Power integrity enhancement in mixed-signal PDNs using diamond-based via-loaded square power island metamaterial structures

1 Introduction

Power distribution networks (PDNs) in multilayer printed circuit boards (PCBs) and electronic packages constitute a fundamental infrastructure for ensuring stable and reliable power delivery in modern high-speed digital and mixed-signal systems. Typically formed by closely spaced power and ground (P/G) planes, PDNs provide low-impedance paths to support the operation of digital logic, as well as sensitive analog and radio-frequency (RF) circuits. However, the continuous scaling of operating frequencies, increasing integration density, and faster signal transition times have significantly exacerbated the challenges associated with maintaining PDN stability (Wu et al., 2010; Wu et al., 2004).

A major factor limiting PDN performance is simultaneous switching noise (SSN), which originates from rapid current transients in high-speed integrated circuits such as processors, field-programmable gate arrays (FPGAs), and application-specific integrated circuits (ASICs). These abrupt current variations excite parasitic inductive elements within the PDN, leading to transient voltage fluctuations that compromise power integrity (PI) (Shen et al., 2016; Zhang et al., 2020). Moreover, the P/G plane pair behaves as a parallel-plate waveguide capable of supporting cavity resonance modes over a broad frequency spectrum. The excitation of these resonances facilitates lateral noise propagation across the PDN, which can couple into adjacent signal traces and sensitive analog/RF components, thereby inducing electromagnetic interference (EMI) and degrading signal integrity (SI) (Zhu et al., 2018; Uma Maheswari et al., 2022). Similar challenges associated with high-speed switching, device scaling, and performance optimization have also been reported in advanced semiconductor and nanoelectronic structures (Panigrahi et al., 2018), (Amani et al., 2024).

Conventional SSN mitigation techniques, including the extensive use of discrete decoupling capacitors, are inherently limited in high-frequency regimes due to parasitic inductance and mounting constraints (Wu et al., 2010). Consequently, electromagnetic bandgap (EBG) and metamaterial-inspired structures have emerged as promising solutions for suppressing SSN by introducing stopband characteristics that inhibit the propagation of cavity modes. A variety of compact EBG configurations—such as cascaded spiral patches (Shen et al., 2016), double-square geometries (Zhang et al., 2020), spiral-slot structures (Zhu et al., 2018), pinwheel and meandered plane designs (Han et al., 2018), and planar compact EBG filters (Bansode and Rathod, 2005)—have demonstrated substantial improvements in broadband noise suppression (Aishwaryaa et al., 2026; Chitra et al., 2026).

Despite these advances, existing approaches predominantly emphasize geometrical optimization while relying on conventional dielectric substrates such as FR4. Such materials exhibit relatively high loss tangent, poor thermal conductivity, and limited high-frequency performance, thereby constraining the overall effectiveness of SSN mitigation. In contrast, diamond has recently emerged as a highly promising dielectric material for high-frequency electronic applications due to its exceptional physical properties, including ultra-low dielectric loss, extremely high thermal conductivity (∼2000 W/mK), and stable permittivity characteristics (Wang et al., 2025; Liu and Ma, 2020; Tharini and Kannammal, 2022). The advantages of advanced materials and process-compatible integration approaches have also been demonstrated in Cu–Cu bonding and microfabrication studies for next-generation electronic platforms (Panigrahy et al., 2024; K et al., 2017). These attributes not only enhance electromagnetic performance but also enable efficient thermal management, which is increasingly critical in high-density electronic systems. Related developments in sensing and intelligent electronic systems further highlight the growing demand for reliable and low-noise interconnect architectures (Adiraju et al., 2021).

1.1 Research gap and problem statement

Notwithstanding the significant progress in metamaterial-based PDN design, the synergistic integration of advanced dielectric materials and engineered electromagnetic structures remains insufficiently explored. In particular, existing solutions fail to simultaneously address wideband SSN suppression and thermal management within a unified design framework suitable for high-frequency mixed-signal environments.

