A new study of right-handed and composite right/left-handed metamaterial transmission lines (TL) using their equivalent circuits and a new approach of the wave concept iterative process method is presented. This approach has the advantage of simulating all the periodic structures by only simulating one basic cell thanks to the surrounding periodic walls. A suitable choice of the cell length is necessary to work with the current as well as voltage and to approach the real behavior of the TL. The simulation results of these circuits, such as the calculation of current, voltage and the parameters S, helped to validate all the theoretical study.