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This paper discusses the problem of determining a thermal model of an electronic system based on the spectral analysis of its step temperature response. The proposed method yields equivalent RC Cauer ladder thermal models, which consist of only a few RC stages, but produce very accurate estimates of circuit temperature. Moreover, the values of model elements have physical significance. Such a thermal model can be easily used in the SPICE simulator for joint electro-thermal simulations of an electronic system. The entire process of the reduced model creation is illustrated in the paper on the practical example of an ASIC packaged and soldered to a PCB.