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 a differential transmission line, a large common-mode radiation is excited due to its asymmetry. In this paper, the imbalance difference model, which was proposed by the authors for estimation of common-mode radiation, is extended to apply to the differential signaling systems. The authors focus on a differential transmission line with asymmetric property, which consists of an adjacent return plane and two signal lines which are placed close to an edge of the return plane. Three orthogonal transmission modes, a normal mode, a primary common mode and a secondary common mode, are defined. Among these transmission modes, the secondary common mode is dominant in radiation, and a mechanism of the secondary common-mode generation is explained. The radiated emission which was calculated using the imbalance difference model was in good agreement with that obtained by full wave calculation.

We propose a novel technique of matching at both ends of the guard trace to suppress resonance. This approach is derived from the viewpoint that the guard trace acts as a transmission line. We examined that matched termination suppresses guard-trace resonance through simulating a circuit and measuring radiation. We found from these results that the proposed method enables guard-trace voltages to remain low and hence avoids increases in radiation. In addition, we demonstrated that "matched termination at the far end of the guard trace" could suppress guard-trace resonance sufficiently at all frequencies. We eventually found that at least two vias at both ends of the guard trace and only one matching resistor at the far end could suppress guard-trace resonance. With respect to fewer vias, the method we propose has the advantage of reducing restrictions in the printed circuit board layout at the design stage.

An equivalent-circuit model is an effective tool for the analysis and design of metamaterials. This paper describes a systematic and theoretical method for the circuit modeling of meta-atoms. We focus on the structures of wired metallic spheres and propose a method for deriving a sophisticated equivalent circuit that has the same topology as the wires using the partial element equivalent circuit (PEEC) method. Our model contains the effect of external electromagnetic coupling: excitation by an external field modeled by voltage sources and radiation modeled by the radiation resistances for each mode. The equivalent-circuit model provides the characteristics of meta-atoms such as the resonant frequencies and the resonant modes induced by the current distribution in the wires by an external excitation. Although the model is obtained by a very coarse discretization, it provides a good agreement with an electromagnetic simulation.

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.

A guard trace placed near a signal line reduces common-mode 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.