基于忆阻器的可编程矩阵行列式求解电路设计及应用  

Design and application of a programmable matrix determinantsolving circuit based on memristors

作　　者：肖平旦 洪庆辉 杜四春 孙辰 黎俊 张吉良[3] Pingdan XIAO;Qinghui HONG;Sichun DU;Chen SUN;Jun LI;Jiliang ZHANG(School of Physics and Eletronics,Hunan University,Changsha 410082,China;College of Computer Science and Electronic Engineering,Hunan University,Changsha 410082,China;College of Semiconductors(College of Integrated Circuits),Hunan University,Changsha 410082,China)

机构地区：[1]湖南大学物理与微电子科学学院,长沙410082 [2]湖南大学信息科学与工程学院,长沙410082 [3]湖南大学半导体学院(集成电路学院),长沙410082

出　　处：《中国科学：信息科学》2023年第5期1008-1025,共18页Scientia Sinica(Informationis)

基　　金：国家自然科学基金(批准号:62001163,62122023,U20A20202,61874042);湖南省自然科学基金(批准号:2020JJ4221,2021JJ40111,2022JJ30160);湖南省创新型省份建设专项资金(批准号:2020JK4046,2022SK2007);湖南省重点研发计划(批准号:2021RC4019)资助项目。

摘　　要：矩阵行列式的求解在工程应用中具有重要的意义并得到了广泛的应用,如何高效快速地求解矩阵行列式成为物联网大数据时代的迫切需求.为此,本文提出了一种基于忆阻器的可编程模拟电路,可一步完成任意阶行列式的计算.首先,本工作给出了二阶行列式和三阶行列式的计算电路.在此基础上,通过组合电路的方式得到任意阶数行列式求解电路.同时,该电路还可以通过调节忆阻器的电导和输入电压源来实现可编程的功能. PSPICE的仿真结果表明,该电路的精度在99.4%以上,运行时间比MATLAB仿真快3个数量级,即便在10.0%的误差干扰的情况下,其精度仍能超过93%.相比于数字处理器,该电路在面积开销与功耗上具有显著优势.最后,该电路可通过各个卫星的余弦参数来计算多卫星构成的空间矩阵行列式以辅助定位卫星组合的选择,其计算结果的平均精度可达99.7%.The determinant of a matrix is of great significance in engineering applications and has been widely used.Obtaining the matrix determinant efficiently and quickly is a major requirement in the IoT and big data era.This paper proposes a programmable analog circuit based on a memristor,which can calculate the determinant of any order in one step.First,we present circuits for second and third order determinants.Circuits for determinants of any order are obtained by combining these circuits.The circuit can also be made programmable by adjusting the conductance of the memristor and varying the input voltage source.PSPICE simulation results show that the accuracy of the circuit is more than 99.4%,and it runs three orders of magnitude faster than the MATLAB simulation.Even when the error interference is 10.0%,the accuracy can still exceed 93%.The circuit has lower area overheads and power consumption than digital processors.Finally,the circuit can calculate the spatial matrix determinant,composed of data from multiple satellites,using the cosine parameters of each satellite to assist in the selection of positioning satellite combinations,and the average accuracy of the calculation results can reach 99.7%.

关 键 词：忆阻器 电路设计 可编程 行列式 卫星定位 

分 类 号：TN60[电子电信—电路与系统] TN710