In the previous chapter, we started with an infinitesimal, z-directed, constant current1 to derive the vector potential. From there we generalized the vector potential by allowing an arbitrary orientation and the current to be distributed over a source volume. For deriving the dipole radiation pattern, we will start again with the infinitesimal, z-directed, constant current. From there, we will lengthen the dipole, include a feeding point and from an assessment of the current distribution calculate the radiation pattern. As well as the radiation pattern, from a system point of view, we also want to know the input impedance. Since the derivation of the input impedance is beyond the scope of this book, we will summarize a few approximate equations for this parameter.
5.1 Elementary Dipole
The starting point of the dipole antenna discussion will be the elementary or Hertz dipole. This elementary dipole is (here) a z-directed current with constant amplitude I0 over infinitesimal length l, see Figure 5.1(a), that we also used to start the discussion of the vector potential and radiation fields, see Figure 4.1.
Before we proceed, ...