The hybrid boundary element method, based on the equivalent electrodes method and the boundary element method, is presented in this article. This method is applied on several examples for calculating the characteristic impedance of transmission lines. It should be emphasized that the combination of the equivalent electrodes method and a new variant of the boundary element method can be efficiently implemented in quasi-transverse electromagnetic analysis of transmission lines without loss of accuracy. All results for the characteristic impedance of the observed transmission lines are compared to corresponding ones obtained by the finite-element method.
The hybrid boundary element method is applied for the calculation of the characteristic impedance of 2D microstrip lines with a finite width dielectric layer and with finite width or infinite ground planes. Even though these forms of microstrips are very typical in practice, they have not been investigated very often. The basic idea of this method is that an arbitrary shaped electrode can be replaced by equivalent electrodes, and an arbitrary shaped boundary surface between any two dielectric layers can be replaced by discrete equivalent total line charges placed in the air. The discretization technique is similar to the method of moments and is well known. As a contribution to the boundary element method, we combine it with the equivalent electrodes method, creating in that way a new hybrid boundary element method. This method could be applied to a large variety of very complex 2D problems, regarding microstrip lines with or without symmetry. The quasi TEM analysis is applied. We compare values of characteristic impedance obtained applying our method with the corresponding ones obtained by the finite element method and values already reported in the literature. Relative error less than 0.5%, fast convergence of the results and several times shorter computation time comparing to the time required by finite element method make our method very efficient in the calculation of parameters of 2D microstrip lines.
Characteristic parameters of a covered microstrip line with ground planes of finite width are determined using hybrid boundary element method (HBEM). This method, developed at the Faculty of Electronic Engineering of Niš is based on the combination of equivalent electrodes method (EEM) and boundary element method (BEM). Results for the characteristic impedance of the observed microstrip line are compared with the corresponding ones obtained by the finite element method.
In a lot of countries and regions there are requirements regarding electromagnetic emissions from electrical equipment. Such emissions can be looked at under two aspects: the emissions might interfere with other equipment in the vicinity causing potential malfunction (EMC aspect), or might be considered with regard to human exposure (EMF aspect). Limitation of such emissions related to the EMC aspect is part of EMC activities and is mostly due to the need to protect radio services from being interfered. Applicable limits depend on the type of equipment under concern and of the locations where equipment is intended to be operated. However, more and more such emissions are looked at also under a human exposure point of view within the frame of EMF regulations. As both aspects deal with entirely different objective targets consequently different limits, different measurement procedures and different assessment methods are to be applied. This could mean in practice that basically two kinds of measurements have to be carried out. This paper introduces an approach how to use results obtained by means of EMC measurements for the purpose of EMF assessments. As an example for an assessment the EMC data in the frequency range between 30 MHz and 230 MHz are used as part of an EMF assessment.
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