Rigorous Derivation of Imbalance Difference Theory for Modeling Radiated Emission Problems

The imbalance difference theory provides both physical insight and a powerful technique for modeling the conversion from differential-mode signals to common-mode noise, especially for radiated emission problems. Although the theory has been successfully used to model a wide variety of important EMC problems over the past 14 years, it has not been rigorously derived. This paper provides a strict derivation of the theory and carefully defines the important quantities. The derivation demonstrates that imbalance difference calculations are exact provided that the differential-mode propagation is TEM and the current division factor, h, represents the actual ratio of currents on the two transmission line conductors excited by a common-mode source. The paper also discusses the acquisition of the current division factor from 2-D calculations of the cross section of the transmission line.