Feedback Theory-Some Properties of Signal Flow Graphs

Mason, S. J.

doi:10.1109/jrproc.1953.274449

Cited by 608 publications

(211 citation statements)

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“…Mathematically, an SFG is just a graphical representation of an equation system, which can even be manipulated and simplified graphically [6]. But as Mason stated there, it can also be used to visualise causal relationships-if it is drawn in the right way.…”

Section: Signal-flow Graphs and Mason's Gain Rulementioning

confidence: 99%

“…The DPSFG was introduced in 1998 [5] when Ochoa combined driving-point impedance techniques with Mason signal-flow graphs (SFGs) [6,7]. Ochoa used auxiliary voltage generators (which we call auxiliary voltage sources or aux sources) and explained the SFG derivation by first splitting schematics into sub-circuits and then coupling the sub-circuits with voltage-controlled current sources.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of switched-capacitor circuits using driving-point signal-flow graphs

Schmid

Huber

2018

Analog Integr Circ Sig Process

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This paper extends the driving-point signal-flow graphs to switched-capacitor (SC) circuits by introducing a new theoretical element: an auxiliary voltage source that transfers no charge. In contrast to existing SFG methods, our method has no restrictions as to what types of SC circuits can be analysed, it requires no equivalent circuits or tables, and it works with two-phase as well as multi-phase SC circuits of any complexity. Compared to charge-equation matrix methods, it requires more effort, but is better suited for hand analysis because it makes causal relationships visible. Three illustrative examples are given to show the efficiency of the method and present a few application hints: a voltage doubler, the standard SC integrator, and a four-phase circuit simulating an inductor.

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Section: Signal-flow Graphs and Mason's Gain Rulementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analysis of switched-capacitor circuits using driving-point signal-flow graphs

Schmid

Huber

2018

Analog Integr Circ Sig Process

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“…The bulk of these improvements took place in the decades of 1950's and 1960's, when the classical topological formulas were modified to fit passive networks containing mutual couplings and active networks. For example, methods for solving a system of indefinite linear algebraic equations by applying a directed weighted graph, known as a signal-flow graph, were proposed in [7,12,13,16,18,23]. Successive efforts were done to develop the graph description by means of matrix techniques [4,31].…”

Section: Introductionmentioning

confidence: 99%

On the Use of Graph Theory for Railway Power Supply Systems Characterization

2015

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Over the years, graph theory has proven to be a key tool in power systems modeling and analysis. In this paper, the authors propose a systematic method for railway power supply systems (RPSS) description that can be applied to any AC/DC system. This method represents the different elements of the RPSS with a set of subgraphs. Merging these subgraphs, the representative graph of the whole RPSS and its associated adjacency and incidence matrices will be obtained. Once these matrices are obtained, Kirchhoff's laws can be easily implemented. In this work, the method is applied to a DC light traction system. The AC system that feeds the traction network through power transformers combined with rectifiers is also included. With the proposed approach, the variability problems in the system topology and dimensions are overcome, obtaining an invariant system, even when the trains change their relative position, or when a new train enters into or exits the system.

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“…Since an interaction graph has dimension one if and only if it is a tree [2] the 1-index q x is the analogous of Mason's index [9] for undirected graphs The indexes q h (h ^ 2) may be regarded as generalizations.…”

mentioning

confidence: 99%