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 in Control System
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.
Table of Content
- What is Mason’s Gain Formula?
- Mason’s Gain Formula
- Important Terminologies of Mason Gain Formula
- Solved Examples on Mason Gain Formula
- Advantages & Disadvantages of Mason’s Gain Formula
- Application of Mason’s Gain Formula: