Time-Domain Analysis Techniques for Characterizing Discontinuities in High-Speed Digital Systems

Abstract

High-speed digital systems increasingly rely on dense interconnects, layered substrates, and heterogeneous packaging whose discontinuities dominate link behavior. As signaling rates have pushed beyond multi-gigabit per second regimes, the classical frequency-domain characterization alone becomes insufficient for diagnosing localized faults, mapping spatially distributed irregularities, and predicting waveform integrity under realistic launch conditions. Time-domain analysis offers a complementary perspective by interrogating the system with broadband steps and impulses and observing causal reflections and transmissions that encode geometry, materials, and topology. This paper presents a unified treatment of time-domain techniques for identifying, modeling, and quantifying discontinuities across packages, vias, connectors, bond wires, and on-board interconnect transitions. Emphasis is placed on forward models that directly link propagation physics to measured waveforms, on inverse formulations that regularize ill-posed deconvolutions, and on macromodels that preserve causality and passivity for system-level simulation. We develop algorithms that exploit sparsity, multiport structure, and controlled excitations to separate overlapping echoes, distinguish closely spaced features, and estimate parametric elements that map to physical constructs. Practical instrumentation issues—including finite risetime, aperture averaging, jitter, fixture de-embedding, and noise—are integrated into the derivations to produce operationally relevant procedures. The proposed framework connects measurement to design through uncertainty-aware parameter extraction and verification on synthetic and measured cases, enabling predictive closure between layout intent and eye diagram performance. The resulting methods translate raw reflectometry and transmission data into actionable models for layout optimization, compliance evaluation, and failure analysis without reliance on extensive frequency sweeps.