Seiichiro Moro

Synchronization phenomena in RC oscillators coupled by one resistor

There have been many investigations of the mutual synchronization of oscillators. Especially, we have analyzed N van der Pol type LC oscillators coupled by one resistor, and confirmed that this system can take a huge number of steady states. In this study, we analyze N Wien-bridge oscillators with the same natural frequency mutually coupled by one resister by both of computer calculations and circuit experiments. Because there is no inductor in this system, it is suitable for VLSI implementation. Moreover, the system has many more phase states than that of the system with van der Pol type LC oscillators when N is not so large. So we can utilize this system as a structural element of cellular neural networks.<<ETX>>

Transient response of Colpitts-VCO and its effect on performance of PLL system

In this paper, we investigate the frequency step response of the Colpitts-voltage-controlled oscillator (VCO) by solving its third-order circuit state equation. The result shows that after the capacitance change, its oscillation frequency changes to its steady state value with vibration. We also establish a more accurate transfer function of the Colpitts-VCO by considering its transient response with the assumption that the change of the capacitance is small. Moreover, we also introduce the idea of VCO time constants which represent a degree of the transient response of the VCO. Finally, to evaluate how the transient response of VCO influences on performance of phase-locked loops (PLLs), we investigate acquisition processes of PLL model using our new transfer function. In the high-speed PLL, transient response of the VCO affects acquisition performance. There might be the case where response of the acquisition changes to its steady state with vibration, even in case where there is only overshoot in conventional analysis with conventional idealized VCO model.

Reachability analyses in Petri nets by Groebner bases

Finding a non-negative integer solution x /spl notin/ Z/sub +//sup n/spl times/1/ for Ax = b (A /spl isin/ Z/sup m/spl times/1/, b /spl isin/ Z/sup m/spl times/1/) in Petri nets is NP-complete. Being NP-complete, even algorithms with theoretically bad worst case and average complexity can be useful for a special class of problems. A Groebner basis approach to integer programming problems was proposed in 1991 and some symbolic computation systems have become useful tools for ideals, varieties, and algorithms for algebraic geometry. In this paper, two kinds of examples are given to show how the Groebner basis approach can be applied to reachability problems in Petri nets.

A modified method for circuit analysis using haar wavelet transform with adaptive resolution — For circuits with waveform with sharp convex ranges—

In this paper, we propose a modified method for the circuit analysis using wavelet transform with adaptive resolutions. Recently, many approaches to the circuit analysis using the wavelet transform have been proposed. Previously, we proposed method which can choose adaptive resolution automatically using multiresolution analysis. However, the method cannot be applied when the waveform has the sharp convex ranges. The proposed method improves the way to pick out the range and achieves more accurate and efficient calculations.

Synchronization in chaotic circuits mutually full-coupled by capacitors

In this study, synchronization in simple chaotic circuits full-coupled by capacitors with a tetrahedron structure is investigated. We consider several types of systems by changing the chaotic circuits. By carrying out circuit experiments and numerical simulations, entirely different synchronization modes can be observed. Further, we confirmed other types of synchronization modes by just changing coupling points. We pay attention to the shapes of attractors generated by subcircuits to compare the three systems. In the proposed systems, there are many interesting synchronization states including different types of synchronization from results reported before.

Bifurcation phenomena in Wien-bridge oscillators coupled by one resistor

In this paper we investigate the bifurcation phenomena in two Wien-bridge oscillators with the same natural frequency mutually coupled by one resistor. Analysis of coupled oscillator systems have played an very important role in nonlinear science and it is important that the coupled RC oscillator systems are suitable for VLSI implementation in practical applications such as neural networks because they do not include any inductors. In the proposed circuit we can see very complex bifurcation phenomena when the coupling resistance varies which we have not seen in coupled LC oscillator systems. Therefore we believe that this research will play very important role in the various fields concerning nonlinear science.

Analysis of PLL frequency synthesizer considering transient response of the VCO represented as Van der Pol equation

With the increasing demand for high speed technology in modern communication systems, PLL frequency synthesizers with a faster acquisition speed have been required. In the past, many analyses of PLLs have been carried out with the assumption that there is no delay between the input voltage and the output frequency in the VCO. However, when the PLLs with high speed acquisition are considered, one must know more accurately the VCO transfer function. The paper shows a more accurate VCO transfer function by solving the circuit state equations of the VCO, and investigates the effect of the VCO transient response on the frequency switching performance of the PLL frequency synthesizer.

Analysis method of periodic solution using Haar wavelet transform for autonomous nonlinear circuits

Recently, much attemtion has been paid to the methods for circuit analysis using wavelet transform. In particular, we have proposed the analysis methods using Haar wavelet transform. Haar wavelet can be easily treated, be adapted to time varying and nonlinear circuits and we can be easily derived differential and integral operator matrices by using block pulse functions. Furthermore, it can analyze a region near singular points more precisely. Therefore, we consider that it is suitable to analyze nonlinear time-varying circuits. In this paper, we propose the method to analyze the numerical solution of the periodic solution of the autonomous nonlinear circuit.

MULTI-PHASE OSCILLATION IN RF CMOS LC OSCILLATORS COUPLED BY MUTUAL INDUCTORS

When the oscillators are coupled, coupling methods are very important and influence some factors, for example, increasing or decreasing of noise and whether multi-phase synchronization phenomena can be observed or not due to the number of oscillators and so on. In this paper, multi-phase synchronization phenomena which are generated in RF CMOS LC oscillators with mutual inductor couplings and the stability of various oscillatory modes in the proposed model are investigated. In the proposed system, multi-phase synchronization phenomena can be observed regardless of the number of oscillators in RF region due to setting up the sign of the mutual inductance properly, and the each oscillatory mode is stable.

Synchronization in chaotic oscillators based on classical oscillator coupled by one resistor

We propose the system of the simple chaotic oscillators which are based on Wien-bridge oscillator coupled by one resistor and investigate synchronization in the proposed system. Further, we propose the system of the simple chaotic oscillators which are based on van der Pol oscillator coupled by one resistor. In the system of chaotic oscillators which are based on Wien-bridge oscillator, N-phase synchronization cannot be observed but in-phase and anti-phase synchronization can be observed regardless of N. In synchronization of chaos, these synchronization phenomena are the first observations as far as we know. In case of the system of chaotic oscillators which are based on van der Pol oscillator, N-phase synchronization can be observed. From the results, it is seen that the synchronization of the classical oscillators and that of the chaotic oscillators based on them have common characteristics when classical oscillator is Wien-bridge oscillator or van der Pol oscillator.