电路原理第五版邱关源罗先觉第五版课件最全包括所有章节及习题

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1、电路原理第五版,邱关源,罗先觉第五版课件最全包括所有章节及习题.This article is contributed by kk0126Third chaptersA keyGeneral analysis of resistance circuitFamiliar with the method of column writing of circuit equation: Mastering the method of column writing of circuit equation: loop current method and node voltage methodprimary

2、 coverageBasic concepts, independent equations of KCL and KVL, independent equations of KCL and KVL, branch current method, loop current method, node voltage methodGeneral analysis methods for linear circuits(1) (2) universality: applicable to any linear circuit. Universality: applies to any linear

3、circuit. Systematicness: the method of calculation is regular. Systematicness: the method of calculation is regular.Basis of methodsConnection of circuits - KCL, KVLs law, KCLs law. (1) connection relation of circuit - KCL, KVLs law. Voltage and current relation characteristics of components. (2) vo

4、ltage and current relation of component. The general analysis method of complex circuits is based on the general analysis method of complex circuits of KCL, KVL and yuan, which is based on the series equations of voltage and current of KCL, KVL and KCL, and solves the equations. Series equations and

5、 solution equations of voltage and current closure. According to the column equation, the difference of the selected variables can be divided into branch current method and the selected variables, which can be divided into branch current method, loop current method and node voltage method. Nodal vol

6、tage method.graph theoryGraph theory is a branch of topology, graph theory is a branch of topology, and it is a very interesting and widely used subject. A very wide range of interests and applications.AB DAC BKonigsberg Seven Bridges problemDC3.1 circuit diagramA circuit diagram (Graph) is a diagra

7、m used to represent the geometric structure of a circuit and a graphical circuit to represent the geometric structure of a circuitIEightR1 R5 R2 + uS R6 _R3Component properties152ThreeA component acts as a branch4635R471N=5B=8Directed graphFourThe components are connected in series and in parallel a

8、s a branch26N= 4B=6Path (path) (path)From a graph of G along some branch continuously moves from one node graph of some branches along the continuous moving to branch through another node of path. Move to branch through another node of path.Connected graphs (connected graphs (connected, graph)At lea

9、st one line at least one arbitrary path graph G two nodes called two nodes called connected graph, non connected graph has at least two separate parts. Connected graphs, at least two separated parts of unconnected graphs.Subgraph: if all branches and nodes in figure G are graphs G Subgraph: if all b

10、ranches and nodes in Figure 1 are graphsThe branch and the node in the branch are called the branch and the node, and then G1 is called the subgraph of the subgraph of GGG1G2The tree (Tree) T is a subgraph of connected graph, satisfying a subgraph of connected graph, and a subgraph of connected grap

11、hColumn condition: column condition:Connectivity contains all nodes without closed pathstreeNot treeTree branch (tree tree branch) (tree branch): Branch Branch of a tree (link) belongs to G, but not to the branch branch (link) that does not belong to T (T): a branch that belongs to G and does not be

12、long to a.Features: corresponding to a graph, there are many trees, corresponding to a graph, there are a lot of trees, the number of branches is a certain tree count: tree count: even count: even count:BT = n? 1BL = b = BT = B? (n, 1)Loop (Loop)L is a subgraph of a connected graph, a closed path, m

13、eet: is a subgraph of a connected graph, a closed path, meet: (1) (2) each connected node associated with each node connectivity, 2 (1) with (2) each node associated with 2 branches not is the 12312 loop 3768542loopFive7854Features: features:Corresponding to a graph, there are many loops, the number

14、 of basic loops is certain, and the number of basic loops for connecting numbers is certain. For planar circuits, for planar circuits, the mesh number is the basic loop numberBasic circuit (single continuous branch circuit) basic loop (single continuous support circuit)The basic loop has an exclusiv

15、e link of 64213131, 522356Conclusion: branch number = tree number + conclusion: branch number = tree number + even numberThe number of nodes and nodes 1 = basic loop numberNode, node, branch and basic loop relationB = n + L = 1exampleHere is a diagram of the circuit. It is shown as a diagram of the

16、circuit, and draw three possible trees and their corresponding basic circuits. Basic circuit of response.15867285, 674836FourThree4823The independent equations and independent equations of two and KCL and KVLKCLs independent equations, KCL equation equations: KCL equations for each node:12341164, 43

17、5223I1, I4, I6 = 0, I1, I2 +, I3 = 0, I2 +, i5 +, I6 = 0, I3 + I4, i5 = 0One234 = 0Conclusion: conclusion:KCL equation for n nodes of the circuit, the independent KCL equation is n-1, all nodes of the circuit, independent KCL equation is nThe number of independent equations =b independent equations

