Sergey Tkachenko

Coupling of Stochastic Electromagnetic Fields to a Transmission Line in a Reverberation Chamber

A new method for the numerical simulation of the stochastic electromagnetic environment of a mode-stirred chamber is presented in this paper. This method is based on the plane-wave integral representation for the fields and uses a Monte Carlo simulation to replace the analytical integration by numerical summation. Therefore, a field generator is implemented as a program. The numerically generated field distributions and spatial correlation functions are compared to the analytical solutions for the validation of the field generator. With this generator, the field coupling to a simple transmission-line structure can be numerically simulated. The coupled current or voltage has to be regarded as a stochastic value as well, and therefore, parameters like the mean value and the standard deviation along the line are calculated. For the special case of a matched line, an analytic solution is introduced in order to validate the numerical results. The simulation also allows for investigating the statistical distribution and correlation of the coupled current along the transmission line. Numerous simulated results are compared with measurements.

Generalized Form of Telegrapher's Equations for the Electromagnetic Field Coupling to Finite-Length Lines Above a Lossy Ground

In this paper, a generalized form of the Telegraphers equations for electromagnetic field coupling to finite-length transmission lines above a lossy ground is derived. The approach is fully based on the thin-wire antenna theory. The effect of a lossy half-space is taken into account by means of the reflection coefficient approximation. The conductor losses can also be taken into account via surface impedance per unit length. The resulting equations are handled numerically via the Galerkin--Bubnov indirect boundary element method. Numerical results are presented for induced current along the line, and compared with transmission line (TL) approximation, for the case of lossless conductor. It is shown that the TL approximation can result in a significant underestimation of the induced currents.

Complex-valued transmission-line parameters and their relation to the radiation resistance

In this paper, the telegrapher equations are extended to general modes and very high frequencies to include radiation effects. It is shown, that the new line parameters are gauge dependent. However, there is also a gauge-independent representation of these parameters. In this representation, the per-unit-length capacitance is not correlated with the radiation resistance, only the per-unit-length inductance (strictly speaking, the imaginary part of it) constitutes it. The generalization to multiconductor and to finite straight transmission lines is straightforward.

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).

On the Evaluation of Antenna-Mode Currents Along Transmission Lines

In this paper, we derive an integral equation describing the antenna-mode currents along a two-wire transmission line (TL). We show that when the cross-sectional dimensions of the line are electrically small, the integral equation reduces to a pair of TL-like equations with equivalent line parameters (inductance and capacitance). The derived equations make it possible to compute the antenna-mode currents using any traditional TL coupling code with appropriate parameters. The derived equations are tested against numerical results obtained using numerical electromagnetics code (NEC), and reasonably good agreement is found

Electromagnetic Field Coupling to a Thin Wire Located Symmetrically Inside a Rectangular Enclosure

This paper calculates the current in a conductor inside a cavity, which is induced by lumped and distributed sources. The current is obtained both analytically (Greens function method) and numerically (multilevel fast multipole method). A long parallel wire is chosen that connects two opposite walls of a rectangular resonator. Since the conductor preserves the translational symmetry of the resonator in one principal direction, the current and the total exciting electrical field can be derived from spatial Fourier series formulations. The obtained results clearly show the influence of the walls on the induced current. Resonance peaks of the resonator, which do not arise in normal electromagnetic compatibility laboratory tests, occurred in the current spectra. The numerical results agree very well with the analytical ones; however, the results are obtained much faster using the analytical formulae (by a factor of 1000).

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.

Transient Excitation of Rectangular Resonators Through Electrically Small Circular Holes

In this paper, analytical solutions of response functions for rectangular resonators are investigated in time domain. Emphasis is placed on the study of electromagnetic field coupling to a 3-D cavity through a small circular aperture. The time-dependent parts of the resulting modal Greens functions exhibit typical behavior that is inherent in all resonating/oscillating linear physical systems: namely, they fulfill oscillating ordinary differential equations at any point of the considered resonator. Their solutions contain transient and steady-state parts. The transient parts of the response functions will become important for electromagnetic compatibility tests in particular of modern digital high-speed electronics.

Time-Domain Generalized Telegrapher's Equations for the Electromagnetic Field Coupling to Finite Length Wires Above a Lossy Ground

In this paper, a time-domain variant of the generalized telegraphers equations for transient electromagnetic field coupling to a finite-length wire above a lossy half-space is derived. The approach is fully based on the thin-wire antenna theory. The lossy ground effects are taken into account by means of the reflection coefficient approximation. The obtained equations are handled numerically via the Galerkin-Bubnov indirect boundary element method. Computational examples are presented for the case of a single-wire line excited by an electromagnetic pulse excitation source. The obtained results for the induced current along the line are compared with those obtained using 1) the method of moments solution of the electric field integral equation implemented in the numerical electromagnetics code (NEC-4), and 2) the transmission line (TL) theory. It is shown that the results obtained by the proposed method are in excellent agreement with those of NEC-4. It is also shown that the TL approximation yields in general results which are in reasonably good agreement with the full-wave results, especially for the early time response and even beyond the limits of the accuracy of the TL theory. The TL theory can, however, give accurate results only for times before the arrival of the first reflection from the TL terminations and it fails to reproduce accurately the dispersion effects occurring after the first reflection.