A spin in an external magnetic field

The number of spins N, which are in the upper or lower energy level are related by the Boltzmann equation:

The NMR System

The NMR System is a serial resonance circuit with a coil within or around the target material.
The coil is connected to the capacitor via a transition cable (UT-85).

A change in the polarization value induces a change in the susceptibility of the coil. This causes
a variation of the Q factor of the circuit, which can be measure as an increase or a decrease of the
voltage. This voltage is conditioned with rf- and lf- amplifiers. The signal is obtained by a frequency
 scan (sweep) over the resonance (Larmor) frequency . The prepared signal is detected bya PC
with a Windows OS (95/98/NT). In order to increase the signal to noise ratio, many signals are
accumulated (the noise reduces by the square root of the number of sweeps).

The polarization of a spin 1/2 particle ( proton, electron ...) is given by:

At given magnetic field and temperature the polarization is calculable by formula (1). The area under the
resonance line is proportional to the polarization value P.

The calibration is done at thermal equilibrium (TE), e.g. B=2.5T, T=1K => Pp=0.25%,
Larmor frequency =106 MHz.

The polarization value of enhanced signals, i.e. after dynamic polarization, can be determined
by formula (3).