On the Exactness of Rational Polynomial Chaos Formulation for the Uncertainty Quantification of Linear Circuits in the Frequency Domain

We discuss the general form of the transfer functions of linear lumped circuits. We show 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 demonstrates that rational polynomial chaos expansions provide more suitable models than standard polynomial chaos for the uncertainty quantification of this class of circuits.