Magnetic nanoparticle thermometer: An investigation of minimum error transmission path and AC bias error

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Abstract

The signal transmission module of a magnetic nanoparticle thermometer (MNPT) was established in this study to analyze the error sources introduced during the signal flow in the hardware system. The underlying error sources that significantly affected the precision of the MNPT were determined through mathematical modeling and simulation. A transfer module path with the minimum error in the hardware system was then proposed through the analysis of the variations of the system error caused by the significant error sources when the signal flew through the signal transmission module. In addition, a system parameter, named the signal-to-AC bias ratio (i.e., the ratio between the signal and AC bias), was identified as a direct determinant of the precision of the measured temperature. The temperature error was below 0.1 K when the signal-to-AC bias ratio was higher than 80 dB, and other system errors were not considered. The temperature error was below 0.1 K in the experiments with a commercial magnetic fluid (Sample SOR-10, Ocean Nanotechnology, Springdale, AR, USA) when the hardware system of the MNPT was designed with the aforementioned method.

Figures

  • Figure 1. System structure of the MNPT. DAQ, data acquisition card.
  • Figure 3. Signal transmission path of the magnetic detection module.
  • Figure 4. Harmonic measurement error resulting from the deviation of the parameters, such as the radius of the Helmholtz coils (r0 = 0.1025 m), the turn of the Helmholtz coils (N0 = 168), the AC impedance of the Helmholtz coils (ωL = 44.06247 Ω), the voltage gain of the power amplifier (k1 = 7.8), the attenuation coefficient of the power amplifier within the pass band (k2 = 1) and the signal source (U0 = 5.75 V). The deviation rates of these parameters are 0.01%, 0.05%, 0.1%, 0.5% and 1%, respectively. The MNPs follow a single particle distribution (10 nm); the saturation magnetic moment is MsV = 2.4976 × 10−19 emu; the frequency is 375 Hz; the system has no noise and no AC bias. (a) represents the error of first harmonic amplitude resulting from the deviation of the parameters; (b) represents the error of third harmonic amplitude resulting from the deviation of the parameters; (c) represents the error of harmonic ratio (1st/3rd) resulting from the deviation of the parameters; (d) represents the temperature error resulting from the deviation of the parameters.
  • Figure 5. Temperature measurement error resulting from parameters, such as the turns of the detection coil (n1 = 884, n2 = 884), the cross-sectional area of the detection coil (s1 = 58.99 mm2, s2 = 58.99 mm2), the voltage gain of the preamplifier (k3 = 1000) and the DC bias of the preamplifier (c1 = 8.2 mV). The deviation rates of the parameters are 0.01%, 0.05%, 0.1%, 0.5% and 1%, respectively. The mean particle diameter is 10 nm; the saturation magnetic moment is MsV = 2.4976 × 10−19 emu; the magnetic excitation frequency is 375 Hz; the system has no noise and no AC bias.
  • Figure 6.Cont.
  • Figure 6. Maximum and minimum transmission direction of the temperature error caused by some factors, such as the radius of the Helmholtz coils (r0 = 0.1025 m), the turn of the Helmholtz coils (N0 = 168), the AC impedance of the Helmholtz coils (ω = 44.06247Ω), the voltage gain of the power amplifier (k1 = 7.8), the attenuation coefficient of the power amplifier within the pass band (k2 = 1) and the signal source (U0 = 5.75 V). The deviation of each factor respectively is 0.01%, 0.05%, 0.1%, 0.5%, 1%. (a) represents the maximum transmission direction of the temperature error; (b) represents the minimum transmission direction of the temperature error.
  • Figure 7. The inductance and resistance of Helmholtz coils varied with temperature. The temperature range is from 253 K to 313 K.
  • Figure 8. The error of the MNPT under different temperatures for the chambers. (a–c) represent different measurement error of the MNPT with respect to the temperatures for the chamber of 293 K, 303 K and 313 K.

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APA

Du, Z., Su, R., Liu, W., & Huang, Z. (2015). Magnetic nanoparticle thermometer: An investigation of minimum error transmission path and AC bias error. Sensors (Switzerland), 15(4), 8624–8641. https://doi.org/10.3390/s150408624

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