RLC梯形电路的状态空间建模
State space modeling of RLC ladder circuits
AI总结：
本文针对RLC梯形电路推导线性时不变状态空间模型，讨论大规模二阶微分方程的矩阵结构，通过仿真揭示其固有动力学行为，为大规模电路的简洁描述提供方法。
AI中文摘要：
大规模电路涵盖从微电子高度集成电路到城市及国家电网等广泛研究主题，每增加一个组件复杂度会显著提升，因此需要以易于理解的方式描述大规模电路。本文研究由电阻、电容和电感构成的简单电路级联，即梯形电路，这类电桥在电子学中常用于设计滤波器，也被其他学科用于描述扩散或波动现象。我们为三种简单梯形电路推导线性时不变状态空间模型，讨论大规模二阶微分方程的特定矩阵结构，并通过仿真示例揭示每种梯形电路的固有动力学行为。
英文摘要：
Large-scale electrical circuits span a wide range of research topics from highly integrated circuits in microelectronics up to power grids for cities and countries. As the complexity increases significantly by each additional component, we find a need to describe large-scale circuits in a manner easy to understand. In this article, we study cascades of simple circuits consisting of resistors, capacitors and inductors, which we call ladder circuits. Such electrical ladders are common in electronics to design filters and they are also used in other disciplines, for example to describe diffusion or wave phenomena. In particular, we derive linear time-invariant state space models for three simple ladder types and we discuss the specific matrix structures of the large-scale second-order differential equations. Furthermore, we exemplify our findings with simulations to unveil the intrinsic dynamical behavior of each ladder type.
