Chapter 3.pptx hhoasdhuio sadhuiosad usadhuasdio

Chapter no 5 linear circuit analysis
gsadiyhgsadi sadijhsaiod osdahuasdioh sadknsioahjdsa sadjhiosadjhsaodj joashsaoihjnsaodnsadboidshaoisadujasdiojdsmiosadjiosadjsadiousdajhoisaudhjsdaiohdsiousd

1. 1

2. Methods of Circuit Analysis Two popular and powerful techniques for analyzing circuits are: Nodal analysis: a general procedure to find all the node voltages in a circuit. It is based on KCL and Ohm’s Law. Loop analysis: another general approach to find mesh currents which circulate around closed paths in the circuit. It is based on KVL and Ohm’s Law. 2

3. More Terminology Reference node or ground: a node that is assumed to have a zero potential. – If the reference node is not explicitly indicated on the circuit one can arbitrarily choose any node as the ground. We will soon see how to choose a good ground node . Node voltage is the voltage difference/drop from a given node to the reference node. 3

4. On the Way to Modified Nodal Analysis We identify four general types for branches as follows: (we have seen these before, and here we are just formalizing them by giving them proper names!): R bran c h R V bran c h I br a n c h ( t h i s a l s o i n c l u d e any b r a n c h t h a t c o n s i s t of a current source in series with other components) V branch (also known as evil branch!) Le t ’s s ee i f w e c an c a l c u l a t e t h e c u r rent of t h e s e b r a n c he s based on the end-point node voltages! 4

5. R Branch A branch that consist of only a resistor (or series combination of resistors that can be represented by their equivalent resistors ) I  V b I  V a R R How about the current in the other direction! I  V a I  V b 5

6. RV Branch A branch that consist of a resistor (or series combination of resistors that can be represented by their equivalent resistors) in series with a voltage sourse (or a series combination of voltage coursed that sources that can be represented by their equivalent voltage source) I a How about the current in the other direction? What if the polarity of the voltage source is reversed? b R R ( V b  V s )  V a  V b  V s I  V a 6

7. I Branch I branch: A branch that consists of only a current source! I I  I s Another example of I branch (some times called IR branch): A branch that consists of a resistor (or equivalent resistor) in series with a current source: I I  I s 7

8. V Branch (Evil Branch) A branch that consists of only one voltage source: I a b However, the good news is: Note: The sources in V, RV, I, and RI branch can be either dependent (controlled) or independent sources. I  ? V s  V a  V b 8

9. Nodal Analysis (NA ) A gen e ral t e c hn i q u e t o s o l v e a c i r c u i t ( i . e . , t o f i n d v o l t a g e , current and power of every element in the circuit). Unknowns : controlling variables (for dependent sources) current in V branches (evil branches) voltage of each true node steps : Identify every true node of the circuit. Choose one of them as a reference node (node whose voltage is zero). W r i t e o n e e qua t i on p e r c o n tr o lli ng c u r rent o r v o l t age o f dependant sources. Write the relationship between the two nodes of the V branch . Write one KCL per true node. 9

10. 4 Different Cases CIRCUITS CONTAINING INDEPENDENT VOLTAGE SOURCES CIRCUITS CONTAINING ONLY INDEPENDENT CURRENT SOURCES CIRCUITS CONTAINING DEPENDENT CURRENT SOURCES CIRCUITS CONTAINING DEPENDENT VOLTAGE SOURCES 10

11. CIRCUITS CONTAINING ONLY INDEPENDENT CURRENT SOURCES W r i t e t he e q ua t i o n s t hat l ead t o s o l v e t he f o ll o w i ng c i r c u i t (finding all the currents and voltages). CASE 1 11

12. KCL @ Node 1 12

13. Case 1 (cont’d) 13

14. Solve Learning Assessment Problem 3.1 3.2 3.3 Homework 14

15. CIRCUITS CONTAINING DEPENDENT CURRENT SOURCES W r i t e t he e q ua t i o n s t hat l ead t o s o l v e t he f o ll o w i ng c i r c u i t (finding all the currents and voltages). CASE 2 15

