Design Optimization of a Current Sensing Trace with respect to Skin Effect by FEM Simulations

Abstract

We have developed a new current sensing method, CSRTRI (Current Sensing by Real-Time Resistance Identification), the feasibility of which was demonstrated in [1], where we reported an achieved accuracy of 0.93%...1.10% and a bandwidth of DC…2 MHz. The working principle is based on the in-situ determination of the current-conducting element's temperature dependent, thus continuously changing resistance with the utilization of an auxiliary inductive sensor signal. The resistance identification takes place at AC, typically at the fundamental PWM-frequency, while the calculated value is applied over the whole current signal spectrum. Therefore, it is a prerequisite of the feasibility of the CSRTRI, that the resistance's frequency-dependence is negligible, from DC up to the first couple of ripple-frequency harmonics. In this paper we investigate this frequency dependence for two design variants: first, that of a single Cu-trace with rectangular cross-section, second an antiparallel low-inductance trace-pair. We conducted AC-magnetics FEM-simulations to assess the influence of the skin-effect on the current trace's resistance. Based on the simulation results presented herein, the antiparallel variant's resistance increase over the DC-30 kHz frequency range is as low as 0.1%, which is acceptable, considering the 2 kHz applied fundamental frequency. The single trace, on the other hand, is prone to a 4.28% resistance rise over the same frequency range, implying that it would have been clearly an unacceptable solution. The prototype sensor system including the optimized low-inductance antiparallel trace, as well as the auxiliary coil, the test setup and measurement results detailed in [1] were also summarized.