Maxwell’s Equations are eloquently simple yet excruciatingly complex.
Solving Maxwell’s Equations for real life situations, like predicting the RF emissions from a cell tower, requires more mathematical horsepower than any individual mind can muster.
Like so many of us, Jason Cole was fed up with the spotty internet in his apartment. A PhD student studying physics at Imperial College London, Cole used his mathematical expertise to determine the ideal l... Read More...
The Method of Moments has become one of the most powerful tools in the RF engineer’s arsenal. In this chapter, we make the transition from theory to practice, first by attempting to compute the characteristics of a “short dipole” by hand, and then by demonstrating that a computer can do that in just a few seconds.
It is time to put these equations to work by computing the radiation from a simple structure, a short wire element.
In the preceding chapters we have derived Maxwell’s Equations and expressed them in their “integral” and “differential” form. In different ways, both forms lend themselves to a certain intuitive understanding of the nature of electromagnetic fields and waves. In this installment, we will express Maxwell’s Equations in their “computational form,” a form that allows our computers to do the work.
In Chapter 2, I introduced Maxwell’s Equations in their “integral form.” Simple in concept, the integral form can be devilishly difficult to work with. To overcome that, scientists and engineers have evolved a number of different ways to look at the problem, including this, the “differential form of the Equations.” The differential form makes use of vector operations.
In Chapter I, I introduced Maxwell’s Equations for the static case, that is, where charges in free space are fixed, and only direct current flows in conductors. In this chapter, I’ll make the modifications to Maxwell’s Equations necessary to encompass the “dynamic” case, that is where magnetic and electric fields are changing. Then I will try to explain why things radiate.
Maxwell’s Equations are eloquently simple yet excruciatingly complex. Their first statement by James Clerk Maxwell in 1864 heralded the beginning of the age of radio and, one could argue, the age of modern electronics as well. Maxwell pulled back the curtain on one of the fundamental secrets of the universe. These equations just don’t give the scientist or engineer insight, they are literally the answer to everything RF.