A class of causal model pulses is constructed by applying a causal modulation to a noncausal function with a rectangular spectral diagram. A particularly suitable modulation is the power exponential pulse, the resulting model pulse having a spectral behavior that is practically flat over a controllable bandwidth, with a steep falloff outside the band. Some of the devised pulses are opportune excitations in ultrawideband antenna models, thus representing effective instruments in their performance analysis, and are appropriate as inputs in electromagnetic time-domain simulation packages.