Chirp Excitation

The paper describes the design of broadband chirp excitation pulses in NMR. We first develop a three stage model for understanding chirp excitation in NMR. We then show how a chirp $\pi$ pulse can be used to refocus the phase of the chirp excitation pulse. The resulting magnetization still has some phase dispersion in it. We show how a combination of two chirp $\pi$ pulses instead of one can be used to eliminate this dispersion, leaving behind a small residual phase dispersion. The excitation pulse sequence presented here allow exciting arbitrary large bandwidths without increasing the peak rf-amplitude. Although methods presented in this paper have appeared elsewhere, we present complete analytical treatment that elucidates the working of these methods.