Mason’s Gain Formula
Mason’s gain formula is used to find the overall transmittance or gain of the system from signal flow graph.
[Tex]T=\frac{\Sigma_{k=1}^kP_k\Delta_k }{\Delta} [/Tex]
Where,
- Pk is the forward path gain of kth path from a specified input node to an output node
- [Tex]\Delta_k [/Tex] is the path factor associated with the concerned path and involves all closed loops in the graph which are isolated from the forward path under consideration.
- [Tex]\Delta [/Tex] = 1 – [sum of all individual loop transmittance] + [sum of loop transmittance products of all possible pairs of non-touching loops] – [sum of loop transmittance products of all possible triplets of non-touching loops] + …….
Conversion of Block Diagrams into Signal Flow Graphs
In this article, we will discuss the method of converting the block diagram into a signal flow graph in a control system. We will first discuss about signal flow graph and its terminologies. We also discuss the construction of signal flow graphs from linear equations. We will then discuss about block diagram and its components. We will then discuss the steps for conversion and then see an example. We will discuss the Mason gain formula and its example. Later in the article, we will discuss the advantages, disadvantages, and applications of this method.
Table of Content
- What is a signal flow graph?
- Construction of Signal Flow Graph from linear equation
- What is Block Diagram?
- Steps to draw signal flow graph from block diagram
- Mason’s Gain Formula
- Solved Example
- Application
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