In this paper we deal with the notion of the effective impedance of alternating current (AC) networks consisting of resistances, coils and capacitors. Mathematically such a network is a locally finite graph whose edges are endowed with complex-valued weights depending on a complex parameter λ (by the physical meaning, λ = iω, where ω is the frequency of the AC). For finite networks, we prove some estimates of the effective impedance. Using these estimates, we show that, for infinite networks, the sequence of impedances of finite graph approximations converges in certain domains in \(\mathbb {C}\) to a holomorphic function of λ, which allows us to define the effective impedance of the infinite network.

在本文中，我们讨论了由电阻，线圈和电容器组成的交流电（AC）网络的有效阻抗的概念。数学上这样的网络是一个局部有限图表，其边缘被赋予了根据一个复杂的参数复数值加权λ（由物理意义，λ =我ω，其中ω是AC的频率）。对于有限网络，我们证明了有效阻抗的一些估计。使用这些估计，我们表明，对于无限网络，有限图逼近的阻抗序列在\（\ mathbb {C} \）中的某些域中收敛到λ的全纯函数，这使我们能够定义无限网络的有效阻抗。