Electrical performance of the 3 × 6 ×  n cobweb cascade resistance network

• Published in: International journal of circuit theory and applications 2023-09, Vol.51 (9), p.4071-4084
• Main Authors: Luo, Feng‐Hua, Fang, Yi, Luo, Li‐Jin
• Format: Article
• Language: English
• Subjects: Equivalence
• ISSN: 0098-9886; 1097-007X
• DOI: 10.1002/cta.3632

In this paper, a kind of multi‐stage cobweb resistance network consisting of n single‐stage cobwebs, namely, a 3 × 6 ×  n cobweb cascade resistance network (CCRN), was studied. To calculate the equivalent resistance of such a large‐scale complex network, we used a modified recursion‐transform (MRT) method. Firstly, the resistance network to be solved was simplified to a simple equivalent network. Thereafter, the recursive relation of the equivalent network was established according to the basic law of circuit. Then, the nonlinear recursive relation was transformed into the linear recursive relation by variable transformation technique. Finally, the equivalent resistance was gained by resolving the linear recursive relation. By this method, we obtained the exact analytical expression of the equivalent resistance of the 3 × 6 ×  n CCRN. The computation results show that the 3 × 6 ×  n CCRN's equivalent resistance is decided by the number of circuit stages n , and as n goes to infinity, these equivalent resistances all tend to a definite limit value.