Chapter 4: Fundamentals of Linear Network Analysis 54-1 Fundamentals of network topology analysis 94-2 Methods for Linear Network Analysis 《 Principles of Circuit Analysis》 1. Loop current method Chapter 4: Network Analysis 2: Nodal point voltage method Lecture 2 §51 Network theorell 200911-03 34-3 Large network analysis method: (Nodal analysis Basie network analysis-Introduction to loop Q age Loop impedance Loop current column Loop voltage Mesh eurrent methe Equation establishing according to the structure of tree if the direction of l, and I, are the same, Z, is positive, otherwise pedance) Z: the common branch impedance between loop I andj( his method is easier to learnt si: the algebraic sum of all the voltage source It can only be used in planar network. (increasing voltage) along the loop 地e段么01) (1) Source equivalence(Norton's-Thevenin's) 2)Virtual loop current method (when the current source 0 IIss branch is at the boundary oKthe network (3)Assuming the branch voltage when current source is 0乙20乙z+2+2x(0 not at the bondary ranch) X14Z6 1359x4z6/s20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 2 2009-11-03 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 §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 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 Basic network analysis – Loop or mesh current method Mesh current method Loop current method ‰ Loop current method: Equation establishing according to the structure of tree; It can be used in nonplanar network. ‰ Mesh current method: This method is easier to learn； It can only be used in planar network. Z2 Z3 Z5 Z1 Z4 Z6 Vs1 Vs3 Vs2 + - - + + - 6 3 2 4 5 1 6 3 2 4 5 1 6 3 2 4 5 1 Review*** 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 * = Z1 +Z2 +Z4 Z2 - Z2 +Z3 +Z5 Z4 +Z5 +Z6 Z4 - Z5 - Z2 - Z4 - Z5 - I1 I2 I3 S1 VS2 V - S2 VS3 V - 0 VS Z⋅I = Loop impedance matrix Loop current column vector Loop voltage source column vector Basic network analysis – Introduction to loop current method Review VSi : the algebraic sum of all the voltage source (increasing voltage) along the loop i Zii : sum of the branch impedance in loop i (self impedance) positive Zij : the common branch impedance between loop I and j (mutual impedance) if the direction of Ii and Ij are the same, Zij is positive, otherwise it is negative. 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) Source equivalence(Norton’s →Thevenin’s) (2) Virtual loop current method (when the current source branch is at the boundary of the network) (3) Assuming the branch voltage (When current source is not at the boundary branch) Z1 Z2 Z3 Z6 Z4 Z7 Z8 + Vs7 - Is2 Is5 I3 I4 I1 I5 + Vx - I2 I2=IS2 IS5=I3-I4 Loop current method — dealing with the current source Review 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 Z1 Z2 Z3 Z6 Z4 Z7 Z8 + Vs7 - Is2 Is5 I3 I4 I1 I5 + Vx - I2 I2=IS2 Review (1) Source equivalence(Norton’s →Thevenin’s) (2) Virtual loop current method (when the current source branch is at the boundary of the network) (3) Assuming the branch voltage (When current source is not at the boundary branch) ⎛ ⎞⎛ ⎞ Loop current method + + — dealing with the current source ⎛ ⎞ ⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎜ ⎟ =⎜ ⎟ ⎜ ⎟ + + ⎜ ⎟ ⎜ ⎟ ⎝ ⎠⎝ ⎠ + + ⎝ ⎠ 134 3 4 1 2 S2 3 S5 34 3 7 6 4 6 4 S7 2 6 2685 Z Z Z 0 -Z -Z 0 I 0 0 10 0 0 I I 0 0 1 -1 0 I I -Z -Z 0 Z Z Z Z -Z I V 0 -Z 0 -Z Z Z Z I 0