The shorter the array is, the more different quantities (17) are. This means that as the number of radiators decreases, the amplitude distribution in the array corresponding to the regular part of the current significantly distorts as compared to the amplitude distribution of waves in feeder lines, which excite the radiators. This is the main cause of distortion of the direction diagram of the array with a small number of radiators, which becomes apparent in the increase of level of side lobes. As the size of the array increases, the quantities (17) converge to the same limit, equal to , and the relation between the amplitudes of slot currents, inducted by the partial excitations (16) converge to the relation between the partial excitations. That is why in arrays with large number of radiating elements, level of side lobes of the direction diagram for the regular part of the current converges to the value corresponding to the amplitude distribution of waves, which excite the radiators. Thus, distortions of the direction diagram of the phased array with a small number of radiators can be revealed by analyzing the interaction of radiators in infinite antenna arrays. This does not mean that boundary waves do not distort the direction diagram of a phased array with a large number of radiators. It can be shown that distortions of the direction diagram caused by the radiation of boundary waves in large arrays appear when the maximum of the direction diagram approaches the edges of the scanning sector. Analysis of the radiation field of the slot infinite array and the plots at fig 1,a show that when the beam is approaching the edge of the scanning sector, because of decreasing amplitude of the regular part of the current, the level of the primary maximum of the direction diagram as well as the level of maximum radiation of the boundary wave does not depend on the number of radiators of the slot. Therefore, in the direction of the maximum of radiation of the boundary waves, a side lobe appears, the level of which infinitely grows as the number of radiators increases, as compared to the level of radiation of the regular part of the current in the given direction. The ratio of the maximums of radiation of the regular part of the current to the boundary wave stays almost constant.

Fig 2,c shows relation between the level of maximum of the side lobe related to the radiation of the boundary wave and the level of side radiation of the regular part of the current in the direction of the maximum, and the number of radiators in a uniformly excited slot array, beam of which is deviated to the extreme angle, defined by the expression [3]

(18) |

The charts show that in large arrays, in the area of side lobes with level -30…-50dB, because of the radiation of the boundary wave, an additional side lobe appears, the level of which is -22.5dB, i.e. the level of side radiation in the direction of the maximum of the direction diagram of the boundary wave significantly increases. At fig 2,a (curves *4*, *5*), in the scale of the curve 1, envelopes of the side lobes of the regular part of the current of a uniformly excited slot array with a different number of radiators, beam of which is deviated from the normal to the extreme angle (18), are shown. Because of the significant width of the direction diagram of the boundary wave, an increase in the level of side radiation happens in the quite large angle sector.

Thus, boundary effects caused by the existence of boundary waves on the edges of the radiating curtain lead not only to oscillations of the current of radiators of the boundary area, but also to appearance of additional lobes in the “blinding” direction of the array. The distortions of the direction diagrams appear when the beam of arrays with a large numbers of radiators is deviated to the extreme angle in the sector of single-beam scanning. In arrays with low level of side radiation and small number of radiators, significant change in the level of side lobes is caused by changes of amplitude-phase distribution of the regular part of the current, which is described by the interaction of radiators in an infinite antenna array.