## 1. Introduction

[2] In terms of electromagnetic interference (EMI) in electronics devices, there are various potential radiators of electromagnetic (EM) waves called EMI antennas, such as a printed circuit board (PCB), slot, and chassis, in electronic devices [*Paul*, 1991]. Since power-ground planes in PCB have two parallel planes, it resembles a microstrip antenna. If decoupling and/or grounding in the power-ground plane pair does not work well, certain high frequency current could leak out with the largest amplitude at the resonance of the EMI antenna formed by the parallel plane pair. This kind of radiation from a multilayer PCB is considered as one of the main sources of EMI from electronic devices. Although many literatures have discussed the power integrity problems and power bus noise of the parallel plane pair [*Fan et al.*, 2001; *Wang et al.*, 2005; *Engin et al.*, 2006, 2007; *Leone*, 2003; *Nishida et al.*, 2007], effective design guidelines for suppressing the EM radiation still remain unclear. Effective methods for predicting and suppressing EMI are desirable, which can maintain signal integrity (SI) over a broad band and have a clear physical meaning at the same time.

[3] Although common-mode (CM) component can dominate the total EM radiation at low frequencies (approximately 30 MHz–1 GHz), it has been found that differential-mode (DM) component should be taken into account in predicting EM radiation at the gigahertz frequencies [*Kayano et al.*, 2005]. Nevertheless, since the DM component can be predicted by transmission line theory, correct prediction of CM at low frequencies is the key to the prediction of the total EMI behavior. Some mechanisms by which DM could be converted to CM noise sources have been demonstrated in the works by *Hockanson et al.* [1996], *Kami and Tobana* [1997], *Watanabe et al.* [2000], *Wada* [2003], and *Shim and Hubing* [2005]. These mechanisms include the disturbance of the ground potential due to ground inductance (current-driven) and the formation of a CM current path due to capacitive coupling (voltage-driven) [*Hockanson et al.*, 1996]. The current and voltage-driven mechanisms are models for lower frequencies (below the first resonance of EMI antenna). Some other methods for predicting EM radiation require measurements of the CM current at one point on a cable, and an antenna factor. The imbalance difference model [*Watanabe et al.*, 2000; *Wada*, 2003] is another successful model for predicting the CM radiation from a PCB. The results calculated by the ground-inductance model (current-driven mechanism) and the imbalance difference model were in good agreement at the lower frequencies. Both models adequately represent the phenomenon of the CM generation. However, for mitigation of EMI problems, the identification of the primary coupling mechanisms is not possible in the imbalance difference model, making the method insufficient for developing design guidelines. It is necessary to accumulate a lot of data for the transfer impedance which would be related EMI coupling paths in PCBs, and to make some suggestions for the design guideline. Therefore, a new model for predicting EM radiation from practical multilayer PCBs is needed to overcome the various limitations of the conventional approaches.

[4] Full-wave analysis such as the finite difference time domain (FDTD) method and the Finite Element Method (FEM) is suitable for PCB geometries to estimate their EMI and SI performance in high-speed electronic designs. However, full-wave analysis is time and memory consuming and could be very inefficient due to complex geometry and mixed scales among traces, multilayer planes with gaps, and vias. Hence, an effective physics-based model for predicting SI/EMI, which needs to have clear physical meanings so that EMI and SI design guidelines can be developed, is preferred.

[5] In this paper, characteristics of EM radiation from a stripline with a thin wire is investigated and predicted by an equivalent circuit model. The frequency responses of CM current on the PCB and EM radiation from the stripline structure are studied with FDTD modeling to provide basic considerations for the realization of methods for predicting EM radiation from the stripline structure. Then, an equivalent circuit model for predicting the CM current is proposed from the FDTD results. The equivalent circuit model for prediction is constructed based on the concepts of CM antenna impedance and distributed constant circuit. Finally, the validity of the equivalent circuit model is demonstrated by comparing the predictions with the FDTD simulation results.