Computation of finite array effects in the framework of the Square Kilometer Array project

The Square Kilometer Array (SKA) is a very large radio telescope being planned by an international consortium. It would operate in a very broad frequency band and have a collecting area of one square kilometer. In order to achieve a good resolution, this area will be spread over a few tens of stations, located several tens or hundreds of kilometers apart. The Netherlands Foundation for Research in Astronomy (ASTRON) is studying the possibility of covering the mid-range frequencies (~0.2 to 2 GHz) with an instrument based on the phased-array technology. This technology presents the major advantages of avoiding mechanically moving structures and of enabling very flexible beamforming. One of the envisaged broadband antenna elements is the tapered slot antenna, also called Vivaldi antenna. The design of these antennas is based on infinite array models, which automatically include the mutual coupling effects. As each station will probably be made of a very large number of small arrays, it is important to know how these arrays will behave when they are truncated. We developed a computation scheme for arrays of antennas made of metallic fins. We justify the adopted approach, then details are given for the fast resolution of the resulting equation system. Finally, examples are shown for wide dipoles and comments are made about the extension to Vivaldi antennas