Definition. A diagram which represents a set of simultaneous equations simplifying a complex network in which nodes are connected by directed branches. The graph basically consists of lines and arrows and the transforms of each component written near the line. Signal flow graphs are employed, especially and generally, for multiple input, multiple output control systems.

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Sections: Configuration | BD to SFG | Algebra | Mason's Gain Rule | Example | Student's Corner

Configuration

Source Nodes. Also called, independent nodes or independent variables and have only outgoing branches. In the diagram above, nodes U and V are source nodes.

Sink Nodes. Also called, dependent nodes or dependent variables and have only incoming branches. In the same diagram above, nodes Y and X are sink nodes.

Mixed Nodes. Consists of independent and dependent nodes or variables. In the same diagram above, node W is a mixed node.

Path. Any connected sequence of branches whose arrows flow in the same direction. A forward path is a succession of branches in which a node appears only once. In the diagram above, the path is simply following the arrow that goes from R to G to Y.

Loop. Any connected sequence of branches whose arrows flow from one particular node and back to that particular node. In the diagram above, the loop is simply following the arrow that goes from node a, to transmittance at G, to node b, to transmittance at -H and back to node a, from where it began.

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Sections: Configuration | BD to SFG | Algebra | Mason's Gain Rule | Example | Student's Corner

Translation of Block Diagram to Signal Flow Graph

Methods.
1. All blocks or elements are translated as lines with arrows in the center of line.
2. Transmittances are written near the signal arrows.
3. All summers and take-off points are translated into nodes.
4. Usually, inputs R(s) and final output, Y(s) are designated with transmittance equal to 1.

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Sections: Configuration | BD to SFG | Algebra | Mason's Gain Rule | Example | Student's Corner

Algebra

1. Addition. y = a x.

2. Transmission.
w = au + bv
x = cw
y = dw.

3. Series/Cascade
Combined into one path by multiplying the transmittances.

4. Parallel
Combined into one path by adding the transmittances.

5. Node Absorption
Separation of Y-paths into V-path by multiplying the respective leg transmittance.

5. Feedback Path
Resolution of the feedback transmittance into one common function.

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