In general, tunnel diodes exhibit various types of oscillation mode: the sinusoidal mode or the nonsinusoidal mode which is known as the relaxation oscillation (RO) mode. We derive a condition for generating the RO in resonant tunneling diodes (RTDs) with essential components for equivalent circuit model. A conditional equation to obtain sufficient nonlinearity towards the robust RO is clarified. Moreover, its condition also can be applied in case of a bow-tie antenna integrated RTD, thus a design policy to utilize the RO region for the antenna integrated RTD is established by numerical evaluations of time-domain large-signal nonlinear analysis towards a terahertz transmitter for broadband wireless communications.

New Recommendation and Future Standards highlight the Power Factor Correction (PFC) converter as a basic requirement for switching power supplies. Most high-frequency power factor correctors use resistor emulation to achieve a near-unity power factor and a small line current distortion. This technique requires forcing the input current with an average-current-mode control to follow the input voltage. Stability of this system was discussed previously by using some linear models. However, in this paper, two nonlinear phenomena have been encountered in the PFC circuit, period doubling bifurcation and chaos. Detection of these new instability phenomena in the stable regions predicted by the prior linear PFC models makes us more susceptible towards them, and reveals the need to consider a nonlinear models. A nonlinear model performing the practical operation of a boost PFC converter has been developed. Then, a simplified and accurate nonlinear model has been proposed and verified experimentally. As a result from this model, instability maps have been introduced to determine the boundary between stable and unstable operating ranges. Then, the period doubling bifurcation has been studied through a new proposed technique based on the capacitor storage energy. It is cleared that, As the load lessens, a required extra storage power is needed to achieve the significant increase in the output voltage. Then, if the PFC system can provide this extra energy, the operation can reach stability with new zero-storage energy else the system will have double-line zero energy that is period doubling bifurcation.

A stability of the cascade two-stage Power-Factor-Correction converter is investigated. The first stage is boost PFC converter to achieve a near unity power factor and the second stage is forward converter to regulate the output voltage. Previous researches studied the system using linear analysis. However, PFC boost converter is a nonlinear circuit due to the existence of the multiplier and the large variation of the duty cycle. Moreover, the effect of the second stage DC/DC converter on the first stage PFC converter adds more complexity to the nonlinear circuit. In this issue, low-frequency instability has been detected in the two-stage PFC converter assuring the limitation of the prior linear models. Therefore, nonlinear model is proposed to detected and explain these instabilities. The borderlines between stable and unstable operation has been made clear. It is cleared that feedback gains of the first stage PFC and the second stage DC/DC converters are the main affected parts to the total system stability. Then, a simplified nonlinear model is provided. Experiment confirm the two models with a good agreement. These nonlinear models have introduced new PFC design scheme by choosing the minimum required output capacitor and the feedback loop design.

From the bifurcation viewpoint, this study examines a boost PFC converter with average-current-mode control. The boost PFC converter is considered to be a nonlinear circuit because of its use of a multiplier and its large duty cycle variation for input current control. However, most previous studies have implemented linear analysis, which ignores the effects of nonlinearity. Therefore, those studies were unable to detect instability phenomena. Nonlinearity produces bifurcations and chaos when circuit parameters change. The classical PFC design is based on a stable periodic orbit that has desired characteristics. This paper describes the main bifurcations that this orbit may undergo when the parameters of the circuit change. In addition, the instability regions in the PFC converter are delimited. That fact is of practical interest for the design process. Moreover, a prototype PFC circuit is introduced to examine these instability phenomena experimentally. Then, a special numerical program is developed. Bifurcation maps are provided based on this numerical study. They give a comprehensive outstanding for stability conditions and identify stable regions in the parameter space. Moreover, these maps indicate PFC converter dynamics, power factors, and regulation. Finally, numerical analyses and experimentation show good agreement.

Higher-order harmonics and distortions generated by nonlinearity of capacitance-voltage characteristic of a single varactor and an anti-series-connected varactor pair are analyzed and compared. The effect of linear and parabolic terms of nonlinearity to harmonics outputs and distortions is discussed. It is shown that an anti-series-connected varactor pair has a completely suppressed linear term and reduced parabolic term. The advantage of an anti-series-connected varactor pair is theoretically explained.

A nonlinear Volterra-series analysis of multiple ion-implanted GaAs FETs is given that relates carrier profile parameters of ion-implantation to nonlinear rf characteristics of a FET. Expressions for nonlinear coefficients of transconductance are derived from drain current-voltage characteristics of a multiple ion-implanted FET. Nonlinear transfer functions (NLTFs) are then obtained using Volterra series approach. Using these NLTFs third-order intermodulation distortion and power gain are explicitly given. A good agreement has been found between the calculation and the measurement for a medium power GaAs FET with a total gate width of 800 µm operated at 10-dB back off, verifying the usefulness of the present analysis.

