This paper describes the equivalent-circuit model of a metamaterial composed of conducting spheres and wires. This model involves electromagnetic coupling between the conductors, with retardation. The lumped-parameter equivalent circuit, which imports retardation to the electromagnetic coupling, is developed in this paper from Maxwell's equation. Using the equivalent-circuit model, we clarify the relationship between the retardation and radiation loss; we theoretically demonstrate that the electromagnetic retardation in the near-field represents the radiation loss of the meta-atom in the far-field. Furthermore, this paper focuses on the retarded electromagnetic coupling between two meta-atoms; we estimate the changes in the resonant frequencies and the losses due to the distance between the two coupled meta-atoms. It is established that the dependence characteristics are significantly affected by electromagnetic retardation.
Placing a guard trace next to a signal line is the conventional technique for reducing the common-mode radiation from a printed circuit board. In this paper, the suppression of common-mode radiation from printed circuit boards having guard traces is estimated and evaluated using the imbalance difference model, which was proposed by the authors. To reduce common-mode radiation further, a procedure for designing a transmission line with guard traces is proposed. Guard traces connected to a return plane through vias are placed near a signal line and they decrease a current division factor (CDF). The CDF represents the degree of imbalance of a transmission line, and a common-mode electromotive force depends on the CDF. Thus, by calculating the CDF, we can estimate the reduction in common-mode radiation. It is reduced not only by placing guard traces, but also by narrowing the signal line to compensate for the variation in characteristic impedance due to the guard traces. Experimental results showed that the maximum reduction in common-mode radiation was about 14 dB achieved by placing guard traces on both sides of the signal line, and the calculated reduction agreed with the measured one within 1 dB. According to the CDF and characteristic impedance calculations, common-mode radiation can be reduced by about 25 dB while keeping the characteristic impedance constant by changing the gap between the signal line and the guard trace and by narrowing the width of the signal line.
In this paper, an improved common-mode antenna model is proposed to quickly predict a common-mode excitation and radiation of printed circuit boards (PCBs). The improved common-mode antenna model is based on a common-mode potential distribution over the two-dimensional plane. Although the original common-mode antenna model explains the commonmode excitation well by introducing a "current division factor (CDF)" of a one-dimensional parameter which represents a degree of imbalance of a transmission line, but it is applicable for limited cases of PCB shapes. To remove the shape limitation, the improved model proposed here uses a "common-mode potential conversion factor (CPCF)." The CPCF is a two-dimensional parameter expanded from the CDF. The improved commonmode antenna model attains good accuracy with experimental measurements and numerical calculations using FDTD method in terms of electromagnetic interference (EMI). The calculation done using this model was extremely fast compared to that with the real structure.
SUMMARYA guard trace placed near a signal line reduces commonmode radiation from a printed circuit board. The reduction effect is evaluated by the imbalance difference model, which was proposed by the authors, when the guard trace has exactly the same potential as the return plane. However, depending on interval of ground connection of the guard trace, the radiation can increase when the guard trace resonates. In this paper, the authors show that the increase of radiation is caused by the common mode, and extend the imbalance difference model to explain a mechanism of increase of common-mode radiation. Additionally, the effective via location of the guard trace is proposed to reduce the number of vias. The guard trace voltage due to the resonance excites the common mode at the interface where the cross-sectional structure of the transmission line changes since the common-mode excitation is expressed by the product of the voltage and the difference of current division factors. To suppress the common-mode excitation, the guard trace should be grounded at the point where the cross-sectional structure changes. As a result, the common-mode radiation decreases even when the guard trace resonates.
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