Content for today's lecture 984-3 Large network analysis method(Nodal analysis, just for knowledge) 《 Principles of Circuit Analysis》 i2 Review for the mid-term exam: summary Chapter 4: Network Analysis and discussion Lecture 3 2009-1112 Fundamentale af alys Chapter 4: Fundamentals of Linear Network Analysis Single-link loop(basic loop) 54-1 Fundamentals of network topology analysis In n Single-tree cut set(basic cut set) alysis §42 Methods for Linear Establish kcL Equaylons using tut-sef The origin of large network all the independenyrcut-set I Loop current meth analysis method Establish KVL equations u 2. Nodal point all the independent loop 二二 55-1 Network f is great. But it is mair the sam Establish KCL equations using all the independent nodes analysis Establish KVL equations using Mesh 84-3 Large network analysis method(Nodal analysis all the independent mesl sanalysis< just for knowledge) Planar network Topology analysis methods of the network: Large network analy sis method methods of the network: Large network analysis method 0 Only the nodal analysis Nodal analysis u It will not appear in the exam. Large network analysis method You can choose any node as the reference node . To the computer and solve the other n, nodes. (There should be Input all the branch information of the network(component) n, nodal equations for the nodal analysis. input the structure of the network(node, branch) of tbe network component (It can be applied 2. Correlation matrix (node-branch) Aprogram(Change the data to network equations ind out the relationship between the branch voltag and the nodal voltage E Set up Your method should be applicable to all kinds of complex network 4. Nodal analysis matrix equations
北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 第 ？讲： 复习 北京大学 北京大学 《Principles of Circuit Analysis》 Chapter 4: Network Analysis Lecture 3 2009-11-12 Interest Focus Persistence Originality 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 Ƨ4-3 Large network analysis method (Nodal analysis, just for knowledge) Æ Review for the mid-term exam: summary and discussion Content for today’s lecture 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 §4-1 Fundamentals of network topology analysis §4-2 Methods for Linear Network Analysis 1. Loop current method 2. Nodal point voltage method §5-1 Network theorem Replacement theorem, Superposition theorem, Reciprocity theorem §4-3 Large network analysis method (Nodal analysis Æ just for knowledge) Chapter 4: Fundamentals of Linear Network Analysis Chapter 4: Fundamentals of Linear Network Analysis The origin of large network analysis method It’s simple to use. For the small network, the simplification is great. But it is mainly influenced by human’s mind, and the computers have little to deal with it. 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 analysis Establish KCL equations using all the independent cut-set Cut-set analysis Establish KVL equations using all the independent loop Loop analysis Establish KCL equations using all the independent nodes Nodal analysis Establish KVL equations using all the independent mesh Mesh analysis Planar network only In networks: Fundamentals of network topology analysis tree No tree Single-link loop (basic loop) Single-tree cut set (basic cut set) 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 Topology analysis methods of the network: Large network analysis method Only the nodal analysis It will not appear in the exam. Large network analysis method : To the computer Æinput all the branch information of the network (component) Æinput the structure of the network (node, branch) (It can be applied to all kinds of networks) Æprogram (Change the data to network equations) To youÆthe output☺ Your method should be applicable to all kinds of complex network. 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 Nodal analysis You can choose any node as the reference node, and solve the other nt nodes. (There should be nt nodal equations for the nodal analysis.) Set up equations Input all the information of the network component. Input the structure of the network 1. branch characteristic equations (standard branches)Æ 2. Correlation matrix (node-branch)Æ 3. Find out the relationship between the branch voltage Vb and the nodal voltage En. 4. Nodal analysis matrix Topology analysis methods of the network: Large network analysis method
Nodal analysis: 1. branch characteristic equation odal analysis: 1. branch characteristic equations se a directed line segment to represent each branch in the network 1. branch characteristic equations(standard branches))VCR here are b branches in the netwo Branch voltage Branch current (K-IsK)=Y(VK-VSK) Ib=Y(Vb-Vsb)+Ist IK=YK(K Branch SK)+ column vector atris (bXb) 0 the network: Large network analysis method Nodal analysis 2 Cor 日 Nodal analysis 2. Node the correlation matrix of branches(from KCL) You can choose any node as the reference node node①:I+L2= o output and solve the other n, nodes. (There should be n, nodal equations for the nodal analysis. node②:-I2+I3+I4=0 2. Correlation matrix (node-branch) branches口 3. Find out the relationship between the branch vol and the nodal voltage E Set up o[11000「 outpu quations ②0-1110 =0 4. Nodal analysis atrix input-8l000-11lIs Nodal analysis 2 Correlation matrix(node-branch) methods of the network: Large network analysis method Nodal analysis ①[11000( o11o‖:=0 You can choose any node as the reference node . and solve the othe (o00-11八(x3 n, nodal equations for the nodal analysis. L. branch charaeteristic equations natrix n. xb AL=02② ar the netwerk component 2. Correlation matrix(node-branch) Elements in the correlation matrix a-2 f the ned e node i-and the branch j is getting away from aode L to the node j. and the tranch j bsg and the nodal voltage E f If the node i i not correlated to the nnde
