Chapter 4. Techniques of Circuit Analysis


 Joseph Powers
 3 years ago
 Views:
Transcription
1 Chapter 4. Techniques of Circuit Analysis By: FARHAD FARADJI, Ph.D. Assistant Professor, Electrical Engineering, K.N. Toosi University of Technology Reference: ELECTRIC CIRCUITS, J.W. Nilsson, S.A. Riedel, 10 th edition, 2015.
2 Chapter Contents 4.1. Terminology 4.2. Introduction to the NodeVoltage Method 4.3. NVM and Dependent Sources 4.4. NVM: Some Special Cases 4.5. Introduction to the MeshCurrent Method 4.6. MCM and Dependent Sources 4.7. MCM: Some Special Cases 4.8. NVM Versus MCM 4.9. Source Transformations Thévenin and Norton Equivalents More on Deriving a Thévenin Equivalent Maximum Power Transfer Superposition Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 2
3 4.1. Terminology o To discuss the more involved methods of circuit analysis, we must define a few basic terms. o Planar circuits can be drawn on a plane with no crossing branches. o A circuit that is drawn with crossing branches still is considered planar if it can be redrawn with no crossover branches. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 3
4 4.1. Terminology o Nonplanar circuits cannot be redrawn in such a way that all the node connections are maintained and no branches overlap. o The nodevoltage method is applicable to both planar and nonplanar circuits. o The meshcurrent method is limited to planar circuits. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 4
5 4.1. Terminology Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 5
6 4.1. Terminology Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 6
7 4.1. Terminology Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 7
8 4.1. Terminology Simultaneous Equations How Many? o The number of unknown currents in a circuit equals the number of branches, b, where the current is not known. o We must have b independent equations to solve a circuit with b unknown currents. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 8
9 4.1. Terminology Simultaneous Equations How Many? o If n is the number of nodes in the circuit, we can derive n1 independent equations by applying KCL to any set of n1 nodes. o Application of KCL to the n th node does not generate an independent equation, because this equation can be derived from the previous n1 equations. o Because we need b equations to describe a given circuit and we can obtain n1 of these equations from KCL, we must apply KVL to loops or meshes to obtain the remaining b(n1) equations. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 9
10 4.1. Terminology Simultaneous Equations How Many? o Thus by counting nodes, meshes, and branches with unknown currents, we have established a systematic method for writing the necessary number of equations to solve a circuit. o We apply: KCL to n1 nodes and KVL to b(n1) loops (or meshes). Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 10
11 4.1. Terminology Simultaneous Equations How Many? o These observations also are valid in terms of essential nodes and essential branches. o If n e is the number of essential nodes and b e is the number of essential branches with unknown currents, we can apply: KCL at n e 1 nodes and KVL around b e (n e 1) loops or meshes. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 11
12 4.1. Terminology Simultaneous Equations How Many? o The number of essential nodes is less than or equal to the number of nodes. o The number of essential branches is less than or equal to the number of branches. o Thus it is often convenient to use essential nodes and essential branches, because they produce fewer independent equations to solve. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 12
13 4.1. Terminology The Systematic Approach o We write the equations on the basis of essential nodes and branches. o The circuit has 4 essential nodes and 6 essential branches, denoted i 1 i 6, for which the current is unknown. o We derive 3 of 6 simultaneous equations by applying KCL to any 3 of 4 essential nodes. o Using nodes b, c, and e: Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 13
14 4.1. Terminology The Systematic Approach o We derive the remaining 3 equations by applying KVL around 3 meshes. o Because the circuit has 4 meshes, we need to dismiss one mesh. o We choose R 7 I, because we don't know the voltage across I. o Using the other 3 meshes: Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 14
15 4.1. Terminology The Systematic Approach o By introducing new variables, we can describe a circuit with just n1 equations or b(n1) equations. o These new variables allow us to obtain a solution by manipulating fewer equations. o The new variables are known as node voltages and mesh currents. o Nodevoltage method enables us to describe a circuit in terms of n e 1 equations. o Meshcurrent method enables us to describe a circuit in terms of b e (n e 1) equations. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 15
16 Chapter Contents 4.1. Terminology 4.2. Introduction to the NodeVoltage Method 4.3. NVM and Dependent Sources 4.4. NVM: Some Special Cases 4.5. Introduction to the MeshCurrent Method 4.6. MCM and Dependent Sources 4.7. MCM: Some Special Cases 4.8. NVM Versus MCM 4.9. Source Transformations Thévenin and Norton Equivalents More on Deriving a Thévenin Equivalent Maximum Power Transfer Superposition Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 16
17 4.2. Introduction to NodeVoltage Method o We introduce nodevoltage method by using essential nodes of circuit. o The first step is to make a neat layout of circuit so that no branches cross over and to mark clearly essential nodes on circuit diagram. o This circuit has n e =3essential nodes. o We need 2 or (n e 1) nodevoltage equations to describe the circuit. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 17
18 4.2. Introduction to NodeVoltage Method o The next step is to select one of 3 essential nodes as a reference node. o Although theoretically the choice is arbitrary, practically the choice for the reference node often is obvious. o For example, the node with the most branches is usually a good choice. o We flag the chosen reference node with the symbol. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 18
19 4.2. Introduction to NodeVoltage Method o After selecting reference node, we define node voltages on circuit diagram, i.e., the voltage rise from the reference node to a nonreference node. o We are now ready to generate nodevoltage equations. o We do so by first writing the current leaving each branch connected to a nonreference node as a function of the node voltages and then summing these currents to zero in accordance with KCL. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 19
20 4.2. Introduction to NodeVoltage Method o Nodevoltage equation at node 1 is: o Nodevoltage equation at node 2 is: Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 20
21 4.2. Introduction to NodeVoltage Method o Once the node voltages are known, all branch currents can be calculated. o Once these are known, the branch voltages and powers can be calculated. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 21
22 4.2. Introduction to NodeVoltage Method Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 22
23 Chapter Contents 4.1. Terminology 4.2. Introduction to the NodeVoltage Method 4.3. NVM and Dependent Sources 4.4. NVM: Some Special Cases 4.5. Introduction to the MeshCurrent Method 4.6. MCM and Dependent Sources 4.7. MCM: Some Special Cases 4.8. NVM Versus MCM 4.9. Source Transformations Thévenin and Norton Equivalents More on Deriving a Thévenin Equivalent Maximum Power Transfer Superposition Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 23
