Multi-Time PDEs for Dynamical System Analysis
Many
types of circuits, e.g., switched-capacitor filters, mixers, voltage-controlled
oscillators (VCOs), etc., contain waveforms that change
at widely disparate rates. We show that it is
useful to reformulate such systems in terms of multiple time variables,
thereby transforming
differential-algebraic equations (DAEs) to partial
differential equations (PDEs) which can be easier to solve numerically.
We present multi-time
formulations for non-autonomous systems (like
mixers) and also for forced autonomous systems (like VCOs). If time permits,
we will also describe how multitime formulations are useful for automatic
macromodelling of time-varying systems.. |