On the Periodic Solutions in One Dimensional Cellular Nonlinear Networks Based on Josephson Junctions (JJ´s)

In this paper we consider an autonomous one dimensional cellular nonlinear network (CNN) that consists of chain of N simple cells based on Josephson Junctions (JJ´s) coupled by linear inductors. In fact the subject is the well known Josephson Transmission Line (JTL) that is used in many applications in superconductor electronics and more especially in Rapid Single Flux Quantum (RSFQ) technique. When the last cell is connected with the first one a ring of Josephson Junctions is formed. Using the framework of the cellular nonlinear network we consider the JTL under the umbrella of the system theory. Based on describing functions method we rigorously prove the existence and stability of periodic solutions in the cellular nonlinear network model considered. The results are confirmed by simulations