scholarly journals A Matrix Approach for Analyzing Signal Flow Graph

Information ◽  
2020 ◽  
Vol 11 (12) ◽  
pp. 562
Author(s):  
Shyr-Long Jeng ◽  
Rohit Roy ◽  
Wei-Hua Chieng

Mason’s gain formula can grow factorially because of growth in the enumeration of paths in a directed graph. Each of the (n − 2)! permutation of the intermediate vertices includes a path between input and output nodes. This paper presents a novel method for analyzing the loop gain of a signal flow graph based on the transform matrix approach. This approach only requires matrix determinant operations to determine the transfer function with complexity O(n3) in the worst case, therefore rendering it more efficient than Mason’s gain formula. We derive the transfer function of the signal flow graph to the ratio of different cofactor matrices of the augmented matrix. By using the cofactor expansion, we then obtain a correspondence between the topological operation of deleting a vertex from a signal flow graph and the algebraic operation of eliminating a variable from the set of equations. A set of loops sharing the same backward edges, referred to as a loop group, is used to simplify the loop enumeration. Two examples of feedback networks demonstrate the intuitive approach to obtain the transfer function for both numerical and computer-aided symbolic analysis, which yields the same results as Mason’s gain formula. The transfer matrix offers an excellent physical insight, because it enables visualization of the signal flow.

2016 ◽  
Vol 78 (3) ◽  
Author(s):  
IS Amiri ◽  
SE Alavi ◽  
ASM Supa'at ◽  
J. Ali ◽  
H Ahmad

The Vernier operation with signal flow graph (SFG) is a graphical approach for analyzing the intricate photonic circuits mathematically and quick calculation of optical transfer function. Analysis of a cascaded microring resonators (CMRR) made of InGaAsP/InP semiconductor is presented using the signal flow graph (SFG) method which enables modelling the transfer function of the passive CMRR. These passive filters are mostly characterized by their frequency response. The theoretical calculations of the system is performed by the Vernier effects analysis. Two MRRs with radius of 100 µm which are vertically coupled together are used to generate resonant peaks. Here, the phase, dispersion and group delay of the generated signals are analyzed. 


Sign in / Sign up

Export Citation Format

Share Document