The Switch-Line: A Simple Lumped Transmission Line that can Support Unattenuated Propagation

A "switch-line" is defined as a lumped transmission line containing in each section a series resistor, a shunt capacitor, and a shunt switch (switch open for voltages greater than some fixed threshold; switch closed otherwise). It is proved that this nonlinear, lossy line can propagate a waveform without attenuation and with constant time delay per section. An exact solution for the propagating waveform is derived, and a simple, approximate formula is given for the key result relating the threshold and the time delay per section. This formula is utilized in obtaining a corresponding relation between the parameters of a more general lumped line having a conductance in series with each switch.