An improved method of modeling lossy transmission lines in finite-difference, time-domain analysis

In a recent publication it was shown that the high-frequency (when skin effect is well developed) resistance and internal inductive reactance are not equal for conductors of rectangular cross section such as printed circuit board lands and differ by as much as 30% unlike conductors of circular cross section (wires). The conventional modeling of these losses in the solution of the multiconductor transmission line (MTL) equations via the finite-difference, time-domain (FDTD) method makes use of the representation of this internal impedance of the conductors of the form A+B√s&rlhar2;A+B√jω where s is the Laplace transform variable and ω is the radian frequency of excitation. The validity of this representation assumes that the high-frequency resistance and internal inductive reactance are equal which, it turns out, is not the case for conductors of rectangular cross section. Furthermore, it has recently been demonstrated that the representation A+B√s in itself produces errors even if the assumption of equality of the high-frequency resistance and internal inductive reactance were true. The contribution of this paper is to provide an improved method for modeling this high-frequency loss in the time domain that overcomes the above two deficiencies and is suitable for the finite-difference, time-domain solution of the MTL equations. In addition, we show some typical crosstalk calculations with the new representation to determine whether the above differences are significant