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The increase in processor speeds in the last few years has created a growing need for the accurate characterization of waveform propagation on lossy printed-circuit-board (PCB) transmission lines. Due to the dispersive nature of pulse propagation on lossy transmission lines, approximations of the classic transmission-line model can fail in this application (i.e., lossless or dc losses approximations). This paper will show how an equivalenttransmission-line model can be used to analyze dispersive transmission lines for high-speed digital applications. The equivalentcircuit elements of this transmission-line model incorporate the frequency dependence of the per unit length impedance and admittance caused by the finite conductivity of the conductors as well as the dielectric losses. We will show that these equivalent circuit elements can be readily implemented into finite-difference time-domain (FDTD) transmission-line codes, and we will present such a FDTD implementation.-parameters and pulsed waveforms for a circular wire, coplanar waveguides (CPW) and microstrip lines are shown. Finally, we present approximate expressions for analytically obtaining the resistance and inductance per length of a microstrip line.

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