Block Diagram Reduction Using Signal Flow Graph

Signal Flow Graph

• A Signal Flow Graph (SFG) is a graphical representation of the relationship between the variables of a set of linear algebraic equations.
• It graphically display the transmission of signals through the system, as does the block diagram. But it is easier to draw and therefore easier to manipulate than block diagrams.
• Beside the differences in the physical appearance of the SFG and the block diagram, the signal flow graph is constrained by rigid mathematical rules, whereas the block diagram notation is more liberal.

Block Diagram

Signal Flow Graph

Basic Properties of SFG

1. SFG’s are applicable only to linear systems.
2. The equations for which an SFG drawn must be algebraic equations in the form of cause and effect relationship.
3. Nodes are used to represent variables. Normally, the nodes are arranged from left to right, from input to output, following as succession of cause and effect relations through the system.
4. Signals travel along branches only in the direction described by the arrows of the branches.
5. The branch directing from node X ₁ and X ₂ represents the dependence of X ₂ upon X ₁ , but not the reverse.

Correlation between Block Diagram & SFG

1. Block: A block with transfer function can be represented as branch with gain.

Lamped parameter                 Distributed parameter

2. Summing point: Summing point is represented by a node after making it as neutral.

N= -X1 -X2,    Y1 = N×1   , Y2= N×1

R= XG+RH                         R= X+R   (Inconsistent equation)

R= X-CH

3. Take–off point: It is also represented by a node

Summer	Single node
Take–off point	Single node
	Single no node
	Two different nodes