It is necessary to emphasize that similarly the previous problem of ensuring the required current distribution along the radiator does not mean a rigorous coincidence of an
obtained current distribution with the given distribution, but creating the distribution, closest to the required as far as possible.
Examples of antenna synthesis with the given current distribution, realized in a certain frequency range, were presented in [46]. The calculation was performed for the described in Section 5.5 monopole of height 6 m with ten capacitive loads. Figure 5.14a shows the equivalent lengths measured along the monopole from its free end to the points, where the capacitors must be installed. In Figure 5.14b the capacitances of these capacitors are given. The tasks were considered: creating a linear distribution of current
Figure 5.14 Equivalent length of antenna (a) and capacitances, calculated by approximated method (b).
(curves, along which the equivalent lengths and the magnitudes of the capacitances are presented, are designated by label “lin”) and creating an exponential distribution of current with the logarithmic decrement a = 2 (corresponding curves are designated by label “exp”). The calculations are performed by the approximated method of a long line with loads in accordance with the expressions (5.54) and (5.58) at frequency f = 40 MHz.
These results were used for strict calculating the amplitude and the phase along antennas with the loads. They are given in Figure 5.15a for a linear distribution and in Figure 5.15b for an exponential distribution. As can be seen from the figures, at f = 40 MHz the amplitude distribution is close to the required one, the phase curves have a slight slope. When the frequency changes (at f = 30 and f = 50 MHz), the amplitude and the phase distribution of the current are not conserved.
In order to provide the required current distribution in the continuous range from 40 to 80 MHz, the synthesis of the antenna was made by the method of mathematical programming. The results are shown in Figure 5.16 for the linear (a) and exponential (b) distributions respectively. The amplitude and phase of the current are obtained as result of optimization of electrical characteristics of the antenna. The error function was formed, using the root-mean-square criterion. The values, calculated by a method of the long line with loads at the middle frequency f = 60 MHz, were taken as a zero approximation. In the calculation it was adopted that the number of frequencies in the given range is equal to 9, and the number of the points on the wire is equal to 11.
The results were improved significantly. In each figure the four curves for the current amplitude are drawn: curve, labeled by f0, corresponds to the required distribution, and curves labeled by f = 40, 60 and 80 corresponds to the result of synthesis at frequencies 40, 60 and 80 MHz. As is seen from the figures, the obtained distribution is, on the whole, close to the given distribution, but is not identical to it. However, this difference is not caused by the inexact method. Primarily the reason of this difference is the limited potential opportunities of antennas. Thus, in addition to the successful solution of the problem the method permits to determine the potential opportunities of the antennas.
Figure 5.15 Currents in the antenna with approximate loads designed for creating the linear (a) and exponential (b) distribution of the amplitude at f = 40 MHz.
Figure 5.16 Linear (a) and exponential (b) distributions of the current in the antenna with loads.
The use of loads also gives freedom in choosing the antenna length (taking into account the possibilities of manufacture and installation), since they permit securing the desired characteristics in the required frequency range at given antenna length. The freedom in choosing the radiator length enables weakening the effect of the adjacent metal bodies, e.g. of the superstructures, on the directional pattern of an antenna or an antenna array. Figure 5.17 shows the calculation results for the directional pattern of a monopole, situated near a metal superstructure in a shape of a circular metal cylinder of finite length. The directional patterns in the horizontal plane are calculated at two frequencies of HF range.
Figure 5.17 An antenna near a superstructure (a) and its horizontal pattern (b).
Two options are considered: 1—the monopole without loads of the height 6 m and the diameter 0.016 m, 2—the monopole of the height 12 m and the diameter 0.06 m with 9 capacitive loads, selected with the aim to ensure the optimal electrical characteristics on the frequencies from 8 to 22 MHz. The relative placement of the superstructure and the monopole as well as the superstructure dimensions are shown in Figure 5.17a. The circular cylinder during calculation was replaced with a wire structure from equidistant conductors, located along generatrices of the cylinder and the radii of its end surface.
As is seen from Figure 5.17b, the radiation of an ordinary monopole in the direction of superstructure decreases sharply, and the use of the monopole with loads allows to lessen this effect.
Figure 5.18 demonstrates similar results for the uniform linear array, situated near the superstructure. The mentioned above two variants of monopoles are adopted as radiators of the array. The relative placement of the superstructure and radiators as well as the superstructure dimensions are given in figure, the phase shift between the currents of the radiators is adopted zero. The calculation results show that in the upper part of the frequency range the influence of the superstructure on the directional pattern of array, consisting of the monopoles without loads, is slighter than its influence on the directional pattern of the separate monopole. This is, apparently, related to the fact that the superstructure does not hinder the propagation of electromagnetic waves from the side radiators. Nevertheless, the use of monopoles with loads in this case also allows to reduce the impact of the superstructure and to increase the signal in its direction.
Figure 5.18 A linear array near a superstructure (a) and its pattern in the horizontal plane (b).
6.1 THE SHAPE OF A CURVILINEAR RADIATOR WITH MAXIMUM DIRECTIVITY
In the previous chapter the synthesis problem of a straight radiator with concentrated loads was regarded. Together with loads the radiator shape substantially affects the antenna’s characteristics, in particular its directivity.
One must refine the considered problem. It is the optimization of the shape of the thin radiator with the aim of obtaining maximal signal in the predetermined direction.
Unlike the previous chapter the problem is solved for a single frequency (or for a single electrical length of the radiator). A thin curvilinear radiator of an arbitrary geometry is situated in a lossless medium in the single vertical plane, e.g. in the plane zOy of rectangular coordinate system (Figure 6.1a). For a certainty directivity is calculated in the y-direction. Selecting the radiator shape is limited by the necessity to exclude super directivity in order to decrease the reactance of the antenna. The reason for such restriction is negative properties of the super directive antennas, which impede the realization of small-sized antennas of such kind.
Figure 6.1 Symmetrical radiator of an arbitrary geometry in the shape of a curve (a) and a broken (b) line.