The equation of the problem regarding currents in a single unit of a regular structure with partial excitation is (23). Thus, correlations (23), (24) make it possible to express the solution of problem regarding the excitation of the finite reflective array by solving the problem regarding the excitation of a regular structure.

In case of numerical implementation of this algorithm, the discrete Fourier transforms of the functions in (23), (24) are found with the help of the fast Fourier transform. The necessary number of iterations depends on the required accuracy of determining currents. The practice of calculations shows that in most cases error in determining the characteristics of an antenna array does not get higher than fractions of or several percent if we use the simplified algorithm. This simplification comes down to the fact that we "connect" regular loads to radiators that expand the finite array to an infinite one, in case of which there are practically no currents excited in these radiators. For instance, if we model a dipole antenna, it is enough to "add" infinitely large impedances to the gap of additional dipoles. In this case, it is possible to use existing software for modelling regular radiating structures with minimum tweaks to determine the characteristics of transmissive and reflective antenna arrays both with a small number of radiators and with the number of radiators up to 10⁴ and more.

Fig.1

As an example, in Fig. 1 you can see H-plane diagrams of the radiation pattern of a dipole antenna array with a square radiating curtain containing 256 radiators located above the flat screens in the nodes of a rectangular grid with spacing = 0,8, = 0,6. The amplitude distribution of the waves exciting the grid corresponded to the cosine-squared-on-a-pedestal function ensuring the level of side lobes not higher than -40 dB. To calculate the radiation pattern with the accuracy enough to reproduce side lobes whose level reaches -60 dB, we had to take into account 10 reflections and 32×32 DFT zero points.

With the specified DFT parameters, the problem of regular structure periodic excitation with one period containing 32×32 elements is solved at each stage of the iteration procedure.

The current in radiators expanding the finite array to an infinite one did not get higher than -60 dB relative to the maximum value of current in the radiators of the array under examination.

The computations time with the specified number of reflections was not more than 20 s on an ES-1045 computer. It took 24 min of computational time to calculate the characteristics of a regular array for the specified DFT parameter with the approximation of current distribution on dipoles by three basis functions.

Using the same array of characteristics for a regular dipole structure, it is evidently possible to determine currents both in a degenerate array consisting of one radiator and in an array with any shape of its radiating curtain that fits in some part of a regular structure containing 32×32 elements, including a square array with 1024 elements. Any option will require the same 20 s of computational time on an ES-1045 computer.

If the size of the array with the characteristics of a regular radiating structure does not change, the accuracy of determining the currents of the finite array reduces if the number of radiators increases. However, it should be noted that, in case of amplitude distributions that decrease closer to the edge of the radiating curtain, error in determining the characteristics of finite antenna arrays meeting the ratio specified above between the array of DFT zero points and the area of the radiating curtain barely depends on the number of radiators and the shape of the radiating curtain.

Calculating the inverse discrete Fourier transform (24) has no difficulties because function does not have peculiarities, such as poles, connected with surface waves. There are no peculiarities like these because value corresponds to a regular structure composed of partial radiators with loads in the form of match-terminated transmission lines or multiport transducers with losses. There are no surface waves in structures like these.

The appropriate choice of basis in (2) and the loads of partial radiators makes it possible to study the characteristics of arrays composed of different radiators as well as unequally spaced antenna arrays where distances between elements are divisible by arbitrary constant.