### Abstract:

This thesis presents two new approaches for the broadband, time-domain modeling of lossy transmission lines. Each approach is based on an alternative derivation of delay extraction in order to separate the line's linear phase from its
attenuation and dispersion. Augmentation networks represent the derived attenuation networks as rational function approximations. Final network models are implemented in a SPICE circuit simulator for transient analysis. The first approach to extract delay is based on the properties of the
eigenvectors of the matrix exponential function in the solution to the telegrapher's
equations. The resultant network contains an ideal transmission line cascaded with two asymmetrical delayless attenuation networks. When applied to a single line with constant line parameters, the resultant attenuation networks are inherently non-passive and to which accurate low-order broadband approximations are not possible. The effects of alternative mathematical techniques such as factorization, forcing reciprocity, and eigenvector normalization or scaling, are applied to determine if passive, low-order approximations of the augmentation networks are obtainable. The second approach utilizes a similarity transformation at each transmission
line port to obtain commutable matrix exponentials in order to extract delay. The resulting model includes a cascade of one or more delayless networks, an ideal transmission line of unity characteristic impedance, and transformation networks at
each port. This approach is applied to single and coupled lines at lengths ranging from 5 cm to 10 m and frequencies up to 5 GHz. The resultant time-domain models are accurate with low-order approximations for lines with constant, non-zero per-unit-length
parameters. Lines with zero shunt conductance or frequency-dependent line parameters prove difficult to accurately model at low-orders with this approach.