The theory is given of the voltage output of a Rogowski coil excited by a current pulse flowing along the axis of the coil. In this theory the Rogowski coil is considered as a delay line. The results do not differ from those obtained usually by considering the coil as a voltage sourced&fgr;/dtwith an inductive output impedance. Details are also given of the design of two Rogowski coils and their working modes are fully analyzed.