Time domain analytical modeling of a horizontal wire buried in a lossy medium
Abstract
As part of the dissertation, an analytical solution was developed for the transient response of a thin wire of finite length buried in the center with losses. The model is based on Pocklington’s integro-differential equation. Analytical treatment of the integral operator is performed by approximating the subintegral function, while the resulting differential equation is solved by applying the Laplace transformation. The solution of the equation obtained in the Laplace domain is transformed into the time domain by applying Cauchy’s residue theorem. The relation obtained in this way represents the impulse response of the wire. The reflection of the signal from the border of the two environments is taken into account by applying the reflection coefficient derived from the modified mapping theory. The exciting electromagnetic (EM) wave is modeled by sampling in the frequency domain and transferred to the time domain by inverse Fourier transformation. After that, a discrete convolution is performed between the incident wave and the relation for the impulse response of the wire, and the induced current for the concrete shape of the EM wave is obtained. The response to excitation by a current source connected to one end of the wire, which represents the grounding electrode, is also analyzed. The expression for the transient response of the electrode is derived in a similar way as for EM wave excitation. The induced current function along the electrode is obtained by performing an analytical convolution with the current source function. The obtained results, for both cases, are compared with the numerical results obtained by indirect modeling in the frequency domain in combination with the inverse Fourier transformation.
