This paper presents efficient and easily implementable methods for the characteristic analysis and tolerance analysis of nonlinear resistive circuits using integer programming. In these methods, the problem of finding all characteristic curves or all solution sets (regions of possible operating points) is formulated as a mixed integer programming problem, and it is solved by a high-performance integer programming solver such as CPLEX. It is shown that the proposed methods can easily be implemented without making complicated programs, and that all characteristic curves or all solution sets are obtained by solving mixed integer programming problems several times. Numerical examples are given to confirm the effectiveness of the proposed methods.

A new algorithm is proposed for finding all solutions of piecewise-linear resistive circuits using separable programming. In this algorithm, the problem of finding all solutions is formulated as a separable programming problem, and it is solved by the modified simplex method using the restricted-basis entry rule. Since the modified simplex method finds one solution per application, the proposed algorithm can find all solutions efficiently. Numerical examples are given to confirm the effectiveness of the proposed algorithm.

Homotopy methods are known to be effective methods for finding DC operating points of nonlinear circuits with the theoretical guarantee of global convergence. There are several types of homotopy methods; as one of the most efficient methods for solving bipolar transistor circuits, the variable-gain homotopy (VGH) method is well-known. In this paper, we propose an efficient VGH method for solving bipolar and MOS transistor circuits. We also show that the proposed method converges to a stable operating point with high possibility from any initial point. The proposed method is not only globally convergent but also more efficient than the conventional VGH methods. Moreover, it can easily be implemented in SPICE.

In advance of network communication society by the internet, the way how to send data fast with a little loss becomes an important transportation problem. A generalized maximum flow algorithm gives the best solution for the transportation problem that which route is appropriated to exchange data. Therefore, the importance of the maximum flow algorithm is growing more and more. In this paper, we propose a Maximum-Flow Neural Network (MF-NN) in which branch nonlinearity has a saturation characteristic and by which the maximum flow problem can be solved with analog high-speed parallel processing. That is, the proposed neural network for the maximum flow problem can be realized by a nonlinear resistive circuit where each connection weight between nodal neurons has a sigmodal or piece-wise linear function. The parallel hardware of the MF-NN will be easily implemented.

Finding DC operating points of transistor circuits is a very important and difficult task. The Newton-Raphson method employed in SPICE-like simulators often fails to converge to a solution. To overcome this convergence problem, homotopy methods have been studied from various viewpoints. For efficiency of homotopy methods, it is important to construct an appropriate homotopy function. In conventional homotopy methods, linear auxiliary functions have been commonly used. In this paper, a homotopy method for solving transistor circuits using a nonlinear auxiliary function is proposed. The proposed method utilizes the nonlinear function closely related to circuit equations to be solved, so that it efficiently finds DC operating points of practical transistor circuits. Numerical examples show that the proposed method is several times more efficient than conventional three homotopy methods.

Finding DC operating points of nonlinear circuits is an important and difficult task. The Newton-Raphson method adopted in the SPICE-like simulators often fails to converge to a solution. To overcome this convergence problem, homotopy methods have been studied from various viewpoints. For the global convergence of homotopy methods, it is a necessary condition that a given initial solution is the unique solution to the homotopy equation. According to the conventional criterion, such an initial solution, however, is restricted in some very narrow region. In this paper, considering the circuit interpretation of homotopy equations, we prove theorems on the uniqueness of an initial solution for globally convergent homotopy methods. These theorems give new criteria extending the region wherein any desired initial solution satisfies the uniqueness condition.

This paper surveys the research topics and results on nonlinear theory and its applications which have been achieved in Japan or by Japanese researchers during the last decade. The paticular emphasis is placed on chaos, neural networks, nonlinear circuit analysis, nonlinear system theory, and numerical methods for solving nonlinear systems.

The use of the column-rank of the system sensitivity matrix as a testability measure for parametric faults in linear analog circuits was pioneered by Sen and Saeks in 1970s, and later re-introduced by several others. Its practical use has been limited by how it can be calculated. Numerical algorithms suffer from inevitable round-off errors, while traditional symbolic techniques can only handle very small circuits. In this paper, an efficient method is introduced for the analysis of Sen and Saeks' analog testability. The method employs determinant decision diagram based symbolic circuit analysis. Experimental results have demonstrated the new method is capable of handling much larger analog circuits.

The efficiency and reliability of an ultrasonic motor, operating in longitudinal-torsional degenerate-mode, are investigated. It is essential to miniaturize both longitudinal and torsional mode piezoelectric ceramic elements, in order to produce low-cost ultrasonic motors, and to realize a motor with low battery power consumption. The ultrasonic motor is designed with an accurate mechanical equivalent circuit, which can produce high design precision notwithstanding low computation cost. It is important in this design that the resonant frequencies of longitudinal mode and torsional mode coincide with each other under the pertinent rotor pressing force and longitudinal and torsional mode piezoelectric ceramic elements are located in the vibration nodes for the longitudinal mode and the torsional mode, respectively. As a result, the fabricated motor, whose rotor diameter was 12 mm, produced 480 r.p.m. no-load revolution speed, 0.55 kgfcm maximum torque, 50% maximum efficiency, 2.5 W consumed power and a lifetime over 1000 hours with continuous rotation.

This paper describes a circuit analysis technique that includes all circuit elements used in transistor Colpitts quartz crystal oscillators. This technique is applied to a quartz crystal oscillator that has a tank circuit for selecting the oscillation frequency. The results obtained with this technique are compared with SPICE simulation results. Good agreement in the results clearly shows the validity of our technique.

This paper reviews the historical aspect of contributions on the theory of analysis and diagnosis of linear circuits, which have been made by Japanese researchers in these twenty years. On papers of diagnosis, those related to element-value solvability (or determinability) are mainly reviewed. Some important problems are suggested.