4×n阶网络的2个等效电阻公式

Two Formulas of Equivalent Resistance of 4×n-Network

通过网络分析构建差分方程组模型,并利用矩阵变换方法,得到了4×n阶电阻网络中的电流分布规律.基于不同的边界条件,获得了4×n阶网络等效电阻的2个普适公式,同时得到了无穷情形的2个等效电阻.特例情况下的验证结果表明了方法的可靠性和结果的正确性,同时指出了所得结果与其它相关结果的等价性.

This paper deals with the equivalent resistance of a model of 4 × n- network. Firstly, by analyzing the net- work, a system of difference equations has been constructed. And by using the matrix transform method, a distributing rule of the current in the network has been obtained. Then, according to two different boundary conditions, two universal formulas for the equivalent resistance of the 4× n-network are deduced. Meanwhile, the infinite 4 × n-network is taken into account, and two equivalent resistances in this case are also obtained. Finally, effectiveness and correctness of the methods used in this paper are verified in special cases, and the equivalence of the results obtained here and elsewhere is also pointed out.