Heinz-D. Bruns

State of the art in the method of moments

This article presents new developments in the method of moments (MOM). IT describes some variants of this method which deal with general bodies composed of metallic and dielectric structures. Some procedures are presented which combine the method of moments with analytical methods in order to solve additional problem classes in the area of EMC. Two of these approaches are able to analyse the shielding effectiveness (SE) of electromagnetic shields consisting of nonperfectly conductive materials. Both procedures can be implemented by the method of moments. Two other techniques, which are outlined, are able to treat the induction in lines close to metallic surfaces and to analyse the voltages coupled into cables.

Validation of a flexible causality treatment for transient analysis of nonlinearly loaded structures

In this paper we study the transient analysis of distributed three dimensional structures loaded by lumped elements. Emphasis is put on the combined electromagnetic (EM)/circuit simulation by making use of band-limited frequency responses. First passive structures are investigated within the spectrum of interest, either by simulation or measurements. Then, causal impulse responses are extracted from the truncated spectrum. For the causality correction, we present a flexible treatment by using exponential functions for the spectrum extrapolation. Finally, the approach is verified by incorporating the causal impulse responses into an EM/circuit simulation. Single and multiple nonlinearly loaded examples are analyzed by means of a time marching procedure based on the causal convolution approach. The results show a good agreement with measurements and the results provided by commercial simulators.

A Measurement Setup for Quantification of Electromagnetic Interference in Metallic Casings

In this paper, a test setup is proposed for quantification of electromagnetic interference (EMI) in an enclosure of digital systems. Small probes at the casing walls are used to measure the internal fields and derive network parameters for the typical coupling between internal components. It is shown that the setup is viable for estimating EMI between enclosed components in a frequency range from 10 MHz to 6 GHz. Measurement results from the proposed setup are in excellent agreement with those of analytical and numerical methods. A statistical approach is introduced to evaluate the measurement results from a twelve-port vector network analyzer at high frequencies above the first resonance. Using this approach, typical components in digital systems are analyzed and simplified geometrical models are given. These models allow full-wave simulations of realistic setups with feasible computation times. A good model-to-hardware correlation between simulation and measurement results over the whole frequency range is achieved. It is demonstrated that the proposed measurement and evaluation approach of the fabricated cavity shows the same characteristic behavior of a real office workstation with internal components.

Fast Evaluation of Electromagnetic Fields Using a Parallelized Adaptive Cross Approximation

This communication shows a novel application of the adaptive cross approximation (ACA). A hierarchical ACA is presented for accelerating the evaluation of electromagnetic fields from a known current distribution, as it is required in the post-processing stage of the method of moments. Furthermore, a parallelization which employs a master-worker scheme is outlined, resulting in a highly efficient parallel code. Numerical examples validate the accuracy and efficiency of the method for various electromagnetic problems such as field coupling and radiation problems. It is demonstrated that the proposed approach is applicable in a broad frequency range, where it provides a definable error bound. Moreover, an acceleration factor of more than 200 is achievable, making an extensive field analysis of electrically large objects feasible.

Analysis of High Intensity Radiated Field Coupling into Aircraft Using the Method of Moments

In this paper, electromagnetic effects arising from high intensity radiated fields (HIRF) within realistic aircraft structures are investigated using the method of moments (MoM) and experimental tests. This study focuses on simulation-to-measurement correlation, where two potential error sources are investigated: Accuracy of the numerical techniques and the generation of numerical models. It is shown that the conventional mixed potential electric field integral equation may lead to inaccurate results regarding the field penetration through apertures. An alternative integral equation is introduced which splits the computational domain into an interior and an exterior domain, improving the results for aperture problems. To analyze the accuracy and the range of applicability for these integral equations, a generic aircraft structure is investigated, both numerically and experimentally. Thereby, various modeling aspects required for a meaningful simulation of aircraft are discussed. Following these observations, a real aircraft is analyzed in a broad frequency range from 10 kHz to 1 GHz. It is demonstrated that accurate numerical techniques are as important as modeling and appropriate simplification of the considered structures.

Advanced method of moments based on iterative equation system solvers

The treatment of field and scattering problems by means of method of moments (MoM) produces a system of linear equations which has to be solved. For large-scale structures the numerical effort for an LU decomposition of the system matrix becomes unacceptable. Iterative solvers can be an alternative but they often require a sophisticated preconditioner. A simple but powerful preconditioner can be derived from the physical meaning of the blocks in the impedance matrix and is applicable to a wide range of EMC problems. Using iterative methods can also be of significant advantage in another class of problems.

An extension of Schelkunoff's shielding theory to anisotropic conducting multilayer materials

A wave matrix formulation that describes the coupling through a planar shield of several anisotropic conducting layers is presented in detail. The approach includes all multiple reflections inside the different layers of the shield. The resulting wave matrix can be used to calculate the shielding effectiveness of the shield. As a result it is demonstrated that for specific cases the shielding effectiveness of an anisotropic multilayered shield can be approximated by the shielding effectiveness of an isotropic shield. In addition a finite structure is simulated and it is shown that the method for the infinite structure allows to correctly predict the transition from isotropic to anisotropic shielding effectiveness with respect to frequency.

Applicability of the thin sheet approximation to the analysis of EM emission from coated PCBs

This paper discusses the application of the so-called thin sheet approximation (TSA) for dielectric coatings to the calculation of the 3D coupling of printed circuit boards (PCBs) using the method of moments (MoM). By extending the TSA to open structures, the volume currents in the dielectric layer can be described by surface currents on the PEC conductor and the problem can be reduced to single current layers. As a consequence, the number of unknowns is reduced drastically. In order to verify the TSA approach and its accuracy and to investigate the influence of the layer and conductor thickness of coated PCBs, comparisons to results obtained by the classical MoM computation and a finite element (FEM) solver are given.

Analytical calculation of conduction and displacement current contributions in PCB return current paths

This paper studies the distribution of via return currents in printed circuit boards and packages. Generally, each return current splits into a conduction current through the ground vias of the structure and a displacement current between the reference planes. An analytical method for the calculation of both conduction and displacement current is described together with an equivalent circuit. The application of the calculation method to simple test structures illustrates the fundamental behavior of the return current. In certain frequency ranges, the magnitude of the displacement current in the return path can become considerably larger than the original signal current. The increase of the displacement current is of interest since it may cause e.g. signal integrity problems.

Application of a Hierarchical SVD/ACA Compression Technique to Near-Field Calculations of Monopole Antennas

This paper describes the concept of hierarchical matrices and the application to near-field calculations of voltage or power driven antennas. The hierarchical matrix structure is based upon a binary partition of the structure to be analyzed, where blocks of the matrix can be represented as full matrices or R(k)-matrices, the latter yielding a data reduced representation of the initial block. It has been found that application of only the ACA (adaptive cross-approximation) matrix reduction technique gave bad results in many practical 3D cases and failed to predict the physical current distribution. Way out of this dilemma is to combine ACA with SVD (singular value decomposition), yielding reliable results again. The new compression scheme turns out to be efficient and stable and will be described in detail. By means of examples the validity of the approach is demonstrated, where especially near-field investigations are carried out.