Indian Journal of Science and Technology

Abstract

Objectives: Ladder networks of resistors have been discussed extensively. This paper considers polygons of resistors where the resistors on sides are different from those on spokes. The objective is to find how their physical quantities depend on the parity of the number of the sides. Methods: We calculate attenuations, nodal potentials, and input impedances when a voltage source is connected between a node and the center. We introduce a continuous parameter ρ in equivalent ladder networks where ρ =1 and ρ = 2 correspond to odd and even numbers of sides, respectively. Findings: Attenuations, nodal potentials, and input impedances are expressed in terms of the Chebyshev polynomials of the second kind or the Fibonacci polynomials. The results depend on the parity of the number of sides. The case ρ = 0 interpolates the case with the odd numbers of sides. Application: The method presented in this document can be applicable to networks with inhomogeneous resistances around the sides. 

Keywords: Chebychev Polynomials, Electric Circuit, Fibonacci polynomials, Interpolation, Polygonal Network