An improved proton magnetometer for Earth's magnetic field observation
As a precision instrument to measure the earth magnetic field, proton magnetometer is widely used in different fields such as geological survey, buried objects detection and earth field variations. Due to poor signal to noise ratio (SNR) of the system, proton magnetometer suffers from low sensitivity which directly affects the performance. In order to increase the sensitivity, we present an improved proton magnetometer. First, the effect of matching resistance on Q value is discussed to enhance SNR, and high matching resistance has been chosen to improve the Q value of the resonant circuit. Second, noise induced by pre-amplifier is investigated in order to obtain low noise signal, and we adopt the JFET with noise figure less than 0.5dB as the pre-amplifier. Third, by using band-pass filter, low-noise output signal is obtained. Fourth, the method of period measurement based on CPLD is employed to measure frequency of the square wave shaped from the output sinusoidal signal. High precision temperature compensate crystal oscillator (TCXO) has been used to improve the frequency measurement accuracy. Last, experimental data is obtained through field measurements. By calculating the standard deviation, the sensitivity of the improved proton magnetometer is 0.15nT for Earth’s magnetic field observation. Experimental results show that the new magnetometer is sensitive to earth field measurement.
Experimental research of proton magnetometer
Proton magnetometer is a static magnetic measuring instrument of high sensitivity based on Larmor precession effect and is widely used in the survey of geological environment, underground buried objects and geomagnetic anomaly detection, etc. In this paper, a new method of magnetic measurement based on the system of DSP+CPLD is composed. The tests were conducted to verify the sensitivity of this instrument under ideal and actual conditions. Two types of function signal generators, the GFG-8255A and EE1420DDS, which can supply signal with high signal to noise ratio (SNR) and accurate phase, are used to simulate the local magnetic frequency. Both of them produce the signals that imitate the frequency of the local magnetic field. The precision of 0.0037nT and 0.0054nT with different function signal generators under the ideal condition were achieved. The precision of 0.1nT in an actual environment was obtained. The experimental results indicate that the sensitivity of this instrument approached the level of commercial instrument.
Asymptotic Properties of Solutions to Second-Order Difference Equations of Volterra Type
<jats:p>We consider the discrete Volterra type equation of the form <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>b</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mrow><mml:msubsup><mml:mo stretchy="false">∑</mml:mo><mml:mrow><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msubsup><mml:mrow><mml:mi>K</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:math>. We present sufficient conditions for the existence of solutions with prescribed asymptotic behavior. Moreover, we study the asymptotic behavior of solutions. We use <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi mathvariant="normal">o</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msup><mml:mo stretchy="false">)</mml:mo></mml:math>, for given nonpositive real <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:math>, as a measure of approximation.</jats:p>