论电路齐次定理和叠加定理的关系  

On Relationship between Circuits'Homogeneity Theorem and Superposition Theorem

作　　者：田社平[1] 陈希有[2] 张峰[1] TIAN Sheping;CHEN Xiyou;ZHANG Feng(School of Electrical and Electronic Eng., Shanghai Jiao Tong Univ., Shanghai 200240, China;School of Electrical Engineering, Dalian University of Technology, Dalian 116024, China)

机构地区：[1]上海交通大学电子信息与电气工程学院,上海200240 [2]大连理工大学电气工程学院,辽宁大连116023

出　　处：《电气电子教学学报》2021年第6期95-99,共5页Journal of Electrical and Electronic Education

基　　金：教育部高等学校仪器类专业新工科建设立项项目(2018C052)。

摘　　要：齐次定理和叠加定理是线性线性电路两个重要的定理。通过分析,指出对单一激励的电路,如果该电路满足齐次定理或者叠加定理,那么,该电路一定是线性电路。对单一激励的电路,齐次定理已经充分表达了线性电路的线性性质。对多个激励的电路,如果该电路满足可加性,那么,该电路一定是线性电路。反之,如果电路仅满足齐次定理,则该电路不一定是线性电路。尽管叠加定理是线性系统可加性在电路中的应用,但叠加定理和可加性的内涵是有所区别的,不能通过电路是否满足叠加定理来判定电路的齐次性或电路是否满足齐次定理。本文的讨论可供讲授电路理论课程的教师参考。Homogeneity theorem and superposition theorem are two important theorem sapplying for linear circuits.This paper points out that for a circuit with single excitation,if the circuit satisfies homogeneity theorem or superposition theorem,the circuit must be linear and the homogeneity theorem has sufficiently expressed the linear properties of the linear circuits.For the circuits with multiple excitations,if the circuit satisfies the additivity,the circuit must be linear.On the contrary,if the circuit only satisfies the homogeneity theorem,it is not necessarily a linear circuit.Although the superposition theorem is the application of additivity of linear system in circuits,the connotation of superposition theorem and additivity is different.It can′t judge the homogeneity(theorem)of circuit by whether the circuit satisfies superposition theorem.The analysis results are helpful for the teaching of circuits.

关 键 词：齐次性 可加性 齐次定理 叠加定理 

分 类 号：TM13[电气工程—电工理论与新技术]