16. KCL @ Node 1 1 2 V 2 V 1 Write controlling variables 16

17. 17

18. Solve Learning Assessment Problem 3.4 3.5 3.6 Homework 18

19. CIRCUITS CONTAINING INDEPENDENT VOLTAGE SOURCES Two cases independent voltage source is connected between two non-reference nodes. Independent voltage source is connected to the reference node CASE 3 No need to write KCL for such node Have to form super node 19

20. 20

21. 21

22. Use nodal analysis to find I o in the following circuit: 22

23. Solve Learning Assessment Problem 3.7 3.8 Homework 23

24. CIRCUITS CONTAINING DEPENDENT VOLTAGE SOURCES networks containing dependent (controlled) sources are treated in the same manner as described earlier. CASE 4 24

25. 25

26. Controlling variable of dependent source Equation of Super node Putting value of V 2 from Eq. 1 KCL at Super node KCL at node 3 Multiplying Eq with 1K and simplifying Multiplying Eq with 1K and simplifying   Combining Eq 2 and 3 1 2 3 Solving 26

27. Equation of Super node Controlling variable of dependent source KCL at node 5 KCL at Super node 1 2 3 Combining Eq 1, 2 and 3 27

28. Solve Learning Assessment Problem 3.9 3.10 3.11 3.12 Homework 28

29. LOOP ANALYSIS 29

30. Node Analysis Identify nodes in the circuit. Assign node voltages to every node KCL for every node Unknown parameters are the node voltages Once these node voltages have been calculated, all the other parameters in the network can easily be determined using Ohm’s law. Identify loops in the circuit. Assign loop current to every loop KVL for every loop Unknown parameters are the loop current Once these loop currents have been calculated, all the other parameters in the network can easily be determined using Ohm’s law. Loop Analysis 30

31. How Many KVL Equations?? B − N +1 linearly independent KVL equations for any network, where B  number of branches in the circuit N  number of nodes. B = 8 N = 5 B − N +1 = 8 − 5 +1 =4. 31

32. The branch currents are then determined as Loop Currents and Branch Currents Not the same 32

33. Mesh Analysis and Loop Analysis Mesh analysis is a special case of a more general technique called loop analysis. A mesh is a loop that does not contain any other loops within it . Mesh analysis Loop analysis! All the circuits we will examine in this text will be planar A planar circuit is a circuit that can be drawn in a plane with no branches crossing one another. Example of non-planar circuits: 33

34. CIRCUITS CONTAINING INDEPENDENT CURRENT SOURCES CIRCUITS CONTAINING ONLY INDEPENDENT VOLTAGE SOURCES CIRCUITS CONTAINING DEPENDENT SOURCES 3 Different Cases 34

35. CIRCUITS CONTAINING ONLY INDEPENDENT VOLTAGE SOURCES KVL for Loop 1 12 K I 1 - 6k I 2 = 12 KVL for Loop 2 -6 K I 1 + 9k I 2 = -3 Once these node voltages have been calculated, all the other parameters in the network can easily be determined using Ohm’s law. Selecting loops in an other way should produce same results Home work CASE 1 35

36. 36

37. Solve Learning Assessment Problem 3.13 3.14 Homework 37

38. CIRCUITS CONTAINING ONLY INDEPENDENT CURRENT SOURCES CASE 2 Just as the presence of a voltage source in a network simplified the nodal analysis, the presence of a current source simplifies a loop analysis KVL for Loop 1 KVL for Loop 2 CASE 2 38

39. for Loop 1 for Loop 2 KVL for Loop 3 39

40. select two loop currents I 1 and I 2 such that I 1 passes directly through the 2-mA source , and I 2 passes directly through the 4-mA source, Go through it from book Home work 40

41. Solve Learning Assessment Problem 3.15 3.16 3.17 Homework 41

42. CIRCUITS CONTAINING DEPENDENT SOURCES CASE 3 First, we write the controlling equation for the dependent source. Then we treat the dependent source as though it were an independent source when writing the KVL equations. Controlling equation of dependent source KVL for Loop 1 KVL for Loop 2 CASE 3 42

43. 43

44. Controlling equation of dependent source for Loop 1 for Loop 2 KVL for Loop 3 KVL for Loop 4 -4m 1 2 3 44

45. 45

46. 46