Mason’s Gain Formula
Mason’s gain formula for the determination of the overall system gain is given by:
[Tex]T = \frac{C(s)}{R(s)} = \frac{\sum_{i=1}^{N}P_{i}\Delta_{i}}{\Delta} [/Tex]
where,
N: total number of forward paths
Pi : gain of the ith forward path
∆: determinant of the graph
∆i : path-factor for the ith path
The determinant of the graph (∆) and the path-factor for the ith path (∆i) are defined as follows:
∆i : 1 – (loop gain which does not touch the forward path)
∆: 1 – Σ(all individual loop gains) + Σ(gain product of all possible combinations of two non-touching loops) – Σ(gain product of all possible combinations of three non-touching loops) + ….
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: