Reconstruction of transient currents from magnetic data

Luca Di Rienzo (Dipartimento di Elettrotecnica, Politecnico di Milano, Milano, Italy)
Sergey Yuferev (Nokia Mobile Phones, Tampere, Finland)
Nathan Ida (Department of Electrical Engineering, The University of Akron, Akron, Ohio, USA)
Cesare Mario Arturi (Dipartimento di Elettrotecnica, Politecnico di Milano, Milano, Italy)



To provide a time domain formulation for reconstruction of transient currents flowing in massive parallel conductors from magnetic data collected in the dielectric space surrounding the conductors.


A boundary integral equation (BIE) formulation involving Mitzner's and Rytov's high order surface impedance boundary conditions (SIBCs) is used. Input data of the inverse problem are the magnetic fields at given locations near the conductors. In order to validate the inversion algorithm, the magnetic field data are computed solving the direct problem with FEM for given current waveforms.


The improvement in reconstruction accuracy of the new time domain BIE formulation employing high order SIBCs has been demonstrated numerically in a simple test case. The range of validity of the technique has been extended to current pulses of longer duration and the computational burden has shown to increase only by a factor of 4.

Research limitations/implications

The proposed formulation can be compared with other possible formulations, both in the time and in the frequency domain.

Practical implications

Based on this formulation a new current sensing technique is proposed for realization of low cost current sensors based on magnetic sensor arrays.


The inverse problem addressed in the paper has been solved for the first time.



Di Rienzo, L., Yuferev, S., Ida, N. and Mario Arturi, C. (2005), "Reconstruction of transient currents from magnetic data", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 24 No. 4, pp. 1200-1212.

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Copyright © 2005, Emerald Group Publishing Limited

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