在分析2×n阶梯形电阻网络对称性的基础上,对任意负载电阻的n阶梯形电阻网络构建等效电阻的递推关系,经过简单的等效变换得出n阶梯形电阻网络等效电阻的通项公式,并将该公式和图2电路用于分段计算n阶和2×n阶梯形电阻网络的等效电阻,以及直接用于计算2×n阶梯形电阻网络等效电阻的通项公式.这项研究揭示了n阶、2×n阶梯形电阻网络的内部以及它们之间存在的紧密联系.采用这种方法能使研究过程大为简化. Based on the analysis of symmetry of 2 × n ladder resistor network, the recursion relation of equivalent resistance is built for n ladder resistor network with arbitrary load resistance, and the equivalent resistance of n ladder resistor network is obtained through simple equivalent conversion The formula and the circuit in Figure 2 are used to segment the equivalent resistance of the n-th order and the 2 × n step-resistor networks, and the directly used to calculate the equivalent resistance of the 2 × n step-resistor networks This study reveals the intimate relationships between the n-order, 2 × n ladder resistor networks and their interdependencies, which makes the study much simplified.