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 T2/tau 0, where 1/tau 0 is the rate of radiation damping. This result leads directly to a fundamental formulation of the usual signal-to-noise ratio, (SNR)2 = (m0 B/tau 0)/(4Fk theta delta v), where m0 is the equilibrium magnetic moment, theta 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.