Mason’s gain formula – Knowledge and References

Mason's gain formula

Mason's gain formula, also known as Mason's rule, is a method used to determine the transfer function of a system by analyzing its Signal Flow Graph (SFG). It involves calculating the gain of each individual path in the SFG and combining them to obtain the overall transfer function. This formula is commonly used in the analysis and design of control systems, and is particularly useful for systems with multiple feedback loops.From: Digital and Statistical Signal Processing [2018], Off-axis optical quadruple racetrack resonator: performance optimization [2019], Control System Problems [2012]

Structures for the Realization of Discrete-Time Systems

View Chapter

Purchase Book

Published in Anastasia Veloni, Nikolaos I. Miridakis, Erysso Boukouvala, Digital and Statistical Signal Processing, 2018

Anastasia Veloni, Nikolaos I. Miridakis, Erysso Boukouvala

Mason’s gain formula (1953), or Mason’s rule, is a method for deriving the transfer function of a system through its SFG. By applying Mason’s rule there is no need to use block diagram reduction. The mathematical formulation is given in Equation 4.19: H(z)=∑n=1kTnDnD

Transfer Functions, Block Diagrams, and Signal Flow Graphs

View Chapter

Purchase Book

Published in Anatasia Veloni, Alex Palamides, Control System Problems, 2012

Anatasia Veloni, Alex Palamides

Mason’s gain formula or Mason’s rule is a method for finding the transfer function of a system through its SFG. By Mason’s rule there is no need to use block diagram reduction. The mathematical equation is () G(s)=∑n=1kTnΔnΔ

Signal Flow Graphs

View Chapter

Purchase Book

Published in Wai-Kai Chen, Mathematics for Circuits and Filters, 2000

Krishnaiyan Thulasiraman

Equation (8.14) is known as Mason’s gain formula. In network and systems theory Pn+1,kj is referred to as a forward path from vertex xn+1 to vertex xk. The directed circuits of Gm(A’) are called the feedback loops.

Off-axis optical quadruple racetrack resonator: performance optimization

View Article

Journal Information

Published in International Journal of Modelling and Simulation, 2019

Subhankar Addya, Sabitabrata Dey, Sanjoy Mandal

All the loops in this architecture are formulated employing Mason’s gain formula. The overall transmittance of the of the filter, i.e. transfer function can be expressed through the following relation [31],

Mason's gain formula

Explore chapters and articles related to this topic

Structures for the Realization of Discrete-Time Systems

Transfer Functions, Block Diagrams, and Signal Flow Graphs

Signal Flow Graphs

Off-axis optical quadruple racetrack resonator: performance optimization