18、independent equations independent equations of the number of independent equations of KVL number KVL number = basic loop number = (n-1) -Conclusion: conclusion:N nodes, B branches of the circuit, the only node, the branch circuit, the set of KCL and KVL equations are: the standing KCL and KVL equati

19、ons are: KCL equation for the number of(n, 1) + B? (n = 1) = bThree, branch current method (branch current method)Circuit circuit equation analysis method of circuit nodes and branches to each branch currents as unknown variables, the circuit has n nodes, B branches, require the solution of branch c

20、urrent and branch current, there are B unknown. Just list B independent circuit equations, variables. The circuit equations are then used to solve the B variables.The column of independent equations is writtenSelect n from the N nodes of the circuit, select n-1 nodes from the N nodes of the circuit,

21、 write the KCL equation, select the basic circuit, write the b- (n-1) KVL equation, select the basic circuit columnexampleI2 1There are 6 branch currents, and 6 equations are to be written. KCL branch currents need to write 6 equations. 2 equations: 1 I1 + I2 = I6 = 0 R4 R2 2 I3 I4 + I3 + I4 = 0213

22、R3 = i5 + I6 = 03 R1 I1 34 R5 i5 I2Take the mesh as the basic circuit, take the mesh as the basic circuit, write the equation in the clockwise direction around the row and column KVL, write the equation: the direction of the needle is round, the equation is writtenI6 loop 1Loop 2 loopThe loop 3 loop

23、 combines the component characteristics to eliminate the branch voltage by eliminating the branch voltage with the component characteristics:R6+ U - SU2 + U3, U1 = 0, U4, U5 = U3 = 0, U1 +, U5 +, U6 = uSR2i2 + R3i3 = Ri1 = 01 R4i4 = R5i5 = R3i3 = 0Ri1 + R5i5 + R6i6 = uS 1General steps of branch curr

24、ent method: general steps of branch current method:The calibration of each branch current (voltage) of the reference direction; calibration of branch current (voltage) of the reference direction; selected (n - 1) nodes, writing the KCL equation; node equation; selected nodes selected B - (n - 1) an

25、independent circuit, writing the KVL equation; a independent loop equation; selected independent circuit elements (components) into the characteristics of characteristics by solving the above equation), get the B branch current; branch current; solving the above equations, a branch current to calcul

26、ate branch voltage and other analysis. Further calculation of branch voltage and other analysis.Characteristics of branch current method: characteristics of branch current method:Equation, branch method is written in the KCL column and the KVL equation, so the equation writing is convenient and intu

27、itionistic, but the equation number of writing is convenient and intuitionistic, but more suitable for use in the equation, the branch number of cases. More cases are used.In 1. casesI1 7? + 70V -Calculate the power of each branch current and voltage source. Calculate the power of each branch curren

28、t and voltage source.A I2 1, 6V + - B 211? I3 7?Solution:(1) n - 1=1 KCL equations: Equations: EquationsNode A: node: - I1 - I2+I3=0(2) B - (n - 1) =2 KVL equations: Equations: Equations7I1 - 11I2=70-6=64 11I2+7I3= 6I1 =1218 203 =6AI2 = 406203 = 2AP = 6 * 70 = 420W 70P = 2 * 6 = 12W 6I3 = I1 + I2 =

29、6 = 2 = 4AIn 2. casesI1 7? + 70V -The current equation of the write branch circuit (the circuit contains ideal current source), the current equation of the write branch current circuit contains ideal current source. The circuit contains ideal current source a, I2 1, 6A, B 11, + +?USolution 1.I3 7?(1

30、) n - 1=1 KCL equations: Equations: EquationsNode A: node: - I1 - I2+I3=0(2) B - (n - 1) =2 KVL equations: Equations: Equations_Two7I1 - 11I2=70-U 11I2+7I3= U addition equation: I2=6A addition equation:I3 7? Known, because I2 is known, only two equations are writtenSolution 2.I1 7? + 70V - I2 1 6AA

31、11?Node A: node - - I1+I3=6Avoid the current source branch back road: avoid the current source branch to retrieve the road:B7I17I3=70In 3. casesI1 7? + 70V -The current equation of the write branch (the circuit contains a controlled source), the write branch current equation contains a controlled so

32、urce in the circuit, and the circuit contains a controlled source a, I2 1 +5USolution:I3 11 + 7? _ U- I1 - I2+I3=0 7I1 - 11I2=70-5U 11I2+7I3= 5U addition equation: supplementary equation: U=7I3_ BTwoCircuit with controlled sources, equation writing is divided into two steps: circuit with controlled

