Circuit Oriented Electromagnetic Modeling Using the PEEC Techniques

Chapter 3Maxwell's Equations

3.1 Maxwell's Equations for PEEC Solutions

One set of fundamental techniques necessary for partial element equivalent circuit (PEEC) models is the circuit techniques in Chapter 2. Furthermore, we require EM techniques that are based on Maxwell's equations presented in this chapter. We give a general overview of the different possible forms of Maxwell's equations and the resultant differential and integral equation formulations. Hopefully, this leads to the understanding of various appropriate solutions. In this chapter, we emphasize existing results and conclusions based on Maxwell's equations instead of derivations of the fundamentals on which they are based. Our aim is to provide essential tools for connecting lumped circuit analysis and electromagnetic modeling. We concentrate on solutions that have practical relevance for PEEC modeling. As an example, we can state that the type of problems we want to solve also requires a solution since such connections exist in these problems. Hence, it is important that our approaches include solutions. Hopefully, we include sufficient references for the reader who wants to study the origin of some of the concepts in more details.

3.1.1 Maxwell's Equations in the Differential Form

To start, we choose a general ...