Causality Enforcement Via Periodic Continuations for Package and On-Chip Interconnects

Causality verification and enforcement is of great importance for performance evaluation of electrical interconnects. We introduce a new technique based on Kramers-Krönig dispersion relations, also called Hilbert transform relations, and a construction of causal Fourier continuations using a regularized singular value decomposition (SVD) method. Given a transfer function sampled on a bandlimited frequency interval, nonperiodic in general, this approach constructs highly accurate Fourier series approximations on the given frequency interval by allowing the function to be periodic on an extended domain. The causality is enforced spectrally, which eliminates the necessity to approximate the transfer function behavior as frequency goes to infinity in order to compute Hilbert transform. The performance of the proposed method is tested using a non-smooth frequency response function. The obtained results demonstrate an excellent accuracy and reliability of the proposed technique. We also compare the accuracy of the new method with the polynomial periodic continuation approach developed by authors in [1], [2].