Signal Flow Graphs

Signal Flow Graphs

Signal flow graph is a graphical representation of the relationships between the variables of a set of linear algebric equations.It consists of a network in which nodes representing each of the system variables are connected by directed branches.

Though the block diagram representation of control systems is very effective but For complicated system block diagram representation and block diagram reduction process is very time consuming. So an alternative method which does not require any reduction process  is developed by S.J Mason which is called Signal flow graphs method. In this method flow graph gain formula which relates the input and output system variables form a set of linear algebric equations which can be analyze in mathematical approach.

Basic Elements or various signal flow terms required for formulation of Signal Flow Graph

1. Node
2. Branch
3. Notation
4. Input node or source
5. Output node or sink
6. Path
7. Forward path
8. Loop
9. Non-touching loops
10. Forward path gain
11. Loop gain

Construction of Signal Flow Graph

Mason's Gain Formula 

[tex]T=\frac{C(s)}{R(s)}=\frac{\Sigma ^N _{i=1}P_i\Delta _i}{\Delta}[/tex]

Where,

C(s) is the output node

R(s) is the input node

T is the transfer function or gain between [tex]R(s)[/tex] and [tex]C(s)[/tex]

Pi is the i^th forward path gain