A Refined PDAE Network Model for a CMOS Ring Oscillator

Abstract

Parasitic and second order effects such as transmission line effects can be linked to the common DAE network equations of circuit design by generalized PDE network models. This modeling approach allows for constructing spatial discretization schemes that are appropriate for the respective PDE system and transform the mixed initial-boundary value problem of PDEs and DAEs (PDAE system) into an approximate DAE (ADAE) system. In many simulation packages, however, one is stuck to companion network models that can be regarded as non-adaptive semi discretization schemes applied already at the modeling level. Inspecting the PDAE model and its analytical properties, these approximate DAE system can be classified and possible short-comings can be determined. If necessary, methods to overcome these short-comings are to be proposed, either on the level of spatial discretization (new models) or in the framework of efficient time integration (exploiting multirate potential). In this paper, all steps of this analysis chain are carefully discussed for a benchmark system: a CMOS ring oscillator with transmission line effects.