TABLE OF CONTENTS Now the subject shifts to the mathematics of electric fields and waves. Maxwell's equations will be introduced and explained in enough detail to allow an introduction to tools that calculate fields. The fundamentals of one type of field solver will be explained as an example that introduces issues and requirements involved in choosing and using field solvers. An objective of this chapter is to help you recognize how and why field solvers differ and how they fit with various engineering requirements. When you were working at a few hundred megahertz, almost all the simulations you did could be done with nothing more than a good copy of SPICE. At microwave frequencies, you must to be able to run a field solver, too.
Since the mathematical derivations flow in that direction, they will be followed through the development of the wave equation, the telegrapher's equation, and then the reflection coefficient. By that point the topic diverges somewhat from fields and field solvers, but that's life.
In 1873, James Clerk Maxwell published a set of four equations that have since come to be known as Maxwell's equations. Later analysis has shown that the set can be reduced to two equations, the other two being redundant. I will approach fields from the perspective of Maxwell's two curl equations. One of the two is based on an equation known as Oersted's law, the mathematical formalization of the physical principle that every electric current is accompanied by a magnetic field. A mathematical formulation...
