It is known that the phase center of some antennas can shift its position over frequency. The effects of such a phase center movement on the time-domain behavior of an antenna are studied throughout this letter. By linearizing the shift of the phase center, exact and approximate derivations of the time-domain impulse response are derived and discussed comprehensively. Contrary to expectations, the extent of the antenna impulse response increases with increasing antenna bandwidth under certain conditions. These theoretical findings are discussed in detail using examples .