This paper proposes an efficient reduction method for a substrate network model, which is extracted from layout data, to analize a substrate coupling noise. The proposed method adopts in a reduction operation a hierarchic structure of a substrate RC network model, a computational procedure using matrix elements, and an expression of admittance as polynominal in complex frequency s=jω. These techniques improve computational efficiency and are suitable for an implementation. In the example of a triple well CMOS circuit, a reduced model, from 7500 nodes to 5 nodes, has less than 25% errors up to 1 GHz.

This paper presents the mixed time-frequency steady-state analysis method for efficient simulation of circuits whose excitation frequencies are widely separated. These circuits can be written by multitime partial differential equations. In this paper, an axis of the slow time-scale is formulated in the time domain and another axis of the fast time-scale is formulated in the frequency domain. We show that computational cost, however, is not dependent on the interval of frequencies, whereas for the harmonic balance or transient analysis, it increases as the interval of frequencies increases.

In this paper, we developed saccade-induced line displays including flashing period controllers. The displays speeded up the flashing period of one line using LED drivers and Arduino Uno equipped with AVR microcomputers. It was shown that saccades were easily induced when the observer alternately looks at the two fast flashing line displays apart. Also, we were able to find the optimum flashing period using a controller that can speed up the flashing period and change its speed. We found that the relationship between the viewing angle of the observer and the optimum flashing period is almost proportional.

A line display that utilizes saccade has been proposed. When an observer moves his or her eyes on a one-dimensional fixed line display, two-dimensional information is perceived on the retina. In this paper, a high speed flashing line display was developed using a CPLD and PIC microcontroller. The flashing period was reduced to 20 µs, which was less than half that of our previous system. The relationship between the flashing frequency and the optimum distance that can be perceived with the least distortion was clarified. The results show that the higher the flashing frequency is, the more information can be perceived from a farther position. Calculated values, which were based on the relationship between the flashing period and the width of the light source, were almost identical with measured values at the flashing frequencies from 3.3 kHz to 10 kHz. Due to short flashing period, the developed line display not only was visible at distance of 15 m or more, which is suitable for outdoor use, but also realized 16 gray levels.

This paper describes a method to distinguish phase noise and amplitude noise from total oscillator noise in circuit simulation, and derives general relationships between periodic time-varying transfer functions for oscillators and phase and amplitude noises.