北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 Nodal analysis: 1. branch characteristic equations Use a directed line segment to represent each branch in the network 1. branch characteristic equations (standard branches) ÆVCR ISK YK VSK + - + V - K IK The kth branch in the network (I -I ) Y (V - V ) K SK = K K SK K K K SK SK I = Y (V - V ) + I + V - K IK 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 = diag(y1 Lyb) y1 0 0 yb Yb = b b b Sb) Sb I = Y (V - V + I …① ISK YK VSK + - + V - K IK The kth branch in the network There are b branches in the network: Branch admittance matrix (bXb) Branch current column vector Branch voltage column vector Branch voltage source column vector Branch current source column vector K K K SK SK I = Y (V - V ) + I Nodal analysis: 1. branch characteristic equations 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 Nodal analysis You can choose any node as the reference node, and solve the other nt nodes. (There should be nt nodal equations for the nodal analysis.) Set up equations Input all the information of the network component. Input the structure of the network 1. branch characteristic equations (standard branches)Æ 2. Correlation matrix (node-branch)Æ 3. Find out the relationship between the branch voltage Vb and the nodal voltage En. 4. Nodal analysis matrix Topology analysis methods of the network: Large network analysis method 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 Nodal analysis 2. Correlation matrix (node-branch) ① ③ 2 ② 4 1 3 5 node①: node②: node③: I1 + I2 = 0 -I2 + I3 + I4 = 0 -I4 + I5 = 0 1 1 0 0 0 0 - 1 1 1 0 0 00 -1 1 I1 I5 =0 2.Node － the correlation matrix of branches(from KCL) ① ③ ② nodes branches 135 2 4 output+ inputoutput+ inputoutput+ inputoutput+ input- 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 ① ③ 2 ② 4 1 3 5 0 I1 I5 0 1 1 0 0 0 - 1 1 1 0 0 00 -1 1 = 135 2 4 ① ③ ② A⋅Ib =0 …② Correlation matrix nt×b Branch current column vector Elements in the correlation matrix aij= 1Æ If the node i is correlated to the node j, and the branch j is getting away from node i. -1Æ If the node i is correlated to the node j, and the branch j is getting towards node i. 0Æ If the node i is not correlated to the node j. Nodal analysis 2. Correlation matrix (node-branch) 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 Nodal analysis You can choose any node as the reference node, and solve the other nt nodes. (There should be nt nodal equations for the nodal analysis.) Set up equations Input all the information of the network component. Input the structure of the network 1. branch characteristic equations (standard branches)Æ 2. Correlation matrix (node-branch)Æ 3. Find out the relationship between the branch voltage Vb and the nodal voltage En. 4. Nodal analysis matrix Topology analysis methods of the network: Large network analysis method
3. Find out the relationship between the branch voltage - and the nodal voltage Ee pology analysis methods of the network: Large network analysis method 3. the relationship between the branch voltage V, and the nodal voltage E Nodal analysis branch You can choose any node as the reference node no and solve the other n, nodes. ( There should be 10 n, nodal equations for the nodal analysis. ④e=0 of the network corm v1=e1-e4=e1 00 V2=e1-e2 vvv =e2-e4=e2 v=A·E…③ 3. Find out the relationship hetween the branch voltage and the nodal voltage Er equatons Nodal analysis matrix Nodal analysis: 4. Nodal analysis matrix Nodal analysis: 4. Nodal analysis matrix IDFYb(b/Vsb)+Isb.o AYDA'En=AY Vsb-Alsb- Y,En=Is A(b=0② Let:Y=AYbA nodal admittance matrix y=AE③ Is=AYb)socal Substitute in ( rs in the network-YyIvsb known→ find out e L=Y(AE-Vs)+ls④ Substitute④in② AYbA En=AYb Vsb-Alsb Ib=Yb(vb-Vsb)+Isb Tea break/
北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 Nodal analysis: 3. Find out the relationship between the branch voltage Vb and the nodal voltage En. ① ③ 2 ② 4 1 3 5 ④ 1 1 e4 e1 V = e - = 2 1 e2 V = e - 3 2 e4 e2 V = e - = 4 2 e3 V = e - 5 3 e4 e3 V = e - = e1 e3 Vb 0 1 -1 = e2 1 0 0 0 1 1 0 0 0 0 -1 1 3. the relationship between the branch voltage Vb and the nodal voltage En e4 = 0 node ① ③ ② branch 4 2 1 3 5 n T Vb = A ⋅E …③ Branch voltage column vector Nodal voltage column vector 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 Nodal analysis You can choose any node as the reference node, and solve the other nt nodes. (There should be nt nodal equations for the nodal analysis.) Set up equations Input all the information of the network component. Input the structure of the network 1. branch characteristic equations (standard branches)Æ 2. Correlation matrix (node-branch)Æ 3. Find out the relationship between the branch voltage Vb and the nodal voltage En. 4. Nodal analysis matrix Topology analysis methods of the network: Large network analysis method 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 Nodal analysis: 4. Nodal analysis matrix Substitute ③ in ①: b b n Sb) Sb I = Y (A E - V + I T …④ Substitute ④ in ②: AYbA En = AYbVSb − AISb T b b b Sb) Sb I = Y (V - V + I …① A⋅Ib =0 …② n T Vb = A ⋅E …③ 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 AYbA En = AYbVSb − AISb T Elements parameters in the network→Yb,ISb,VSb Structure parameters in the network →A known→find out En n T Vb = A ⋅E b b b Sb ) Sb I = Y (V - V + I T Yn = AYbA S AYbVSb AISb I = − Let: nodal admittance matrix Nodal current source column vector n n S Y E = I Nodal analysis: 4. Nodal analysis matrix 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 Tea break！ Tea break！