  Numerical inverse Laplace transforms are used to analyze the transient
response of non-ideal transmission lines to a voltage step. We find that the
detailed shape of the transient response is sensitive conductor losses, but
insensitive to dielectric losses. Furthermore, we find that the low-loss
approximations for the transmission line propagation constant and
characteristic impedance in the complex-frequency domain are sufficient to
accurately model the observed transient response. We also investigate the
effects of: (1) a parasitic capacitance terminating the open end of the coaxial
transmission line, (2) the input impedance of the oscilloscope used to make the
measurements, and (3) the finite rise time of the voltage step. Finally, we
cool a semi-rigid coaxial cable in liquid nitrogen so as to reduced conductor
lossless and observe a transient response that is closer to that expected from
an ideal lossless line.
