By using the relations given in [4], we can found the dispersion matrix of the union of two multipoles – attenuator and radiator block. If we specify the amplitude of the wave at the input of the attenuator, we can get the amplitude of the reflected wave and amplitudes of the harmonics in the Floquet channel, using which we can easily calculate the DN of the block of the phased array [1].

In [5], relations are given, which allow finding of the amplitudes of incident and reflected waves in the lines connecting the multipoles and . If we know these amplitudes, in case of the attenuator with absorbing elements, we can find power absorbed in each of the absorbing elements.

We shall note that when implementing the numeric algorithm, the method detailed above turns out to be significantly more efficient compared to the direct solution of the boundary-value problem for the block containing MxN radiators by considering an infinite phased array with the period equal to the block. Indeed, in case of waveguide radiators [1] for example, in the latter case we shall get the system of MxN operator equations, which, using the method of moments, can be reduced to the system containing linear algebraic equations. Using the latter method, we will have to invert matrix sized times. Since, when inverting an n-order matrix using the Gauss method, the number of operations grows as , the gain in machine time will be times.

Based on the mathematical model and the program for calculating characteristics of an infinite plane phased array built of round waveguides, there was developed a program for calculating characteristics of a block phased array. All calculations were performed for an array with square grid of radiators. Distances between waveguides were assumed equal to 0,7, and radius of the waveguide - to 0,34. All mentioned results correspond to the E-plane of waveguide radiators. Fig.3 shows the direction diagrams of the block depending on its size: 1 — for the 1x1 block; 2 — for the 2x2 block and 3 — for the 5x5 radiator block. For calculations, the input-matched attenuator was used, which provided uniform distribution inside the block [4]. For all diagrams, there are dips related to the periodicity of radiator layout and periodicity of blocks. It is known [1] that for a common infinite array, full cutoff is characteristic at the moment of appearance of difractional maximums in the area of real angles. In case of a block array, the zero is only the dip related to the periodicity of radiators ( = 25°), and the rest of the dips are nonzero. Indeed, DN of the block in an infinite block array is determined by the zero Floquet harmonics corresponding to the partial excitation with indices k, l = 0 in (4); this is why the DN of the block suffers the zero dip the same as in the common array. If waves of other partial excitation suffer full reflection, redistribution of values of amplitude coefficients takes place in the formula (4) because of interaction of waveguide radiators through the attenuator and additional dips in the DN of the block appear, which have a nonzero depth. The latter is also related to the fact that a partial excitation corresponds only to a portion of the power for a single block. Because of this, maximums of the reflection coefficient on block input do not reach the unit value unlike the case with a common infinite array. This fact is illustrated by fig. 4, a, which shows dependence of the reflection coefficients at the attenuator input for a 2x2 radiator block, the same dependence for the 5x5 radiator block is shown at fig. 4, b (curve 1).

Especially interesting is the case, when during scanning not only blocks but also block radiators are phased, i.e. when the block radiators are phased in the phasing direction of the entire array. To calculate characteristics of such an array, an input-matched attenuator was used, which has phase inverters installed in its arms. The field value in the main maximum of this array is the same as in the common array with elementwise phasing. However, because of the fact that waves reflected from the aperture are re-reflected from the attenuator, passing through the phase inverters two times, side lobes appear, unlike the case with the array of semiinfinite waveguides. Besides, there is also redistribution of energy between the waveguides in effect, because of the interconnection through the attenuator. The total power of these side lobes, as the computer calculations have shown, can reach 4-6% of the incident power (in a single-beam scanning sector). Because of the fact that part of the reflected energy is re-reflected into the side lobes, such array is better matched at the attenuator input. Dependence of the reflection coefficient module on the scanning angle at the attenuator input for such array (size of the block is 5x5 reflectors) is shown at fig. 4, b (curve 2).

It would be interesting to research characteristics of a phased array with an attenuator containing an absorbing element to provide decoupling of the attenuator outputs. When using such attenuator, a portion of power is dispersed in the absorbing element. Therefore, especially interesting are the energy characteristics of such a phased array. Fig.4, b shows dependence of power dispersed in the attenuator on the input power for an array with the 1x2 radiator block. As the plot shows, the loss of power in the attenuator is especially high at the moments of appearance of diffraction maximums in the area of real angles, when the phase difference between the reflected waves in different waveguides is at maximum.

Thus, the explained method allows for building an efficient algorithm of calculating characteristics of block phased arrays intended for scanning in a limited sector of angles and normal phased arrays with elementwise phasing considering interaction of radiators in the outside space and power wiring circuits.

The given numerical results show the possibility of considering the influence of the attenuator when designing phased antenna arrays.