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Leaky-wave radiation of strongly truncated periodic structures is investigated. Starting with the analysis of an infinite structure with one-dimensional periodicity, the implications of a truncation on the far-field radiation characteristic are pointed out. In particular, the influence on the half-power beamwidth and the direction of maximum radiation is examined. The theoretical results are verified by the design of a transmission-line based leaky-wave antenna. The antenna consists of a microstrip line loaded periodically by inductive short-circuited stubs. The direction of maximum radiation and the half-power beamwidth are determined by the dispersion of the infinite structure and the total length of the antenna, respectively, both parameters representing degrees of freedom for the design. It is also shown how the total efficiency of strongly truncated antennas can be enhanced considerably.