A rational polynomial chaos formulation for the uncertainty quantification of linear circuits in the frequency domain

This paper discusses the general form of the transfer functions of linear lumped circuits. It is shown that an arbitrary transfer function defined on such circuits has a functional dependence on individual circuit parameters that is rational, with multi-linear numerator and denominator. This result is then used to introduce a suitable model for the uncertainty quantification of this class of circuits, namely a rational polynomial chaos expansion in place of the conventional single expansion.