Akio Ushida

Frequency-domain analysis of nonlinear circuits driven by multi-tone signals

An efficient algorithm is given for calculating the steady-state response of a nonlinear circuit driven by multi-tone signals, possibly made up of incommensurable frequencies \omega_{1}, \omega_{2}, \cdots , \omega_{p} . The algorithm is particularly useful when the steady-state response is not periodic, thereby invalidating most existing methods. The algorithm is much more efficient than those given in [1] for circuits containing only a few nonlinear elements (compared to the number of inductors and capacitors). The algorithm is based on a combined application of the harmonic balance and least square approach, and does not require any transient analysis.

An efficient algorithm for finding multiple DC solutions based on the SPICE-oriented Newton homotopy method

It is a very important, but difficult, task to calculate the multiple dc solutions in circuit simulations. In this paper, we show a very simple SFICE-oriented Newton homotopy method which can efficiently find out the multiple de solutions. In the paper, we show our solution curve-tracing algorithm based on the arc-length method and the Newton homotopy method. We will also prove an important theorem about how many variables should be chosen to implement our algorithm. It verifies that our simulator can be efficiently applied even if the circuit scales are relatively large. In Section III, we show that our Newton homotopy method is implemented by the transient analysis of SPICE. Thus, we do not need to formulate a troublesome circuit equation or the Jacobian matrix. Finally, applying our method to solve many important benchmark problems, all the solutions for the transistor circuits could be found on each homotopy path. Thus, our simulator can be efficiently applied to calculate the multiple dc solutions and perhaps all the solutions.

Spatio-temporal chaos in simple coupled chaotic circuits

In this paper, simple autonomous chaotic circuits coupled by resistors are investigated. By carrying out computer calculations and circuit experiments, irregular self-switching phenomenon of three spatial patterns characterized by the phase states of quasi-synchronization of chaos can be observed from only four simple chaotic circuits. This is the same phenomenon as chaotic wandering of spatial patterns observed very often from systems with a large number of degrees of freedom. Spatial-temporal chaos observed from systems of large size can be also generated in the proposed system consisting of only four chaotic circuits. A six subcircuits case and a coupled chaotic circuits network are also studied, and such systems are confirmed to produce more complicated spatio-temporal phenomena. >

Steady-state analysis of nonlinear circuits based on hybrid methods

Two efficient algorithms for calculating the steady-state responses of nonlinear circuits are proposed. They are based on both time-domain and frequency-domain approaches. A nonlinear circuit is partitioned into two subnetworks with substitution sources, and their responses are solved by a combined frequency-domain and time-domain method. The total response of the combined circuit can be calculated by an iterative technique based on either the Newton or the relaxation harmonic balance method. Since the methods are based on both time-domain and frequency-domain algorithms, they are called the Newton and the relaxation hybrid harmonic balance methods, respectively. The methods can be applied efficiently to strong nonlinear circuits containing high-Q subnetworks such as filter circuits and crystal oscillators. When a large-scale circuit is partitioned into large linear subnetworks and small nonlinear subnetworks, the method can also be applied efficiently. >

Quasi-synchronization phenomena in chaotic circuits coupled by one resistor

In this brief, synchronization phenomena observed from simple chaotic circuits coupled by one resistor are investigated. A simple three-dimensional autonomous circuit is considered as a chaotic sub-circuit. By carrying out circuit experiments and computer calculations for two, three or four subcircuits case, various interesting synchronization phenomena of chaos, which are different types from the results reported before, are confirmed to be stably generated. Further, quasi-synchronization of asymmetric chaos are investigated with attention on the number of synchronization states.

Virtual Pain Stimulation of Allodynia Patients Activates Cortical Representation of Pain and Emotions: A Functional MRI Study

Summary:The present study investigated neural correlates of affect processing in allodynia patients (n=8) and healthy controls (n=12) with the aid of virtual tactile stimulation. Whole brain functional magnetic resonance imaging was performed for allodynia patients and healthy volunteers while they were shown a video demonstrating light stimulation of the palm and another stimulation aimed at producing anticipation of palm stimulation. Contrasting with controls, patients displayed activation of the cortical areas related to pain and emotions: prefrontal cortex (Brodmanns area BA 10) and anterior cingulate cortex (BA 24). These findings may indicate involvement of an emotional component of pain perception in all odynia patients.

Frequency response of nonlinear networks using curve tracing algorithm

For designing of nonlinear circuits, it is very important to know the frequency response characteristics and the intermodulation. In this paper, we propose an efficient method for calculating the characteristic curves of nonlinear circuits, which is based on the harmonic balance method and a curve tracing algorithm for solving the determining equation. Firstly, applying the harmonic balance method to each element in the circuit, we obtain the determining equation which is realized by two coupled resistive circuits corresponding to the sine and cosine components. Then, the frequency response characteristic curve is calculated by solving the circuit with a STC (solution curve tracing circuit) of Spice.

An efficient algorithm for finding multiple DC solutions based on Spice oriented Newton homotopy method

For circuit designing, it is very important to calculate the DC operating points. It is known that if the circuit contains positive feedback loops such as flip-flop and negative resistance circuits, it may have many DC solutions. It is very difficult to find all of the solutions for these circuits. In this paper, we show a very simple Spice oriented Newton homotopy method which can efficiently find out the multiple DC solutions, and perhaps all of the solutions.

Analysis of Chua's circuit with transmission line

The purpose of this brief is that, by an application of the method of characteristics, we analyze chaotic phenomena in Chuas circuit with lossy transmission line. The transmission line is replaced by the equivalent lumped circuit and a time-delayed element so that it can be solved efficiently by the Runge-Kutta method. It is found from numerical experiments that the circuit has complicated and interesting chaotic attractors.

Analysis of communication circuits based on multidimensional Fourier transformation

There are many communication circuits driven by multitone signals such as modulators and mixers, and so on. In this case, if frequency components of the modulators are largely different, the brute force numerical integration will take an enormous computation time to get the steady-state responses, because the step size must be chosen depending on the highest frequency input. The same situation happens to mixer circuits which generate very low frequency output. In this paper, an efficient algorithm is shown to solve the communication circuits driven by multitone signals which is based on the frequency-domain relaxation method and the multi-dimensional Fourier transformation. Attenuation of the transient phenomena mainly depends on the reactive elements such as capacitors and inductors, so that we partition the circuit into two groups of the nonlinear resistive subnetworks and the reactive elements using the substitution sources. The steady-state response can he calculated in such a manner that the responses at each partitioning point have the same waveform. We have developed a simple simulator carrying out our algorithm that only uses the transient, dc-analysis and ac-analysis of SPICE. It can be easily applied to relatively large scale integrated circuits, efficiently, We found from many simulation results that the convergence ratio at the iteration of our relaxation method is sufficiently large, and can be applied to wide class of the communication circuits.