Influence of Asymmetric Three-Phase Cable Cross-Sections on Conducted Emission Measurements

This work presents a frequency-domain and modal-domain model to analyze how the length of a three-phase power cable influences conducted emission (CE) voltages measured through a line impedance stabilization network (LISN). The measurement setup considered consists of an equipment under test (EUT) connected to the LISN via a power cable whose cross-section is defined in this study as quadrilateral, namely, four conductors arranged at the corners of a quadrilateral: typically the three phases and the protective earth or neutral conductor. The cable is modeled as a multiconductor transmission line (MTL). To evaluate the system performance both with and without the cable, the concept of voltage insertion ratio (IR) is introduced, defined as the reciprocal of the typical insertion loss. Closed-form expressions are derived for both common mode (CM) and differential mode (DM) emissions. The objective is twofold: to understand under which conditions the LISN measurements overestimate or underestimate the actual emissions at the EUT terminals, and to provide a predictive tool to assess the impact of electrically long cables on CE measurements. The model is validated through numerical simulations of quadrilateral cable configurations considering both a homogeneous and inhomogeneous cross-section, highlighting the need to account for cable length in system design and EMC test interpretation.