We have studied analytically the temporal characteristics of terahertz radiation emitted from a biased largeaperture photoconductive antenna triggered by an ultrashort optical pulse. We have included the effects of the finite lifetime and transient mobility dynamics of photogenerated carriers in the analysis. Succinct explicit expressions are obtained for the emitted radiation in the surface field and in the far field. The dependence of the waveforms of the radiated field on the fluence and duration of triggering optical pulse, carrier relaxation time and carrier lifetime are discussed in detail using the obtained expressions.