Interconnection of Subsystem Reduced-Order Models in the Electrothermal Analysis of Large Systems

Heat conduction in an electronic device is commonly modeled as a discretized thermal system (e.g., finite element or finite difference models) that typically uses large matrices for solving complex problems. The large size of electronic-system heat transfer models can be reduced using model reduction methods and the resulting reduced-order models can yield accurate results with far less computational costs. Electronic devices are typically composed of components, like chips, printed circuit boards, and heat sinks that are coupled together. There are two ways of creating reduced-order models for devices that have many coupled components. The first way is to create a single reduced-order model of the entire device. The second way is to interconnect reduced-order models of the components that constitute the device. The second choice (which we call the "reduce then interconnect" approach) allows the heat transfer specialist to perform quick simulations of different architectures of the device by using a library of reduced-order models of the different components that make up the device. However, interconnecting reduced-order models in a straightforward manner can result in unstable behavior. The purpose of this paper is two-fold: creating reduced-order models of the components using a Krylov subspace algorithm and interconnecting the reduced-order models in a stable manner using concepts from control theory. In this paper, we explain the logic behind the "reduce then interconnect" approach, formulate a control-theoretic method for it, and finally exhibit the whole process numerically, by applying it to an example heat conduction problem