24 4.3. NVM and Dependent Sources o If the circuit contains dependent sources, the nodevoltage equations must be supplemented with the constraint equations imposed by the presence of the dependent sources. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 24
25 4.3. NVM and Dependent Sources Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 25
26 Chapter Contents 4.1. Terminology 4.2. Introduction to the NodeVoltage Method 4.3. NVM and Dependent Sources 4.4. NVM: Some Special Cases 4.5. Introduction to the MeshCurrent Method 4.6. MCM and Dependent Sources 4.7. MCM: Some Special Cases 4.8. NVM Versus MCM 4.9. Source Transformations Thévenin and Norton Equivalents More on Deriving a Thévenin Equivalent Maximum Power Transfer Superposition Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 26
27 4.4. NVM: Some Special Cases o When a voltage source is the only element between 2 essential nodes, the nodevoltage method is simplified. o There are 3 essential nodes. o 2 simultaneous equations are needed. o A reference node has been chosen. o Two other nodes have been labeled. o The 100 V source constrains the voltage between node 1 and the reference node to 100 V. o There is only one unknown node voltage (v 2 ). Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 27
28 4.4. NVM: Some Special Cases o Knowing v 2, we can calculate the current in every branch. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 28
29 4.4. NVM: Some Special Cases o When you use NVM to solve circuits that have voltage sources connected directly between essential nodes, the number of unknown node voltages is reduced. Because the difference between the node voltages at these nodes equals the voltage of the source. o The circuit contains 4 essential nodes. o We anticipate writing 3 nodevoltage equations. o 2 essential nodes are connected by an independent voltage source. o 2 other essential nodes are connected by a dependent voltage source. o There is only 1 unknown node voltage. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 29
30 4.4. NVM: Some Special Cases o We introduce current i because we cannot express it as a function of node voltages v 2 and v 3. o When a voltage source is between 2 essential nodes, we can combine those nodes to form a supernode. o KCL must hold for the supernode: Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 30
31 4.4. NVM: Some Special Cases Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 31
32 4.4. NVM: Some Special Cases o When we used the branchcurrent method of analysis, we faced the task of writing and solving 6 simultaneous equations. o Nodal analysis can simplify our task. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 32
33 4.4. NVM: Some Special Cases o The circuit has 4 essential nodes. o Nodes a and d are connected by an independent voltage source as are nodes b and c. o The problem reduces to finding a single unknown node voltage. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 33
34 4.4. NVM: Some Special Cases Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 34
35 Chapter Contents 4.1. Terminology 4.2. Introduction to the NodeVoltage Method 4.3. NVM and Dependent Sources 4.4. NVM: Some Special Cases 4.5. Introduction to the MeshCurrent Method 4.6. MCM and Dependent Sources 4.7. MCM: Some Special Cases 4.8. NVM Versus MCM 4.9. Source Transformations Thévenin and Norton Equivalents More on Deriving a Thévenin Equivalent Maximum Power Transfer Superposition Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 35
36 4.5. Introduction to MeshCurrent Method o Meshcurrent method (MCM) describes a circuit in terms of b e (n e 1) equations. o A mesh is a loop with no other loops inside it. o MCM is applicable only to planar circuits. o The circuit shown contains 7 essential branches with unknown currents and 4 essential nodes. o To solve it via the MCM, we must write 4 or 7(41) meshcurrent equations. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 36
37 4.5. Introduction to MeshCurrent Method o A mesh current is current that exists only in perimeter of a mesh. o On a circuit diagram, it appears as either a closed solid line or an almostclosed solid line that follows perimeter of appropriate mesh. o An arrowhead on solid line indicates reference direction for mesh current. o Mesh currents automatically satisfy KCL. At any node in circuit, a given mesh current both enters and leaves node. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 37
38 4.5. Introduction to MeshCurrent Method o Identifying a mesh current in terms of a branch current is not always possible. o i 2 is not equal to any branch current, whereas i 1, i 3, and i 4 can be identified with branch currents. o Measuring a mesh current is not always possible. o There is no place where an ammeter can be inserted to measure i 2. o The fact that a mesh current can be a fictitious quantity doesn't mean that it is a useless concept. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 38
39 4.5. Introduction to MeshCurrent Method Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 39
40 4.5. Introduction to MeshCurrent Method Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 40
41 4.5. Introduction to MeshCurrent Method o Above equations are identical in form, with mesh currents i a and i b replacing branch currents i 1 and i 2. o MCM of circuit analysis evolves quite naturally from branchcurrent equations. o MCM is equivalent to a systematic substitution of n e 1 current equations into b e (n e 1) voltage equations. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 41
42 4.5. Introduction to MeshCurrent Method o The circuit has 7 branches (5 essential branches) where current is unknown and 5 nodes (3 essential nodes). o Thus, we need 3 or b(n1)=7(51) or b e (n e 1)=5(31) meshcurrent equations to describe circuit. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 42
43 4.5. Introduction to MeshCurrent Method Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 43
44 Chapter Contents 4.1. Terminology 4.2. Introduction to the NodeVoltage Method 4.3. NVM and Dependent Sources 4.4. NVM: Some Special Cases 4.5. Introduction to the MeshCurrent Method 4.6. MCM and Dependent Sources 4.7. MCM: Some Special Cases 4.8. NVM Versus MCM 4.9. Source Transformations Thévenin and Norton Equivalents More on Deriving a Thévenin Equivalent Maximum Power Transfer Superposition Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 44
45 4.6. MCM and Dependent Sources o If the circuit contains dependent sources, meshcurrent equations must be supplemented by appropriate constraint equations. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 45
46 4.6. MCM and Dependent Sources o Circuit has 6 branches with unknown currents and 4 nodes. o We need 3 mesh currents: Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 46
47 4.6. MCM and Dependent Sources o What if you had not been told to use MCM? o Would you have chosen NVM? o It reduces problem to finding 1 unknownnodevoltage node because of the presence of 2 voltage sources between essential nodes. o We present more about making such choices later. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 47
48 Chapter Contents 4.1. Terminology 4.2. Introduction to the NodeVoltage Method 4.3. NVM and Dependent Sources 4.4. NVM: Some Special Cases 4.5. Introduction to the MeshCurrent Method 4.6. MCM and Dependent Sources 4.7. MCM: Some Special Cases 4.8. NVM Versus MCM 4.9. Source Transformations Thévenin and Norton Equivalents More on Deriving a Thévenin Equivalent Maximum Power Transfer Superposition Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 48
