TEM wave on a lossless coaxial cable with a homogeneous dielectric. Figure 9.2 shows...

TEM wave on a lossless coaxial cable with a homogeneous dielectric. Figure 9.2 shows a cross section of an infinitely long lossless coaxial cable carrying a TEM wave of angular frequency ω. With the z-axis of a cylindrical coordinate system adopted

along the cable axis, the complex rms voltage in the cross section of the cable defined by z = 0 is V ₀. From Eqs.(9.1) and (9.4), the cable voltage and current for an arbitrary coordinate z are

The distribution of the electric and magnetic fields in a cross section of the cable are as in electrostatics and magnetostatics, respectively, so we can write, based on Eqs.(9.3) and the field symmetries in Fig.9.2,

Referring to Fig.9.2, boundary conditions in Eqs.(6.19) give the following expressions for the surface charge and current densities on the conductor surfaces of the cable:

Finally, using Eqs.(6.32), (9.2), (6.33), and (6.31), the time-average Poynting vector (the complex Poynting vector is purely real), P, at an arbitrary location in the dielectric of the cable (Fig.9.2) and the total time-average power flow along the cable, P, come out to be

Implement in MATLAB Eqs.(9.6)–(9.9), and compute the values of all quantities considered in the analysis for the following numerical data: a = 1 cm, b = 3 cm, c = 3.5 cm, ε_r = 2.1, V₀ = 1 V,

Display the results in the Command Window

Reference: Equation (9.1) and (9.4), (9.3)