On Checking Causality of Tabulated $S$-Parameters

The existing formulation for the causality testing of tabulated S-parameters can be oversensitive to non-causality, in that it can report causality violations for data that may not result in an inaccurate transient simulation. Existing numerical procedures that implement the present formulation can result in false-positive test outcomes (i.e., causal data being declared as noncausal). A mechanism to reduce the over-sensitivity in the formulation and new testing procedures that minimize false positives are proposed. Over-sensitivity is reduced significantly if the target fitting error (of the macromodel to tabulated data) is chosen as the minimum amplitude of the non-causality to be detected. Sources of false-positive outcomes are identified, and four procedures that minimize false positives are proposed. These procedures differ in resolution, accuracy, and computational requirements. Numerical results demonstrating the proposed modifications to the formulation and numerical results comparing and contrasting the different procedures are presented.