Removing the Froissart Doublets in a Rational Interpolation for S-parameters

A Loewner matrix based rational interpolation is combined with the finite element method (FEM) to fit the S-parameters over a wide frequency band. However, numerical errors in S-parameters may lead to Froissart doublets in the rational expression, which look like a spike in the curve. This paper proposes a novel technique to remove these doublets. The interpolated barycentric rational expression is converted into the sum of many partial fractions. The fraction with the smallest imaginary part of the pole and relatively large absolute value will be identified as the Froissart doublets. Removing these doublets leads to a smooth rational polynomial, which is verified by an example of a passive circuit.