Theoretical study on the number of solutions and the stability on transistor circuits

晶体管电路解数及稳定性的理论研究

• 批准号: 13650414
• 负责人: NISHI Tetsuo
• 金额: $ 2.05万
• 依托单位: Kyushu University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13650414/
• 关键词: transistor circuits; no-of solutions; stability; stability condition for CNN; global stability; CNNによる信号処理; 大域安定; 離散時間2値システム

This study aims to pursue two subjects on nonlinear active circuits including transistor circuits. One is to investigate the maximum number of solutions of transistor circuits under the prescribed topology. This problem was proposed by the Technical Committee on Nonlinear Circuits and Systems of the IEEE CAS Society several years ago.. The other is to investigate the stability conditions for general active circuits including transistor circuits. The main results of this research are summarized as follows:1.We showed that the algebraic equations which have two variables and whose nonlinear terms are exponential functions of the variables have at most five solutions. This type of equations come from transistor circuits.. The above result show that the well-known conjecture does not hol in general.2.We give some sufficient conditions for the denominator polynomial of active RC circuits including transistor circuits not to yield negative coefficients due to parasitic elements. This result then shows some conditions for stability of this class of circuits.3.We give the necessary and sufficient conditions for a one-dimensional discrete-time cellular neural network, which is a class of active analog circuits.4.We give the necessary and sufficient condition for the second-order differential equations to be globally stable.

本研究旨在探讨两个关于非线性主动电路（包括电晶体电路）的主题。一个是研究晶体管电路在给定拓扑下的最大解数。这个问题是几年前由IEEE CAS学会的非线性电路与系统技术委员会提出的。二是研究包括晶体管电路在内的一般有源电路的稳定性条件。本文的主要研究结果如下：1.证明了非线性项为变量的指数函数的二元代数方程至多有五个解。这种类型的方程来自晶体管电路。上述结果表明著名的猜想一般不成立。2.给出了有源RC电路（包括晶体管电路）的分母多项式不因寄生元件而产生负系数的充分条件。3.给出了一类有源模拟电路--一维离散细胞神经网络的稳定性的充分必要条件; 4.给出了二阶微分方程全局稳定的充分必要条件.

项目成果

Norikazu Takahashi, Tetsuo Nishi: "On the Global Stability of Two-Cell Cellular Neural Networks with Opposite-Sign Connections"Proceedings of the 15th European Conference on Circuit Theory and Design. vol.3. 93-96 (2001)

Norikazu Takahashi、Tetsuo Nishi：“论具有异号连接的双细胞细胞神经网络的全局稳定性”第 15 届欧洲电路理论与设计会议论文集。

Ryoma Bise, Norikazu Takahashi, Tetsuo Nishi: "An Improvement of the Design Method of Cellular Neural Networks Based on Generalized Eigenvalue Minimization"IEEE Transactions on Circuits and Systems-I. vol.50,no.12. 1569-1574 (2003)

Ryoma Bise、Norikazu Takahashi、Tetsuo Nishi：“基于广义特征值最小化的细胞神经网络设计方法的改进”IEEE Transactions on Circuits and Systems-I。

Norikazu Takahashi, Tetsuo Nishi: "Effect of Biases on the Complete Stability of Planar Dynamical Systems related to CNNs"Proceedings of the 2003 Workshop on Nonlinear Dynamics of Electronic Systems, May. 263-266 (2003)

Norikazu Takahashi、Tetsuo Nishi：“偏差对与 CNN 相关的平面动力系统的完全稳定性的影响”2003 年电子系统非线性动力学研讨会论文集，5 月。

Hidenori Sato, Tetsuo Nishi, Norikazu Takahashi: "Signal Processing by One-dimensional Discrete-time Binary Cellular Neural Networks with A- and B-Template"Proceedings of the 2001 International Technical Conference on Circuits/System, Computers and Commun

Hidenori Sato、Tetsuo Nishi、Norikazu Takahashi：“使用 A 和 B 模板进行一维离散时间二元细胞神经网络的信号处理”2001 年电路/系统、计算机和通信国际技术会议论文集

Tetsuo Nishi, Norikazu Takahashi: "Necessary and Sufficient Conditions for a One-Dimensional Binary CNN to be Stable Under Fixed Boudaries"Proc. 2002 Int. Workshop on Informations & Electrical Engineering. 184-189 (2002)

Tetsuo Nishi、Norikazu Takahashi：“一维二值 CNN 在固定边界下稳定的必要和充分条件”Proc。