shown in Figure 1.
Picture 1
What is shown in the figure above is also called the spatial diagrammatic directivity, which is the surface of the volume and can have several maxima. The main maximum, highlighted in red in the figure, is called the main lobe of the diagram and corresponds to the direction of the main radiation (or reception). Accordingly, the first minimum or (less often) zero values of the field strength around the main lobe determine its boundary. All other maximum field values are called sidelobes.
In practice, there are various antennas that can have several directions of maximum radiation, or have no side lobes at all.
For the convenience of the image (and technical application), the MDs are usually considered in two perpendicular planes. As a rule, these are the planes of the electric vector E and the magnetic vector H (which are perpendicular to each other in most media), Figure 2.
Picture 2
In some cases, the BP is considered in the vertical and horizontal planes with respect to the plane of the Earth. Plane diagrams are depicted by polar or Cartesian (rectangular) coordinate systems. In polar coordinates, the diagram is more visual, and when superimposed on a map, you can get an idea of the coverage area of the radio station antenna, Figure 3.
Figure 3
The representation of the radiation pattern in a rectangular coordinate system is more convenient for engineering calculations; such a construction is more often used to study the structure of the diagram itself. For this, the diagrams are built normalized, with the main maximum reduced to one. The figure below shows a typical normalized reflector antenna pattern.
Figure 4
In the case where the intensity of the side radiation is rather low and it is difficult to measure the side radiation on a linear scale, a logarithmic scale is used. As you know, decibels make small values large and large values small, so the same diagram on a logarithmic scale looks like the following:
Figure 5
A fairly large number of characteristics that are important for practice can be pulled out of the radiation pattern alone. Let's examine in more detail the diagram shown above.
One of the most important parameters is the zero-emission main lobe θ 0 and the half-power main lobe θ 0.5. Half the power is 3 dB, or 0.707 in field strength.
Figure 6
Figure 6 shows that the width of the main lobe for zero radiation is θ 0 = 5.18 degrees, and the width at the half-power level is θ 0.5 = 2.15 degrees.
Also, the diagrams are evaluated by the intensity of the side and back radiation (the power of the side and back lobes), hence two more important parameters of the antenna follow - this is the coefficient of protection, and the level of the side lobes.
Coefficient of protection is the ratio of the field strength radiated by the antenna in the main direction to the field strength radiated in the opposite direction. If the orientation of the main lobe of the diagram is considered in the direction of 180 degrees, then the opposite one is at 0 degrees. Any other directions of radiation are also possible. Let's find the coefficient of protective action of the diagram under consideration. For clarity, we will depict it in a polar coordinate system (Figure 7):
Figure 7
On the diagram, markers m1, m2 represent the radiation levels in the reverse and forward directions, respectively. The protective action coefficient is defined as:
In relative units. Same dB value:
Side-lobe level (LBL) is usually specified in dB, thereby indicating how weak the side-lobe level is compared to the level of the main lobe, Figure 8.
Figure 8
These are two important parameters of any antenna system, which directly follow from the definition of the directional pattern. KND and KU are often confused with each other. Let's move on to considering them.
Directional factor
Directional action factor (CDI) is the ratio of the square of the field strength created in the main direction (E 0 2) to the mean value of the square of the field strength in all directions (E cf 2). As is clear from the definition, directivity characterizes the directional properties of the antenna. LPC does not take into account losses, as it is determined by the radiated power. From the above, you can indicate the formula for calculating the KND:
D = E 0 2 / E cf 2
If the antenna works for reception, then the directivity indicator shows how many times the signal-to-noise power ratio will improve when replacing a directional antenna with an omnidirectional one, if the interference comes uniformly from all directions.
For a transmitting antenna, the directivity figure shows how many times the radiation power must be reduced if the omnidirectional antenna is replaced with a directional one, while maintaining the same field strengths in the main direction.
The directivity of an absolutely omnidirectional antenna is obviously equal to one. Physically, the spatial radiation pattern of such an antenna looks like an ideal sphere:
Figure 9
Such an antenna radiates equally well in all directions, but in practice it is not feasible. Therefore, it is a kind of mathematical abstraction.
Gain
As mentioned above, the directivity does not take into account the antenna loss. The parameter that characterizes the directional properties of the antenna and takes into account the loss in it is called the gain.
The gain (KU) G is the ratio of the square of the field strength created by the antenna in the main direction (E 0 2) to the mean value of the square of the field strength (E oe 2) created by the reference antenna, when the powers supplied to the antennas are equal. We also note that when determining KU, the efficiency of the reference and measured antenna is taken into account.
The concept of a reference antenna is very important in understanding gain, and different types of reference antennas are used in different frequency bands. In the range of long / medium waves, a vertical monopole quarter-wavelength vibrator is taken as the standard (Figure 10).
Figure 10
For such a reference vibrator, D e = 3.28, therefore, the gain of the long-wave / medium-wave antenna is determined through the directivity as follows: G = D * ŋ / 3.28, where ŋ is the antenna efficiency.