49 4.7. MCM: Some Special Cases o When a branch includes a current source, MCM requires some additional manipulations. o We defined mesh currents i a, i b, and i c, and voltage across 5 A current source. o Circuit contains 5 essential branches with unknown currents and 4 essential nodes. o We need to write 2 or 5(41) meshcurrent equations to solve circuit. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 49
50 4.7. MCM: Some Special Cases o Presence of current source reduces 3 unknown mesh currents to 2 such currents. o It constrains difference between i a and i c to equal 5 A. o If we know i a, we know i c, and vice versa. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 50
51 4.7. MCM: Some Special Cases o For mesh a: o For mesh c: o Adding the above equations: o For mesh b: o For current source branch: o Solving equations: Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 51
52 4.7. MCM: Some Special Cases o We can solve the problem without introducing unknown voltage v by using the concept of a supermesh. o To create a supermesh, we mentally remove current source from circuit by simply avoiding this branch when writing meshcurrent equations. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 52
53 4.7. MCM: Some Special Cases o We express voltages around supermesh in terms of original mesh currents: Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 53
54 4.7. MCM: Some Special Cases o Circuit has 4 essential nodes and 5 essential branches with unknown currents. o Circuit can be analyzed in terms of 5(41) or 2 meshcurrent equations. o Although we defined 3 mesh currents, dependent current source forces a constraint between mesh currents i a and i c. o We have only 2 unknown mesh currents. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 54
55 4.7. MCM: Some Special Cases Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 55
56 Chapter Contents 4.1. Terminology 4.2. Introduction to the NodeVoltage Method 4.3. NVM and Dependent Sources 4.4. NVM: Some Special Cases 4.5. Introduction to the MeshCurrent Method 4.6. MCM and Dependent Sources 4.7. MCM: Some Special Cases 4.8. NVM Versus MCM 4.9. Source Transformations Thévenin and Norton Equivalents More on Deriving a Thévenin Equivalent Maximum Power Transfer Superposition Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 56
57 4.8. NVM Versus MCM o The greatest advantage of both NVM and MCM is that they reduce the number of simultaneous equations that must be solved. o They also require the analyst to be quite systematic in terms of organizing and writing these equations. o When is NVM preferred to MCM and vice versa? o There is no clearcut answer. o Asking a number of questions, may help you identify the more efficient method. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 57
58 4.8. NVM Versus MCM o Does one of the methods result in fewer simultaneous equations to solve? o Does the circuit contain supernodes? If so, using NVM will permit you to reduce the number of equations to be solved. o Does the circuit contain supermeshes? If so, using MCM will permit you to reduce the number of equations to be solved. o Will solving some portion of the circuit give the requested solution? If so, which method is most efficient for solving just the pertinent portion of the circuit? o Some time spent thinking about the problem in relation to the various analytical approaches available is time well spent. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 58
59 4.8. NVM Versus MCM o Find the power dissipated in R = 300. o We need to find either current or voltage of resistor. o MCM yields current in the resistor. o MCM requires solving 5 simultaneous mesh equations. o In writing the 5 equations, we must include the constraint i = i b. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 59
60 4.8. NVM Versus MCM o Find the power dissipated in R = 300. o The circuit has 4 essential nodes. o Only 3 NV equations are required. o Because of dependent voltage source between 2 essential nodes, we have to sum currents at only 2 nodes. o Problem is reduced to writing 2 NV equations and a constraint equation. o NVM requires only 3 simultaneous equations, it is the more attractive approach. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 60
61 4.8. NVM Versus MCM Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 61
62 4.8. NVM Versus MCM o Find the voltage v o in the circuit. o Circuit has 4 essential nodes and 2 voltagecontrolled dependent sources. o NVM requires solving 3 NV equations and 2 constraint equations. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 62
63 4.8. NVM Versus MCM o Find the voltage v o in the circuit. o Circuit contains 3 meshes. o We can use leftmost one to calculate v o. o If i a denotes leftmost mesh current, v o = i a. o Presence of 2 current sources reduces problem to solving a single supermesh equation and 2 constraint equations. o MCM is the more attractive technique here. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 63
64 4.8. NVM Versus MCM Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 64
65 4.8. NVM Versus MCM Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 65
66 Chapter Contents 4.1. Terminology 4.2. Introduction to the NodeVoltage Method 4.3. NVM and Dependent Sources 4.4. NVM: Some Special Cases 4.5. Introduction to the MeshCurrent Method 4.6. MCM and Dependent Sources 4.7. MCM: Some Special Cases 4.8. NVM Versus MCM 4.9. Source Transformations Thévenin and Norton Equivalents More on Deriving a Thévenin Equivalent Maximum Power Transfer Superposition Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 66
67 4.9. Source Transformations o Even though NVM and MCM are powerful techniques, we are still interested in methods that can be used to simplify circuits. o Seriesparallel reductions and toy transformations are already on our list of simplifying techniques. o We begin expanding this list with source transformations. o A source transformation, allows a voltage source in series with a resistor to be replaced by a current source in parallel with same resistor or vice versa. o A source transformation is bilateral. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 67
68 4.9. Source Transformations o We need to find relationship between v s and i s that guarantees 2 configurations are equivalent with respect to nodes a, b. o Equivalence is achieved if any R L experiences same current, and same voltage, if connected between nodes a, b: o If polarity of v s is reversed, orientation of i s must be reversed to maintain equivalence. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 68
69 4.9. Source Transformations o Circuit has 4 essential nodes and 6 essential branches with unknown currents. o We can find current in branch containing 6 V source by solving either 3 = [6(41)] meshcurrent equations, or 3 = [41] nodevoltage equations. o We can also simplify circuit by using source transformations. o We must reduce circuit in a way that preserves identity of branch containing 6 V source. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 69
70 4.9. Source Transformations i s = (19.26)/16 = A i s Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 70
71 4.9. Source Transformations o What happens if there is an R p in parallel with voltage source? o What happens if there is an R s in series with current source? o In both cases, resistance has no effect on equivalent circuit that predicts behavior with respect to terminals a, b. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 71
72 4.9. Source Transformations p 8A (developed) = (60)(8) = 480 W Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 72
73 4.9. Source Transformations o 125 and 10 resistors do not affect the value of v o but do affect the power calculations! Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 73