To bridge this gap, this work proposes a diamond-based via-loaded square power island (SPI) metamaterial structure for enhanced PDN performance. By incorporating diamond as the dielectric medium and integrating via-loaded metamaterial features, the proposed design introduces tailored inductive–capacitive characteristics that give rise to a wide electromagnetic stopband. This enables effective suppression of SSN over a broad frequency range while simultaneously improving thermal dissipation.

The proposed structure achieves a peak noise suppression of approximately −72 dB and maintains suppression better than −30 dB across the 8–20 GHz frequency band. The performance is evaluated using full-wave electromagnetic simulations, which demonstrate the effectiveness of the proposed design in suppressing noise propagation. These results indicate that the proposed approach provides a robust and scalable solution for enhancing both power integrity and thermal reliability in next-generation high-speed mixed-signal PDNs.

2 Design of metamaterial unit cell

The design specifications of the proposed structure include a 30 × 30 mm² board size, a two-layer PCB configuration, and a diamond-based substrate characterized by a dielectric constant of εr ≈ 5.5–5.7, an ultra-low loss tangent of tanδ ≈0.0001, and an exceptionally high thermal conductivity of approximately 2000 W/mK. The substrate thickness is selected as h ≈ 0.five to one mm to ensure mechanical stability and optimal electromagnetic performance. The via dimensions include a radius of ∼0.2–0.3 mm and a pitch optimized for effective inductive loading, while the square power island (SPI) unit cell size is designed in the range of 3–5 mm, enabling subwavelength operation and efficient suppression of high-frequency noise.

The proposed metamaterial unit cell consists of a square metallic patch interconnected by narrow bridge lines, forming a periodic lattice on the power distribution plane (Figure 1). This engineered geometry introduces inherent stopband characteristics that suppress noise propagation in the power distribution network through parallel LC resonance.

The equivalent circuit model of a single unit cell is shown in Figure 2, where the bridge lines primarily contribute the inductance LLL, and the gap coupling between adjacent patches provides the capacitance CCC. The center frequency of the stopband can be approximated by the parallel LC resonance conditionwhere ​ f 0 denotes the stopband center frequency. The inductance L increases with longer and narrower bridge lines, while the capacitance C depends on the patch geometry, inter-patch gap, substrate thickness, and dielectric constant, and can be approximated aswhere εr​ is the substrate permittivity, A is the effective overlapping area, and g is the gap spacing.

f 0 = 1 2 π L C (1)

C ∝ ε r A g (2)

As indicated by (1) and (2), parametric variations in bridge length, bridge width, and inter-patch gap directly control the resonant frequency and stopband bandwidth. Increasing the bridge-line inductance shifts the stopband toward lower frequencies and broadens the suppression bandwidth, while reducing the gap-coupling capacitance further enhances broadband noise attenuation. These analytical trends are verified through full-wave electromagnetic simulations, which show strong qualitative agreement with the LC model despite the omission of higher-order coupling and fringing-field effects, thereby validating the proposed metamaterial design methodology.

3 Power integrity analysis with square power island metamaterial structure

The Square power island metamaterial structure is investigated under cascading, long-bridged, and long-bridged-with-via configurations to evaluate its effectiveness in suppressing power/ground noise in high-frequency power distribution networks.

3.1 Analysis of power integrity for square power island metamaterial unit cell

Figure 3 illustrates the structure of the square power island metamaterial unit cell, in which a subwavelength square metamaterial pattern is etched on the power plane, while a signal trace is implemented on the ground plane beneath it. From an electromagnetic perspective, the square power island introduces a distributed inductive effect due to the elongated current path, while the narrow gaps between adjacent square turns and the coupling between the power and ground planes contribute to distributed capacitance. Together, these effects form an effective LC resonant network within the unit cell.

The signal trace on the ground plane provides a well-defined current return path, ensuring controlled signal propagation and reducing unintended current spreading across the power plane. At resonance, the LC behavior of the square metamaterial significantly increases the impedance of the power distribution path, thereby inhibiting the propagation of high-frequency noise. As a result, electromagnetic interference and simultaneous switching noise are effectively suppressed within the stopband frequency range, leading to improved power integrity performance.

