Analytical stability condition of the latency insertion method for nonuniform GLC circuits

The latency insertion method (LIM) is a transient simulation technique for circuits and is based on a finite-difference formulation, like the well-known finite-difference time-domain (FDTD) method for solving Maxwells equations. The LIM, like the FDTD method, is only conditionally stable resulting in an upper bound for the time step of the transient simulation. This bound on the time step is a function of the circuit topology and the circuit element values. It is critical to know this bound analytically for a given circuit. However, stability conditions of the LIM have been proven only for 1-D, infinitelylong, distributed uniform RLC circuits, employed in transmission line modeling. For nonuniform circuits, these conditions have been predicted and have been observed experimentally as well but have not been possible to prove using the existing stability analysis techniques. Recently, analytical stability conditions of the LIM for nonuniform RLC circuits have been proven using the Lyapunovs direct method (LDM). However, when a conductance to ground (G) is added to a node of an LC or RLC circuit, the stability conditions cannot be derived using the Lyapunov function proposed. In this brief, analytical stability condition of the LIM is derived for the first time for nonuniform GLC circuits using the LDM with a new Lyapunov function.