An accurate, robust and intuitive technique to detect causality violations in broadband frequency measurements

Abstract

Dispersion relations with filtering were recently proposed to reliably test the causality of sampled scattering parameters obtained with a direct measurement or a full-wave simulation. Owing to the use of a simple low-pass filter, this novel form of relations is much easier to implement and understand than previous approaches. In this paper, we demonstrate, through a rigorous theoretical analysis and numerical tests, that the novel method provides a better estimation of the detected violation. The proposed analysis also elucidates the effect of the low-pass filter on the causality test.