Instrumentation & Measurement Magazine 23-5 - 41

A Frequency Measurement Method
Using Rising-Falling Edge of
Square Wave for Increasing Proton
Magnetometer Precision
Chao Tan, Chenguang Wu, Yanchun Xu, Xiaofei Gong, and Liqing Pan

o improve the measurement precision of the proton
magnetometer (PM), a multi-average multi-cycle
frequency measurement (M-MFM) method using
both rising and falling edge of square wave is proposed in
this study. First, the M-MFM method using Rising-Falling
edge of square wave is presented based on the multi-cycle
frequency measurement (MFM) method, and the formula of
frequency measurement is deduced. Then, the relative error of
the proposed method is analyzed, and the proposed method is
optimized by solving the minimum value of the relative error
formula. Finally, the implementation process of the proposed
method in STM32 is introduced. The experimental results
of the frequency measurement demonstrate that the measurement precision for low SNR sine signals is significantly
increased by the proposed method. The experimental results
of the magnetic field measurement show that the sensitivity
is about 0.11 nT/Hz1/2@0.25 Hz in the range of the geomagnetic field while the proposed method is adopted by the PM,
which is better than that of the other methods and the commercial instruments.

frequency is proportional to the strength of the magnetic field.
The relationship between the magnetic field strength B with
the precession frequency fp is given as follows:

B
2  f p  p 
23.4874  fp (1)

where γp is the gyromagnetic ratio. Therefore, the magnetic
field strength can be measured by measuring the precession
frequency. However, the magnitude of the precession frequency induced by the coils in sensor is extremely weak [9],
usually in the order of a few microvolts with an exponential
decay, and it is drowned by noise after approximately one second, so the precession frequency signal is called FID signal. An
amplified FID signal is displayed in Fig. 1. As shown, the magnitude of the signal decays exponentially over time, and the
amplitude envelope of the FID signal is not a smooth exponential curve, which indicate that the signal contains noise and
the SNR is very low. Overall, the precision of the PM is mainly
dependent on the frequency measurement precision of low
SNR FID signal in a limited window of time. Therefore, how to

Introduction
The proton magnetometer (PM) is a quantum weak magnetic
field measuring instrument with superior stability [1]. It has
been widely used in the detection of static or quasistatic weak
magnetic field in applications such as space exploration and
geology [2]-[4]. There are two types of PM: ordinary and dynamic nuclear polarization (DNP). The differences between
these lie in the different excitation mode and the working substance in the sensor. The working substance for the ordinary
PM is a proton-rich solution, such as aviation kerosene, where
protons in solution are polarized by a dc magnetic field [5]. The
sample solution in a DNP magnetic field sensor is a mixture
of free radicals and a large number of protons. The free radicals in solution are first polarized by radio-frequency magnetic
field [6]-[8], then protons in solution are excited by polarized
free radicals. While the polarization condition is removed, the
polarized protons in solution will precess with angular frequency of ω in the target magnetic field, where the precession
August 2020

Fig. 1. The amplified FID signal waveform output from a PM sensor.

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