Well-Posed Device Models for Electrical Circuit Simulation
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This document provides guidelines for creating computational device models that work well in simulation. We build our discussion around the mathematical notion of “well-posedness”. We show that the requirements for a model to be well-posed stem from the internal working mechanisms of simulators. Therefore, our main aim is to provide insight into the numerical procedures used by simulators in order to help model developers avoid ill-posedness issues. We start our discussion with an example that shows how an ill-posed Verilog-A model can produce different simulation results in different simulators. We then provide a step-by-step simulation case study. In this case study, we illustrate the role of device models in simulations by examining the steps a simulator goes through, from taking a netlist as input to producing a simulation result as output. Finally, we distill our discussion in a functional definition of a well-posed model. As an extension to our theoretical discussion, we also provide practical guidelines that should be followed by Verilog-A models in order to avoid ill-posedness issues.
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