Wave propagation in a high frequency region, f_e < f < f_s, shows transition between TEM and TE or TM modes in calculated results by the TL approach and by the numerical electromagnetic code NEC in a frequency domain. FDTD method confirms the transition is from TEM to TM mode. In a frequency lower than the critical frequency f_c, the wave propagation is dominated by the earth-return path, and it is called “earth-return wave propagation”. In a frequency higher than the frequency f_c, so-called “surface wave” (TM mode) propagation or Sommerfeld-Goubau propagation, which is determined by the conductor internal impedance, is completed. The phenomenon was pointed out by Kikuchi in 1950s.

In a high frequency region, f > f_s, where the surface wave is completed, the earth-return impedance has minor contribution to the wave propagation. Thus, the earth-return impedance can be approximately neglected in the TL approach in this frequency region.

A numerical electromagnetic analysis method such as NEC can give, in general, a more accurate result than a conventional TL theory approach. However, the accuracy of NEC depends on the mesh size and terminating conditions which may result in numerical instability. On the contrary, the TL approach is more stable but it is applicable only to a limited frequency range.

A TL approach with Wise's earth-return admittance and the accurate earth-return impedance together with the conductor internal impedance can deal with wave propagation from a low frequency in the power engineering field to a high frequency in the communication engineering field including mode transition and Sommerfeld-Goubau propagation as predicted by Kikuchi. The TL approach is expected to be effective to study electromagnetic noises in a very high frequency region produced by transmission/distribution lines and gas-insulated substations.