Physical Interpretation of Impedance Formulas for Conductors Enclosed in a Cylindrical Tunnel

Based on a comparison of earth models and conductor impedance equations, a physical interpretation of the self and mutual impedance for conductors enclosed in a cylindrical tunnel with peripherally infinite homogeneous earth is put forward. The inherent relations between Carson´s formulas and Tylavsky´s formulas are revealed through a rigorous mathematical justification. A new concept of complex radius, which is similar with the complex depth, is introduced to explain the simplified approximate impedance expressions.