关键词: T形网络, 电位公式, 等效电阻, 差分方程

Abstract: The arbitrary n-order T-shaped resistor network (TRN) has significant value in the fields of circuits and microwaves. The article considers the electrical characteristics (including equivalent resistance and voltage at any node) of an n-order TRN with feedback resistor, achieving method extension and theoretical innovation. The main research method adopted is to establish recursive equation models and boundary condition equation models with node voltage as a variable. Through rigorous mathematical calculations, the general and specific solutions of the differential equation are derived, and the voltage analytical formula for any node of the TRN is derived. At the same time, the equivalent resistance formula between any two nodes is derived, and the special case of the conclusion is analyzed and discussed.

Key words: T-shaped network, potential formula, equivalent resistance, differential equation