Compact nonlinear thermal modeling of packaged integrated systems

This paper proposes a new thermal nonlinear modeling technique for packaged integrated systems. Thermal behavior of complicated systems like packaged electronic systems may exhibit nonlinear and temperature dependent properties. As a result, it is difficult to use a low order linear model to approximate the thermal behavior of the packaged integrated systems without accuracy loss. In this paper, we try to mitigate this problem by using piecewise linear (PWL) approach to characterizing the thermal behavior of those systems. The new method (called ThermSubPWL), which is the first proposed approach to nonlinear thermal modeling problem, identifies the linear local models for different temperature ranges using the subspace identification method. A linear transformation method is proposed to transform all the identified linear local models to the common state basis to build the continuous piecewise linear model. Experimental results validate the proposed method on a realistic packaged integrated system modeled via the multi-domain/physics commercial tool, COMSOL, under practical power signal inputs. The new piecewise models can lead to much smaller model order without accuracy loss, which translates to significant savings in both the simulation time and the time required to identify the reduced models compared to applying the high order models.