Transient Response of a Transmission Line Containing An Arbitrary Number of Small Capacitive Discontinuities

A uniform, loss-free transmission line, across which an arbitrary number of lumped capacitors have been connected at equal intervals, is subjected to an exponential step without a carrier
[1 - e-{\beta t}]
and to an exponential step which is superimposed upon a carrier:
[1 - e-{\beta t}] \sin \omega t
. The response of the line is evaluated analytically and numerically. The results can be applied directly to situations where long transmission lines with many discontinuities, such as insulators or flanges, are used. A typical application is the response of the coaxial transmission line between a TV transmitter and its antenna.