平面无穷正多边形等值电阻网格分析

Infinite Planar Regular-polygonal Lattice Networks of Identical Resistor

本文首先证明了平面无穷正多边形等值电阻网格有正三角形、正方形和正六边形三类。然后,根据三类网格的特点,分别进行合理的坐标系选取,并利用傅里叶变换推导了平面无穷正三角形等值电阻网格任意两节点间等效电阻的解析解。最后,利用Matlab软件进行了数值分析,验证了公式的合理性。

This paper briefly proves that only three regular polygons can produce tessellations： equilateral triangles,squares,regular hexagons. The appropriate coordinates are chosen for each infinite planar lattice networks of identical resistor,respectively. Using Fourier transform,the formulas of the equivalent resistance between two arbitrary points in the infinite triangular,square and hexagonal lattice networks of identical resistor are deduced. The numerical analysis results by Matlab prove the rationality of the formulas.