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研究了一类多功能n阶蜂巢型电阻网络模型,该问题一直未被解决。通过调节电路参数,该网络模型可以转化为含有多种功能的数个不同网络模型,例如一个规则的梯形网络、一个n阶三角形网络,等。我们导出了电阻网络的2个新的等效电阻公式,同时导出了LC网络的等效复阻抗公式,它们都属于分数阶范畴。首先,将一个复杂网络简化为一个简单的等效模型;其次,应用基尔霍夫定律,建立一个分式差分方程模型;再次,采用等效变换方法,给出非线性差分方程的通解。在实际应用中,获得了数个有趣的特殊结论。特别地,讨论分析了一个n阶LC复阻抗网络,发现了许多新的等效复阻抗特性。
A multi-functional n-order honeycomb resistor network model is studied, which has not been solved yet. By adjusting circuit parameters, the network model can be transformed into several different network models with multiple functions, such as a regular trapezoidal network, an n-th order triangular network, and the like. We derive two new equivalent resistance equations for the resistor network and derive the equivalent complex impedance equations for the LC network, all of which belong to the fractional order category. First, a complex network is simplified as a simple equivalent model. Secondly, Kirchhoff’s law is applied to establish a model of fractional difference equation. Thirdly, the equivalent solution is used to obtain the general solution of the nonlinear difference equation. In practical application, we obtained several interesting special conclusions. In particular, the discussion analyzed an n-order LC complex impedance network and found many new equivalent complex impedance characteristics.