Signal Flow Graphs

Signal flow graph is a graphical representation of algebraic equations. In this chapter, let us discuss the basic concepts related signal flow graph and also learn how to draw signal flow graphs.

Basic Elements of Signal Flow Graph

Nodes and branches are the basic elements of signal flow graph.

Node

Node is a point which represents either a variable or a signal. There are three types of nodes — input node, output node and mixed node.

·        Input Node − It is a node, which has only outgoing branches.

·        Output Node − It is a node, which has only incoming branches.

·        Mixed Node − It is a node, which has both incoming and outgoing branches.

Example

Let us consider the following signal flow graph to identify these nodes.

·        The nodes present in this signal flow graph are y1, y2, y3 and y4.

·        y1 and y4 are the input node and output node respectively.

·        y2 and y3 are mixed nodes.

Branch

Branch is a line segment which joins two nodes. It has both gain and direction. For example, there are four branches in the above signal flow graph. These branches have gains of a, b, c and -d.

Construction of Signal Flow Graph

Let us construct a signal flow graph by considering the following algebraic equations −

  


 

Conversion of Block Diagrams into Signal Flow Graphs

Follow these steps for converting a block diagram into its equivalent signal flow graph.

·        Represent all the signals, variables, summing points and take-off points of block diagram as nodes in signal flow graph.

·        Represent the blocks of block diagram as branches in signal flow graph.

·        Represent the transfer functions inside the blocks of block diagram as gains of the branches in signal flow graph.

·        Connect the nodes as per the block diagram. If there is connection between two nodes (but there is no block in between), then represent the gain of the branch as one. For example, between summing points, between summing point and takeoff point, between input and summing point, between take-off point and output.

Example

Let us convert the following block diagram into its equivalent signal flow graph.

With the help of Mason’s gain formula (discussed in the next chapter), you can calculate the transfer function of this signal flow graph. This is the advantage of signal flow graphs. Here, we no need to simplify (reduce) the signal flow graphs for calculating the transfer function.