In PCB and packaging interconnect design, electromagnetic analysis tools have evolved from optional aids to essential instruments over the last two decades, driven by data rates exceeding 6 Gbps. Today, as standard rates surpass 6 Gbps and approach 448 Gbps, these tools are indispensable for ensuring reliable interconnect performance. The objective of interconnect analysis is straightforward: identify potential failures at target data rates and facilitate effective troubleshooting and resolution. The most efficient method for such pass-fail assessments is Decompositional Electromagnetic Analysis (DEA), which isolates signal degradation factors to streamline analysis and problem-solving. This article outlines the fundamental elements of DEA, examines the conditions for its accuracy, and highlights its growing importance in the future of interconnect design.

Introduction

Data rates in PCB and packaging (PKG) interconnects continue to rise across all major signaling protocols (PCIe, DDR, Ethernet, USB, SAS, CEI, OIF, UCIe, 5G, etc.). Many of these high-speed standards now operate beyond 6 Gbps (or GT/s), with some reaching 448 Gbps, pushing signal spectra deep into microwave and millimeter-wave bandwidths. Accurately predicting the behavior of such interconnects is practically impossible without rigorous electromagnetic (EM) analysis. The primary goal of EM analysis is to identify and resolve transmission issues by ensuring compliance in both frequency and time domains.

Interconnects, by design, function as waveguiding structures, and the most efficient modeling approach leverages decomposition into multiport representations of transmission lines and discontinuities. Originally introduced for analyzing closed waveguiding systems,¹ partitioning was later successfully applied to microwave (MIC) and millimeter wave integrated circuits (MMIC) using decompositional EM analysis² and other design-oriented EM models³ for open waveguiding systems like microstrip and stripline interconnects.

Despite the similarities between digital PCB/PKG interconnects and MIC/MMIC structures, SI tools in the early 2000s relied primarily on transmission line models (XTK, ICX, HyperLynx). As data rates exceeded 6 Gbps, these tools failed to deliver sufficient accuracy, with the analysis requiring correlation to measurements up to 10 to 20 GHz—beyond the capabilities of traditional SI approach. To bridge this gap, Simbeor became the first electromagnetic signal integrity software specifically developed for accurate interconnect modeling, incorporating a systematic analysis-to-measurement validation framework.⁴ The key principles of DEA were established⁵ and later formalized into a structured methodology for design of predictable interconnects.⁶

DEA is a rigorous field-theory-driven approach that optimally reduces problem complexity by leveraging the underlying physics of wave propagation. It enables precise separation of signal degradation factors, allowing for accelerated pass/fail EM analysis and troubleshooting—even on a standard laptop. This article highlights recent advancements in digital interconnect analysis using DEA.

While partitioning methodologies similar to DEA have emerged in other SI tools (“cut and stitch,” “divide and conquer,” “HFSS regions”), they are often mischaracterized as approximate techniques. Their accuracy depends on implementation details and the nature of the simulated structures, as discussed further in this paper. EM analysis without decomposition has recently been made feasible through formal domain decomposition in finite element methods⁷ and algebraic matrix reduction in integral equation methods,^8,9 alongside high-performance computing. These brute-force solutions mark significant progress, but remain computationally and financially prohibitive for most electronics designers, who continue to rely on traditional SI software or empirical design rules. A full-wave electromagnetic analysis of interconnects without decomposition accounts for additional effects such as radiation and distant coupling. While this approach captures more physical phenomena, it comes at a significant cost: extended simulation times and higher computational demands. DEA, on the other hand, is designed to identify and eliminate sources of distant coupling that enhances its accuracy. In this approach, accuracy and the goal of reliable interconnect design are inherently aligned, making them mutually beneficial.

