Modeling the electrical properties of three-dimensional printed meshes with the theory of resistor lattices

Abstract

The electrical properties of conducting meshes are investigated numerically by solving the related Kirchhoff equations with the Lanczos algorithm. The method is directly inspired by the recursion technique widely used to study the electronic and vibrational spectra of solids. The method is demonstrated to be very efficient and fast when applied to resistor networks. It is used to calculate equivalent resistances between arbitrary pairs of nodes in simple resistive lattices. When the resistance fluctuates statistically from bond to bond, the method makes it possible to evaluate the fluctuations of the electrical properties of the network. It is also employed to assign an effective bulk resistivity to a discrete conducting three-dimensional mesh.

Interaction of Multiwalled Carbon Nanotube Aerogels with Quasi‐Optical Terahertz Beams

“…In an earlier study, we proposed to use the model of a regular wire medium as a structural model of an aerogel medium. However, unlike the previous work, the conductors forming such a medium in ref. [29] were nanowires equivalent to MWCNTs.…”

“…In a previous study, the effective medium model for 2D periodic arrays of CNTs was considered. The 3D lattice of macroscopic conductors for calculating the parameters of composites fabricated by 3D printing technology was considered in a previous study . However, in our opinion, the most adequate model of an aerogel media is the 3D wire lattice model with contacts at the intersection points …”

Resistance Theory of General 2 × n Resistor Networks

“…For example, in literature, [ 2 ] the photonic crystal circuits have been studied, and 2D and 3D resistor networks have been explored. Topological properties of linear circuit lattices have been studied in literature; [ 3 ] literature [ 4 ] has studied the electrical properties of 3D‐printed meshes by using resistance lattice theory simulation. In addition, in terms of theoretical research on resistor networks, literature [ 5 ] established crystal Green's function technology to study the equivalent resistance of infinite networks.…”

Electrokinetic Properties of 3D-Printed Conductive Lattice Structures

“…Under this condition, the resistance of a rod is R = σ −1 0 l/Ω with l and Ω being the length and cross-sectional area (see Figure 1b), respectively, and σ 0 being the conductivity of the polymer nanocomposite used for the fabrication. The mesh can therefore be considered as a network of resistors [38].…”

“…The limit y → 0+ of individual elements of the resolvent matrix may be difficult to evaluate, especially in 2D. One can get rid of this difficulty by rewriting the right-hand side of Equation (4) as a diagonal element of the resolvent matrix [38]. Values of R eq mn can be obtained analytically for a few simple 3D lattices: sc [44], bcc [45], fcc [46] (the equivalent resistances tabulated in [46] must be divided by a factor of two), and diamond [47].…”