Progress in Decompositional Electromagnetic Analysis of Digital Interconnects

In the realm of PCB and packaging interconnect design, electromagnetic analysis tools have transitioned from optional to essential over the last two decades, as data rates soared beyond 6 Gbps. Today, with standard data rates eclipsing 6 Gbps and reaching thresholds of 224 Gbps, these tools are indispensable for designing reliable interconnects. The goals of the interconnect analysis are simple: identify interconnects that may fail at the target data rate and allow troubleshooting and fixing the problem. The most efficient approach to such pass-fail analysis is the Decompositional Electromagnetic Analysis (DEA). It allows separation of the signal degradation factors for faster analysis and troubleshooting. This paper outlines the basic elements of DEA, discusses conditions for its accuracy and underscores its significance in the future of interconnect design.

💡 Research Summary

The paper presents a comprehensive view of Decompositional Electromagnetic Analysis (DEA) as a practical, high‑performance methodology for digital PCB and package interconnect design in the era of multi‑gigabit data rates. It begins by highlighting the shift from optional to mandatory electromagnetic (EM) verification as link speeds have risen beyond 6 Gbps and now approach 224 Gbps, stressing that traditional transmission‑line‑based signal‑integrity (SI) tools cannot reliably predict behavior up to the required 10–20 GHz bandwidth.

DEA is introduced as a physics‑based domain‑decomposition technique that separates an interconnect into two classes of sub‑domains: (1) long transmission‑line sections that can be modeled with multi‑conductor line theory, and (2) localized discontinuities (pads, vias, bumps, etc.) that demand full 3‑D EM simulation. An automated pattern‑recognition step identifies the wave‑guiding channel, defines wave‑port boundaries, and classifies each polygonal conductor. Transmission‑line segments are characterized by modal characteristic impedance and propagation constant, producing block‑diagonal matrices; discontinuities are solved with either a method‑of‑lines solver (3DML) or a Trefftz finite‑element solver (3DTF). By embedding wave ports in all directions, reflections at domain interfaces are suppressed, extending accuracy to higher frequencies.

The resulting system matrix has a five‑band block‑diagonal structure, which can be solved with a frontal algorithm in O(N) time relative to the number of layers, dramatically reducing both CPU time and memory compared with brute‑force full‑wave solvers. Frequency‑domain (FD) results are converted to compact rational models (RCMs) using a selective interpolative sweep; only frequencies that improve the RCM fit are simulated, cutting the number of required frequency points. These RCMs provide continuous S‑parameter representations that can be used directly in time‑domain (TD) analysis, or transformed into SPICE macro‑models for system‑level simulation.

A multi‑pass design flow is advocated. In the first pass, the designer checks impedance matching, “localization” (the frequency below which a discontinuity’s loss remains confined), and local coupling using fast transmission‑line or coupled‑line models. Localization is quantified by the frequency at which leaked power exceeds a chosen threshold (e.g., 10 %). Problems identified at this stage are corrected before proceeding. The second pass employs DEA’s 3‑D EM models for the remaining critical discontinuities, delivering accurate predictions of broadband material loss (P_abs) and reflection (P_refl). A final pass can optionally add wave ports to model unavoidable distant crosstalk.

Accuracy is anchored on three pillars: (1) localization, (2) broadband material modeling, and (3) manufacturing variations. Broadband dielectric and conductor‑roughness models are extracted automatically via GMS‑parameters, separating dielectric and conductor losses and building statistical material models that remain valid up to 224 Gbps. Manufacturing tolerances are incorporated through the “sink or swim” systematic validation approach, and model similarity is quantified with a modified Hausdorff distance metric applied to S‑parameters. The authors note that comparable systematic validation is lacking for other commercial SI tools.

The paper concludes that DEA, now fully automated in the Simbeor suite, enables a “design‑by‑analysis” workflow where routing, verification, and compliance reporting occur simultaneously on a laptop without high‑performance computing. The authors envision extending DEA to massive design‑space exploration: by generating millions of link models with varied geometries and material parameters, machine‑learning algorithms can learn the feasible design envelope, allowing real‑time compliance checks during layout. Ultimately, the traditional “connect‑by‑trace” paradigm would be replaced by a wave‑guiding‑structure paradigm that inherently respects reference conductors, impedance, and coupling constraints, dramatically improving predictability and productivity for next‑generation high‑speed electronic systems.