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arxiv: 2606.02878 · v1 · pith:D6SJSNY4new · submitted 2026-06-01 · 📡 eess.SY · cs.SY

Package-Embedded Coupled Inductor Arrays for High-Performance Computing Power Delivery

Rami Rasheedi , Salma Abdelzaher , Inna Partin-Vaisband This is my paper

Pith reviewed 2026-06-28 12:59 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords package-embedded inductorscoupled inductor arraysvertical power deliveryhigh-performance computinginductance densitypower converter efficiencymulti-phase convertersinductance-island methodology
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The pith

Package-embedded arrays of coupled inductors deliver 5.65 percent average efficiency gains in multi-phase power converters.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents a framework that places arrays of spiral inductors inside the package and connects them to multiple converters operating in the same phase. Inductors share a common magnetic rod to increase coupling, and the power network is split into islands each serving one phase of the load current. This produces 250 nH/mm² inductance density and 10 A/mm² current density while the inductor itself reaches 97.4 percent efficiency at 10 MHz. When the extracted inductor netlist is co-simulated with the converter circuitry, the overall system improves efficiency by 5.65 percent on average and 11.04 percent at 40 A compared with an otherwise identical design that uses uncoupled inductors.

Core claim

The central claim is that an array of tightly coupled spiral square inductors sharing one magnetic rod, placed inside the package and paired with an inductance-island partitioning method, simultaneously raises both inductance density and current density while cutting conversion losses in vertical power delivery networks for high-performance computing.

What carries the argument

The package-embedded coupled inductor array in which multiple spiral square inductors share a common magnetic rod and serve converters of the same phase, optimized jointly with the active circuitry through 3D electromagnetic extraction and circuit co-simulation.

If this is right

  • The inductance-island approach allows the power delivery network to scale by adding more islands without redesigning the entire converter.
  • Joint optimization of the coupled passive array and the active switches produces concrete efficiency gains that grow with load current.
  • The topology maintains an average quality factor of 23.6 while operating at 10 MHz, supporting the high switching frequencies needed for compact converters.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the simulated gains hold in hardware, the method could reduce the fraction of total system power lost in delivery, freeing budget for more compute cores or higher clock rates.
  • The shared-rod geometry may be adapted to other multi-phase buck or boost stages that already use vertical power paths.
  • Successful physical validation would open a route to further density improvements by exploring different rod materials or spiral geometries within the same package constraints.

Load-bearing premise

The 3D electromagnetic simulations and subsequent circuit co-simulations accurately capture all relevant parasitics, material properties, and fabrication effects so the reported densities and efficiency numbers will appear in physical silicon.

What would settle it

Fabricate the described inductor array in silicon, measure its inductance density, current density, and efficiency at the stated operating point, and compare the results directly to the simulated values of 250 nH/mm², 10 A/mm², and 97.4 percent.

Figures

Figures reproduced from arXiv: 2606.02878 by Inna Partin-Vaisband, Rami Rasheedi, Salma Abdelzaher.

Figure 1
Figure 1. Figure 1: Power conversion loss components in high-power [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of embedded inductor design space across [PITH_FULL_IMAGE:figures/full_fig_p001_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Circuit schematic of a two-phase buck converter with [PITH_FULL_IMAGE:figures/full_fig_p002_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: A five-inductor section of the proposed inductor array. [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Coupling coefficients between two inductors separated [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Magnetic characteristics of TY-M5: (a) B-H relation and relative permeability, (b) relative permeability vs. frequency, [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: Island-based multi-phase power delivery scheme uti [PITH_FULL_IMAGE:figures/full_fig_p006_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Performance characteristics of a two-turn segment [PITH_FULL_IMAGE:figures/full_fig_p006_9.png] view at source ↗
Figure 7
Figure 7. Figure 7: Individual inductor dimensions after optimization. [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 10
Figure 10. Figure 10: Temperature map of the inductor array at 2 A DC [PITH_FULL_IMAGE:figures/full_fig_p007_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Inductor island-driven power conversion, (a) hybrid converter architecture [ [PITH_FULL_IMAGE:figures/full_fig_p008_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Performance of a single hybrid converter, (a) output [PITH_FULL_IMAGE:figures/full_fig_p008_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Performance of the individual converters in the proposed coupled power delivery system with ten distributed converters, (a) peak-to-peak output current ripple, and (b) power efficiency gain. Average, minimum, and maximum performance values across the ten converters are reported on the right as referenced to the baseline system Together, these mechanisms introduce an additional high￾frequency loss of 0.335… view at source ↗
read the original abstract

