Medium frequency transmission line (MF TL) communications
in circular cylindrical underground tunnels critically
depend on the soil return impedance. The soil impedance can
be approximately calculated using a very simple closed-form
expression based on an image method–the so-called Dubanton
approach. In this paper, we present an analytical exact method,
based on electromagnetic field analysis, using Bessel and Hankel
functions to correctly evaluate the soil impedance and the wave
propagation parameters (attenuation, phase velocity, and characteristic
impedance) that characterize the fundamental quasi-
TEM mode propagating along circular tunnels. By comparing
the computation results of both methods we have been able to
quantify the errors involved in the Dubanton approach. The
approximation developed by Wait is also used for verification
purposes.