## Date of Award

12-2014

## Document Type

Dissertation

## Degree Name

Doctor of Philosophy (PhD)

## Legacy Department

Automotive Engineering

## Committee Chair/Advisor

Hubing, Todd

## Committee Member

Prucka , Robert

## Committee Member

Onori , Simona

## Committee Member

Pisu , Pierluigi

## Abstract

This dissertation describes three related studies regarding the imbalance difference theory in modeling the conversion between differential mode and common mode/antenna mode signals. The topics covered are: rigorous derivation of imbalance difference theory for modeling radiated emission problems, modeling the conversion between differential mode and common mode propagation in transmission lines, and modeling the loading impedance on differential mode signals due to radiated emissions. The imbalance difference theory describes a method for calculating the coupling between differential mode signals and common mode signals due to changes in electrical balance on a transmission line. It provides both physical insight and a simple technique for modeling the conversions between the two modes. The first chapter presents a rigorous derivation of imbalance difference theory for modeling radiated emission problems. Although the theory has been successfully used to model a wide variety of important EMC problems over the past, it has not been rigorously derived. The derivation carefully defines the important quantities and 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. This chapter also discusses the acquisition of the current division factor from 2D calculations of the cross-section of the transmission line. The second chapter provides a rigorous development of the imbalance difference theory for three-conductor transmission lines where both the differential mode and common mode exhibit TEM propagation. It also derives expressions for the mode conversion impedances, which account for the energy converted from one mode to the other. They are essential for modeling the conversion between the two modes when they are strongly coupled. The third chapter introduces conversion impedance to the existing imbalance difference theory model for modeling radiated emission problems, so that when the coupling between differential mode and antenna mode are strong, the imbalance difference theory can more accurately estimate the antenna mode current. All three papers are about confirming, enriching and expanding the imbalance difference theory. The first chapter focuses on the rigorous derivation of theory for its most common application, radiated emission problems. The second chapter expands the theory to multi-conductor transmission line structure when the two modes are strongly coupled. The last chapter introduces conversion impedance to the theory in modeling radiated emission problems and improves the accuracy of the model at resonant frequencies. This dissertation describes three related studies regarding the imbalance difference theory in modeling the conversion between differential mode and common mode/antenna mode signals. The topics covered are: rigorous derivation of imbalance difference theory for modeling radiated emission problems, modeling the conversion between differential mode and common mode propagation in transmission lines, and modeling the loading impedance on differential mode signals due to radiated emissions. The imbalance difference theory describes a method for calculating the coupling between differential mode signals and common mode signals due to changes in electrical balance on a transmission line. It provides both physical insight and a simple technique for modeling the conversions between the two modes. The first chapter presents a rigorous derivation of imbalance difference theory for modeling radiated emission problems. Although the theory has been successfully used to model a wide variety of important EMC problems over the past, it has not been rigorously derived. The derivation carefully defines the important quantities and 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. This chapter also discusses the acquisition of the current division factor from 2D calculations of the cross-section of the transmission line. The second chapter provides a rigorous development of the imbalance difference theory for three-conductor transmission lines where both the differential mode and common mode exhibit TEM propagation. It also derives expressions for the mode conversion impedances, which account for the energy converted from one mode to the other. They are essential for modeling the conversion between the two modes when they are strongly coupled. The third chapter introduces conversion impedance to the existing imbalance difference theory model for modeling radiated emission problems, so that when the coupling between differential mode and antenna mode are strong, the imbalance difference theory can more accurately estimate the antenna mode current. All three papers are about confirming, enriching and expanding the imbalance difference theory. The first chapter focuses on the rigorous derivation of theory for its most common application, radiated emission problems. The second chapter expands the theory to multi-conductor transmission line structure when the two modes are strongly coupled. The last chapter introduces conversion impedance to the theory in modeling radiated emission problems and improves the accuracy of the model at resonant frequencies.

## Recommended Citation

Niu, Li, "STUDIES OF IMBALANCE DIFFERENCE THEORY IN MODELING CONVERSION BETWEEN DIFFERENTIAL MODE AND COMMON MODE SIGNALS" (2014). *All Dissertations*. 1456.

https://open.clemson.edu/all_dissertations/1456

#### Included in

Electrical and Computer Engineering Commons, Operations Research, Systems Engineering and Industrial Engineering Commons