Transform matrix approach for path gain in signal flow graph

Shyr Long Jeng*, Wei Hua Chieng

*此作品的通信作者

研究成果: Conference contribution同行評審

摘要

Mason's gain formula can grow factorial 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 derived the transfer function of the signal flow graph to the ratio of different cofactor matrices of the augmented matrix. Example of feedback networks demonstrates 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.

原文English
主出版物標題Proceedings of the 3rd IEEE International Conference on Knowledge Innovation and Invention 2020, ICKII 2020
編輯Teen-Hang Meen
發行者Institute of Electrical and Electronics Engineers Inc.
頁面348-351
頁數4
ISBN(電子)9781728193335
DOIs
出版狀態Published - 21 8月 2020
事件3rd IEEE International Conference on Knowledge Innovation and Invention, ICKII 2020 - Kaohsiung, Taiwan
持續時間: 21 8月 202023 8月 2020

出版系列

名字Proceedings of the 3rd IEEE International Conference on Knowledge Innovation and Invention 2020, ICKII 2020

Conference

Conference3rd IEEE International Conference on Knowledge Innovation and Invention, ICKII 2020
國家/地區Taiwan
城市Kaohsiung
期間21/08/2023/08/20

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