74 Chapter Contents 4.1. Terminology 4.2. Introduction to the NodeVoltage Method 4.3. NVM and Dependent Sources 4.4. NVM: Some Special Cases 4.5. Introduction to the MeshCurrent Method 4.6. MCM and Dependent Sources 4.7. MCM: Some Special Cases 4.8. NVM Versus MCM 4.9. Source Transformations Thévenin and Norton Equivalents More on Deriving a Thévenin Equivalent Maximum Power Transfer Superposition Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 74
75 4.10. Thévenin and Norton Equivalents o Sometimes, we want to concentrate on what happens at a specific pair of terminals. o For example, when we plug a toaster into an outlet, we are interested primarily in voltage and current at terminals of toaster. o We have little or no interest in effect that connecting toaster has on voltages or currents elsewhere in circuit supplying outlet. o We then are interested in how voltage and current delivered at outlet change as we change appliances. o We want to focus on the behavior of circuit supplying outlet, but only at outlet terminals. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 75
76 4.10. Thévenin and Norton Equivalents o Thévenin and Norton equivalents are circuit simplification techniques that focus on terminal behavior. o They are extremely valuable aids in circuit analysis. o Here we discuss resistive circuits, but Thévenin and Norton equivalent circuits may be used to represent any circuit made up of linear elements. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 76
77 4.10. Thévenin and Norton Equivalents o Letters a and b denote pair of terminals of interest. o A Thévenin equivalent circuit is an independent voltage source V Th in series with a resistor R Th, which replaces an interconnection of sources and resistors. o If we connect same load across terminals a and b of each circuit, we get same voltage and current at terminals of the load. o This equivalence holds for all possible values of load resistance. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 77
78 4.10. Thévenin and Norton Equivalents o We must be able to determine V Th and R Th. o If load resistance is infinitely large, we have an opencircuit condition. The opencircuit voltage at the terminals a and b is V Th in circuit (b). It must be same as opencircuit voltage at terminals a and b in original circuit. o To calculate V Th, we simply calculate opencircuit voltage in original circuit. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 78
79 4.10. Thévenin and Norton Equivalents Reducing load resistance to zero gives us a shortcircuit condition. o In circuit (b), shortcircuit current directed from a to b is: o This shortcircuit current must be identical to shortcircuit current that exists in a short circuit placed across terminals a to b of original network. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 79
80 4.10. Thévenin and Norton Equivalents o Thévenin resistance is ratio of opencircuit voltage to shortcircuit current: o If shortcircuit current is directed from b to a is, a minus sign must be inserted in the equation. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 80
81 4.10. Thévenin and Norton Equivalents o When terminals a and b are open, there is no current in 4 resistor, and v ab is identical to v 1. o Thévenin voltage for circuit is 32 V. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 81
82 4.10. Thévenin and Norton Equivalents o The shortcircuit current (i sc ) is found easily once v 2 is known. o Problem reduces to finding v 2 with the shortcircuit in place: Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 82
83 4.10. Thévenin and Norton Equivalents o If a 24 resistor is connected across terminals a and b in original circuit, voltage across resistor is 24 V and current in the resistor is 1 A, as would be the case with Thévenin circuit. o This same equivalence between circuits holds for any resistor value connected between nodes a and b. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 83
84 4.10. Thévenin and Norton Equivalents o A Norton equivalent circuit consists of: an independent current source in parallel with Norton equivalent resistance. o We can derive it from a Thévenin equivalent circuit simply by making a source transformation. o Norton current equals shortcircuit current at terminals of interest. o Norton resistance is identical to Thévenin resistance. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 84
85 4.10. Thévenin and Norton Equivalents o Sometimes, we can make effective use of source transformations to derive a Thévenin or Norton equivalent circuit. o This technique is most useful when the network contains only independent sources. o The presence of dependent sources requires retaining identity of controlling voltages and/or currents. o This constraint usually prohibits continued reduction of circuit by source transformations. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 85
86 4.10. Thévenin and Norton Equivalents o Thévenin Equivalent: o Norton Equivalent: Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 86
87 4.10. Thévenin and Norton Equivalents o Find the Thévenin equivalent for the circuit containing dependent sources. o Current i x must be 0. Note the absence of a return path for i x to enter lefthand portion of circuit. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 87
88 4.10. Thévenin and Norton Equivalents o Find the Thévenin equivalent for the circuit containing dependent sources. o With short circuit shunting 25, all current from dependent current source appears in short circuit: Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 88
89 Chapter Contents 4.1. Terminology 4.2. Introduction to the NodeVoltage Method 4.3. NVM and Dependent Sources 4.4. NVM: Some Special Cases 4.5. Introduction to the MeshCurrent Method 4.6. MCM and Dependent Sources 4.7. MCM: Some Special Cases 4.8. NVM Versus MCM 4.9. Source Transformations Thévenin and Norton Equivalents More on Deriving a Thévenin Equivalent Maximum Power Transfer Superposition Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 89
90 4.11. More on Deriving a Thévenin Equivalent o Technique for determining R Th we discussed is not always the easiest method available. o 2 other methods generally are simpler to use. o The first is useful if network contains only independent sources. o To calculate R Th for such a network, we: deactivate all independent sources, calculate resistance seen looking into network at designated terminal pair. o A voltage source is deactivated by replacing it with a short circuit. o A current source is deactivated by replacing it with an open circuit. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 90
91 4.11. More on Deriving a Thévenin Equivalent First alternative procedure to find R Th Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 91
92 4.11. More on Deriving a Thévenin Equivalent o If circuit or network contains dependent sources, an alternative procedure for finding R Th is as follows: We first deactivate all independent sources. We apply either a test voltage source or a test current source to Thévenin terminals a and b. Thévenin resistance equals ratio of voltage across test source to current delivered by test source. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 92
93 4.11. More on Deriving a Thévenin Equivalent Second alternative procedure to find R Th Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 93
94 4.11. More on Deriving a Thévenin Equivalent o We can use a Thévenin equivalent to reduce one portion of a circuit to greatly simplify analysis of larger network. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 94
95 4.11. More on Deriving a Thévenin Equivalent o This modification has no effect on branch currents i 1, i 2, i B, and i E. o We replace circuit made up of V CC, R 1, and R 2 with a Thévenin equivalent, with respect to terminals b and d. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 95
