Analytical Solution in Complicated Volumes for Detailed Compact Thermal Model Construction

Abstract

Original recursive construction and series acceleration techniques are presented for an analytically exact solution of temperature response at any point in an arbitrary N-level, finite, rectangular multi-layer. This enhanced solution is fast and robust and provides accurate calculation of thermal resistance for packaged and mounted power FETs and MMICs. The model is validated against liquid crystal measurements. It forms the basis for quasi-analytical construction of the global thermal impedance matrix for complicated microwave systems by spectral, domain decomposition. Construction costs can be O(I), where I is the number of subvolume heating and interface elements. An original recursive convolution technique is presented producing transient simulation after pre-computation at O(N) cost, where N is the number of time steps. The method is illustrated by simulation of a mounted, packaged and metallised FET. This represents the most detailed quasi-analytical thermal simulation ever presented. This generalised network parameter description provides immediately boundary condition independent (BCI) compact dynamic thermal models for electrothermal CAD