Silvestar Sesnic

Generalized Form of Telegrapher's Equations for the Electromagnetic Field Coupling to Buried Wires of Finite Length

In this paper, a generalized form of telegraphers equations for electromagnetic field coupling to buried wires is derived. The presented approach is based on thin-wire antenna theory. The effect of a dissipative half-space is taken into account via the reflection/transmission coefficient approximation. The conductor losses can be taken into account via the surface impedance per unit length. The derived equations are treated numerically via the Galerkin-Bubnov indirect boundary element method. Numerical results are presented for induced current along the wire, and compared with transmission-line (TL) and modified TL (MTL) approximations, respectively, for the case of perfectly conducting electrode buried in a lossy medium. It is shown that the TL and MTL approximations can result in an inaccurate induced current distribution along the conductor at HFs and for shorter electrode lengths, respectively.

TIME DOMAIN ANALYTICAL MODELING OF A STRAIGHT THIN WIRE BURIED IN A LOSSY MEDIUM

This paper deals with an analytical solution of the time domain Pocklington equation for a straight thin wire of ¯nite length, buried in a lossy half-space and excited via the electromagnetic pulse (EMP) excitation. Presence of the earth-air interface is taken into account via the simplified reflection coefficient arising from the Modified Image Theory (MIT). The analytical solution is carried out using the Laplace transform and the Cauchy residue theorem. The EMP excitation is treated via numerical convolution. The obtained analytical results are compared to those calculated using the numerical solution of the frequency domain Pocklington equation combined with the Inverse Fast Fourier Transform (IFFT).

Analytical Modeling of a Transient Current Flowing Along the Horizontal Grounding Electrode

This paper deals with an analytical solution of the time domain Pocklington integro-differential equation for the transient current flowing along the horizontal grounding electrode of finite length. The electrode is excited with an equivalent current source representing the lightning strike current. Presence of the earth-air interface is taken into account through the formulation, via simplified reflection coefficient arising from the modified image theory. The analytical solution is carried out using the Laplace transform and the Cauchy residue theorem, respectively. Results obtained by the analytical solution are compared to those calculated using numerical solution of the corresponding frequency domain Pocklington equation in conjunction with the Inverse Fast Fourier Transform. The results obtained via different methods agree satisfactorily.

A comparison of finite-difference, finite-integration, and integral-equation methods in the time-domain for modelling ground penetrating radar antennas

Development of accurate models of GPR antennas is being driven by research into more accurate simulation of amplitude and phase information, improved antenna designs, and better-performing forward simulations for inversion procedures. Models of a simple dipole antenna, as well as more complex models similar to a GSSI 1.5GHz antenna and a MALA Geo-science 1.2GHz antenna were investigated in free space and over lossless and lossy dielectric half-spaces. We present comparisons of simulated data using the Finite-Integration Technique, the Finite-Difference Time-Domain method, and a Time-Domain Integral Equation approach, as well as measured data. For each scenario, phase, amplitude, and the shape of the waveform were compared. Generally we found very good agreement between the different simulation techniques, and good agreement between experimental and simulated data. Differences that were evident highlight the significance of understanding how features such as antenna feeding and material dispersion are modelled. This degree of match between experimental and simulated data cannot be attained by using just an infinitesimal dipole model in a simulation - a model including the structure of the antenna is required. This is important for the many GPR applications which operate in the near-field of the antenna, where the interaction between the antenna, the ground, and targets is important.

Direct time domain modeling of the transient field transmitted in a dielectric half-space for GPR applications

The paper deals with the study of a transient electric field transmitted into the dielectric half-space by means of the time domain analysis method. The time domain formulation is based on the space-time Hallen integral equation. The numerical solution is carried out via the space-time scheme of the Galerkin-Bubnov variant of the Indirect Boundary Element Method (GB-IBEM). Once determining the current along the dipole antenna, it is possible to determine the field reflected from the interface and the field transmitted into lower medium by solving the corresponding field integrals. Some illustrative numerical results for the reflected/transmitted field are presented in the paper.

A Stochastic Analysis of the Transient Current Induced along the Thin Wire Scatterer Buried in a Lossy Medium

The paper deals with the stochastic collocation analysis of a time domain response of a straight thin wire scatterer buried in a lossy half-space. The wire is excited either by a plane wave transmitted through the air-ground interface or by an equivalent current source representing direct lightning strike pulse. Transient current induced at the center of the wire, governed by corresponding Pocklington integrodifferential equation, is determined analytically. This antenna configuration suffers from uncertainties in various parameters, such as ground properties, wire dimensions, and position. The statistical processing of the results yields additional information, thus enabling more accurate and efficient analysis of buried wire configurations.

Stochastic Collocation Analysis Of The Transient Current Induced Along The Wire Buried In A Lossy Medium

The paper deals with the stochastic collocation analysis of a time domain response of a straight thin wire scatterer buried in a lossy half-space. The wire is excited by a plane wave transmitted through the air-ground interface. Transient current induced at the centre of the wire, governed by corresponding Pocklington integro-differential equation is determined. This configuration, as is the case with many electromagnetic compatibility (EMC) issues, suffers from uncertainties in various parameters, such as ground properties, wire dimensions, position, etc. The obtained results yield additional statistical information thus enabling more accurate and efficient analysis of buried wire configurations.

Transient statistics from the lightning strike current flowing along grounding electrode

This paper aims to couple analytical solution of the Pocklington integro-differential equation with stochastic techniques for the statistics of transient current flowing along horizontal grounding electrode. The electrode is excited with a current source representing a lightning strike current. This problem, as it is the case for electromagnetic compatibility (EMC) issues, is governed by many uncertain parameters (lightning source profile and location, ground properties, electrode position and length, etc.). The proposed results yield additional statistical information which enable more accurate and efficient design of a grounding systems.

A simple antenna model of the human nerve

An antenna model of the human nerve has been proposed. The model is based on the Pocklington integro-differential equation for the coated straight wire immersed in a finitely conducting medium. The corresponding Pocklington equation is solved via the Galerkin-Bubnov Boundary Element Method (GB-IBEM). Some illustrative computational examples are presented throughout the paper.

Electromagnetic field coupling to buried wires: Comparison of frequency domain wire antenna and transmission line model

The paper deals with different frequency domain approaches for the analysis of electromagnetic field coupling to finite length buried wires based on the wire antenna theory, and the transmission line method (TLM). The wire antenna formulation deals with the corresponding Pocklington integro-differential equation, while the transmission line model uses the Telegraphers equations. The Pocklington equation is solved via the Galerkin-Bubnov scheme of the indirect boundary element method (GB-IBEM), while the transmission line equations are treated using the chain matrix method. Some illustrative numerical results for the frequency response of the buried conductor of finite length, obtained via different approaches, are presented in this paper.