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Despite the fact that active electrically small antenna based on Superconducting Quantum Array forms output voltage which is independent of the antenna size to wavelength ratio, a small size effect can appear and limit antenna linearity with the ratio increase. We analyze and discuss impact of the size effect on the antennas of both the transformer and transformer-free types. In the case of transformer antenna, this effect can be associated with a finite phase delay of the input signals coming to the cells which are coupled to opposite sides of the superconducting transformer. This delay is substantial for differential network. In transformer-less antenna, every quantum cell operates independently with input flux applied directly to the cell area. If the quantum cell has only one main loop as in the case of bi-SQUID, the size effect is negligibly small. However, this effect can not be neglected in cases of the differentially connected cells and the cells containing parallel arrays of Josephson junctions. Owing to the size effect, the flux distribution along the array-based cell can get an asymmetry which noticeably affects the linearity characteristics despite smallness of the asymmetry.