## 1 Introduction  
In current high-speed and mixed-signal electronics, the processor speed and communication data rate have been extremely increased to achieve massive computing platforms with high bandwidth data transfers. For instance, consumer electronics such as mobile phones and tablet PCs possess a CPU with several giga-hertz (GHz) clock speeds and a serial communication device with multi-giga byte per second (GBps) data rates. The significant increases in switching speeds and data rates also induce a wideband switching noise called simultaneous switching noise (SSN) or ground bounce noise (GBN). Commonly, SSN bandwidth is more than several GHz frequencies, thus causing a serious electromagnetic interference (EMI) problem including the logic failure of digital devices and voltage margin reduction in analog devices. Moreover, the SSN characteristics of wideband bandwidth and high frequency harmonics allow it to be easily coupled to signal lines, which results in signal waveform distortion, low bit error rate (BER), and low reliability.  
Numerous studies have focused on suppressing the parallel plate waveguide (PPW) modes in packages and PCBs because SSN is mainly generated when a switching device excites a PPW,which is commonly employed as a power/ground plane pair for the DC power supply in high-speed packages and PCBs. To mitigate PPW modes, various techniques such as decoupling capacitors, slotted planes, and electromagnetic bandgap (EBG) structures have been presented [1; 2; 3; 4; 5; 6; 7; 8; 9]. Among these, EBG structures are prominent approaches for suppressing PPW modes over wideband frequency ranges. EBG structures have the advantages of wideband suppression, a high level of suppression, small effect on high-frequency parasitics, ease of fabrication, and cost effectiveness. Since the first design, the mushroom-type EBG (MT-EBG), EBG structures have continuously evolved to improve their bandgap characteristics. Early development studies [6; 7; 8; 9; 10; 11] mainly focused on extending the stopband bandwidth.  
In [10], heterogeneous EBG cells were combined to superimpose different stopbands for an effectively wideband stopband. However, this resulted in an inevitable substantial increase in board size. In [11], multiple vials equally distributed on the patch were used. This improved the stopband bandwidth, however, the low cut-off frequency was increased, which increased the EBG unit cell (UC) size. Even though the EBG is desirable for widening the stopband bandwidth, reducing the UC size is particularly important for the practical application of EBG structures. To address this, the DGS technique was introduced in [12; 13]. These techniques achieved both a wideband stopband and reduction in UC size. However, the size reduction was not enough to permit the use of EBG structures in high-speed packages and PCBs of certain applications. Moreover, the DGS may cause a signal integrity problem.  
In [14] and [15], high dielectric-constant materials and inter-level branches, respectively, were employed to improve the stopband bandwidth by only decreasing the low cut-off frequency. However, these methods increased manufacturing cost and led to complex design issues. Consequently, a new EBG structure is needed which includes a small sized UC, low cost, good signal integrity, and simple analysis.  
In this paper, we propose a miniaturized EBG structure using an inductance-enhanced patch (IEP) for the suppression of PPW modes in high-speed packages and PCBs. The proposed IEP technique substantially reduces the EBG-UC size without increasing manufacturing cost, degrading signal integrity characteristics, or increasing design complexity. A dispersion analysis based on [PERSON]'s theorem was conducted to examine the IEP effects on a stopband. The performance of the proposed IEP-EBG structure was verified through measurements.