A new reliable approximation method for expanded symbolic network functions

A method is presented to generate approximate expressions for expanded symbolic network functions which is more reliable than previous methods. The expressions are approximated with a user-defined error on the magnitude and phase over a continuous frequency range of interest. The method makes use of sensitivities of the magnitude and phase of the network function with respect to the different coefficients of the network function. The method can be used both for simplification strategies where the exact expanded network function is generated before approximation, and for strategies where the network functions are simplified during generation. Experimental results illustrate that the method generates reliable results for circuits where classical approximation methods give large inaccuracies.