Noncausality of AR-Extrapolated S-Parameters

The autoregression (AR) model has been recently used for S-parameter extrapolation to improve TDR stability and reduce the edge effect of time-gating. In this paper, several simulated and measured data are extrapolated using AR, and then causality is examined using the dispersion relation with subtraction. Some cases indicate that AR may give noncausal responses; the results thus raise concerns about the general applicability of AR, and call for solution on fixing the causality.