Figure 4 presents the simulated S21 response of the square power island metamaterial unit cell, highlighting its role in mitigating simultaneous switching noise within the power distribution network. In SSN theory, rapid and concurrent switching of digital circuits induces transient current spikes that excite resonant modes in the power–ground plane cavity, leading to voltage fluctuations and noise propagation across the PDN. Effective suppression of SSN therefore requires a significant increase in the transfer impedance between noise sources and sensitive circuit regions.

The deep attenuation notch of approximately −59 dB observed at 10 GHz corresponds to a resonance-induced peak in the effective power-plane impedance introduced by the square metamaterial unit cell. The distributed inductive–capacitive behavior of the square geometry impedes the propagation of high-frequency transient currents generated during simultaneous switching events. As a result, noise energy is confined locally and prevented from spreading across the power plane.

Furthermore, the sustained attenuation better than −30 dB over the 8–20 GHz frequency range indicates broadband impedance enhancement, which is essential for suppressing wideband SSN components arising from fast edge rates in modern high-speed digital systems. This behavior confirms that the proposed metamaterial unit cell effectively attenuates both resonant and broadband SSN, thereby significantly improving overall power integrity.

3.2 Design of square power island cascading metamaterial structure

Figure 5 illustrates the power plane incorporating the square power island cascading metamaterial configuration, in which multiple identical metamaterial unit cells are arranged sequentially along the power distribution path. Cascading these unit cells effectively increases the electrical length of the noise propagation path and results in the accumulation of distributed inductive and capacitive effects. Consequently, multiple resonant impedance peaks are introduced, leading to a wider stopband and enhanced broadband attenuation.

Compared to a single unit-cell configuration, the cascading arrangement significantly improves isolation characteristics by progressively attenuating noise as it propagates through successive metamaterial sections. This multi-stage filtering behavior suppresses both resonant and broadband components of simultaneous switching noise, thereby enhancing overall power integrity. As a result, the cascaded square power island metamaterial structure demonstrates superior wideband noise suppression performance and is well suited for high-frequency power distribution network applications.

3.3 Design of square power island long-bridged metamaterial structure

Figure 6 illustrates the square power island long-bridged metamaterial configuration, in which adjacent metamaterial unit cells are interconnected using extended bridge lines. The long-bridge connections increase the effective current path length l, thereby introducing additional series inductance, which can be approximated bywhere w and t represent the width and thickness of the bridge conductor, respectively (Equation 3). As the bridge length increases, the effective inductance between neighboring cells increases proportionally, leading to stronger inductive coupling.

L ∝ μ o l ln 2 l w + t − 1 (3)

This increase in inductance shifts the resonant frequency of the metamaterial structure toward lower frequencies and contributes to the formation of a wider stopband. From a power integrity standpoint, the higher series inductance raises the power-plane transfer impedance, thereby limiting the propagation of high-frequency transient currents associated with simultaneous switching noise. As a result, the long-bridged configuration provides enhanced noise isolation and improved broadband attenuation compared to non-bridged or short-bridge configurations, making it particularly effective for high-speed mixed-signal power distribution networks.

3.4 Design of square power island metamaterial in long bridge with vias

Figure 7 depicts the square power island long-bridged metamaterial structure incorporating vertical vias that connect the power and ground planes. The vias introduce additional vertical current paths, increasing the effective inductance of the power distribution network. The via inductance can be approximated aswhere h is the substrate thickness and d is the via diameter (Equation 4). Combined with the inductive effects of the long-bridge connections, this added inductance significantly increases the power-plane impedance.

L v i a ≈ μ 0 h 2 π ln 4 h d , (4)

Moreover, the vias enhance capacitive coupling between the power and ground planes, forming a three-dimensional LC resonant network that shifts the resonant frequency and broadens the stopband. From a simultaneous switching noise perspective, the additional current return paths confine transient switching currents locally, thereby reducing noise propagation. Consequently, the via-loaded long-bridged metamaterial structure provides improved broadband noise isolation and superior SSN suppression compared to the configuration without vias.

