Ralf Vick

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.

Closed-Form Formulas for the Stochastic Electromagnetic Field Coupling to a Transmission Line With Arbitrary Loads

A simple model of intrinsic stochastic electromagnetic fields and a simple transmission line model are combined to analytically derive closed-form expressions for the average field coupling to a transmission line. The results are valid under the assumptions of transmission line theory for a line with general load resistances. The theoretical analysis starts with the calculation of the mean squared current magnitude along the line and at the ends. This result is transferred to the coupled voltage. Then, the characteristics of the statistic distribution can be used to calculate other important parameters like the variance or the maximum value.

Estimation of the Mathematical Parameters of Double-Exponential Pulses Using the Nelder–Mead Algorithm

Transient pulses for electromagnetic compatibility problems, such as the high-altitude electromagnetic pulse and ultrawideband pulses, are often described by a double-exponential pulse. Such a pulse shape is specified physically by the three characteristic parameters rise time tr, pulsewidth tfwhm (full-width at half-maximum), and maximum amplitude Emax. The mathematical description is a double-exponential function with the parameters α, β, and E0. In practice, it is often necessary to transform the two groups of parameters into each other. This paper shows a novel relationship between the physical parameters tr and tfwhm on the one hand and the mathematical parameters α and β on the other. It is shown that the least-squares method in combination with the Nelder-Mead simplex algorithm is appropriate to determine an approximate closed-form formula between these parameters. Therefore, the extensive analysis of double-exponential pulses is possible in a considerably shorter computation time. The overall approximation error is less than 3.8%.

Electromagnetic compatibility for device design and system integration

Motivation and Overview.- Thinking in Voltages, Currents, Fields and Impedances.- Electric Fields.- Magnetic Fields.- Electromagnetic Fields.- The Interference Model.- Intrasystem Measures.- Atmospheric Noise, Electromagnetic Environment and Limit Values.- EMC Engineering and Analysis.- Numerical Techniques for Field Calculation.- Model for Immunity Testing.- Electric Fields of Rod Arrangements.- Magnetic Stray Fields.- Self and Mutual Inductances.- Elementary Dipoles.- The Polarization Ellipsis.- Skin Effect and Shielding Theory of Schelkunoff.- Example of an EMC-Design Guide for Systems.- 25 EMC-Rules for the PCB-Layout and the Device Construction.- Easy-to-use Procedure for Predicting the Cable Transfer Impedance.- Capacitances and Inductances of Common Interest.- Reports of Electromagnetic Incompatibilities.- Solutions to the Exercises.- Physical Constants and Conversion Relations.

Modeling and testing of immunity of computerized equipment to fast electrical transients

One of the major problems associated with testing computerized equipment for immunity stems from the fact that their susceptibility to electrical transients is time-variant. This paper develops an improved statistical model for the susceptibility of computerized equipment to electrical transients and illustrates a few affordable methods for estimating the mean and maximum malfunction probability in an operational cycle. Reinforcement learning algorithms are used to estimate the maximum susceptibility efficiently. These algorithms automatically restrict testing to the most susceptible time windows. This allows affordable testing for safety-related equipment and also supports effective redesign.

Simulation of the stochastic electromagnetic field coupling to an unshielded twisted pair of wires

The twisting of signal pairs in cables is among shielding a typical countermeasure against the coupling of external fields into transmission lines. For the simulation a twisted pair can be modeled as a bifilar helix and the incident field can be approximated by a plane wave. With these simplifications the field-to-wire coupling can be calculated analytically. This method, which is based on classical transmission line theory, is known from the literature and is validated against a numerical simulation using the method of moments. In a next step the analytical method is used to calculate the coupling of stochastic electromagnetic fields into a twisted pair cable. Therefore the incident field is modeled by a superposition of plane waves. As a result also the coupled current becomes a stochastic quantity, whose statistical properties and dependencies are analyzed.

Singularity expansion method (SEM) for long terminated transmission lines

This paper deals with the calculation of first layer SEM poles of a long loaded transmission line above conducting ground excited by high frequency electromagnetic fields. This set of poles yields the main contribution to the susceptibility of the transmission line to the pulse excitations. For the case of an open-circuit wire, SEM poles are obtained in explicit form. The comparison of the results of this SEM approach with those of a numerical simulation gives a good agreement.

HF coupling to a transmission line inside a rectangular cavity

The coupling of high-frequency electromagnetic fields with thin wire structures - transmission lines and antennas - inside a resonator is considered. For the analytical solution of the EFIE we used the method of analytical regularization, hybrid representation of the resonator Greens function, and transmission-line approximation.

High-Frequency Electromagnetic Field Coupling to a Long, Finite Wire With Vertical Risers Above Ground

The main goal of this paper is the analytic approximation of the singularity expansion method poles of a long finite wire with vertical risers above a perfectly conducting ground. For wavelengths in the same order of magnitude or smaller than the height of the wire above the ground, the classical transmission-line theory is not valid. Therefore, an asymptotic approach is used to approximate the current on the thin wire, which is expressed in terms of current reflection and scattering coefficients. The perturbation theory is used for their analytic calculation. The complex current is analytically approximated and compared to a numerical simulation for illustration purposes. A very good agreement between the analytic approximations and the numerical ones from literature and simulations is observed.

Numerical simulation of the stochastic electromagnetic field coupling to transmission line networks

Based on transmission line theory a closed-form solution for the terminal currents of an arbitrarily oriented single-wire transmission line above a perfectly conducting ground plane is presented. The line is excited by a single plane wave. The result is generalized for transmission line networks of single-wire lines above a ground plane in form of the BLT equation and validated against the method of moments. Using a plane wave representation the coupling of stochastic electromagnetic fields to an exemplary network of three lines is simulated numerically. Different configurations of the network are analyzed and the average squared magnitude of the coupled current at the terminals is calculated and discussed.