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This article is devoted to the analysis of multiconductor transmission lines (MTLs), a type of structure that is encountered in many applications concerning RF and microwave engineering. Our aim is to provide the reader with a self‐contained presentation of the subject; we start by establishing the time‐domain equations of multiconductor transmission‐line systems and then progress step by step to the final objective of determining the frequency‐domain solution to those equations. Matrix techniques are made intense‐use in order to permit a compact analysis of the problem. Solutions to MTL equations are presented in two different useful formats. At first we consider a solution in the form of a superposition of natural modes of propagation; later, a relationship between voltages and currents at the MTL structure ports is established by employing a transmission matrix. The analysis presented in this article is not limited to the simple case of uniform line structures, as it also encompasses the important problem of nonuniform MTLs.
This article is devoted to the analysis of multiconductor transmission lines (MTLs), a type of structure that is encountered in many applications concerning RF and microwave engineering. Our aim is to provide the reader with a self‐contained presentation of the subject; we start by establishing the time‐domain equations of multiconductor transmission‐line systems and then progress step by step to the final objective of determining the frequency‐domain solution to those equations. Matrix techniques are made intense‐use in order to permit a compact analysis of the problem. Solutions to MTL equations are presented in two different useful formats. At first we consider a solution in the form of a superposition of natural modes of propagation; later, a relationship between voltages and currents at the MTL structure ports is established by employing a transmission matrix. The analysis presented in this article is not limited to the simple case of uniform line structures, as it also encompasses the important problem of nonuniform MTLs.
This research and tutorial paper is the second part of a work dedicated to the analysis and computation of the electromagnetic behavior of inductor windings operating at high-frequency regimes-a critical issue for very fast transient overvoltage studies. The inductor winding, wound around a ferromagnetic core, containing a total number of N dielectric coated cylindrical turns, is modeled by using a multiconductor transmission line (MTL) approach (proximity effects being accounted) whose constitution and characterization was presented in a former paper. In the present work, we make use of the R, G, L, and C constitutive matrices of the structure in order to develop a modal analysis technique-based formulation aimed at the evaluation of the winding's input impedance in the frequency-domain. Results obtained show that the input impedance critically depends not only on the number of layers of the winding but also, and, more importantly, on the frequency, where resonance phenomena play a key role. Frequency-domain analysis is complemented with simulation results in the time-domain that clearly illustrate how critical and sensitive the system response can be under minute changes of the winding's excitation current. are different). In addition, in paper [3], the system partial capacitances are grouped into only three types C g , C k , and C s -this is a crude simplifying approximation, since, in general an N-turn winding is to be characterized by N(N+1)/2 partial capacitances.In a recent paper [4], we developed a new MTL model of an inductor winding that takes into account a multitude of effects, such as, conductor proximity, dielectric heterogeneities, capacitive and inductive coupling among all winding turns, dielectric and conductor losses, eddy currents in the core, etc. Our complete model [4] provides the user with frequency-dependent per-unit-length (PUL) constitutive matrices R, G, C, and L that are crucial to the development of modal analysis techniques on which MTL results rely.The reader is referred to (Figure 1 in Reference [4]) to recall the geometry of the actual inductor winding whose analysis we are going to develop-the winding, which is wound around a ferromagnetic core of radius r, consists of m layers, each layer comprising n turns; the total number of winding turns is N ¼ nm; each individual turn is a dielectric coated cylindrical conductor whose cross-section outer radius is R 0 , the radius of the internal conductor itself is r.The configuration of the MTL model adopted to represent the winding structure is shown in Figure 1. The model consists of N parallel conductors above a conducting plane-the ferromagnetic corewhich is taken as the reference conductor (0) of the MTL. The longitudinal length l of the structure is made equal to the average value of the perimeters of the turns, that is, l ¼ 2pðr þ mR 0 Þ. The total length of the winding is l w ¼ Nl.This paper is organized into five sections, the first of which is introductory. In Section 2, we present a review of the modal analysis matrix techniqu...
Coupled‐mode analysis of multiconductor microstrip lines, based on quasi‐TEM approximations, leads to a wave solution usually obtained by superposition of exponential elementary waves. This paper shows that critical situations exist where such simple exponential waves cannot describe the propagation phenomenon. Particular relationships among the quasistatic parameters of a two‐conductor asymmetrical microstrip line are obtained allowing the synthesis of a physically realizable critical situation where an anomalous wave solution is required.
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