ABSTRACT
Hoult and Richards (1976) first formulated a method of calculation of the induced signal in a nuclear magnetic resonance (NMR) experiment. Considering the radio frequency (RF) field B 1 at point P in space, produced by a coil C carrying a unit current, the presence of a rotating magnetic moment m at point P will induce an electromotive force (EMF) in the coil conductor given by () EMF = − ∂ ∂ t ( B 1 ⋅ m ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429173653/28d7b5a0-981b-413e-bd5e-1f02359f0b03/content/eq192.tif"/> () m = M o e − j ω o t https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429173653/28d7b5a0-981b-413e-bd5e-1f02359f0b03/content/eq193.tif"/> Therefore, for a given sample of volume V s , the total EMF induced is given by the equation above. For a magnetization vector rotating at the Larmor frequency ω o , the above expression simplifies to () EMF = ω o B 1 M o e − j ω o t https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429173653/28d7b5a0-981b-413e-bd5e-1f02359f0b03/content/eq194.tif"/> where M o is the total magnetic moment for the volume of the sample under consideration. Calculation of the signal voltage necessitates the knowledge of an expression for the magnetic field B 1 produced by a unit current flowing in the detection coil. The latter is, of course, a function of coil geometry. Therefore, an important design aspect of RF coils is the choice of such coil geometry to achieve maximization of the relative ratio of the B 1 field to the total resistance of the coil.