The proposed diamond-based via-loaded SPI metamaterial achieves −72 dB noise suppression at 14 GHz through the combined effect of electromagnetic bandgap (EBG) behavior and LC resonance. The periodic diamond cells and metallized vias form an equivalent inductive–capacitive network, where via inductance and inter-cell capacitance create a stopband that blocks high-frequency noise propagation in the PDN. The resulting high surface impedance and localized field confinement suppress surface-wave and switching-noise transmission, while the diamond geometry improves current redistribution and enhances stopband depth.

3.5 Comparison results

Figures 8, 9 compare the simulated S21 responses of the cascaded and long-bridged square power island metamaterial structures, and the long-bridged EBG with the via-loaded square configuration, respectively. The square power island structure consistently outperforms the modified straight-line long-bridged design across the entire frequency band.

As shown in Figure 8, a maximum attenuation of approximately −65 dB is achieved at 19 GHz, with suppression remaining better than −30 dB over 8–20 GHz due to the increased electrical path length and enhanced inductive coupling introduced by the square geometry. Figure 9 demonstrates that the inclusion of vertical vias further improves performance, yielding a peak attenuation of approximately −72 dB at 14 GHz as a result of added via inductance and three-dimensional LC coupling.

From a simultaneous switching noise perspective, the combined effects of square geometry, long-bridge interconnections, and vias increase power-plane impedance and confine transient switching currents locally, thereby significantly reducing noise propagation and improving broadband power integrity.

Compared with FR4 and Rogers substrates, the diamond dielectric improves PDN performance due to its low dielectric loss and high thermal conductivity. Simulation results indicate lower S21 loss, reduced voltage ripple, improved current return paths, and lower temperature rise, leading to enhanced power integrity and thermal stability under high-frequency operation.

Tolerance and yield analysis confirm that the proposed structure is robust to fabrication variations and via parasitics. Parametric and statistical process variation simulations show only small resonance shifts under dimensional and process deviations, while suppression performance remains largely unchanged. The results indicate high fabrication yield and stable operation, supporting practical mixed-signal PCB implementation.

The proposed metamaterial PDN effectively suppresses SSN by reducing PDN resonances and electromagnetic coupling. Simulation results show lower voltage ripple and reduced ground bounce under high switching conditions, improving power integrity and operational stability in 5G, AI, and FPGA platforms.

4 Conclusion and future work

4.1 Conclusion

The proposed diamond-based via-loaded square power island (SPI) metamaterial achieves effective wideband noise suppression in high-frequency PDNs, with up to −72 dB attenuation and better than −30 dB over 8–20 GHz. Leveraging diamond’s low loss and high thermal conductivity, the design enhances both electromagnetic and thermal performance. Integration into multilayer PCBs and 2.5D/3D IC packages is challenged by via density, alignment tolerance, and interconnect parasitics. However, the compact unit-cell geometry, compatibility with standard PCB processes, and high thermal conductivity of diamond support feasible integration in advanced package-level PDN designs. The results, validated through full-wave simulations, confirm its effectiveness for improving power integrity in compact high-speed mixed-signal systems.

4.2 Future work

The proposed diamond-based via-loaded SPI metamaterial provides strong noise suppression and thermal performance but is limited by high cost, fabrication complexity, and use of a two-layer PCB without real-time SSN validation.

Future work will focus on experimental validation, FPGA-based implementation, wideband suppression enhancement, and integration with package-level PDNs and 2.5D/3D systems. Further studies will also evaluate thermal reliability and AI-assisted design optimization for adaptive noise mitigation.

Generative AI statement

The author(s) declared that generative AI was not used in the creation of this manuscript.

Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Footnotes

Edited by: Marco Girolami, National Research Council (CNR), Italy

Reviewed by: Asisa Kumar Panigrahy, ICFAI Foundation for Higher Education, India

M. Malagonda.SivaKumar, Jawaharlal Nehru Technological University Anantapur College of Engineering Pulivendula, India