In the range of short waves, a symmetrical half-wave vibrator is taken as a reference antenna, for which De = 1.64, then KU:
G = D * ŋ / 1.64
In the microwave range (and this is almost all modern Wi-Fi, LTE and other antennas), an isotropic emitter, giving D e = 1, and having a spatial diagram shown in Fig. 9, is taken as a reference emitter.
The gain is a determining parameter of transmitting antennas, since it shows how many times it is necessary to reduce the power supplied to the directional antenna, in comparison with the reference, so that the field strength in the main direction remains unchanged.
KND and KU are mainly expressed in decibels: 10lgD, 10lgG.
Conclusion
Thus, we have considered some of the field characteristics of the antenna resulting from the radiation pattern and power characteristics (directivity and control). The antenna gain is always less than the directional action, since the gain takes into account the antenna loss. Losses can arise due to the reflection of power back into the feed line of the feed, currents flowing through the walls (for example, a horn), shading of the diagram by the structural parts of the antenna, etc. In real antenna systems, the difference between the LPC and KU can be 1.5-2 dB.
Let the current distribution along the length of the antenna be constant:
Real antennas (for example, slotted waveguide) or printed antenna arrays often have this current distribution. Let's calculate the radiation pattern of such an antenna:
Now let's construct a normalized DN:
(4.1.)
Rice. 4.3 Linear antenna pattern with uniform current distribution
In this radiation pattern, the following areas can be distinguished:
1) The main lobe is the area of the radiation pattern where the field is maximum.
2) Lateral petals.
The following figure shows the polar pattern in which 
has a more visual form (Figure 4.4).
Rice. 4.4 The radiation pattern of a linear antenna with a uniform current distribution in a polar coordinate system
A quantitative estimate of the antenna directivity is considered to be the width of the antenna's main lobe, which is determined either by the level of -3 dB from the maximum or by zero points. Determine the width of the main lobe at the level of the zeros. Here, we can roughly assume that for highly directional antennas: 
... The condition for the equality of the system factor to zero can be approximately written as follows:
Considering that 
, the last condition can be rewritten as follows:
For large values of the electrical length of the antenna (for small values of the half-width of the main antenna lobe), taking into account the fact that the sine of a small argument is approximately equal to the value of the argument, the last relation can be rewritten as:
Whence we finally get the ratio between the width of the main lobe and the size of the antenna in fractions of the wavelength:
An important conclusion follows from the last relation: for an in-phase linear antenna at a fixed wavelength, an increase in the antenna length leads to a narrowing of the radiation pattern.
Let us estimate the level of side lobes in this antenna. From relation (4.1), we can obtain the condition for the angular position of the first (maximum) side lobe:
(-13 dB)
It turns out that in this case the level of the side lobes does not depend on the antenna length and frequency, but is determined only by the form of the amplitude distribution of the current. To reduce the UBL, one should abandon the accepted form of the amplitude distribution (from a uniform distribution), and go to a distribution that falls to the edges of the antenna.
5. Linear antenna array
5.1. Deriving an expression for dn lar
Expression 4.2. allows you to easily switch from the field of a linear continuous antenna system to the field of a discrete antenna array. To do this, it is sufficient to set the current distribution under the integral sign in the form of a lattice function (a set of delta functions) with weights corresponding to the amplitudes of excitation of the elements and the corresponding coordinates. In this case, the result is the antenna array radiation pattern as a discrete Fourier transform. Master students are given the opportunity to implement this approach on their own as an exercise.
6. Synthesis of afr for a given day.
6.1. Historical overview, features of antenna synthesis problems.
Often, in order to ensure the correct operation of radio engineering systems, special requirements are imposed on the antenna devices that are their integral part. Therefore, designing antennas with specified characteristics is one of the most important tasks.
Basically, the requirements are imposed on the directional pattern (BP) of the antenna device and are of a very diverse nature: a specific shape of the antenna pattern main lobe (for example, the form of a sector and cosecant), a certain level of side lobes, a dip in a given direction or in a given range of angles may be required. The section of antenna theory devoted to solving these problems is called the theory of antenna synthesis.
In most cases, the exact solution to the synthesis problem has not been found, and we can talk about approximate methods. Such problems have been studied for a long time and many methods and techniques have been found. Certain requirements are also imposed on the methods for solving problems of antenna synthesis: to speed; stability, i.e. low sensitivity to minor changes in parameters (frequency, antenna sizes, etc.); practical feasibility. The simplest methods are considered: partial diagrams and the Fourier integral. The first method is based on the analogy of the Fourier transform and the relationship between the amplitude-phase distribution and the MD, the second is based on the expansion of the MD series in basis functions (partial MDs). Often, the solutions obtained by these methods are difficult to apply in practice (antennas have poor instrumentation, a difficult-to-implement amplitude-phase distribution (AFD), the solution is unstable). In and considered methods to take into account the restrictions on PRA and avoid the so-called. "Superdirectional effect".
Separately, it is worth highlighting the problems of mixed synthesis, the most important of which is the problem of phase synthesis, that is, finding the phase distribution at a given amplitude, leading to the required DP. The relevance of the problems of phase synthesis is explained by the large use of phased antenna arrays (PAR). Methods for solving such problems are described in, and.