A novel power delivery framework, comprising a package-embedded inductor topology and an inductance-island methodology, is introduced to maximize both inductance and current densities in vertical power delivery (VPD). The framework leverages multiple multi-phase converters, a common strategy in high-performance computing systems, to enhance efficiency and scalability. The proposed topology employs an array of tightly coupled spiral square inductors sharing a common magnetic rod, serving multiple converters operating in the same conversion phase. The array is optimized to maximize coupling and minimize conversion losses, achieving superior inductance and current densities of 250 nH/mm^2 and 10 A/mm^2, respectively. At the system level, the inductance-island methodology partitions the power delivery network into multiple islands, each dedicated to a converter phase and supplying a portion of the load current, thereby enabling scalable and efficient distribution. To validate the framework, the inductor array is designed and simulated in ANSYS Maxwell 3D and Mechanical, exhibiting an average quality factor of 23.6 and efficiency of 97.4% at 2 A load current, 6 V input, and 10 MHz switching frequency. The inductor array netlist is extracted from ANSYS and co-designed in Cadence Virtuoso with a distributed dual-phase power conversion system, ensuring joint optimization of passive and active components. The co-designed converter achieves a significant efficiency gain of 5.65% on average and up to 11.04% at 40 A load over a similar converter with uncoupled inductors, demonstrating the practical benefits of the approach.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a package-embedded array of tightly coupled square spiral inductors sharing a common magnetic rod, combined with an 'inductance-island methodology' that partitions the power delivery network into phase-dedicated islands. The design is intended for vertical power delivery in high-performance computing multi-phase converters. All quantitative results—inductance density of 250 nH/mm², current density of 10 A/mm², inductor efficiency of 97.4 % at 2 A / 10 MHz, and converter efficiency gains of 5.65 % average (up to 11.04 % at 40 A) versus an uncoupled baseline—are obtained from ANSYS Maxwell 3D electromagnetic extraction followed by Cadence Virtuoso co-simulation of a dual-phase converter.

Significance. If the reported simulation fidelity holds in fabricated hardware, the coupled-inductor array and island partitioning could improve both power density and conversion efficiency in package-level VPD, a relevant direction for HPC systems. The explicit use of commercial 3D EM and circuit solvers with stated operating points is a methodological strength, but the complete absence of measured prototypes or independent analytical benchmarks limits the immediate engineering impact.

major comments (2)
  1. [Simulation results and co-design sections (as described in the abstract and validation narrative)] The headline claims (250 nH/mm² inductance density, 10 A/mm² current density, 97.4 % inductor efficiency, and the 5.65 % / 11.04 % system efficiency gains) rest exclusively on the accuracy of the ANSYS Maxwell 3D model at 10 MHz for a shared-rod, package-embedded geometry. No mesh-convergence data, material-property validation, 2-D analytical cross-check, or measured prototype is provided, so any systematic error in skin-effect, proximity-effect, or inter-winding capacitance extraction propagates directly into the central performance assertions.
  2. [System-level co-simulation results] The comparison to the 'similar converter with uncoupled inductors' is performed entirely within the same simulation framework. Without an independent baseline (either measured or analytically derived) or a sensitivity study on coupling-coefficient mismatch, it is unclear whether the reported relative gain is robust to realistic fabrication variations in the shared magnetic rod.
minor comments (2)
  1. The term 'inductance-island methodology' is introduced without a concise algorithmic description or pseudocode; a short dedicated subsection would clarify how the partitioning is performed and how it interacts with the multi-phase converter scheduling.
  2. Figure captions and text should explicitly state the exact load current, input voltage, and switching frequency at which each efficiency number is reported to avoid ambiguity when comparing the 2 A inductor efficiency figure with the 40 A system-level figure.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major comment below and indicate where revisions will be made to strengthen the validation sections.

