FDTD Formulation Based on High-Order Surface Impedance Boundary Conditions for Lossy Two-Conductor Transmission Lines

• Published in: IEEE transactions on electromagnetic compatibility Vol. 62; no. 1; pp. 194 - 203
• Main Authors: Huangfu, Youpeng, Di Rienzo, Luca, Wang, Shuhong
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.02.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Boundary conditions; Boundary element method; Boundary element method (BEM); Conductors; Convolution; Discretization; Fast Fourier transformations; Finite difference methods; Finite difference time domain method; Fourier transforms; High frequencies; High pass filters; high-order surface impedance boundary conditions; Impedance; lossy transmission lines; Mathematical analysis; Mathematical model; Propagation losses; Proximity effect (electricity); Time domain analysis; Transmission lines
• ISSN: 0018-9375; 1558-187X
• DOI: 10.1109/TEMC.2018.2885208

This paper presents a finite difference time domain formulation incorporating conductor losses due to skin and proximity effects for a uniform lossy two-conductor transmission line. At high frequency the per-unit-length effective internal impedance model is based on a boundary element method formulation enforcing high-order surface impedance boundary conditions. A smooth transition from the low to the high frequency model is obtained using first-order low- and high-pass filters. The effective internal impedance model is implemented into the finite difference time domain method via the discretization of the convolution. Finally, a computationally efficient finite difference time domain discretization of the two-conductor transmission line equation is obtained applying a recursive convolution technique. The proposed formulation is validated by comparison with the conventional inverse fast Fourier transform method and shows an improvement with respect to the well-known Paul's method, which does not consider the proximity effect.