A coupled resonator model of the detection of nuclear magnetic resonance: Radiation damping, frequency pushing, spin noise, and the signal‐to‐noise ratio

Magnetic resonance involves two coupled resonating systems: the spins and the tuned receiver coil. We simulate the spin system by an equivalent electrical resonator. An analysis of coupled resonators leads to a straightforward derivation of properties such as radiation damping, frequency pushing, and spin noise. The theory is applied to recent experiments (M. Guéron and J. L. Leroy, J. Magn. Reson. 85 , 209–215 (1989)). The sensitivity of the spin noise experiment is shown to be T 2 /τ 0 , where 1/τ 0 is the rate of radiation damping. This result leads directly to a fundamental formulation of the usual signal‐to‐noise ratio,\documentclass{article}\pagestyle{empty}\begin{document}$$({\rm SNR)}^{\rm 2} = (m_0 B/\tau _0)/(4Fk\theta \delta \nu),$$\end{document}where m 0 is the equilibrium magnetic moment, θ is the temperature, and F is the noise figure of the receiver. An equivalent electrical resonator can also be used to describe the active medium of masers. © 1991 Academic Press, Inc.