We demonstrate how resonant planar coils may be used as sensors to detect and quantify magnetic nanoparticles reliably. A coil's resonant frequency depends on the adjacent materials' magnetic permeability and electric permittivity. A small number of nanoparticles dispersed on a supporting matrix on top of a planar coil circuit may thus be quantified. Such nanoparticle detection has application detection to create new devices to assess biomedicine, food quality assurance, and environmental control challenges. We developed a mathematical model for the inductive sensor response at radio frequencies to obtain the nanoparticles' mass from the self-resonance frequency of the coil. In the model, the calibration parameters only depend on the refraction index of the material around the coil, not on the separate magnetic permeability and electric permittivity. The model compares favourably with three-dimensional electromagnetic simulations and independent experimental measurements. The sensor can be scaled and automated in portable devices to measure small quantities of nanoparticles at a low cost. The resonant sensor combined with the mathematical model is a significant improvement over simple inductive sensors, which operate at smaller frequencies and do not have the required sensitivity, and oscillator-based inductive sensors, which focus on just magnetic permeability.
Keywords: coil; electric permittivity; impedance; inductive sensor; magnetic lateral flow immunoassays; magnetic nanoparticles; magnetic permeability; nanoparticles; refraction index; self-resonant frequency.