April 15, 2014

Goubau (1950) analyzes the TM propogation wave for a coated wire configuration. To calculate the power extension radially of the wave in the external medium ρ > a2 , the calculation, which involves numerical solution of a transcendental equation, is performed initially assuming an ideal conductor (perfect conductivity) to determine the real propogation constant

there the axial power flow between radius ρ and infinity, normalized to total current squared in the wire cross section is:

where β

The fraction of the total external power flowing axially between the outside of the coating layer and an external radius

(Note: Pz(ρ) above is the time-averaged power which contains an extra factor of 1/2 compared to Goubau's result).

A calculator can be used to solve for the TM mode and calculate the power extension.

The graph below shows the dependence of

**Electromagnetic Theory**, J. Stratton, 1941, McGraw Hill, pp. 524-536, 546-554

**Surface Waves and Their Application to Transmission Lines**, G. Goubau, J. Appl. Phys, V21, 1950, p.1119

**Electrodynamics**, A. Sommerfeld, Lectures on Theoretical Physics, 1952, VIII Academic Press, pp 177-185

**Field Theory of Guided Waves**, R. E. Collin, 1991, IEEE Press, pp.697-700, 718-720