read point-by-point responses

  1. Referee: [Simulation results and co-design sections (as described in the abstract and validation narrative)] The headline claims (250 nH/mm² inductance density, 10 A/mm² current density, 97.4 % inductor efficiency, and the 5.65 % / 11.04 % system efficiency gains) rest exclusively on the accuracy of the ANSYS Maxwell 3D model at 10 MHz for a shared-rod, package-embedded geometry. No mesh-convergence data, material-property validation, 2-D analytical cross-check, or measured prototype is provided, so any systematic error in skin-effect, proximity-effect, or inter-winding capacitance extraction propagates directly into the central performance assertions.

    Authors: We agree that additional simulation validation is warranted. In the revised manuscript we will add mesh-convergence results from ANSYS Maxwell showing stabilization of inductance and AC resistance with increasing mesh density, explicit material-property values drawn from the simulator library, and a 2-D analytical cross-check for single-spiral inductance using established formulas. These additions will be placed in a new subsection of the validation section. Measured prototypes remain outside the scope of the present simulation study. revision: partial

  2. Referee: [System-level co-simulation results] The comparison to the 'similar converter with uncoupled inductors' is performed entirely within the same simulation framework. Without an independent baseline (either measured or analytically derived) or a sensitivity study on coupling-coefficient mismatch, it is unclear whether the reported relative gain is robust to realistic fabrication variations in the shared magnetic rod.

    Authors: We will add a sensitivity study in the revised manuscript that varies the coupling coefficient by ±10 % around the extracted value and reports the resulting range of efficiency gains. The uncoupled baseline is obtained by setting mutual inductance to zero within the identical extracted netlist, preserving consistency of all other parasitics. While an independent analytical model for the full 3-D array geometry is not feasible, the sensitivity results will quantify robustness to rod-related variations. revision: yes

standing simulated objections not resolved
  • Provision of measured prototype data or hardware validation, as the work is entirely based on electromagnetic and circuit simulation.

Circularity Check

0 steps flagged

No circularity: results are direct simulation outputs

full rationale

The paper's central claims (250 nH/mm² inductance density, 10 A/mm² current density, 97.4% inductor efficiency, 5.65% avg / 11.04% peak system efficiency gain) are obtained from ANSYS Maxwell 3D EM simulation, netlist extraction, and Cadence Virtuoso co-simulation of the dual-phase converter. These quantities are not algebraically forced by any fitted parameters, self-citations, or input definitions; they are independent numerical outputs of external solvers. No self-definitional equations, fitted-input predictions, load-bearing self-citations, uniqueness theorems, or ansatz smuggling appear in the text. The derivation chain is self-contained against the simulation benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The framework rests on the assumption that commercial EM and circuit simulators faithfully represent the fabricated device; no new physical constants or entities with external falsifiability are introduced.

axioms (1)
  • standard math Maxwell's equations and the material models inside ANSYS Maxwell 3D govern inductor behavior
    Invoked by the 3D electromagnetic simulation step that produces the reported inductance, coupling, and quality factor.
invented entities (1)
  • inductance-island methodology no independent evidence
    purpose: Partitioning the power delivery network into phase-dedicated islands for scalability
    Presented as a new system-level technique without independent experimental evidence outside the simulation.

pith-pipeline@v0.9.1-grok · 5823 in / 1416 out tokens · 35091 ms · 2026-06-28T12:59:33.013987+00:00 · methodology

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