Numerical analysis of lossy nonuniform interconnect lines in modern integrated circuits by multistep θ-method and Runge-midpoint method

With the rapid evolution of system-on-chip technology and with fast switching speeds, the resistance, conductance, capacitance and inductance of interconnections have a dominant impact on coupling noise and signal integrity. Interconnections can be from various levels of design hierarchy, such as on chips, packaging structures, multi-chip modules and PCBs (printed circuit boards). In this paper, we present an effective numerical method for the transient analysis of lossy coupled nonuniform interconnection lines for several technology nodes. In order to eliminate the oscillations that are a result of the simple FDTD (finite difference time domain) of our system and to provide an accurate solution, we propose a resolution system by coupling the finite difference θ-method scheme with the optimized time advancement Runge-midpoint algorithm. The proposed algorithm is implemented using MATLAB programming language. To validate our proposed method, various numerical results are presented and compared with traditional FDTD numerical results. These simulations show that our new schemes are stable under CFL (Courant–Friedrich–Levy) conditions and that their height order is accurate in space and time.