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In order to design a small radiating nuclear electromagnetic pulse simulator with fast rise time,we have investigated the application of TEM horn antenna in this kind of simulator.The TEM horn antenna is excitated by the integral double exponential pulse.Farfield response in time domain is analyzed based on the step response formula which is derived from the equivalent transmission line model of TEM horn antenna.Principle of antenna parameters selection is determined.The results of numerical calculation give a show of the radiation waveform and some problems.Then experiments are implemented and results are compared with the radiation waveforms generated by double exponential pulse excitation.