Abstract
In this work a method called “signal flow graph (SFG)” is presented. A signal-flow graph describes a system by its signal flow by directed and weighted graph; the signals are applied to nodes and functions on edges. The edges of the signal flow graph are small processing units, through which the incoming signals are processed in a certain form. In this case, the result is sent to the outgoing node. The SFG allows a good visual inspection into complex feedback problems. Furthermore such a presentation allows for a clear and unambiguous description of a generating system, for example, a netview. A Signal Flow Graph (SFG) allows a fast and practical network analysis based on a clear data presentation in graphic format of the mathematical linear equations of the circuit. During creation of a SFG the Direct Current-Case (DC-Case) was observed since the correct current and voltage directions was drawn from zero frequency. In addition, the mathematical axioms, which are based on field algebra, are declared. In this work we show you in addition: How we check our SFG whether it is a consistent system or not. A signal flow graph can be verified by generating the identity of the signal flow graph itself, illustrated by the inverse signal flow graph (SFG−1). Two signal flow graphs are always generated from one circuit, so that the signal flow diagram already presented in previous sections corresponds to only half of the solution. The other half of the solution is the so-called identity, which represents the (SFG−1). If these two graphs are superposed with one another, so called 1-edges are created at the node points. In Boolean algebra, these 1-edges are given the value 1, whereas this value can be identified with a zero in the field algebra.
Highlights
There are various methods in the circuit technology to ca1culate transfer functions of electrical circuits such as Kirchhoff’s laws, two-port network theory, nodal analysis method [1] and time constant method [2]
Two signal flow graphs are always generated from one circuit, so that the signal flow diagram already presented in previous sections corresponds to only half of the solution
For the analysis of a network the Signal Flow Graph (SFG)-method provides an important alternative, since you are saving in complex systems long calculus, and get a most suitable overview in the interaction of the system components and spare parts
Summary
There are various methods in the circuit technology to ca1culate transfer functions of electrical circuits such as Kirchhoff’s laws, two-port network theory, nodal analysis method [1] and time constant method [2]. In this paper we repeat the mathematical methodology for the symbolic analysis of real electronic circuits on the basis of a given real circuitry It is based on graph theory, the so called SFG method. The signal flow graph (SFG) is a vividly method to present the internal structure of a system or the interaction of several systems. This presentation allows a better understanding of the function as well as the interrelations of one or more systems. Signal flow graphs are formally defined graphs [3] Such a mapping enables a one-to-one (local-bijective) and understandable description of a generating system. The results and the core outline of the work are summarized again and an outlook is given
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