Threshold voltages for hyperbolic secant inversion pulses.

Spin inversion produced by hyperbolic secant RF pulses is independent of pulse amplitude once a threshold value is exceeded. A semi-empirical formula for these pulses has been derived by application of analytical solutions to the Bloch equations. This predicts the required coil voltages for inversion as a function of inversion bandwidth and side-to-width parameter mu, based on knowledge of a reference voltage for the loaded coil. The voltage required is shown to increase linearly with bandwidth but to fall with the mu, approximately as (1/mu)0.4. Experimental confirmation is presented, and factors affecting choice of pulse parameters are discussed.