DEA Technology Evolution

The DEA is the domain decomposition (DD) technique that is based on the physics of the wave propagation. DEA is the wave approach to the DD. First, structures that can be simulated with transmission line (t-line) models and structures that require 3D EM analysis (discontinuities) are identified. It can be done by following the signal propagation direction between components within some boundaries around signal conductors (waveguiding channel) and setting wave boundaries between all elements as illustrated in Figure 1. It is a pattern recognition problem that requires fast algorithms to convert polygonal conductors into EM models. All reference conductor discontinuities within the waveguiding channel (illustrated as pink lines in Figure 1) are included either in t-line or into discontinuity models. Coupling to the other links within a specified coupling distance can be also included in such model with either coupled t-lines or coupled discontinuities (pads or viaholes). To facilitate the geometry optimization, vertical transitions are identified and parameterized as multi-vias. That allows comparison and model reuse to accelerate the analysis of multiple links (usually, most of the transitions to the same layer are identical). Models for the transmission lines are also compared and re-used. Discontinuity boundaries and boundary conditions, wave ports between the discontinuities and t-lines, external component ports are automatically defined. The transmission line ports are created both for transitions to planar t-lines in the XY-plane and for the Z-directed transitions to BGA and connector pins. The ports in all directions are de-embedded to eliminate the reflections between the domains. Comparing to the analysis with lumped component ports, the wave ports in all directions extend the accuracy of the DEA to higher frequencies.

The main reason for the decomposition into t-lines and discontinuities is to increase the accuracy and accelerate analysis of long traces. It is computationally expensive to achieve high accuracy in the analysis of long planar t-line segments with the brute force approach due to peculiarities of current distribution in strips and reference planes. It is faster and often more accurate to extract modal characteristic impedances and propagation constants for multiconductor t-lines and use them to model the segments.

The major element of PCB/PKG interconnects are vertical transitions or vias through multi-layered media. Such structures require fast and accurate analysis and optimization. The wave approach to the DD is used to accelerate the analysis of multi-layered discontinuities. The layers are treated as separate domains with the wave channels defined at the partially metallized layers. That turns the matrices describing the whole problem into block band matrices with five block diagonals. Matrices describing blocks are fully populated in the method of lines solver (3DML) and are sparse in the Trefftz finite elements solver (3DTF). The band matrices are solved with the frontal algorithm in both solvers. The complexity of such solution grows linearly with the number of layers in the structure. Overall, that approach accelerates analysis orders of magnitude and substantially reduces the memory requirement. 

Figure 1. Differential link decomposition along the waveguiding channel.

The analysis of digital interconnects is done in the frequency-domain (FD), but the time-domain (TD) analysis is also required both at the system-level and at the level of each discontinuity. Multiport models require seamless transition between FD and TD. The approximation of S-parameters with rational functions or rational compact models (RCM) enables such analysis in both domains.⁵ It is used to accelerate the frequency sweeps by selecting frequencies only where they improve the quality of RCMs. This interpolative sweep reduces the number of frequency points and produces frequency-continuous RCM models for each discontinuity. That allows fast and accurate TD analysis of each discontinuity. At the system-level, RCMs are either used directly for both FD and TD analysis, or converted into SPICE models to remove the model dependency on the discretization and the limited bandwidth.

The DEA analysis and acceleration techniques outlined here are implemented in Simbeor software.¹⁴ It enables design exploration and interactive or automated analysis even on a laptop—no HPC is required! To further reduce the simulation time, 3D EM solvers are accelerated with the distributed computing. The analysis of frequency points is parallelized in a local computer or cloud network of computers. 

Predictable Interconnect Design with DEA

The interconnects should be designed as the waveguiding structures with the constant characteristic impedance and minimized effect of discontinuities. In reality, it is often not the case. Before running an expensive broadband EM analysis, possible defects should be found and fixed first with inexpensive and fast EM models. This can be done with the multi-pass approach to interconnect design based on a decomposition of signal degradation effects illustrated by the balance of power:

P_out = P_in - P_abs - P_refl - P_leaked + P_coupled

Here, P_in is the power delivered by a transmitter to the interconnect and P_out is the power delivered to a receiver (degraded signal). All other terms in the balance of power equation describe signal distortion. P_refl characterises the power reflected to the receiver—the major contributors to the reflection are the impedances of traces, pads, and viaholes that can be computed and compared with the target impedance at just one frequency point first (signal Nyquist frequency, for instance). The problems discovered during such analysis should be addressed in the first pass. P_leaked and P_coupled are two terms that describe a link coupling to neighbor structures (local coupling) as well as to remote structures through parallel-plane waveguides (distant coupling). The structures with possible distant coupling prevent predictability of interconnects with any method and, thus, should be identified and eliminated during the first pass, too. It can be done by evaluating localization frequency for each viahole and discontinuity in reference conductors. The structures are predictable with higher confidence over the frequency bandwidth up to the localization frequency. They are also relatively independent from the boundary conditions used to solve the problem in isolation. The leakage from the conditionally localized structures grows with the frequency and the localization frequency can be formally defined as the frequency where P_leaked exceeds some threshold (10%, for instance). In cases of high data rates (28 to 448 Gbps), it may be physically impossible to localized vias on PCBs, and we usually need to build models with the bandwidth exceeding the localization limit. Absorption of the lost energy with the low impedance boundary conditions is required to model such structures with the gradual loss of localization. That approximates the behavior of the power delivery planes, and also eliminates the numerical resonances caused by other types of boundary conditions.

