We consider a multipurpose n-step network with cross resistors that is a profound problem that has not been resolved before. This network contains a number of different types of resistor network model. This problem is resolved by three steps: First of all, we simplify a complex graphics into a simple equivalent model; next, we use Kirchhoff's laws to analyse the network and establish a nonlinear difference equation; and finally, we construct the method of equivalent transformation to obtain the general solution of the nonlinear difference equation. In this paper, we created a new concept of negative resistance for the needs of the equivalent conversion and obtain two general resistance formulae of a multipurpose ladder network of cross resistors. As applications, several interesting specific results are produced. In particular, an n-step impedance LC network is discussed. Our method and the results are suitable for the research of complex impedance network as well.
The resistance between two arbitrary nodes of a network of resistors is studied when the network is perturbed by connecting an extra resistor between two arbitrary nodes in the perfect lattice. The lattice Green's function and the resistance of the perturbed network are expressed in terms of those of the perfect lattice by solving Dyson's equation. A comparison is carried out between numerical and experimental results for a square lattice.
This paper presents two new fundamentals of the 2×n and ,×n circuit network. The results of a plane 2×n resistor network can be applied to a ,×n circuit network, which has not been studied before. We first study the 2×n resistor network by modeling a differential equation and obtain two equivalent resistances between two arbitrary nodes of the 2×n network. Next, the ,×n cube network is transformed to the 2×n plane network equivalently to achieve two resistance formulae between two arbitrary nodes of the ,×n cube network. By applying the resistance results to the ,×n LC cube network, the complex impedance characteristics of the LC network, which includes oscillation characteristics and resonance properties, are discovered.
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