A Complex-Envelope FDTD Formulation Using Alternating In-Phase and Quadrature Field Variables

Autor:	Qi Liu, Paul M. Goggans
Rok vydání:	2015
Předmět:	Partial differential equation Field (physics) Tridiagonal matrix Frequency domain Mathematical analysis Finite difference method Finite-difference time-domain method Electrical and Electronic Engineering Envelope (mathematics) In-phase and quadrature components Mathematics
Zdroj:	IEEE Transactions on Antennas and Propagation. 63:5169-5175
ISSN:	1558-2221 0018-926X
DOI:	10.1109/tap.2015.2477430
Popis:	Real-valued partial differential equations (PDEs) are obtained by substituting the rectangular form of the complex envelope (CE) field and source quantities into the CE versions of Faraday’s and Ampere’s laws, and then separating each resulting complex PDE into real and imaginary parts. These real-valued PDEs result in a CE FDTD scheme that uses only real numbers and operations. As presented here, this CE FDTD scheme alternates at intervals of half a time step between solving for the real and imaginary portions of the CE fields, exactly as the Yee grid alternates spatial components of the fields at half spatial steps. The scheme is demonstrated here for the two-dimensional (2-D) transverse-magnetic case. A split-step method is used in the implicit formation such that only tridiagonal matrices have to be solved. FDTD results are presented for a 2-D cavity with an electric current source.
Databáze:	OpenAIRE
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