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1752 results in Circuits and systems

Page 41 of 88

  • 14 - Multiconductor TEM transmission lines

  • Dante C. Youla
  • Book:
    Theory and Synthesis of Linear Passive Time-Invariant Networks
    Published online:
    05 November 2015
    Print publication:
    05 November 2015, pp 481-524

  • Summary

    Introduction

    The validity of lumped circuit analysis hinges critically on the assumption that all electrical signals, such as voltage and current, although time-dependent, do not vary continuously with position. Such will indeed be the case if the physical size of any component in the network is much less than the wavelength of the excitation produced in the component by external sources. In the microwave band, however, frequencies range from 1 to 10 GHz and corresponding wavelengths vary from 0.3 to 0.03 meters. It is often impossible, or prohibitively expensive to accurately design discrete components whose dimensions are negligibly small compared with 3 centimeters. Our study of the 1-dimensional TEM line with the aid of field theory will reveal that low-frequency techniques are sometimes applicable, in the small.

    Analytical formulation

    A transverse electromagnetic or TEM wave is one in which the electric and magnetic field vectors lie in a plane perpendicular to the direction of propagation (which we shall assume to be along the longitudinal z-axis). This is the principal type of wave supported by the structures in Figs. 14.1 (a, b, and c) formed by embedding n + 1 parallel ideal cylindrical conductors in a homogeneous isotropic dielectric. Naturally, even excellent conductors such as gold and platinum are not perfect and have finite conductivities σ(ω). And, of course, neither are they infinitely long. This combination of loss and end-effects inevitably leads to the appearance of longitudinal field components and propagation is not truly TEM. Nevertheless, these z-components attenuate very rapidly as they progress into the interior of such metals and in general contribute negligibly to the field in the bulk of the dielectric.

Theory and Synthesis of Linear Passive Time-Invariant Networks
  • Dante C. Youla
  • Published online:
    05 November 2015
    Print publication:
    05 November 2015
  • Exploring the overlap of mathematics and engineering network synthesis, this book presents a rigorous treatment of the key principles underpinning linear lumped passive time-invariant networks. Based around a series of lectures given by the author, this thoughtfully written book draws on his wide experience in the field, carefully revealing the essential mathematical structure of network synthesis problems. Topics covered include passive n-ports, broadband matching, the design of passive multiplexes and two-state passive devices. It also includes material not usually found in existing texts, such as the theoretical behavior of transverse electromagnetic (TEM) coupled transmission lines. Introducing fundamental principles in a formal theorem-proof style, illustrated by worked examples, this book is an invaluable resource for graduate students studying linear networks and circuit design, academic researchers, and professional circuit engineers.

Page 41 of 88