Abstract
Increasing attention has been paid to the study of electromagnetic (EM) phenomena in complicated wire networks [e.g., metamaterials and EM compatibility (EMC)]. However, their lack of physical insights usually prevents systematic analysis of the phenomena. To address this, this article describes a transmission line (TL) model of a finite-length single conductor without a return current path to be applied as a fundamental physical model. The model includes radiation effects in a self-consistent way (i.e., its radiation reaction is included in an explicit way), and it is based on Sommerfeld principal wave propagation (strictly speaking, its behavior is asymptotic as the wire's conductivity approaches infinity). This formulation naturally leads to the consequence that the current flowing along a single conductor illuminated by an incident EM field is classified into three components, which are dominated by physically distinct principles, the principal wave itself (I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">tr</sub> , the traveling wave), the one reinduced by the traveling wave radiation (I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">re</sub> , the radiation reaction), and the one that directly scatters the incident field (I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sc</sub> , the scattering wave). The EM energies of the traveling wave and radiation reaction components are stored in the TL and propagate, while the scattering component indicates an instantaneous scattering process. These components reveal the dynamical characteristics of a single-conductor TL model that includes radiation phenomena.
Highlights
C LASSICAL transmission line (TL) theory [1], [2] addresses the transmission of electromagnetic (EM) waves with specific modes that are characterized by the transverse shape and dimensions of the guiding structure
A single-conductor TL model was developed by deriving a homogeneous TL equation for an infinite single conductor, the solution to which corresponds to the Sommerfeld principal wave
Based on the application of classical EM field scattering theory, the effect of the external field is included in the inhomogeneous term of the TL equation
Summary
C LASSICAL transmission line (TL) theory [1], [2] addresses the transmission of electromagnetic (EM) waves with specific modes that are characterized by the transverse shape and dimensions of the guiding structure. The governing equations of the generalized TL methods [3], [6] strictly follow the full-wave solution to Maxwell’s equations with certain structural assumptions, they have difficulty in providing satisfactory explanations for consistent causality pertaining to radiation losses in the framework of TL theory (i.e., how radiation occurs, in what dynamical ways it contributes to losses, and how it is different from the ohmic losses) This is the case for the methods presented in [23]–[25], which derive TL equations for a single conductor or the common-mode in multiconductor lines. They consistently explain the dynamics of a single-conductor TL, including radiation, allowing the model to be applicable to the design of EM phenomena around wiring structures with bends and branches
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More From: IEEE Transactions on Electromagnetic Compatibility
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