A stabilized leapfrog scheme for circuit-based analysis of power delivery network

This paper describes an explicit leapfrog scheme that is stabilized for an arbitrary time step size in the fast transient simulation of a power delivery network (PDN). A time step size used in a basic explicit leapfrog scheme becomes too small if there exist extremely-small reactances in a circuit. Because such small reactances are usually extracted from small meshes, the basic leapfrog scheme is not suitable for the simulation including electrically-small objects, such as small apertures on a conductor plane of a PDN. The proposed stabilized leapfrog scheme can remove instability related to the low reactances and enables to use a relatively-large time step size which is not limited by a numerical stability condition. The proposed method is applied to the transient simulation of an example PDN to demonstrate its accuracy and efficiency. Numerical results show that our approach successfully avoids the time step size limitation and can perform much faster simulation than existing solvers.