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This paper addresses theoretically and methodologically the electrical characteristics (including node voltage and equivalent resistance) of a class of n-ladder resistor networks with external load. The authors establish, with node voltage as a variable, the second-order difference equation model and boundary condition equation model based on Kirchhoff’s law. They propose the general and specific methods of solution for different equations and at once obtain the voltage formula of any node in the n-ladder network with external load and the equivalent resistance formula between any two nodes as well. Special cases in the conclusion section are analyzed and discussed. In particular, they find the oscillation and resonance characteristics of the LC network under different conditions by carrying out an analysis and research into the equivalent complex impedance characteristics of the LC network.

The electrical characteristics (including node voltage, branch current, equivalent resistance) of a complex n-ladder network are studied by establishing recursive model with voltage parameters. On this network, not only a load is embedded on any node, but also an arbitrary right boundary resistance is contained. In this paper, the difference equation model of voltage is first established by network analysis, and then the boundary condition equation model is established according to the constraints. The general solution and solution of the difference equation are derived, and then the voltage formula of any node, branch current and equivalent resistance are obtained. The formula obtained in this paper is multifunctional and universal, and the results of many special cases are contained. The equivalent complex impedance of LC ladder network is further studied, and its irregular oscillation and resonance characteristics are revealed. Keywords: Ladder network, Kirchhoff's law, Difference equation, Electrical properties

This paper investigates the electrical properties of a class of n-order triangular resistor network model. The authors establish, by constructing equivalent model, the second-order nonlinear difference equation model. We propose, by using equivalent transformation method, the general and specific methods of solution for the nonlinear difference equation and at once obtain an accurate equivalent resistance formula of n-order triangular resistor network, and a series of special conclusions are analyzed and compared. Finally, we study the oscillation and resonance characteristics of the triangular LC network under different conditions, where the method used is variable substitution by using the equivalent resistance results obtained. This study reveals the electrical characteristics of triangular LC network and establishes a new theoretical foundation for related disciplines.