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

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.