J-Fraction Approach for Calculating Thermal Structure Functions

Transient thermal testing is an established technique for thermal analysis of electronic components. While much attention has been paid to the experimental handling of transient measurements, the subsequent data analysis with network identification by deconvolution is also very challenging and should be performed with great care. One crucial step is the transformation from a Foster to a Cauer network which is usually done by polynomial long division. Here, polynomials of degree one hundred and more have to be handled. To guarantee sufficient numerical accuracy for these computations, arbitrary-precision arithmetic is applied. In turn, this increases computation times significantly, in particular for polynomials of higher order, i. e. longer RC lines. In this work, two alternative approaches for the Foster-to-Cauer transformation are investigated. The established method of polynomial long division is compared to Khatwani's method and Sobhy's method with respect to speed and accuracy. The results show a significant speed advantage of Sobhy's method over polynomial long division for identical accuracies.