Método para a determinação de capacitâncias parasitas em sistemas eletromagnéticos

Abstract

This Doctoral Thesis presents a detailed study about stray capacitances in electromagnetic systems, with a special focus on inductors and transformer windings. The main objective of research is the development of a method for evaluating stray capacitances in multiconductor systems, more exactly self-capacitances and parasitic capacitors between turns. The proposed technique is based on the use of standard cells to be applied in a matching routine of turn, layer or macrolevel arrangements along the length of a coil. A standard cell is defined as a minimal and basic turn, layer or macrolevel arrangement that represents the main patterns of electrostatic energy stored on a multiconductor system. Therefore, standard cells enable the adequate calculation of the capacitive relations established in a multiconductor system, substantiated by the concept of an equivalent capacitive coupling matrix. The standard cell embraces mathematical rules for determining stray capacitances. These expressions are derived by means of a curve fitting approach through a set of Finite Element Analysis (FEA) simulations under the FEMM 4.2 (Finite Element Method Magnetics 4.2) environment and complementary computations on Mathematica 11.1.1.0. As a first step of this research process, a contextualization regarding the representation and estimation of parasitic capacitances is provided, together with an overview of analytical techniques currently available in the scientific literature and FEA simulations. As a second step, four inductor prototypes and their SPICE and EMTP-ATP (ElectroMagnetic Transients Program – Alternative Transients Program) implementations are verified. The equivalent circuits of the prototypes and the proposed technique are validated by comparing frequencyand time-domain (step transient response) characteristics, as well as the equivalent series impedance obtained from simulations and laboratory measurements. The proposed technique corroborates with other researches about medium- and high-frequency modeling of multiconductor systems. This technique also contributes with discussions about the electrostatic behavior of inductors through the concept of a capacitive coupling matrix. Based on standard cells, the proposed technique is feasible to be adapted for distinct turn, layer or macro level arrangements, provided that a pattern may be evaluated and replicated.