电网络基本元件的群论导出和确定

In this project it is the first time to lead theory of group into electric-network theory research. Using theory of group study multi-port electric-network devices and converters, defining the group relation between multi-port electric-network devices and converters. Using the result of theory of group research define multi-port electric-network basic devices system, the induction and prove of theorem of group of multi-port electric-network basic devices. This project gives theory basic to the definition of electric-network basic devices and induction of new devices, promoting the perfect research of electric-network theory system a big step. This project proves that the set of 2n-port transformer can compose a IT(2n) group, and induced the coset devices of 2n-port transformer, 2n-port gyrator, discussing the realization and application of them. Using theory of group proves that 2n-port gyrator and (p+q) -port gyrator are the basic circuit devices of electric-network theory, but 2n-port transformer and (p+q)-port transformer are not belong to basic circuit devices. This project gives the application methods and concrete circuit from 2n-port gyrator or (p+q)-port gyrator to 2n-port transformer or (p+q)-port transformer, and proves that using this new way to realize 2n-port transformer of (p+q) transformer from 2n-port gyrator or (p+q) gyrator can only have half of basic circuit devices which directly synthesize the circuit basing on the method of Pro. Cai. Using (p+q)-port gyrator can synthesize multi-port network function matrix, n-port circulator, 2n-port rotator, reflector and other useful devices, that can't be synthesized before. At last this project study the realized circuit of normalization of (p+q)-port gyrator, giving a new way of design and multi-port basic circuit devices for analog LSI designation..This project induced complex frequency domain intepretation and it's circuit realization of 2n-port scalor converter, inducing a new kind of multi-port devices --n-port circulator, giving it's definition, character and circuit realization method, studying the method that can use 2-port network and 3-port network to realize multi-port network. This project study the theory and method of signal process, using the character of paracitic capacitor, paracitic resistor of MOSFET to realize multifunction filter which have single input, multi output and other multi-port signal process network. This project give basis of theory and method for the realization of multi-port signal process network..

本项目在以往用器件造型导出电网络元件的基础上用群论的完备性和完美性导出电网络元件，并用群论方法确定以往导出的电网络元件和本项目导出的电网络元件中哪些属于基本电网络元件，最后确定电网络基本元件体系。.电网络基本元件是大规模集成电路和网络设计的基石，因此导出和确定电网络基本元件对电话络理论的完善和网络设计具有决定性指导意义。