Determining elements of lossy ladder networks

Quantitative Performance Comparison of Thermal Structure Function Computations

“…Truncating the recovered structure function when the theo-retical structure function ends puts a bias into m S to favor divergences at higher R Σ in the recovered structure function, i.e., it is biased to overestimate the total thermal resistance. For this reason, the limits are defined as in (26).…”

“…Measuring the accuracy of structure functions via (25) means that the absolute accuracy of the total thermal resistance is not reflected in m S . The upper integration limit is defined by the point of the divergence via (26). Only the shape of the divergence is taken into account and not its relative position.…”

“…For these reasons, an additional measure of accuracy is used to characterize the total resistance belonging to the recovered structure function. The difference in total resistance, ∆R Σ , is calculated by comparing the theoretically expected resistance R Σ,th to R Σ,max as defined in (26),…”

“…An approach using polynomial long division is described in detail in [25]. A state-space method is laid out in [26]. A tridiagonalization method is presented by Codecasa in [24].…”

Physical interpretation and numerical approximation of structure functions of components and packages

“…The structure function of a one-port passive lumped thermal network is defined by the continued fraction expansion of its impedance function [5]. Two methods are reported in literature for determining this continued fraction expansion: the polynomial long division classical method and the state-space method [11]. Both methods are numerically ill-conditioned [6] and thus can be applied only to one-port passive lumped thermal networks of small orders.…”