33、sources, equation writing is divided into two steps: the first controlled source as an independent source column equation; (1) the first controlled source as an independent source column equation; will control with unknown, and substituting listed in (equation (2) will control the amount with the un

34、known quantity said, and substituting (1) listed in equation, eliminating intermediate variables. Go to intermediate variables.Four, mesh current method (mesh current method)Method for analyzing circuit by writing circuit equation with mesh current as unknown quantitybasic thoughtTo reduce the numbe

35、r of unknowns (equations), in order to reduce the number of unknowns (equations), it is assumed that there is a mesh current in each mesh. There is a mesh current. The current of each branch can be represented by a linear combination of mesh currents to obtain the solution of the circuit. A linear c

36、ombination representation is used to obtain the solution of the circuit.AThere are two meshes in the drawing, and there are two meshes in the branch current diagram:I1, R1, uS1 + -I2, R2, IM1 + uS2 - B im2I3 R3I1 = IM1I3 = im2I2 = im2? IM1Equations listedThe branch current can be expressed as an alg

37、ebraic sum of the mesh currents, so the branch currents can be expressed as algebraic sums of mesh currents and automatically satisfied. KCL automatically meets. The mesh current method is to mesh writing KVL equation: process equation: B? (n? 1) equation: writing equations of writing: mesh 1 mesh 1

38、:R1 im1+R2 (im1- im2) -uS1+uS2=0 2:R2 (im2- IM1 mesh 2 mesh) + R3 IL2 -uS2=0 finishing finishing: (R1+ R2) im1-R2im2=uS1-uS2 - R2im1+ (R2 +R3) im2 =uS2I1, R1, uS1 + - I2, R2, IM1 + uS2 - B, im2, R3, a, I3,.Compared with the branch current method, the method reduces the number of equations and reduce

39、s the number of equations by n-1 compared with the branch current methodSummary: summary:Self resistance of R11=R1+R2 mesh 1. A self resistance equal to the sum of all resistances in mesh 1. Equal to the self resistance of the mesh 1 R22=R2+R3 mesh 2. A self resistance equal to the sum of all resist

40、ances in mesh 2. Equal to mesh 2Since the total resistance is R12= R21= - R2 1 mesh 2 mesh 1 mesh, 2 mesh between the mutual resistance when the two loop current flows through the relevant branch of the same direction, when the two loop mutual electrical current flows through the relevant branch of

41、the same direction, take the positive or negative resistance.The positive or negative resistance. Algebraic us11= uS1-uS2 mesh all voltage source voltage in the 1 and 1 us22= uS2 algebraic mesh mesh 2 mesh 2 all voltage source voltage and source voltage when the voltage of the loop direction and dir

42、ection, from a negative voltage source voltage; when the direction of the loop direction, take the negative and the positive. And take a plus.Equation of standard form: equation of standard form:R11im1+R12im2=uS11 R12im1+R22im2=uS22A circuit for a mesh, for circuits having l=b- (n-1) meshes:Of which

43、: Rkk: self resistance (positive), self resistance (positive)Rjk: mutual resistanceR11im1+R12im1+. +R1m imm=uS11 R21im1+R22im1+. +R2m imm=uS22. Rm1im1+Rm2im1+. +Rmm imm=uSmm+: the two meshes flowing through each other have the same current direction - the two meshes flowing through each other, the c

44、urrent opposite, 0: NoneExample 1. solution 1The current I. circuit has three meshes, as shown in the diagram: the circuit has three meshes as shown: (RS + R + R4) I1 = Ri2 = US = 11 R4i3Ri1 + (R + R2 + R) I2 = R, I3 = 01155R4i1, R, I2 + (R +, R4 + R), I3 = 0535I = I2? I3RS + US R1 _I1R4R5I2 i3R2Sho

45、w: indicate:The linear network Rjk=Rkj without controlled source, and the coefficient matrix is symmetric matrix. When the mesh currents are in the same direction (or inverse), they are negative when the mesh currents are clockwise (or counterclockwise) clockwise. In the direction of the needle, Rjk

46、 is negative.IR3General steps of mesh current method: general steps of mesh current method:Determine the direction of each mesh bypass circuit in the bypass circuit; determine the direction of each mesh in the mesh to mesh current; as the unknown, the mesh to mesh currents as unknown variables, the

47、equation of KVL writing; writing the KVL equation KVL equation; solving the above equations, a mesh current; solving the above equation. Get a l mesh current; for each branch current (represented by a mesh current) for each branch current (represented by a mesh current); other analysis. Other analys