96 4.11. More on Deriving a Thévenin Equivalent Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 96
97 4.11. More on Deriving a Thévenin Equivalent Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 97
98 Chapter Contents 4.1. Terminology 4.2. Introduction to the NodeVoltage Method 4.3. NVM and Dependent Sources 4.4. NVM: Some Special Cases 4.5. Introduction to the MeshCurrent Method 4.6. MCM and Dependent Sources 4.7. MCM: Some Special Cases 4.8. NVM Versus MCM 4.9. Source Transformations Thévenin and Norton Equivalents More on Deriving a Thévenin Equivalent Maximum Power Transfer Superposition Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 98
99 4.12. Maximum Power Transfer o We assume a resistive network containing independent and dependent sources and a designated pair of terminals a and b, to which a load R L, is to be connected. o Problem is to determine value of R L that permits maximum power delivery to R L. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 99
100 4.12. Maximum Power Transfer o Replacing original network by its Thévenin equivalent greatly simplifies task of finding R L. o Derivation of R L requires expressing power dissipated in R L as a function of 3 circuit parameters V Th, R Th, and R L : Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 100
101 4.12. Maximum Power Transfer Derivative is 0 and p is maximized when: Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 101
102 4.12. Maximum Power Transfer R L = 25 Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 102
103 4.12. Maximum Power Transfer Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 103
104 Chapter Contents 4.1. Terminology 4.2. Introduction to the NodeVoltage Method 4.3. NVM and Dependent Sources 4.4. NVM: Some Special Cases 4.5. Introduction to the MeshCurrent Method 4.6. MCM and Dependent Sources 4.7. MCM: Some Special Cases 4.8. NVM Versus MCM 4.9. Source Transformations Thévenin and Norton Equivalents More on Deriving a Thévenin Equivalent Maximum Power Transfer Superposition Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 104
105 4.13. Superposition o A linear system obeys principle of superposition, i.e., whenever a linear system is excited, or driven, by more than one independent source of energy, total response is sum of individual responses. o An individual response is result of an independent source acting alone. o Because we are dealing with circuits made up of interconnected linearcircuit elements, we can apply superposition directly to analysis of such circuits. o At present, we restrict the discussion to simple resistive networks. o Principle is applicable to any linear system. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 105
106 4.13. Superposition o Superposition is applied in both analysis and design of circuits. o In analyzing a complex circuit with multiple independent voltage and current sources, there are often fewer, simpler equations to solve by applying superposition. o Applying superposition can simplify circuit analysis. o Sometimes, applying superposition actually complicates analysis, producing more equations to solve. o Superposition is required only if independent sources in a circuit are fundamentally different. o When all independent sources are dc sources, superposition is not required. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 106
107 4.13. Superposition o Superposition is applied in design to synthesize a desired circuit response that could not be achieved in a circuit with a single source. o If desired circuit response can be written as a sum of two or more terms, response can be realized by including one independent source for each term of response. o This approach to design of circuits with complex responses allows a designer to consider several simple designs instead of one complex design. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 107
108 4.13. Superposition Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 108
109 4.13. Superposition Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 109
110 4.13. Superposition Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 110
111 4.13. Superposition Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 111
112 4.13. Superposition o When applying superposition to linear circuits containing both independent and dependent sources, you must recognize that dependent sources are never deactivated. Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 112
113 4.13. Superposition Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 113
114 4.13. Superposition Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 114
115 4.13. Superposition Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 115
116 4.13. Superposition Electric Circuits 1 Chapter 4. Techniques of Circuit Analysis 116
ECE2262 Electric Circuits
ECE2262 Electric Circuits Equivalence Chapter 5: Circuit Theorems Linearity Superposition Thevenin s and Norton s Theorems Maximum Power Transfer Analysis of Circuits Using Circuit Theorems 1 5. 1 Equivalence
More informationECE2262 Electric Circuits. Chapter 5: Circuit Theorems
ECE2262 Electric Circuits Chapter 5: Circuit Theorems 1 Equivalence Linearity Superposition Thevenin s and Norton s Theorems Maximum Power Transfer Analysis of Circuits Using Circuit Theorems 2 5. 1 Equivalence
More informationChapter 4: Techniques of Circuit Analysis
Chapter 4: Techniques of Circuit Analysis This chapter gies us many useful tools for soling and simplifying circuits. We saw a few simple tools in the last chapter (reduction of circuits ia series and
More informationChapter 5. Department of Mechanical Engineering
Source Transformation By KVL: V s =ir s + v By KCL: i s =i + v/r p is=v s /R s R s =R p V s /R s =i + v/r s i s =i + v/r p Two circuits have the same terminal voltage and current Source Transformation
More informationLecture Notes on DC Network Theory
Federal University, NdufuAlike, Ikwo Department of Electrical/Electronics and Computer Engineering (ECE) Faculty of Engineering and Technology Lecture Notes on DC Network Theory Harmattan Semester by
More informationUNIT 4 DC EQUIVALENT CIRCUIT AND NETWORK THEOREMS
UNIT 4 DC EQUIVALENT CIRCUIT AND NETWORK THEOREMS 1.0 Kirchoff s Law Kirchoff s Current Law (KCL) states at any junction in an electric circuit the total current flowing towards that junction is equal
More informationElectric Circuits II Sinusoidal Steady State Analysis. Dr. Firas Obeidat
Electric Circuits II Sinusoidal Steady State Analysis Dr. Firas Obeidat 1 Table of Contents 1 2 3 4 5 Nodal Analysis Mesh Analysis Superposition Theorem Source Transformation Thevenin and Norton Equivalent
More informationD C Circuit Analysis and Network Theorems:
UNIT1 D C Circuit Analysis and Network Theorems: Circuit Concepts: Concepts of network, Active and passive elements, voltage and current sources, source transformation, unilateral and bilateral elements,
More informationNotes for course EE1.1 Circuit Analysis TOPIC 4 NODAL ANALYSIS
Notes for course EE1.1 Circuit Analysis 200405 TOPIC 4 NODAL ANALYSIS OBJECTIVES 1) To develop Nodal Analysis of Circuits without Voltage Sources 2) To develop Nodal Analysis of Circuits with Voltage
More information3.1 Superposition theorem
Many electric circuits are complex, but it is an engineer s goal to reduce their complexity to analyze them easily. In the previous chapters, we have mastered the ability to solve networks containing independent
More informationCHAPTER 4. Circuit Theorems
CHAPTER 4 Circuit Theorems The growth in areas of application of electrical circuits has led to an evolution from simple to complex circuits. To handle such complexity, engineers over the years have developed
