Complex-Valued Transmission-Line Parameters and Their Relation to the Radiation Resistance

Extension of the Transmission Line Theory Application With Modified Enhanced Per-Unit-Length Parameters

“…parameters of a single transmission line (TL) which were first explicitly extracted from [6]. This modification was necessary since the enhanced parameters only enable to split the energy propagating on the TL into TEM and radiated modes.…”

“…Then, from [6] and using some Bessel functions properties, we can easily find: (4) Here J 0 and Y 0 are, respectively, the 0-order Bessel functions of first and second kind. Now, using the expansion form of Y 0 as given in [9]:…”

“…The classical approximation for this integral consists in assuming that all terms are negligible with respect to the first one on the right-hand side of (6). In the following these terms are considered as a correction factor.…”

“…parameters defined in [6] allow taking into account higher-order modes for uniform transmission lines using a rigorous derivation of the integral of the Green's function. However, these enhanced p.u.l.…”

“…Indeed, putting the complex p.u.l. parameters defined in [6] under a resistance, inductance, capacitance, conductance (RLCG) form leads only to the decomposition of the modes in terms of TEM modes supported by the real part of the characteristic impedance, and radiating modes (or antenna mode) supported by the imaginary part of the characteristic impedance. Therefore, in this paper, we will also present a modified version of these enhanced parameters that will converge to the solution of the differential currents at the ends of the TL.…”