# Chirp Excitation

## TL;DR

This paper presents a comprehensive analytical framework for broadband chirp excitation pulses in NMR, enabling large bandwidth excitation without increasing peak RF amplitude, and introduces a sequence of two chirp π pulses to reduce phase dispersion.

## Contribution

It provides a complete analytical understanding of chirp excitation methods in NMR, including phase refocusing techniques using two chirp π pulses.

## Key findings

- Chirp excitation can achieve large bandwidths without higher peak RF.
- Two chirp π pulses effectively reduce phase dispersion.
- Analytical models clarify the working of chirp excitation methods.

## Abstract

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.