48、is.Five, loop current method (loop current method)Method for analyzing circuit by writing circuit equation by circuit current unknown in basic circuit. Equation analysis method of a circuit.AdvantageThe mesh current method is only suitable for planar circuits. The loop current law and the hole curre

49、nt method are only suitable for planar circuits, and are applicable to planar or nonplanar circuits. Suitable for planar or nonplanar circuits.basic thoughtTo reduce the number of unknowns (equations), in order to reduce the number of unknowns (equations), it is assumed that there is a loop current

50、in each loop. There is a loop current. The branch currents can be represented by a linear combination of loop currents. To find the solution of the circuit. Combination representation. To find the solution of the circuit.Equations listedThe loop current is closed in the independent loop, and the loo

51、p current is closed in the independent circuit for each associated node, and flows into the flow once and then automatically. All flow into the flow once, so the KCL automatically meets.Therefore, the loop equation, the equation number is: the current method is the independent loop column written KV

52、L equation, the equation is:B? (n, 1)The number of independent circuits is 2, and the number of independent circuits is 2. Select the two I 1 independent circuits of the diagram. The branch current can be expressed as an independent loop, and the branch current can be expressed as: RA, I2, R2, IL1 +

53、 uS2 - B, IL2, I3, R3OneI = IL1, IL 21, I2 = IL1, I3 = IL 2US1+ -Write: equation equation writing: loop 1: loop: R1 (il1- IL2) +R2il1-uS1+uS2=0 + 2: loop circuit: R1 (il2- IL1) + R3 IL2 +uS1=0: tidy tidy: (R1+ R2) il1-R1il2=uS1-uS2 - R1il1+ (R1 +R3) IL2 =-uS1A, I1, R1, uS1 + - I2, R2, IL1 + uS2 - B,

54、 IL2, R3, I3,.Summary: summary:The self resistance of the R11=R1+R2 loop 1 is equal to the self resistance of all resistance sum loop 1 in loop 1, and the self resistance of the R22=R1+R3 loop 2 is equal to the self resistance of all resistance sum loop 2 in circuit 2,Since the total resistance is R

55、12= R21= - R1 loop 1, loop mutual resistance between 2 and two when the loop current flows through the relevant branch of the same direction, when the two loop current flowing through the relevant branch of the same direction, the mutual resistance is negative or positive. Take the positive or negat

56、ive.Ul1= uS1-uS2 ul2= -uS1The algebraic sum of all voltage source voltages in loop 12 all voltage source voltage loop algebra and when the voltage source voltage and the direction of loop direction, when the voltage source voltage and the direction of loop direction, and take a negative. And take po

57、sitive numbers.The resulting canonical form equation: the resulting canonical form of equation: R11il1+R12il2=uSl1R12il1+R22il2=uSl2Circuit of a loop, for circuits having l=b- (n-1) circuits:Of which: Rkk: self resistance (positive), self resistance (positive) +: the two circuits flowing through eac

58、h other have the same current directionRjk: mutual resistance - the two circuits flowing through each other opposite the current direction0: nothing to do withR11il1+R12il1+. +R1l ill=uSl1 R21il1+R22il1+. +R2l ill=uSl2. Rl1il1+Rl2il1+. +Rll ill=uSllExample 1. solutions:Solving current by loop curren

59、t method i.Let only one loop current pass through the R5 branch(RS + R + R4) I1, Ri2, (R + R4) I3 = US 111Ri1 + (R + R2 + R) I2 + (R + R2) I3 = 01151(R + R4) I1 + (R + R2) I2 + (R + R2 + R + R4) I3 = 01113I = I2RS + US R1 _I1R4R5I2R2IFeatures: features:Reduce the amount of computationI3R3The recogni

60、tion of mutual resistance is more difficult, and the identification of mutual resistance is more difficult, and it is easy to miss each otherThe general steps of loop method: general steps of loop method: selected l=b- (n-1) independent loop, and determine the direction of bypass; independent loop,

61、and determine the direction of bypass; independent loop to loop currents as unknown variables, the L independent loop, for the unknown quantity in the loop current,Writing the KVL equation; equation; solving the above equations, get l loop current; loop current; solving the above equation for the cu

62、rrent of each branch (represented by current loop) for each branch current (represented by current loop); other analysis. Other analysis.The treatment of the branch of a non current source: the processing of a branch of a non current source:The current source voltage is introduced, and the current s

63、ource voltage is introduced to increase the relation equation between the loop current and the current source current. Relational equation. (RS + R + R4) I1 = Ri2 = R4i3 = US case 11Ri1 + (R + R2) I2 = U 11R4i1 + (R + R4) I3 = U 3RS + US _ R1 R2 current source as voltage source column equationI1R4IS I2_ + USupplementar