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A Complete Multimode Equivalent-Circuit Theory for Electrical Design.

Dylan F Williams1, Leonard A Hayden1, Roger B Marks1

  • 1National Institute of Standards and Technology, Boulder, CO 80303.

Journal of Research of the National Institute of Standards and Technology
|January 1, 1997
PubMed
Summary
This summary is machine-generated.

This study introduces a comprehensive equivalent-circuit theory for lossy multimode transmission lines, simplifying complex electrical behavior. It provides new mathematical expressions for key transmission line parameters and noise characteristics.

Keywords:
conductor currentconductor representationconductor voltageelectromagnetic modesimpedance matrixmodal representationmulticonductor transmission line

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Area of Science:

  • Electrical Engineering
  • Electromagnetics
  • Circuit Theory

Background:

  • Multimode transmission lines are crucial in high-frequency applications.
  • Existing models often struggle to accurately represent lossy line behavior.
  • A unified theoretical framework is needed for advanced analysis.

Purpose of the Study:

  • To develop a complete equivalent-circuit theory for lossy multimode transmission lines.
  • To provide novel expressions for impedance matrices and source representations.
  • To incorporate thermal noise analysis for passive multiports.

Main Methods:

  • Formulating voltages and currents using linear combinations of normalized modal quantities.
  • Deriving new expressions for transmission line impedance matrices.
  • Developing representations for source conditions and thermal noise.

Main Results:

  • A complete equivalent-circuit theory for lossy multimode transmission lines.
  • New expressions for impedance matrices, symmetry, and lossless conditions.
  • Inclusion of source representations and thermal noise of passive multiports.

Conclusions:

  • The presented theory offers a unified and accurate method for analyzing lossy multimode transmission lines.
  • This framework facilitates the design and simulation of complex high-frequency circuits.
  • The new expressions enhance the understanding of noise in passive multiport networks.