This paper describes the simulation, design, realization, and experimental test of a tapered transmission line (TL) for adapting a broad-band impulse generator to a radiating antenna, for a frequency range of 50 MHz-1 GHz. Two different taper geometries are considered and discussed in the analysis: exponential and logarithmic. Two analysis methods are also used: 1) analytical equations obtained by applying the TL theory and 2) full-wave numerical simulations in both frequency and time domains using Comsol. It is shown that, in general, an exponential taper performs better than a logarithmic one, particularly at high frequencies. Time-domain simulations reveal that, for fast transient subnanosecond pulses, both tapers can be used equivalently and the signal does not suffer from any significant distortion while traveling along the tapers. We also show that analytical equations obtained using the TL theory are in very good agreement with full-wave simulation results and can be used advantageously in the design of tapers. This paper also presents the mechanical design and the realization of an exponential taper used for the connection of a 50-Omega pulser to a half-impulse radiating antenna (HIRA) having an input impedance of 100-Omega. The realized taper is fully characterized in the frequency domain using a vector analyzer and in the time domain using a reflectometer and shown to be performing in agreement with the simulations.