A theoretical study of magnetic and ultrasonic sensors: Dependence of magnetic potential and acoustic pressure on the sensor geometry

In this paper, we describe a model based on a spatial distribution of point sources, called "DPSM" (Distributed Point Sources Method), applied to magnetic and ultrasonic sensors modelling. Magnetic and acoustic fields are theoretically generated for two types of sensors. The sensor surface is discretized into a finite number of elemental surfaces. A point source is placed at the centroid position of every elemental surface. Point source strength is proportional to the elemental surface area for acoustic sensors and it is obtained by inverting a matrix to satisfy the equipotential boundary conditions for magnetic sensors. Total field is computed at a given point by adding fields generated by all sources. The main difference between the magnetic and acoustic field modelling is that for a magnetic sensor the magnetic potential remains constant on the sensor surface and the magnetic flux varies from point to point, while for the acoustic sensor the particle velocity remains constant on the sensor surface and the acoustic pressure varies. This difference causes an additional matrix inversion in the magnetic field modelling, which is not necessary for the acoustic field modelling. Like other numerical modelling schemes, accuracy of the computation depends on the sensor surface discretization or mesh generation. Effect of the spacing between two neighbouring point sources on the accuracy of the field computation is studied and the optimum spacing for accurate numerical computation is given. For accurately modelling acoustic fields the spacing between two neighbouring sources should be less than the acoustic wavelength. Flat sensors with circular and rectangular cross-sections as well as point focused concave sensors have been modelled by this technique.