梯形电阻网络等效电阻及节点电压的递推计算通式

Calculation of Equivalent Resistance and Node Voltage on Ladder Resistance Network

通过求解梯形电阻网络中的递推关系,推导出梯形电阻网络中等效电阻及节点电压 的计算通式;证明了无穷梯形电阻网络等效电阻为常数,且给出其计算公式;提出梯形电 阻网络按无穷网络简化计算的条件.

By analyzing recursion relation of ladder resistance network, the formulas of calculating equivalent resistance and node voltages on ladder resistance network have been derived. It was proved that equivalent resistance of infinity ladder resistance network is a constant, its calculating formula has been derived. Furthermore, the condition to simplify calculation of equivalent resistance on ladder resistance network by treating this network as infinity ladder resistance one was proposed in this paper.