Research Of Some Structural Properties Of Electrical Networks Over F(z) And Development Of Aided Analysis Software

System controllability and observability are two important characteristics to show system structural property in linear system theory. Radio engineers never consider whether networks are controllable or observable, but circuits they design work well, because they meet the electrical networks structural controllable condition. It is the conclusion by electrical networks research over F(z). Different to traditional over real number, it is only related to networks structures and indicates structural property alone.At present, lots of specialists and scholars are researching electrical networks structural property. They use different methods and get many achievements. But their research methods usually can't describe more general system. In this paper, author uses rational function matrix in multi-parameters (also named matrix over F(z)) to describe electrical networks, studies its structural controllability and observability etc. and overcomes their shortcomings. Because the components of networks never take a real number value, the operation is symbolic algebraic operation. To a complex electrical network, the task of count is arduous, and can't be done by manpower, so it is necessary to develop corresponding computer aided analysis software. The main content and the research achievement of this paper include two parts, one is the results of theoretical investigations, and the other is to develop the computer aided analysis software.â… . Theoretical investigation partâ…°)Deduce the state equation over F(z). In order to study the electrical networks structural property over F(z), we often use its state equation. Author deduces the state equation of active and passive networks in detail. Though the mathematic model which is given in paper is simple, but its meaning and process to deduce is complex. It is a very important tool to study networks structural controllability in linear system theory. At the same time, it is a proper mathematic model for computer aided analysis software.â…±)Deduce the output equation of RLC networks with independent source and without independent source over F(z). It is a very important condition to analyze structural observability of networks. In this paper, firstly, author deduces the output mathematic model of any two nodes voltage of networks with independent source in detail, which is used to study structural observability and bring out the output equation with software. Secondly, author uses the output equation without sources to study the obervability of any state in networks and gets some structural properties and conditions.â…²)Primary research for controllability of electrical networks with zero modes. If a network has zero modes structures, then the coefficient matrix A of the state equation would have zero characteristic roots. The preconditions of some research conclusions about electrical networks over F(z) often are networks which don't include zero mode structure. At first, paper studies the structural characters of networks with zero modes, and then draws a conclusion on how this character shows in state equation. At last, paper writes out the criterion of structural controllability of electrical networks with zero modes. Based on networks graph theory, author does some early study on how to distinguish the independent all-capacitor cut-set and all-inductor loop.â…¡. Developing aided analysis software partPaper firstly indicates that it is necessary and pressing to develop computer aided analysis software, and then points out the requirement analysis and the test plan for it according to software engineering requirement. The requirement analysis makes known the basal function and frame of it, and by comparing to other familiar circuits analysis software to show its advantage and innovation. Topological analysis function of electrical networks is the most important in software functions. Paper particularly expatiates on each algorithm in networks topological analysis, mainly includes judging abnormal connection (for example, components short circuit, all independent voltage sources loop, all independent current sources cut-set, etc), judging graph conjunction relationship (for instance, determining the number of connection graph, marking nodes, confirming twigs and links, etc), judging special structures (such as all-capacitor cut-set and loop, all- inductor cut-set and loop, etc).Soft test is an important component in software developing process, the final verify to requirement analysis and coding, and the key steps to guaranteeing its quality before client using. Author tests the software in customer layer, application layer and function layer respectively, and gives the results, and uses the test point to show where has been paid more attention. The valid code rate and system test indicates that the software is canonical and dependable.