A coaxial line consists of two concentric cylindrical conductors (see Figure 4.2), where Ri and Ro are the inner and outer radius, respectively. The two conductors are separated by a homogeneous dielectric material with a relative permittivity of εr. The voltage U between the inner and outer conductor corresponds to a radial electric field strength ER and the current I in the conductors produces a circulating magnetic field strength Hφ.
In the following sections we will derive the transmission line parameters of a coaxial line. The cylindrical symmetry of the problem allows a mathematically quite simple treatment using cylindrical coordinates. In our considerations we employ our knowledge of electromagnetic theory from Chapter 2 and the definitions from the transmission line theory in Chapter 3.
Let us consider a loss-less transmission line. We can calculate the characteristic impedance Z0 from the inductance per unit length L′, the material parameters εr and μr and the light speed in vacuum c0 (see Equation 3.69).
Technical transmission lines commonly use dielectric, non-magnetic materials. Hence, we set μ ...