More informationChapter 10 AC Analysis Using Phasors
Chapter 10 AC Analysis Using Phasors 10.1 Introduction We would like to use our linear circuit theorems (Nodal analysis, Mesh analysis, Thevenin and Norton equivalent circuits, Superposition, etc.) to
More informationCircuit Theorems Overview Linearity Superposition Source Transformation Thévenin and Norton Equivalents Maximum Power Transfer
Circuit Theorems Overview Linearity Superposition Source Transformation Thévenin and Norton Equivalents Maximum Power Transfer J. McNames Portland State University ECE 221 Circuit Theorems Ver. 1.36 1
More informationBasic Electrical Circuits Analysis ECE 221
Basic Electrical Circuits Analysis ECE 221 PhD. Khodr Saaifan http://trsys.faculty.jacobsuniversity.de k.saaifan@jacobsuniversity.de 1 2 Reference: Electric Circuits, 8th Edition James W. Nilsson, and
More informationMAE140  Linear Circuits  Fall 14 Midterm, November 6
MAE140  Linear Circuits  Fall 14 Midterm, November 6 Instructions (i) This exam is open book. You may use whatever written materials you choose, including your class notes and textbook. You may use a
More informationChapter 3. Loop and Cutset Analysis
Chapter 3. Loop and Cutset Analysis By: FARHAD FARADJI, Ph.D. Assistant Professor, Electrical Engineering, K.N. Toosi University of Technology http://wp.kntu.ac.ir/faradji/electriccircuits2.htm References:
More informationCHAPTER FOUR CIRCUIT THEOREMS
4.1 INTRODUCTION CHAPTER FOUR CIRCUIT THEOREMS The growth in areas of application of electric circuits has led to an evolution from simple to complex circuits. To handle the complexity, engineers over
More informationChapter 10: Sinusoidal SteadyState Analysis
Chapter 10: Sinusoidal SteadyState Analysis 10.1 10.2 10.3 10.4 10.5 10.6 10.9 Basic Approach Nodal Analysis Mesh Analysis Superposition Theorem Source Transformation Thevenin & Norton Equivalent Circuits
More informationNotes for course EE1.1 Circuit Analysis TOPIC 10 2PORT CIRCUITS
Objectives: Introduction Notes for course EE1.1 Circuit Analysis 45 Reexamination of 1port subcircuits Admittance parameters for port circuits TOPIC 1 PORT CIRCUITS Gain and port impedance from port
More informationELECTRICAL THEORY. Ideal Basic Circuit Element
ELECTRICAL THEORY PROF. SIRIPONG POTISUK ELEC 106 Ideal Basic Circuit Element Has only two terminals which are points of connection to other circuit components Can be described mathematically in terms
More informationModule 2. DC Circuit. Version 2 EE IIT, Kharagpur
Module 2 DC Circuit Lesson 5 Nodevoltage analysis of resistive circuit in the context of dc voltages and currents Objectives To provide a powerful but simple circuit analysis tool based on Kirchhoff s
More informationCURRENT SOURCES EXAMPLE 1 Find the source voltage Vs and the current I1 for the circuit shown below SOURCE CONVERSIONS
CURRENT SOURCES EXAMPLE 1 Find the source voltage Vs and the current I1 for the circuit shown below EXAMPLE 2 Find the source voltage Vs and the current I1 for the circuit shown below SOURCE CONVERSIONS
More informationChapter 10 Sinusoidal Steady State Analysis Chapter Objectives:
Chapter 10 Sinusoidal Steady State Analysis Chapter Objectives: Apply previously learn circuit techniques to sinusoidal steadystate analysis. Learn how to apply nodal and mesh analysis in the frequency
More informationWriting Circuit Equations
2 C H A P T E R Writing Circuit Equations Objectives By the end of this chapter, you should be able to do the following: 1. Find the complete solution of a circuit using the exhaustive, node, and mesh
More informationNotes for course EE1.1 Circuit Analysis TOPIC 3 CIRCUIT ANALYSIS USING SUBCIRCUITS
Notes for course EE1.1 Circuit Analysis 200405 TOPIC 3 CIRCUIT ANALYSIS USING SUBCIRCUITS OBJECTIVES 1) To introduce the Source Transformation 2) To consider the concepts of Linearity and Superposition
More informationSinusoidal Steady State Analysis (AC Analysis) Part II
Sinusoidal Steady State Analysis (AC Analysis) Part II Amin Electronics and Electrical Communications Engineering Department (EECE) Cairo University elc.n102.eng@gmail.com http://scholar.cu.edu.eg/refky/
More informationDC STEADY STATE CIRCUIT ANALYSIS
DC STEADY STATE CIRCUIT ANALYSIS 1. Introduction The basic quantities in electric circuits are current, voltage and resistance. They are related with Ohm s law. For a passive branch the current is: I=
More informationElectric Circuits I. Midterm #1
The University of Toledo Section number s5ms_elci7.fm  Electric Circuits I Midterm # Problems Points. 3 2. 7 3. 5 Total 5 Was the exam fair? yes no The University of Toledo Section number s5ms_elci7.fm
More informationChapter 2. Engr228 Circuit Analysis. Dr Curtis Nelson
Chapter 2 Engr228 Circuit Analysis Dr Curtis Nelson Chapter 2 Objectives Understand symbols and behavior of the following circuit elements: Independent voltage and current sources; Dependent voltage and
More informationSinusoidal Steady State Analysis (AC Analysis) Part I
Sinusoidal Steady State Analysis (AC Analysis) Part I Amin Electronics and Electrical Communications Engineering Department (EECE) Cairo University elc.n102.eng@gmail.com http://scholar.cu.edu.eg/refky/
More informationSeries & Parallel Resistors 3/17/2015 1
Series & Parallel Resistors 3/17/2015 1 Series Resistors & Voltage Division Consider the singleloop circuit as shown in figure. The two resistors are in series, since the same current i flows in both
More information6. MESH ANALYSIS 6.1 INTRODUCTION
6. MESH ANALYSIS INTRODUCTION PASSIVE SIGN CONVENTION PLANAR CIRCUITS FORMATION OF MESHES ANALYSIS OF A SIMPLE CIRCUIT DETERMINANT OF A MATRIX CRAMER S RULE GAUSSIAN ELIMINATION METHOD EXAMPLES FOR MESH
More informationSystematic Circuit Analysis (T&R Chap 3)
Systematic Circuit Analysis (T&R Chap 3) Nodevoltage analysis Using the voltages of the each node relative to a ground node, write down a set of consistent linear equations for these voltages Solve this
More informationIn this lecture, we will consider how to analyse an electrical circuit by applying KVL and KCL. As a result, we can predict the voltages and currents
In this lecture, we will consider how to analyse an electrical circuit by applying KVL and KCL. As a result, we can predict the voltages and currents around an electrical circuit. This is a short lecture,
More informationChapter 2 Direct Current Circuits
Chapter 2 Direct Current Circuits 2.1 Introduction Nowadays, our lives are increasingly dependent upon the availability of devices that make extensive use of electric circuits. The knowledge of the electrical
More informationEIT Review. Electrical Circuits DC Circuits. Lecturer: Russ Tatro. Presented by Tau Beta Pi The Engineering Honor Society 10/3/2006 1
EIT Review Electrical Circuits DC Circuits Lecturer: Russ Tatro Presented by Tau Beta Pi The Engineering Honor Society 10/3/2006 1 Session Outline Basic Concepts Basic Laws Methods of Analysis Circuit
More informationChapter 5 Objectives
Chapter 5 Engr228 Circuit Analysis Dr Curtis Nelson Chapter 5 Objectives State and apply the property of linearity State and apply the property of superposition Investigate source transformations Define
More informationThevenin Norton Equivalencies  GATE Study Material in PDF
Thevenin Norton Equivalencies  GATE Study Material in PDF In these GATE 2018 Notes, we explain the Thevenin Norton Equivalencies. Thevenin s and Norton s Theorems are two equally valid methods of reducing
More informationENGG 225. David Ng. Winter January 9, Circuits, Currents, and Voltages... 5
ENGG 225 David Ng Winter 2017 Contents 1 January 9, 2017 5 1.1 Circuits, Currents, and Voltages.................... 5 2 January 11, 2017 6 2.1 Ideal Basic Circuit Elements....................... 6 3 January
