###### Abstract  
In modern printed electronics, the performances of a circuit and a device are severely deteriorated by the electromagnetic noise in the gigahertz (GHz) frequency range, such as the simultaneous switching noise and ground bounce noise. A compact and multi-stack electromagnetic bandgap (CMS-EBG) structure is proposed to suppress the electromagnetic noise over the GHz frequency range with a short distance between a noise source and a victim on multilayer printed circuit boards (MPCBs). The original configuration of the stepped impedance resonators is presented to efficiently form multiple stacks of EBG cells. The noise suppression characteristics of the CMS-EBG structure are rigorously examined using Floquet-Bloch analysis. In the analysis, dispersion diagrams are extracted from an equivalent circuit model and a full-wave simulation model. It is experimentally verified that the CMS-EBG structure suppresses the resonant modes over the wideband frequency range with a short source-to-victim distance; thus, this structure substantially mitigates GHz electromagnetic noise in compact MPCBs. electromagnetic bandgap; multi stack; noise suppression; printed circuit boards +
Footnote †: journal: Applied Physics Letters  
_Applied Physics Letters_  
problem [6; 7; 8; 9]. In mixed-signal MPCBs, DC power buses are essential for properly delivering power to the circuits. Power buses connect the chips with power sources such as the regulator and DC/DC converter. The power buses are patterned on any metal layer in the MPCBs. The power buses are mostly designed by using solid metal planes to reduce the design complexity. Considering the electromagnetic wave theory, the electromagnetic characteristics of the previous power buses are equivalent to a parallel plate waveguide (PPW). In a PPW-based power bus of mixed-signal MPCBs, numerous resonant modes in the wideband frequency range are excited, which induces the GHz electromagnetic noise couplings between a noise source and a victim [6; 7; 8; 9]. Moreover, the short horizontal distance from a noise source to a victim device for a compact system results in a severe electromagnetic interference. Consequently, wideband noise suppression with a short distance between the noise source and the victim is required for the high performance of MPCBs. Numerous studies are presented to suppress the resonant modes of a PPW in the GHz frequency range. In particular, electromagnetic bandgap (EBG) structures show vastly superior characteristics to suppress the resonant modes in a wideband frequency range [10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20]. The EBG structure is the engineered material used to obtain a broad stopband, where the propagation of a GHz noise wave is prevented. In the EBG structure, unit cells (UCs) are periodically arranged in the same horizontal plane. The UCs may include an equivalent LC resonator or a stepped impedance resonator to suppress the GHz electromagnetic noise. The previous EBG structures have the advantage of a wideband stopband in the GHz frequency range. However, the previous EBG structures are designed based on a planar structure, so they require a sufficiently large number of UCs that are placed horizontally between a noise source and a noise victim. In other words, a large horizontal distance from the source to the victim is required. As shown in Figure 1, the source-to-victim distance is equivalent to the product of the number and the size of EBG UCs, which are substantially large. To reduce the horizontal area of the EBG structure, the multi-layer EBG structures with LC resonators are presented [21; 22]. However, they did not focus on reducing the source-to-victim distance. To maintain or enhance the characteristics of the previous EBG structures, it is inevitable to place the large number of EBG UCs, which increase the horizontal distance between the source and the victim.