Harmonic balance (HB) method is well known principle for analyzing periodic oscillations on nonlinear networks and systems. Because the HB method has a truncation error, approximated solutions have been guaranteed by error bounds. However, its numerical computation is very time-consuming compared with solving the HB equation. This paper proposes an algebraic representation of the error bound using Grobner base. The algebraic representation enables to decrease the computational cost of the error bound considerably. Moreover, using singular points of the algebraic representation, we can obtain accurate break points of the error bound by collisions.

This paper presents the several bifurcation phenomena generated in nonlinear three-phase circuit with symmetry. The circuit consists of delta-connected nonlinear inductors, capacitors and three-phase symmetrical voltage sources. Particular attention is paid to the subharmonic oscillations of order 1/2. We analyze the bifurcations of the oscillations from both theoretical and experimental points. As a tool of analysis, we use the homotopy method. Additionally, by comparing with single-phase and single-phase-like circuits, the special feature of the three-phase circuit is revealed.

This paper presents the several bifurcation phenomena of harmonic oscillations occurred in nonlinear three-phase circuit. The circuit consists of delta-connected nonlinear inductors, capacitors and three-phase symmetrical voltage sources. We analyze the bifurcations of the oscillations by the homotopy method. Additionally, we confirm the bifurcation phenomena by real experiments. Furthermore, we reveal the effect of nonlinear couplings of inductors by the comparison of harmonic oscillations in a single-phase circuit.

This paper describes how the symmetry of a three-phase circuit prevents the symmetric modes of several subharmonic oscillations. First, we make mathematically it clear that the generation of symmetrical 1/3l-subharmonic oscillations (l=1,2,) are impossible in the three-phase circuit. As far as 1/(3l+1)-subharmonic oscillations (l=1,2,) and 1/(3l+2)-subharmonic oscillations (l=0,1,) are concerned, the former in negative-phase sequence and the latter in positive-phase sequence are shown to be impossible. Further, in order to confirm the above results, we apply the method of interval analysis to the circuit equations and obtain all steady state solutions with unsymmetric modes.

This paper presents efficient applications of invariants to harmonic balance (HB) methods using Grobner base. The Grobner base is a powerful tool based on ideal theory. Using the Grobner base, we can obtain the solutions of the HB equation. However, its computation is very time-consuming when the equation has equivalent different solutions based on symmetries of the system. We show that invariants enable to transpose the equivalent different solutions to a unique solution. The bifurcation diagram of the invariant is simpler than the original bifurcation diagram, and its computation is considerably decreased. Further, we can obtain the relation among the amplitudes of each frequency component using the invariants. We propose a method for finding the circuit parameters using the amplitude relation.

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.

Power and ground planes on multilayer PCBs can effectively radiate electromagnetic fields excited by the IC simultaneous switching noise. The high frequency electromagnetic radiation is often calculated from the electric field along the edge of the PCB, which can be estimated with a cavity model using magnetic walls. The excitation of the cavity modes is related to the via current passing through the power bus planes at the interconnection between IC package and PCB. Usually the attention is focused on the differential-mode current of the package pins, but in the present paper it is shown that the common-mode current flowing out from package pins plays a very important role in the excitation of cavity modes, and its neglect implies a fatal underestimation of the electromagnetic radiation from the power bus planes in some circumstances. A second important contribute to the radiation is given by the common mode current on the pins, together with the current flowing on the PCB ground plane. With the proposed equivalent circuit, the effectiveness of decoupling inductors depending on their location and on the value of the parasitic capacitance is studied.

High-speed flash ADCs are useful in high-speed applications such as communication receivers. Due to offset voltage variation in the sub-micron processes, the power consumption and the area increase significantly to suppress variation. As an alternative to suppressing the variation, we have developed a flash ADC architecture that selects the comparators based on offset voltage ranking for reference generation. Specifically, with the order statistics as a basis, our method selects the minimum number of comparators to obtain equally spaced reference values. Because the proposed ADC utilizes offset voltages as references, no resistor ladder is required. We also developed a time-domain sorting mechanism for the offset voltages to achieve on-chip comparator selection. We first perform a detailed analysis of the order statistics based selection method and then design a 4-bit ADC in a commercial 65-nm process and perform transistor-level simulation. When using 127 comparators, INLs of 20 virtual chips are in the range of -0.34LSB/+0.29LSB to -0.83LSB/+0.74LSB, and DNLs are in the range of -0.33LSB/+0.24LSB to -0.77LSB/+1.18LSB at 1-GS/s operation. Our ADC achieves the SNDR of 20.9dB at Nyquist-frequency input and the power consumption of 0.84mW.