During the second pass, the local coupling between parallel traces can be accurately modelled with the coupled transmission line models—such analysis does not require 3D EM models. The local coupling between adjacent vias can be also evaluated separately at this pass with the 3D EM models. If the local coupling exceeds a coupling compliance condition, it should be fixed.   

Only after the impedance, localization, and local coupling problems are identified and corrected, can more accurate broadband analysis with 3D models of discontinuities be used to evaluate the overall losses caused by material absorption (P_abs) and the reflection (P_refl) over the bandwidth of the signal. Again, if problems are detected, they have to be fixed before the final analysis of multiple links with the local viahole and t-line coupling. If the localization of viaholes is not sufficient, the distant crosstalk can be evaluated and fixed, if necessary. Though, this is the most expensive and often not possible type of the analysis. Thus, the key in that multi-pass approach is the localization. The improvement of localization makes interconnects more predictable with any method, including DEA. To support the multi-pass approach to interconnect analysis, SI Compliance Analyzer tool was implemented in Simbeor.¹⁴ It allows for finding and fixing the problems without resorting to the brute force 3D EM analysis.

DEA Accuracy and Validation 

In context of PCB/PKG interconnect analysis, the accuracy can be defined as a possibility to predict interconnect behavior. Three major elements define the predictability: localization, broadband material models, and manufacturing adjustments and variations. The localization condition was discussed in the previous section. The broadband dielectrics and conductor roughness models were required even for 10 to 20 Gbps links.⁴ To address this need, the broadband material model identification with GMS-parameters was introduced.¹⁰ It enabled automatic model identification with separation of dielectric and conductor losses and building statistical material models, as demonstrated in Reference 11. Such models include material and some geometric manufacturing variations and are essential for predictability of 28 to 448 Gbps interconnects. Possible manufacturing adjustment are also important for the predictability, as demonstrated in Reference 6, where the systematic “sink or swim” approach to the accuracy validation was formally introduced and used to validate Simbeor solvers. As of now, there are no published reports on the systematic validation of the other SI tools with the process repeatable by a user. To further formalize and facilitate the validation process, S-parameters similarity metric was introduced in Reference 12.

Conclusion and Future of DEA

(DEA is not just a theoretical framework introduced about 12 years ago⁵—it is fully implemented in Simbeor electromagnetic signal integrity software.¹⁴ That allowed the compliance analysis automation for pre-layout analysis and in post-layout from the design geometry import to the pass-fail report. The outlined multi-pass approach to interconnect design allows elimination of the structures with possible distant coupling and makes the final DEA analysis as accurate as necessary by design. 

The outlined DEA opens multiple possibilities to make interconnect compliant by design and to eliminate the need in SI software as it currently exists. First, the fast DEA enables the model-driven routing, running analysis simultaneously with the layout and making interconnect compliant immediately.

Second, the fast DEA allows the analysis of millions of links in order to populate solution spaces with all possible geometry and material parameters variations, as well as the use of machine learning algorithms to build ranges where interconnects stay compliant.¹³ Only the validation of the ranges is required in this approach. Though, for both approaches, the process of connecting two components with traces as it is done now in the layout tools should be replaced with the process of connecting by waveguiding structures that, in addition to the traces, include relevant reference conductors.

Last but not least, DEA is accessible through C, Matlab, and Python APIs in Simbeor SDK. This capability serves as a foundational technology for developing AI-driven agents capable of performing signal integrity analysis. Companies are already leveraging Simbeor’s technology to create autonomous AI engineers, transforming signal integrity workflows and enhancing design efficiency. By enabling automation through rigorous electromagnetic analysis, Simbeor is paving the way for intelligent, AI-assisted interconnect design, ensuring reliability at ever-increasing data rates. 

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