Mathias Magdowski

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%.

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.

Corrections to “Boundary Fields in Reverberation Chambers” [May 05 281-290]

In the above paper, the plane-wave integral representation for well-stirred fields in reverberation chambers was extended to apply near the chamber walls. Several analytical terms for the mean of squared field magnitudes were derived. The formulas are inaccurate for describing the conditions near the chamber walls and need to be corrected, since they lead to non-physical negative values for the mean of squared magnitudes for small input values kx, ky, or kz.

Modeling the skin effect in the time domain for the simulation of circuit interconnects

The skin effect is characterized by a reduction of a conductors effective cross-sectional area and is of great importance for the losses in electrical interconnection systems. Many well-known solutions exist for its modeling in the frequency domain. Based on the method of full spectrum convolution macromodeling a new skin-effect model is developed for an efficient numerical time-domain analysis. The integration of this model into the transmission line model and into the PEEC model is studied in two examples. Thereby the influence of skin effect on the simulation of interconnection systems with transient current and voltage responses is investigated.

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.

Efficient analytical calculation of the plane wave coupling to uniform transmission lines with arbitrary load resistances in time domain

An efficient calculation scheme for the plane wave coupling to a lossless and uniform transmission line in time domain is presented. The method is based on closed-form formulas and a finite sum. It is applicable for a single-wire transmission line above a perfectly conducting ground plane as well as for a double-wire line in free space. The line can be terminated with arbitrary linear load resistances. The exciting plane wave can be described by any time function that must be integrable. In comparison with a solution in the frequency domain and a subsequent inverse Fourier transform, the presented method is much faster, more exact and very comprehensible.

High frequency electromagnetic field coupling to small antennas in a cylindrical resonator

In this paper we outline our researches of high-frequency electromagnetic field-coupling to small antennas in cylindrical cavities. This problem has many practical applications in EMC, e.g., for airplanes, etc.

Transient simulation of the low-frequency and high-frequency behavior of asynchronous machines in SPICE

The aim of this investigation is the model-based description of an asynchronous motor by a general equivalent circuit that can be used in SPICE. The model incorporates the dynamic behavior of the motor including possible mechanical loads and the high-frequency behavior at the connecting terminals. The parametrization is explained and some comparative measurements with a real motor are presented and discussed. The presented method allows simulating an entire drivetrain of an electric or hybrid vehicle, which consists of a traction battery, an inverter and at least one electrical machine, including electromagnetic compatibility phenomena like fast transients of the stator current.