Time Domain Response of a Sphere in the Field of a Coil: Theory And Experiment

Abstract

The time-harmonic solution for the anomnalous vector potential due to a conducting permeable sphere in the field of a currentcarrying loop is used to derive the corresponding step response. The step response is then used to obtain analytical expressions for the voltage induced in a second loop due to a chosen exciting current pulse train. The voltage induced in an actual system of coils is obtained by superposition. The effect of the measurement system is included in the analysis in order to experimentally verify the model. Measured responses of a number of aluminum and steel spheres at various distances from the coils are compared with theoretical predictions. The agreement between the two is generally good. I. INTRODUCTION THE USE OF electromagnetic induction in detecting conducting objects is well established in geophysics [1], nondestructive testing [2], [3], treasure hunting [4], and mine detection [5], among other disciplines. A conducting object is exposed to a time-varying (usually in the hertz to kilohertz range) magnetic field produced by a current-carrying primary coil. The resulting eddy currents in the object produce a secondary magnetic field, which is detected by another coil. A particular choice of time variation of the primary current and the number and relative positions of coils is dictated by operational considerations and ease of data interpretation in a given application. The work reported here is directed towards detectors of buried artillery shells, which are small (diameters -0.02-0.15 m, lengths -0.05-0.70 m, masses -0.1-45 kg), metallic (a-107 S/m) objects at shallow depths (0-2 m). For this application, a pulse train of primary current and a vertical coaxial sensor geometry, as shown in Fig. 1, are considered most suitable [6], [7]. Detectors of this type are commercially available and simplified analysis of signals induced in them by metallic objects are reported [8]. However, detailed analysis taking into account the effects of pulse shape, finite coil size, and measurement system parameters is not available. This paper presents such an analysis for a metallic sphere. This would provide a useful model for predicting detector performance and for possible processing of measured signals to extract information about a detected object such as its depth, size, or material properties.

On the wideband EMI response of a rotationally symmetric permeable and conducting target

“…For the time dependence assumed, this implies that the EMI resonant modes decay exponentially with time. This is consistent with the well known late-time characteristics of transient EMI excitation of conducting and permeable targets [1].…”

“…At induction frequencies [1], [2], the displacement current can be neglected and the wavenumber inside the target satisfies , where is the free-space permeability, is the relative permeability, is the conductivity, and is the angular frequency. The source-free fields inside the target satisfy (1) where denotes either the electric or magnetic fields. This source-free wave equation can be solved for the resonant modes of the target, from which the target resonant frequencies and fields can be computed.…”

“…Of more importance from a practical standpoint, simple algorithms have been developed for calculation of the resonant modes of high-permittivity rotationally symmetric dielectric resonators [6]- [8], with that previous work transitioned here for characterization of the EMI modes of rotationally symmetric highly conducting and permeable targets. While the restriction to rotationally symmetric targets is clearly a limitation, such are of interest for many conducting and permeable land mines and unexploded ordnance (UXO) [1], [2].…”

“…In the context of subsurface sensing, EMI is used to sense buried metal mines as well as unexploded ordnance (UXO) [1], [2]. Since the conductivity of such targets is typically many orders of magnitude larger than the conductivity of soil, the target can usually be analyzed in free space.…”

Robust and Efficient 3D Model of an Electromagnetic Induction (EMI) Sensor

“…In contrast to experimental systems, 3D simulation models don't have such limitations, but rather other disadvantages like model flexibility and huge computation times. Theoretical models, on the other hand, exist only for the simplest shapes such as a permeable conductive spheroid or a sphere [3], [4].Many papers [1], [5], [7] contributed to modeling of such systems by using the advantage of the computational 3D capability and still implementing theoretical models where necessary to preserve the accuracy required and provide the robustness and fast computational time needed. Similarly, the current approach focuses on modeling a detection sensor, in this case, made of Printed Circuit Board (PCB) sender and receiver coils.…”