## Date of Award

1-1-2014

## Document Type

Thesis

## Degree Name

M.S. in Engineering Science

## Department

Electrical Engineering

## First Advisor

Paul Goggans

## Second Advisor

Alexander B. Yakovlev

## Third Advisor

Richard Gordon

## Relational Format

dissertation/thesis

## Abstract

Use of the complex-envelope (CE) representation of band-pass limited sources and their resulting fields increases the allowable time-step in finite-difference time-domain (FDTD) simulations. The complex envelope representation transforms band-pass limited fields and sources to complex-valued low-pass limited form and Maxwells equations from real-valued partial differential equations (PDEs) to complex-valued PDEs. Previous CE FDTD schemes have used complex valued difference equations in terms of complex valued field quantities to approximate these complex PDEs. This choice requires the use of complex numbers and complex operations in the computer program implementing the solution. An alternative CE FDTD scheme using only real numbers and operations can be derived from the real valued PDEs obtained by substituting the rectangular form of the complex field and source quantities into the complex PDEs and then separating each resulting complex PDE into its two equivalent real valued PDEs. The formulation of the CE FDTD using real values is demonstrated for a two-dimensional geometry where the electric field has only a z component. This implicit formulation requires only the solution of tridiagonal matrices. Results are presented for a 2D cavity problem with an electric current source. A reference solution for this problem is obtained by first solving the problem in the frequency domain and then transform it to the time-domain using the inverse fast Fourier transform (IFFT). Comparison of the two solutions demonstrates the accuracy of the new formulation.

## Recommended Citation

Liu, Qi, "A Complex-Envelope FDTD Formulation Using Real-Valued Field-Variables" (2014). *Electronic Theses and Dissertations*. 1299.

https://egrove.olemiss.edu/etd/1299

## Concentration/Emphasis

Emphasis: Electrical Engineering