A transmission line consisting of a parallel connection of shunted Josephson junctions is one of the base elements in the new Rapid Single Flux Quantum (RSFQ) logic. When an additional bias current is applied to the edge junction of the transmission line it generates and injects series of flux quanta on the line. This kind of pulse generators have important applications for testing RSFQ devices at high frequencies. In such experiments unwanted steps always show up in theI‐Vcurve of the generator junction. This problem has been experimentally and numerically investigated for parallel arrays of identical junctions. Steps with extremely low differential resistance are found to be due to the self‐induced magnetic field produced by the edge current. The underlying mechanism is that the non‐uniform field divides the array into domains consisting of several (unit) cells each containing the same number of flux quanta. The influence of an applied homogeneous external magnetic field and a uniformly distributed bias current is also considered.