What determines the level of side lobes? Phase radiation pattern
Let the current distribution along the length of the antenna be constant:
Real antennas (for example, slot waveguides) or printed antenna arrays often have exactly this current distribution. Let's calculate the radiation pattern of such an antenna:
Now let's build a normalized pattern:
(4.1.)
Rice. 4.3 Radiation pattern of a linear antenna with uniform current distribution
The following areas can be distinguished in this radiation pattern:
1) The main lobe is the section of the radiation pattern where the field is maximum.
2) Side petals.
The following figure shows the radiation pattern in the polar coordinate system, in which 
has a more visual appearance (Fig. 4.4).
Rice. 4.4 Radiation pattern of a linear antenna with uniform current distribution in a polar coordinate system
A quantitative assessment of the antenna directivity is usually considered to be the width of the main lobe of the antenna, which is determined either by a level of -3 dB from the maximum or by zero points. Let's determine the width of the main lobe based on the level of zeros. Here we can approximately assume that for highly directional antennas: 
. The condition for the system multiplier to be equal to zero can be approximately written as follows:
Considering that 
, the last condition can be rewritten this way:
For large values of the electrical length of the antenna (for small values of the half-width of the main lobe of the antenna), taking into account the fact that the sine of the small argument is approximately equal to the value of the argument, the last relation can be rewritten as:
From where we finally get the relationship connecting the width of the main lobe and the size of the antenna in fractions of the wavelength:
An important conclusion follows from the last relationship: for an in-phase linear antenna at a fixed wavelength, increasing the antenna length leads to a narrowing of the radiation pattern.
Let's 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 type of amplitude current distribution. For reduction of UBL one should abandon the accepted form of amplitude distribution (uniform distribution), and move to a distribution that decreases towards the edges of the antenna.
5. Linear antenna array
5.1. Deriving the expression for day lar
Expression 4.2. allows you to easily move from the field of a linear continuous antenna system to the field of a discrete antenna array. To do this, it is enough to specify the current distribution under the integral sign in the form of a lattice function (a set of delta functions) with weights corresponding to the excitation amplitudes of the elements and the corresponding coordinates. In this case, the result is the antenna array radiation pattern as a discrete Fourier transform. Master's students are left to implement this approach independently as an exercise.
6. Synthesis of afr on a given day.
6.1. Historical review, features of antenna synthesis problems.
Often, to ensure the correct operation of radio systems, special requirements are imposed on the antenna devices that are part of them. Therefore, designing antennas with specified characteristics is one of the most important tasks.
Basically, the requirements are imposed on the radiation pattern (DP) of the antenna device and are very diverse: a specific shape of the main lobe of the pattern (for example, in 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 antenna synthesis theory.
In most cases, an exact solution to the synthesis problem has not been found and we can talk about approximate methods. Such problems have been studied for quite a long time and many methods and techniques have been found. Methods for solving antenna synthesis problems are also subject to certain requirements: speed; sustainability, 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 connection between the amplitude-phase distribution and the pattern; the second is based on the expansion of the pattern series into basis functions (partial patterns). Often, the solutions obtained by these methods are difficult to apply in practice (antennas have poor instrumentation characteristics, the amplitude-phase distribution (APD) is difficult to implement, the solution is unstable). Methods that allow taking into account restrictions on PRA and avoiding the so-called are considered. "overdirectional effect".
Separately, it is worth highlighting the problems of mixed synthesis, the most important of which is the problem of phase synthesis, i.e. finding the phase distribution for a given amplitude, leading to the required pattern. The relevance of phase synthesis problems can be explained by the widespread use of phased array antennas (PAA). Methods for solving such problems are described in, and.
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.
Relative (normalized to the maximum radiation pattern) level of antenna radiation in the direction of the side lobes. As a rule, UBL is expressed in decibels; less commonly, UBL is determined "by power" or "on the field".
An example of an antenna radiation pattern and radiation pattern parameters: width, directivity, UBL, relative level of rear radiation
The pattern of a real (finite size) antenna is an oscillating function in which a global maximum is identified, which is the center main petal DP, as well as other local maxima of DP and the corresponding so-called side lobes DN. Term side should be understood as side, and not literally (petal directed “sideways”). The DN petals are numbered in order, starting with the main one, which is assigned the number zero. The diffraction (interference) lobe of the pattern that appears in a sparse antenna array is not considered lateral. The minima of the pattern that separate the lobes of the pattern are called zeros(the level of radiation in the directions of the nulls of the pattern can be arbitrarily small, but in reality radiation is always present). The lateral radiation region is divided into subregions: near side lobe region(adjacent to the main lobe of the pattern), intermediate area And posterior lateral lobe region(the entire rear hemisphere).
- UBL is understood as relative level of the largest side lobe of the pattern. As a rule, the largest side lobe is the first one (adjacent to the main one).
For antennas with high directivity they also use average lateral radiation level(the pattern normalized to its maximum is averaged in the sector of lateral radiation angles) and level of far side lobes(relative level of the largest sidelobe in the region of the rear sidelobes).
For longitudinal radiation antennas to assess the radiation level in the “backward” direction (in the direction opposite direction main lobe of the pattern) the parameter is used relative rear radiation level(from English front/back, F/B- forward/backward ratio), and this radiation is not taken into account when assessing the UBL. Also, to estimate the level of radiation in the “sideways” direction (in the direction perpendicular to the main lobe of the pattern), the parameter relative lateral radiation(from English front/side, F/S- front/side ratio).
UBL, as well as the width of the main lobe of the radiation pattern, are parameters that determine the resolution and noise immunity of radio engineering systems. Therefore, in the technical specifications for the development of antennas, these parameters are given great importance. The beam width and UBL are controlled both when the antenna is put into operation and during operation.
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
- The low-level antenna provides the system with greater electromagnetic compatibility with other radio-electronic means 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.
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
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.
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 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.
