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Silicon on-chip integrated antennas have been developed for intra- and inter-chip signal transmission. However, the radiation efficiency and transmission gain of the antenna were degraded due to conductive loss of Si substrates. In order to solve these problems, a bypass planar wave guide which was composed of a high dielectric constant substrate was developed to reduce the propagation loss through Si chips. In this paper the effects of dielectric constant and thickness of the dielectric wave guide on radiation efficiency and transmission gain of integrated antenna are investigated.