More informationThevenin equivalent circuits
Thevenin equivalent circuits We have seen the idea of equivalency used in several instances already. 1 2 1 2 same as 1 2 same as 1 2 R 3 same as = 0 V same as 0 A same as same as = EE 201 Thevenin 1 The
More informationChapter 4 Circuit Theorems
Chapter 4 Circuit Theorems 1. Linearity and Proportionality. Source Transformation 3. Superposition Theorem 4. Thevenin s Theorem and Norton s Theorem 5. Maximum Power Transfer Theorem Mazita Sem 1 111
More informationChapter 5: Circuit Theorems
Chapter 5: Circuit Theorems This chapter provides a new powerful technique of solving complicated circuits that are more conceptual in nature than node/mesh analysis. Conceptually, the method is fairly
More informationLecture #3. Review: Power
Lecture #3 OUTLINE Power calculations Circuit elements Voltage and current sources Electrical resistance (Ohm s law) Kirchhoff s laws Reading Chapter 2 Lecture 3, Slide 1 Review: Power If an element is
More informationNetwork Topology2 & Dual and Duality Choice of independent branch currents and voltages: The solution of a network involves solving of all branch currents and voltages. We know that the branch current
More informationMidterm Exam (closed book/notes) Tuesday, February 23, 2010
University of California, Berkeley Spring 2010 EE 42/100 Prof. A. Niknejad Midterm Exam (closed book/notes) Tuesday, February 23, 2010 Guidelines: Closed book. You may use a calculator. Do not unstaple
More informationBFF1303: ELECTRICAL / ELECTRONICS ENGINEERING. Alternating Current Circuits : Basic Law
BFF1303: ELECTRICAL / ELECTRONICS ENGINEERING Alternating Current Circuits : Basic Law Ismail Mohd Khairuddin, Zulkifil Md Yusof Faculty of Manufacturing Engineering Universiti Malaysia Pahang Alternating
More informationECE 1311: Electric Circuits. Chapter 2: Basic laws
ECE 1311: Electric Circuits Chapter 2: Basic laws Basic Law Overview Ideal sources series and parallel Ohm s law Definitions open circuits, short circuits, conductance, nodes, branches, loops Kirchhoff's
More informationEECE251 Circuit Analysis I Lecture Integrated Program Set 3: Circuit Theorems
EECE251 Circuit Analysis I Lecture Integrated Program Set 3: Circuit Theorems Shahriar Mirabbasi Department of Electrical and Computer Engineering University of British Columbia shahriar@ece.ubc.ca 1 Linearity
More informationPOLYTECHNIC UNIVERSITY Electrical Engineering Department. EE SOPHOMORE LABORATORY Experiment 2 DC circuits and network theorems
POLYTECHNIC UNIVERSITY Electrical Engineering Department EE SOPHOMORE LABORATORY Experiment 2 DC circuits and network theorems Modified for Physics 18, Brooklyn College I. Overview of Experiment In this
More informationMAE140  Linear Circuits  Winter 09 Midterm, February 5
Instructions MAE40  Linear ircuits  Winter 09 Midterm, February 5 (i) This exam is open book. You may use whatever written materials you choose, including your class notes and textbook. You may use a
More informationUNIVERSITY F P RTLAND Sch l f Engineering
UNIVERSITY F P RTLAND Sch l f Engineering EE271Electrical Circuits Laboratory Spring 2004 Dr. Aziz S. Inan & Dr. Joseph P. Hoffbeck Lab Experiment #4: Electrical Circuit Theorems  p. 1 of 5  Electrical
More informationmywbut.com Mesh Analysis
Mesh Analysis 1 Objectives Meaning of circuit analysis; distinguish between the terms mesh and loop. To provide more general and powerful circuit analysis tool based on Kirchhoff s voltage law (KVL) only.
More informationPreamble. Circuit Analysis II. Mesh Analysis. When circuits get really complex methods learned so far will still work,
Preamble Circuit Analysis II Physics, 8 th Edition Custom Edition Cutnell & Johnson When circuits get really complex methods learned so far will still work, but they can take a long time to do. A particularly
More informationSOME USEFUL NETWORK THEOREMS
APPENDIX D SOME USEFUL NETWORK THEOREMS Introduction In this appendix we review three network theorems that are useful in simplifying the analysis of electronic circuits: Thévenin s theorem Norton s theorem
More informationModule 2. DC Circuit. Version 2 EE IIT, Kharagpur
Module 2 DC Circuit esson 8 evenin s and Norton s theorems in the context of dc voltage and current sources acting in a resistive network Objectives To understand the basic philosophy behind the evenin
More informationR 2, R 3, and R 4 are in parallel, R T = R 1 + (R 2 //R 3 //R 4 ) + R 5. CC Tsai
Chapter 07 SeriesParallel Circuits The SeriesParallel Network Complex circuits May be separated both series and/or parallel elements Combinations which are neither series nor parallel To analyze a circuit
More information4/27 Friday. I have all the old homework if you need to collect them.
4/27 Friday Last HW: do not need to turn it. Solution will be posted on the web. I have all the old homework if you need to collect them. Final exam: 79pm, Monday, 4/30 at Lambert Fieldhouse F101 Calculator
More informationBASIC NETWORK ANALYSIS
SECTION 1 BASIC NETWORK ANALYSIS A. Wayne Galli, Ph.D. Project Engineer Newport News Shipbuilding SeriesParallel dc Network Analysis......................... 1.1 BranchCurrent Analysis of a dc Network......................
More informationElectric Circuits I. Nodal Analysis. Dr. Firas Obeidat
Electric Circuits I Nodal Analysis Dr. Firas Obeidat 1 Nodal Analysis Without Voltage Source Nodal analysis, which is based on a systematic application of Kirchhoff s current law (KCL). A node is defined
More informationSolution: Based on the slope of q(t): 20 A for 0 t 1 s dt = 0 for 3 t 4 s. 20 A for 4 t 5 s 0 for t 5 s 20 C. t (s) 20 C. i (A) Fig. P1.
Problem 1.24 The plot in Fig. P1.24 displays the cumulative charge q(t) that has entered a certain device up to time t. Sketch a plot of the corresponding current i(t). q 20 C 0 1 2 3 4 5 t (s) 20 C Figure
More informationEE40 KVL KCL. Prof. Nathan Cheung 09/01/2009. Reading: Hambley Chapter 1
EE40 KVL KCL Prof. Nathan Cheung 09/01/2009 Reading: Hambley Chapter 1 Slide 1 Terminology: Nodes and Branches Node: A point where two or more circuit elements are connected Branch: A path that connects
More informationCIRCUIT ANALYSIS TECHNIQUES
APPENDI B CIRCUIT ANALSIS TECHNIQUES The following methods can be used to combine impedances to simplify the topology of an electric circuit. Also, formulae are given for voltage and current division across/through
More informationDEPARTMENT OF COMPUTER ENGINEERING UNIVERSITY OF LAHORE
DEPARTMENT OF COMPUTER ENGINEERING UNIVERSITY OF LAHORE NAME. Section 1 2 3 UNIVERSITY OF LAHORE Department of Computer engineering Linear Circuit Analysis Laboratory Manual 2 Compiled by Engr. Ahmad Bilal
More informationEE201 Review Exam I. 1. The voltage Vx in the circuit below is: (1) 3V (2) 2V (3) 2V (4) 1V (5) 1V (6) None of above
EE201, Review Probs Test 1 page1 Spring 98 EE201 Review Exam I Multiple Choice (5 points each, no partial credit.) 1. The voltage Vx in the circuit below is: (1) 3V (2) 2V (3) 2V (4) 1V (5) 1V (6)
More informationChapter 5 Solution P5.22, 3, 6 P5.33, 5, 8, 15 P5.43, 6, 8, 16 P5.52, 4, 6, 11 P5.62, 4, 9
Chapter 5 Solution P5.22, 3, 6 P5.33, 5, 8, 15 P5.43, 6, 8, 16 P5.52, 4, 6, 11 P5.62, 4, 9 P 5.22 Consider the circuit of Figure P 5.22. Find i a by simplifying the circuit (using source transformations)
More informationEE292: Fundamentals of ECE
EE292: Fundamentals of ECE Fall 2012 TTh 10:0011:15 SEB 1242 Lecture 4 120906 http://www.ee.unlv.edu/~b1morris/ee292/ 2 Outline Review Voltage Divider Current Divider NodeVoltage Analysis 3 Network Analysis
More informationQUIZ 1 SOLUTION. One way of labeling voltages and currents is shown below.
