Jürgen Nitsch

New propagation models for electromagnetic waves along uniform and nonuniform cables

This paper discusses the mathematical modeling of the propagation of electromagnetic energy along nonuniform transmission lines. This electromagnetic energy can either be transmitted signals or disturbances caused by electromagnetic interference. Emphasis is laid on the basic ideas behind the transmission-line super theory and the solution of the corresponding telegrapher equations. We show how to establish these telegrapher equations for nonuniform transmission lines and how to calculate the per-unit-length parameters. Afterwards we discuss several solution methods, like numerical integration techniques and semi-analytical approaches. With selected examples we demonstrate the application of our new tools.

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.

Statistical interpretation of autocorrelation coefficients for fields in mode-stirred chambers

The autocorrelation function of electrical field strengths for different boundary conditions (tuner positions) at a given special position is proposed in the IEC standard 61000-4-21 as a measure for the determination of the number of uncorrelated boundary conditions in mode-stirred chambers. Additionally, an upper limit for the autocorrelation coefficient is given for a fixed number N of measured tuner positions only. In this paper, we analyze an approach given in the literature that includes the treatment of different N, but still gives results that are inconsistent with the daily measurement practice in mode-stirred chambers. A slight modification of this approach is proposed that leads to consistent results. This paper gives critical values for the autocorrelation coefficients for any number of measured tuner positions based on a statistical analysis of the well known probability distribution of autocorrelation coefficients. The degree of determination and the significance level remain as free parameters that have to be established by the community. The authors propose values for these parameters that are consistent with the example given in the standard

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).

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.

High frequency electromagnetic field coupling to small antennas in rectangular resonator

The integral-differential equation for the current of an electrically small antenna inside a resonator, which is induced by given sources, is solved by the so-called “Method of Small Antenna”. The calculated input impedance of the antenna in the resonator and the calculated coefficients of the mutual coupling between two antennas are compared to experimental measurements, performed within the mode-stirred chamber at the University of Magdeburg. For low resonances, when the assumption of electrically small antennas is justified, a good agreement is found.

Application of the Transmission-Line Super Theory to Multiwire TEM-Waveguide Structures

Open TEM-waveguides are often realized by multiwire structures instead of conducting planes. Especially for large-scale nuclear electromagnetic pulse (NEMP) simulators the wire structure is common. In this paper, a generic open TEM-waveguide structure is analyzed using the transmission-line super theory (TLST). The concept of the numerical implementation is thoroughly described independent of a particular programming language. The TLST comprises full Maxwells equations assuring that higher order modes and radiation effects are included. Currents along the lines and the total radiated power outside the simulator are calculated. Inside the simulator the magnetic field is estimated in the working volume, and the result is verified by experiment. The presented theory is applicable not only to the described simulator structure but also to a variety of wire-based problems in electromagnetic compatibility.

High frequency model for the transfer impedance based on a generalized transmission-line theory

The transfer impedance and transfer admittance as the characterizing parameters of cables in an electromagnetic environment have been subject of intensive research in EMC. Usually the shields of those cables are composed of braided wires. Existing computational models for the transfer impedance are based on models of the braided shield itself. With the nonuniform transmission line theory it becomes possible to consider these shields as nonuniform multiconductor transmission lines, and to derive the transfer impedance and transfer admittance from the primary per-unit-length parameters of the cable. With this approach the local, location dependent per-unit-length transfer values can be obtained. This paper presents the first step towards such model for the transfer impedance.

Transmission-Line Super Theory as Antenna Theory for Linear Structures

A new generalized transmission-line theory is presented to treat multiconductor as well as antenna systems. Maxwell’s equations are cast into the form of classical telegrapher’s equations. Two quite different examples are calculated to illustrate the wide use of this theory.

High-Frequency Electromagnetic Field Coupling to Small Antennae in a Rectangular Resonator

The integral-differential equation for the current of an electrically small antenna inside a resonator, which is induced by given sources, is solved by the so-called “Method of Small Antenna”. The calculated input impedance of the antenna in the resonator and the calculated coefficients of the mutual coupling between two antennas are compared to experimental measurements, performed within the mode-stirred chamber at the University of Magdeburg. For low resonances, when the assumption of electrically small antennas is justified, a good agreement is found.