Important Terminologies of Mason Gain Formula

The important terminologies which will be used in Mason Gain Formula are:

• Path: It is that traversal of the connected branches where no node can be encountered more than once.
  
• Forward Path: It is the traversal of the path from input to output node.
  
• Forward Path Gain: While moving through forward path the product of the gain encountered in traversing this path is called as the forward path gain.
  
• Loop: It is the traversal of the path which originates and terminates at the same node.
  
• Non Touching Loops: Loops which do not share the common node.
  
• Loop Gain: It is the gain of the path traversed along a loop.

Let us consider a signal flow graph for understanding the above elements:

Forward Path

Form the above signal flow graph (SFG) image, there are two forward paths with their path gain as:

• P1=ACEH
• P2=AGH

Loop

There are 4 individual loops in the above SFG with their loop gain as:

• L1=BC
• L2=EHD
• L3=F
• L4=GHDB

Non-Touching Loops

There are ONE possible combinations of the non-touching loop with loop gain product as –

• L1.L3=BCF

In above SFG, there are no combinations of three non-touching loops, 4 non-touching loops and so on.

Where,

• ∆₁ = 1 (since all loops are touching P₁)
• ∆₂ = 1 (since all loops are touching p2)
• ∆ = 1- [L1+L2+L3+L4] + [L1.L3]
• ∆=1 – (BC + EHD + F + GHDB) + BCF

Transfer Function:

[Tex]\frac{C}{R}= \frac{P_{1}∆_{1}+P_{2}∆_{2}}{∆} [/Tex]

[Tex]\frac{C}{R} = \frac{ACEH+AGH}{1-(BC+EHD+F+GHDB)+BCF} [/Tex]

Mason’s Gain Formula, also known as Mason’s Rule or the Signal Flow Graph Method, is a technique used in control systems and electrical engineering. It provides a systematic way to analyze the transfer function of a linear time-invariant (LTI) system, especially those with multiple feedback loops and complex interconnections. Let’s delve deeper into Mason’s Gain Formula with a more detailed explanation. In this article, we will learn Mason’s Gain Formula and problem-solving with the help of a signal flow graph by Mason’s Gain Formula.