Printed circuit board (PCB) model using the thin-wire method to compute conducted EMI in power electronic systems

This paper describes a method for modelling the printed conductors employed in high-frequency (range 10 kHz-1 MHz), medium-power (several kW) static converters, in order to simulate their conducted interference emissions. The principle of this method is to divide the circuit's layout into elementary rectangles. These rectangles are then substituted by a bundle of thin cylindrical wires. Afterwards, it becomes possible to determine an electrical equivalent circuit for each bundle, which integrates inductive, capacitive and resistive effects. In the first section of this paper, the theoretical development, with respect to a single rectangular conductor, is presented. The printed conductor and the thin-wire bundle equivalence conditions are then specified in the second section, and the validity of this principle is experimentally verified. The third section is devoted to modelling the coupling phenomena between two printed conductors. Special attention has been paid to separating strong and negligible couplings, in order both to reduce the computing time and to extract equivalent circuits for a complex layout. Quantitative coupling criteria, based on geometrical and current quantities, are proposed; they establish the complexity of the equivalent circuits and thereby the simulation time. The paper's final section focuses on the experimental aspects of this research work. A chopper has been developed on a PCB. Experimental and theoretical results are also compared: the impedance curves of the entire circuit and the conducted emission spectrum of the converter are presented and discussed. The role played by the PCB in the conducted EMI is clearly revealed and allows the designer to optimise the printed circuit pattern.