An Enhanced Transmission Line Model for Conducting Wires

The “standard” transmission line model describes accurately the propagation of electric signals along conducting wires, if the distance between them is much smaller than both their length and the smallest characteristic wavelength of the signals. This paper presents an “enhanced” transmission line model that is able to describe the propagation along perfectly conducting wires in a homogeneous dielectric, and also when the distance between the wires is comparable with the smallest characteristic wavelength of the signals. The enhanced model is obtained, with suitable approximations, starting from a full-wave analysis of the problem and using an integral formulation based on the electromagnetic potentials satisfying the Lorentz gauge. It differs from the standard transmission line model, only in its constitutive relations, that is, in the relation between the per unit length (p.u.l.) magnetic flux and the current intensity, and in the relation between the electric voltage and the p.u.l. electric charge. In the standard model, these relations are of the algebraic type, and in the enhanced one they are of the convolution type, expressing nothing more than a very simple physical fact: the values of the p.u.l. flux and voltage at the generic abscissa along the wires depend on the entire distribution of the current and the p.u.l. charge, respectively. The kernels of the convolution integrals have the logarithmic singularity typical of the surface distributions and takes into account proximity effects. The solution of the enhanced model highlights the high-frequency effects due to dispersion and radiation that the standard model is unable to provide. Good agreement with the solutions obtained by a full-wave electromagnetic numerical code is achieved.