CHAPTER 3 电路原理课件.ppt

3.1 Introduction NETWORK TOPOLOGY Tree（树）：A set of branches which does not contain any loops and connects every node to every other nodes. Cotree（余树）：After a tree has been specified, those branches that not part of the tree form the cotree. Link（连支）：Any branch belonging to the cotree. 3-2 结点电压法Node-Voltage Analysis / Nodal Analysis  一、Steps： 1. Select a node as the reference node. Assign voltages V1,V2,…,Vn-1 to the remaining n-1 nodes . 2. Apply KCL to each of the n-1 nonreference nodes. Use Ohm’s law to express the branch currents in terms of node voltages. 3. Solve the resulting simultaneous equations to obtain the unknown node voltages. G11U①+G12U②+G13U③+G15U⑤= (G1+G3+G4+G5+G6)U①-G1U②-G3U③-G4U④-(G5+G6)U⑤ = G1US1- G6US6+IS2-IS4+G4US4 (G1+G3+G5+G6)U①-G1U②- G3U③-( G5+G6)U⑤= G1US1- G6US6+IS2-IS4 改进节点法 MODIFIED NODAL ANALYSIS US2：无伴电压源 Assign an unknown current to the branch which contains the voltage source. a：Ua=US1 (1) bc：I3+I4= I5+ I6 Example：R1=R2=R3=R4=R6=2?，R7=6?，US1=4V，US5=10V，IS7=1A，IS8=4A，?＝2， ?＝2. Find the node voltages. Mesh(网孔)：A loop which does not contain any other loops within it. 支路电流法 BRANCH ANALYSIS 以支路电流为未知量，直接应用KCL和KVL建立电路方程，从方程中解出各支路电流。 Example： R1=1?，R3=2?，US1=2V，IS2=0.5A，find I3，PU，PI。 Example： R2=2?，R3=3?，US3=3V，gm=1S，find the currents I2，I3。 以基本回路电流为独立变量，在基本回路中建立KVL方程，解方程组得回路电流，随后确定支路电流。 基本回路电流：在基本回路（单连支回路）中，由连支电流形成的环流，简称回路电流。 I1：-US1+US6=R1I1+R6I6+R5I5+ R4I4 ∵I4= I1+I2， I5=I4-I3=I1+I2-I3， I6=I1-I3 ∴ I1：(R1+R4+R5+R6)I1+(R4+R5) I2 -(R5+R6)I3= -US1+US6 I2：(R4+R5)I1+(R4+R5)I2-R5I3= -US2 I3：-(R5+R6) I1-R5I2+(R3+R5+R6) I3= -US6 ：Sum of all independent voltage sources in loop 1，with voltage rise treated as positive. Example： R1=1?，R2=2?，R3=3?，R4=4?，IS5=5A. What value of gm is required to give the current I3 of 0A. 网孔电流法 Mesh Analysis A loop is any closed path, and a mesh is a loop which does not contain any other loops within it. A mesh current is a current that flows only