An efficient large-signal modeling method of FET using load-line analysis is proposed, and it is applied to non-linear characterization of FET. In this method, instantaneous drain-source voltage Vds(t) and drain-source current Ids(t) waveforms are determined by load-line analysis while non-linear parameters in a large-signal equivalent circuit of FET are defined as the average values over one period corresponding to instantaneous Vds(t) and Ids(t). Output power (Pout), power added efficiency (ηadd), and phase deviation calculated by using such an equivalent circuit of FET agree well with the measured results at 933.5 MHz. Phase deviation mechanism is explained based on the large-signal equivalent circuit of FET, and it is shown how non-linear parameters, such as trans-conductance (gm), drain-source resistance (Rds), gate-source capacitance (Cgs), and gate leak resistance (Rig) contribute to positive or negative phase deviations. The difference between small-signal and large-signal S-parameters (S11, S12, S21, S22) is also discussed. The proposed large-signal modeling method is considered to be useful for the design of high power, high efficiency, and low distortion amplifiers as well as the investigation of the behavior of FET in large-signal operating conditions.

This report introduces a new approach to the time domain analysis of the magnetostatic wave in ferrite materials. The time domain analysis is carried out by the finite difference time domain (FDTD) method. To include the gyromagnetic properties which is the origin of magnetostatic wave, direct differentiation of magnetic dipole moment equation in time and space domains without any approximation are carried out and is combined with Maxwell's equation under the FDTD method. As a result, the possibilities of the analysis on the magnetostatic wave with the FDTD method are confirmed and the validities of this approach are confirmed by some inspections. In addition, the analyses of the nonlinear characteristics on the magnetostatic backward volume waves (MSBVW) are carried out and clarify the dependance of the space profile on the input power.

This paper describes a new approach to analyze nonlinear characteristics of propagating waves in a ferrite material. As to the formulation of the wave in a ferrite medium, the analysis in this paper is not taken under the assumption of a sinusoidal steady state using Polder tensor permeability, but taken by directly differentiating the gyromagnetic equation in time domain without any linear approximations. Then it is combined with Maxwell equation in FDTD procedure. As a result, intensity-dependent nonlinear responses of the propagating wave are confirmed, and the nonlinearity is seen in only the right-hand polarization wave. It is also found that an effect of the damping term in the equation of the motion of the magnetization has nonlinear characteristics for wave propagation.

This paper reviews two topics of nonlinear system analysis done in Japan. The first half of this paper concerns with nonlinear system analysis through the nondeterministic operator theory. The nondeterministic operator is a set-valued or fuzzy set valued operator by K. Horiuchi. From 1975 Horiuchi has developed fixed point theorems for nondeterministic operators. Using such fixed point theorems, he developed a unique theory for nonlinear system analysis. Horiuchi's theory provides a fundamental view point for analysis of fluctuations in nonlinear systems. In this paper, it is pointed out that Horiuchi's theory can be viewed as an extension of the interval analysis. Next, Urabe's theory for nonlinear boundary value problems is discussed. From 1965 Urabe has developed a method of computer assisted existence proof for solutions of nonlinear boundary value problems. Urabe has presented a convergence theorem for a certain simplified Newton method. Urabe's theorem is essentially based on Banach's contraction mapping theorem. In this paper, reformulation of Urabe's theory using the interval analysis is presented. It is shown that sharp error estimation can be obtained by this reformulation. Both works discussed in this paper have been done independently with the interval analysis. This paper points out that they have deep relationship with the interval analysis. Moreover, it is also pointed out that these two works suggest future directions of the interval analysis.

The purpose of the present paper is to review a state of the art of nonlinear analysis with the self-validating numerical method. The self-validating numerics based method provides a tool for performing computer assisted proofs of nonlinear problems by taking the effect of rounding errors in numerical computations rigorously into account. First, Kantorovich's approach of a posteriori error estimation method is surveyed, which is based on his convergence theorem of Newton's method. Then, Urabe's approach for computer assisted existence proofs is likewise discussed. Based on his convergence theorem of the simplified Newton method, he treated practical nonlinear differential equations such as the Van der Pol equation ahd the Duffing equation, and proved the existence of their periodic and quasi-periodic solutions by the self-validating numerics. An approach of the author for generalization and abstraction of Urabe's method are also discribed to more general funcional equations. Furthermore, methods for rigorous estimation of rounding errors are surveyed. Interval analytic methods are discussed. Then an approach of the author which uses rational arithmetic is reviewed. Finally, approaches for computer assisted proofs of nonlinear problems are surveyed, which are based on the self-validating numerics.