Jeong, Jaehoon (2006-12). Analytical time domain electromagnetic field propagators and closed-form solutions for transmission lines. Doctoral Dissertation. Thesis uri icon

abstract

  • An analytical solution for the coupled telegrapher's equations in terms of the voltage and current on a homogeneous lossy transmission line and multiconductor transmission line is presented. The resulting telegrapher's equation solution is obtained in the form of an exact time domain propagator operating on the line voltage and current. It is shown that the analytical equations lead to a stable numerical method that can be used in the analysis of both homogeneous and inhomogeneous transmission lines. A numerical dispersion relation is derived proving that this method has no numerical dispersion down to the two points per wavelength Nyquist limit. Examples are presented showing that exceptionally accurate results are obtained for lossy single and multiconductor transmission lines. The method is extended to represent the general solution to Maxwell's differential equations in vector matrix form. It is shown that, given the electromagnetic field and boundary conditions at a given instant in time, the free space time domain propagator and corresponding dyadic Green's functions in 1-, 2-, and 3-dimensions can be used to calculate the field at all subsequent times.
  • An analytical solution for the coupled telegrapher's equations in terms of the
    voltage and current on a homogeneous lossy transmission line and multiconductor
    transmission line is presented. The resulting telegrapher's equation solution is obtained
    in the form of an exact time domain propagator operating on the line voltage and current.
    It is shown that the analytical equations lead to a stable numerical method that can be
    used in the analysis of both homogeneous and inhomogeneous transmission lines. A
    numerical dispersion relation is derived proving that this method has no numerical
    dispersion down to the two points per wavelength Nyquist limit. Examples are presented
    showing that exceptionally accurate results are obtained for lossy single and
    multiconductor transmission lines. The method is extended to represent the general
    solution to Maxwell's differential equations in vector matrix form. It is shown that,
    given the electromagnetic field and boundary conditions at a given instant in time, the
    free space time domain propagator and corresponding dyadic Green's functions in 1-, 2-,
    and 3-dimensions can be used to calculate the field at all subsequent times.

publication date

  • December 2006