Properties of some convolution algorithms for the thermal analysis of semiconductor devices

This paper deals with three kinds of convolution algorithms designed for the thermal analysis of semiconductor devices and electronic circuits with the use of the lumped thermal models. Such kind of models and algorithms is especially convenient to analyse the electronic circuits consisting of a high number of thermally sensitive devices. The fundamental features, such as: stability, convergence and accuracy of these algorithms, are considered and investigated in the paper. In the investigations the exponential test function describing the dissipated power is taken into account. It was analytically proved that the considered algorithms are stable and convergent. The analytical formulas describing the values of the local and total cut off error of the algorithms are proposed. The theoretical considerations are accompanied by some calculation results illustrating the influence of the values of thermal parameter models and the size of the analysis step on the accuracy of calculations carried out with the considered algorithms.