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The characteristics of photogenerated terahertz radiation from a current-biased superconducting YBa2Cu3O7-δ (YBCO) bow-tie antenna were investigated using a free-space electrooptic sampling technique. Picosecond electromagnetic pulses about 450 fs wide were obtained. The frequency spectrum derived by Fourier transforming the picosecond pulses spans over 0.1-4 THz. The dynamics of the quasi-particles optically induced by the ultrafast laser pulse primarily determines the performances of the transient terahertz radiation generated under different operating parameters. The results indicate a characteristic quasi-particle relaxation time of about 2.5 ps close to the critical temperature Tc, and a faster time at lower temperatures.