Classical radiation theory

Electromagnetic boundary value problems that incorporate a source of, or a sink for, electromagnetic waves are examined in Chap. 3 by adopting the 'source-present' Maxwell equations. It is shown that the resultant inhomogeneous second-order vector differential equations can be solved by employing analogies with statics, and by borrowing the mathematical forms derived there, particularly those which relate static electric and magnetic fields to charge and current. This leads to the formulation of the retarded scalar electric, and vector magnetic, potentials, which are demonstrated to be solutions of the source-present Maxwell equations. The retarded potentials are applied to the classical 'short current element' or Hertzian dipole, which is a useful building block in the mathematical modelling of a range of antennas of the 'wire' or reflector type (see Chap. 4). It is shown that the fields surrounding the current element resolve into near-field and far-field forms. In the far-field k_or > 1, the solution is predominantly in the form of TEM waves radiating maximally in the plane bisecting the element and minimally in the axial directions. The pattern is 'dough-ring' shaped. The radiated energy density obeys the inverse square law, and in circuit terms, the power radiated can be represented by a radiation resistance. In the near field, components of E and H other than the radiated fields exist. These fields diminish very rapidly with distance from the source and are negligible for k_or> 1. They represent capacitive (electric dipole) and inductive stored energy, which means that in circuit terms, an antenna can present reactive impedance to the feed line. The significance of radiation pattern and radiation resistance to the collection of electromagnetic waves, when the antenna becomes a sink rather than a source, is also elaborated upon in the chapter. This, of course, is the essential problem represented by solar power collection, which is examined in Chaps. 7, 8, 9 and 10.