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1、Chapter 4 Formulation and Dynamic Behavior of Electrical Systems,Syllabus 4.1 Element Laws 4.2 Interconnection Laws 4.3 Obtaining the System Model 4.4 Analogue Relation对应关系 Among Different Systems,2021/9/1,1,4.1,electrical circuit电子电路 resistor电阻器 resistance电感 Ohms ()欧姆 capacitor电容器 capacitance电容 Far
2、ad (F)法拉 inductor电感器 inductance电感 Henries (H)亨利 source电源,2021/9/1,2,Passive elements无源元件 Active element有源元件 terminal端子 current电流 curve 曲线 versus 对 Ohms law欧姆定律 charge电荷 integral积分 Derivative导数 flux linkage磁链,2021/9/1,3,4.1 Element Laws,The elements in the electrical circuit电子电路 are resistors电阻器, cap
3、acitors电容器, inductors电感器 and sources电源.,Passive elements 无源元件,Resistor Capacitor Inductor,Because: cant introduce additional energy,Source,Active element 有源元件,Because: can introduce energy into the circuit电路 and serve as the input,Mechanical system,Dashpot Mass Spring,Force Displacement,Electrical s
4、ystem,4.1.1 Resistor,A resistor is an element for which there is an algebraic relationship between the voltage across its terminals端子 and the current电流 through it-that is, an element that can be described by a curve 曲线of UR versus 对i.,A linear resistor is one for which the voltage and current are di
5、rectly proportional to each other-that is, one described by Ohms law欧姆定律:,(4.1),where R is the resistance电感 in Ohms ()欧姆,(4.2),Figure 4.2 A resistor and its variables.,2021/9/1,5,4.1.2 Capacitor,A capacitor is an element that obeys an algebraic relationship between the voltage and the charge电荷, wher
6、e the charge is the integral积分 of the current.,For a linear capacitor, the current and voltage are related by,(4.3),Figure 4.3 A capacitor and its variables.,where C is the capacitance电容 in Farads (F)法拉.,2021/9/1,6,4.1.3 Inductor,An inductor is an element for which there is an algebraic relationship
7、 between the voltage across its terminals and the derivative of the flux linkage磁链的导数.,For a fixed linear inductor, the current and voltage are related by,(4.5),where L is the inductance电感 with units of Henries (H)亨利.,Figure 4.4 An inductor and its variables.,2021/9/1,7,4.2,Kirchhoffs Voltage Law基尔霍
8、夫电压定律 Kirchhoffs Current Law与基尔霍夫电流定律 circuit node电路节点 closed path闭合回路 Partial circuits部分电路 illustrate说明 Likewise同样地 equivalent等价的,2021/9/1,8,Nodal Method节点法 Electrical Network Analysis电网分析 Integro-differential equations积微分方程 Procedure步骤 establish建立 Normalize标准化 Arrange排列 descendent order降幂 ascenden
9、t order升幂,2021/9/1,9,4.2 Interconnection Laws,Two interconnection laws are used in conjunction with the appropriate element laws in modeling electrical circuits. These laws are known as Kirchhoffs Voltage Law基尔霍夫电压定律and Kirchhoffs Current Law基尔霍夫电流定律: The algebraic sum of voltages around a closed-lo
10、op equals zero. The algebraic sum of currents flowing into a circuit node电路节点equals zero.,2021/9/1,10,4.2.1 Kirchhoffs Voltage Law,When a closed path闭合回路 - that is, a loop - is traced through any part of a circuit, the algebraic sum of the voltages across the elements that make up the loop must equa
11、l zero.,(4.7),around any loop,where Uj denotes the voltage across the jth element in the loop.,It follows that summing the voltages across individual elements in any two different paths from one point to another will give the same result.,2021/9/1,11,Figure 4.5 Partial circuits部分电路to illustrate说明Kir
12、chhoffs voltage law.,Summing the voltages around the loop, going in a counterclockwise direction, and taking into account the polarities indicated on the diagram give,Reversing the direction in which the loop is traversed yields,Likewise同样地, going from point B to point A by each of the two paths sho
13、wn gives,which is equivalent等价的 to both of the foregoing loop equations前面两个回路方程.,2021/9/1,12,4.2.2 Kirchhoffs Current Law,(4.8),When the terminals of two or more circuit elements are connected together, the common junction is referred to as a node. All the joined terminals are at the same voltage an
14、d can be considered part of the node. The algebraic sum of the currents at any node must be zero at all times.,at any node,where the summation is over the currents through all elements joined to the node. a plus sign: a current arrow directed away from the node. a minus sign: a current arrow directe
15、d toward the node.,Figure 4.6 Partial circuits to illustrate Kirchhoffs current law.,Applying (4.8) at the node to which the three elements of the figure 4.5 are connected gives,2021/9/1,13,4.2.3 The Nodal Method of Electrical Network Analysis 电网分析的节点法,In the nodal method of electrical network analy
16、sis, one node in the network is usually chosen as the reference node and voltages between the reference node and other node are defined.,The rules for writing the integro-differential equations积微分方程 for each node are summarized as follows:,The number of equations required equals the number of unknown node voltages. One equation is written for each node.,2021/9/1,14,Procedure步骤 to establish建立 differential equation of a physical system is listed as follows: Analyze the principle of the practical s
