The order of complexity of electrical networks
The order of complexity of electrical networks
复制标题
电力网络的复杂性顺序
DOI：
10.1049/pi-c.1959.0031
复制
发表时间：
1959
期刊：
影响因子：
--
通讯作者：
P. Bryant
中科院分区：
文献类型：
--
作者：
P. Bryant
定义了电网络的固有频率，这些固有频率的个数称为网络的复杂程度。考虑RLC网络，其复杂性顺序σ由σ=BL+N+S−SC−给出。其中，BL是网络中电感的数目，N是节点数，S、SC和SCR是连通性，即给定网络和仅由电容器和电阻组成的子网络的独立部分的数目。文中还给出了σ的其他表达式，证明了其复杂性顺序也是网络方程完全解中任意积分常数的个数和动态独立的网络变量个数。这种动态独立变量的完整集合是通过从网络方程中消去的过程获得的。一种特定类型的成套设备按拓扑结构进行分类，这些设备由跨电容器的电压和流过电感的电流组成，这些电压形成了通过开路所有电阻器和电感而获得的纯电容器网络的丛林，而流过电感的电流形成了通过短路所有电容器和电阻器而获得的仅电感网络的一组弦。
The natural frequencies of an electrical network are defined, and the number of these natural frequencies is called the order of complexity of the network. RLC networks are considered, and the order of complexity, σ, is shown to be given byσ = BL + N + S − SC − SCR.Here, BL is the number of inductors in the network, N is the number of nodes, S, SC and SCR are the connectivities, i.e. the number of separate parts of, respectively, the given network and those subnetworks formed of the capacitors only and of the capacitors and resistors only. Other expressions for σ are also obtained.It is shown that this order of complexity is also the number of arbitrary integration constants in the complete solution of the network equations, and the number of dynamically-independent network variables. Complete sets of such dynamically-independent variables are obtained by a process of elimination from the network equations. A particular type of complete set is classified topologically, such sets being made up of voltages across capacitors forming a forest of the capacitor-only network obtained by open-circuiting all the resistors and inductors, together with the currents through inductors forming a set of chords of the inductor-only network obtained by short-circuiting all the capacitors and resistors.