Abstract
We analyze the scale factor linearity, steady-state, transient, and noise characteristics of a nuclear magnetic resonance oscillator coupled with the phase-locked loop, which makes its performance improvement possible by a balanced strategy in optimizing parameters based on the proposed model. The numerical simulation indicates that the simple oscillator system gives a better scale factor linearity and transient response than the coupled system, while the steady-state solution is similar between the two with experimental validation. The phase and magnetic noise suppression is necessary to ensure the dynamic response of the coupled system. The characteristic analysis not only facilitates the rapid-response optimization of the coupled oscillator system under a dynamic environment but also enlightens corresponding steady-state tracking precision.
Highlights
The nuclear spin of a single atom is too weak to be detected by currently available methodology; an ensemble of atoms is applied as the sensitive medium to be hyperpolarized by spin exchange optical pumping (SEOP)13–15 to form the detectable macroscopic magnetization vector along the longitudinal direction
We focus on the mostly applied secondorder phase-locked loop (PLL) as the tracking approach, which typically consists of a phase detector (PD), a loop filter (LF), and a voltage-controlled oscillator (VCO), while a similar procedure can be obtained with other types of PLL or tracking approaches
We analyze the characteristics of a nuclear magnetic resonance (NMR) oscillator coupled with the PLL to study the scale factor linearity, steady-state, transient, and noise response of the output frequency compared with the pure NMR oscillator
Summary
High performance nuclear magnetic resonance (NMR) oscillators benefit various applications such as NMR spectroscopy, magnetic resonance imaging (MRI), and the NMR gyroscope. The Larmor precession frequency of the detected nuclear species is utilized to enable the signal detection of the NMR oscillator, which is further achieved by measuring nuclear spins with the built-in magnetometer. The nuclear spin of a single atom is too weak to be detected by currently available methodology; an ensemble of atoms is applied as the sensitive medium to be hyperpolarized by spin exchange optical pumping (SEOP) to form the detectable macroscopic magnetization vector along the longitudinal direction. The Larmor precession frequency of the detected nuclear species is utilized to enable the signal detection of the NMR oscillator, which is further achieved by measuring nuclear spins with the built-in magnetometer.. A transverse magnetic field that matches the Larmor frequency of the detected nuclear species needs to be applied to make the magnetization vector precess around the longitudinal direction, enabling the Larmor frequency detection by tracking the applied transverse field. To achieve high performance NMR oscillators, it is crucial to track the Larmor frequency precisely in time with an appropriate tracking approach, e.g., fast Fourier transform (FFT). Besides well-known characteristics of the typical PLL technique, the steady-state characteristic analysis of the NMR oscillator has been reported.. We perform a characteristic analysis of the coupled system compared with the pure oscillator, including scale factor linearity, steady-state, transient, and noise characteristics
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