F 14 1250 QUIZ 1 SOLUTION EX: Find the numerical value of v 2 in the circuit below. Show all work. SOL'N: One method of solution is to use Kirchhoff's and Ohm's laws. The first step in this approach is
More informationExperiment 2: Analysis and Measurement of Resistive Circuit Parameters
Experiment 2: Analysis and Measurement of Resistive Circuit Parameters Report Due Inclass on Wed., Mar. 28, 2018 Prelab must be completed prior to lab. 1.0 PURPOSE To (i) verify Kirchhoff's laws experimentally;
More informationReview of Circuit Analysis
Review of Circuit Analysis Fundamental elements Wire Resistor Voltage Source Current Source Kirchhoff s Voltage and Current Laws Resistors in Series Voltage Division EE 42 Lecture 2 1 Voltage and Current
More informationVoltage Dividers, Nodal, and Mesh Analysis
Engr228 Lab #2 Voltage Dividers, Nodal, and Mesh Analysis Name Partner(s) Grade /10 Introduction This lab exercise is designed to further your understanding of the use of the lab equipment and to verify
More informationErrors in Electrical Measurements
1 Errors in Electrical Measurements Systematic error every times you measure e.g. loading or insertion of the measurement instrument Meter error scaling (inaccurate marking), pointer bending, friction,
More informationELEC 250: LINEAR CIRCUITS I COURSE OVERHEADS. These overheads are adapted from the Elec 250 Course Pack developed by Dr. Fayez Guibaly.
Elec 250: Linear Circuits I 5/4/08 ELEC 250: LINEAR CIRCUITS I COURSE OVERHEADS These overheads are adapted from the Elec 250 Course Pack developed by Dr. Fayez Guibaly. S.W. Neville Elec 250: Linear Circuits
More informationHomework 2. Due Friday (5pm), Feb. 8, 2013
University of California, Berkeley Spring 2013 EE 42/100 Prof. K. Pister Homework 2 Due Friday (5pm), Feb. 8, 2013 Please turn the homework in to the drop box located next to 125 Cory Hall (labeled EE
More informationStudy Notes on Network Theorems for GATE 2017
Study Notes on Network Theorems for GATE 2017 Network Theorems is a highly important and scoring topic in GATE. This topic carries a substantial weight age in GATE. Although the Theorems might appear to
More informationModule 2. DC Circuit. Version 2 EE IIT, Kharagpur
Module DC Circuit Lesson 4 Loop Analysis of resistive circuit in the context of dc voltages and currents Objectives Meaning of circuit analysis; distinguish between the terms mesh and loop. To provide
More informationEE40. Lec 3. Basic Circuit Analysis. Prof. Nathan Cheung. Reading: Hambley Chapter 2
EE40 Lec 3 Basic Circuit Analysis Prof. Nathan Cheung 09/03/009 eading: Hambley Chapter Slide Outline Chapter esistors in Series oltage Divider Conductances in Parallel Current Divider Nodeoltage Analysis
More informationE1.1 Analysis of Circuits ( ) Revision Lecture 1 1 / 13
RevisionLecture 1: E1.1 Analysis of Circuits (20144530) Revision Lecture 1 1 / 13 Format Question 1 (40%): eight short parts covering the whole syllabus. Questions 2 and 3: single topic questions (answer
More informationCOOKBOOK KVL AND KCL A COMPLETE GUIDE
1250 COOKBOOK KVL AND KCL A COMPLETE GUIDE Example circuit: 1) Label all source and component values with a voltage drop measurement (+, ) and a current flow measurement (arrow): By the passive sign convention,
More informationENGR 2405 Class No Electric Circuits I
ENGR 2405 Class No. 48056 Electric Circuits I Dr. R. Williams Ph.D. rube.williams@hccs.edu Electric Circuit An electric circuit is an interconnec9on of electrical elements Charge Charge is an electrical
More informationDiscussion Question 6A
Discussion Question 6 P212, Week 6 Two Methods for Circuit nalysis Method 1: Progressive collapsing of circuit elements In last week s discussion, we learned how to analyse circuits involving batteries
More informationChapter 2 Resistive Circuits
1. Sole circuits (i.e., find currents and oltages of interest) by combining resistances in series and parallel. 2. Apply the oltagediision and currentdiision principles. 3. Sole circuits by the nodeoltage
More informationUniversity of Alabama Department of Physics and Astronomy. Problem Set 4
University of Alabama Department of Physics and Astronomy PH 26 LeClair Fall 20 Problem Set 4. A battery has an ideal voltage V and an internal resistance r. A variable load resistance R is connected to
More informationElectric Circuits I Final Examination
EECS:300 Electric Circuits I ffs_elci.fm  Electric Circuits I Final Examination Problems Points. 4. 3. Total 38 Was the exam fair? yes no //3 EECS:300 Electric Circuits I ffs_elci.fm  Problem 4 points
More informationCapacitance. A different kind of capacitor: Work must be done to charge a capacitor. Capacitors in circuits. Capacitor connected to a battery
Capacitance The ratio C = Q/V is a conductor s self capacitance Units of capacitance: Coulomb/Volt = Farad A capacitor is made of two conductors with equal but opposite charge Capacitance depends on shape
More informationQUESTION BANK SUBJECT: NETWORK ANALYSIS (10ES34)
QUESTION BANK SUBJECT: NETWORK ANALYSIS (10ES34) NOTE: FOR NUMERICAL PROBLEMS FOR ALL UNITS EXCEPT UNIT 5 REFER THE EBOOK ENGINEERING CIRCUIT ANALYSIS, 7 th EDITION HAYT AND KIMMERLY. PAGE NUMBERS OF
More informationMassachusetts Institute of Technology Department of Electrical Engineering and Computer Science : Circuits & Electronics Problem Set #1 Solution
Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.2: Circuits & Electronics Problem Set # Solution Exercise. The three resistors form a series connection.
More informationIntroductory Circuit Analysis
Introductory Circuit Analysis CHAPTER 6 Parallel dc Circuits OBJECTIVES Become familiar with the characteristics of a parallel network and how to solve for the voltage, current, and power to each element.
More informationDesigning Information Devices and Systems I Fall 2018 Lecture Notes Note Introduction: Opamps in Negative Feedback
EECS 16A Designing Information Devices and Systems I Fall 2018 Lecture Notes Note 18 18.1 Introduction: Opamps in Negative Feedback In the last note, we saw that can use an opamp as a comparator. However,
More informationVer 6186 E1.1 Analysis of Circuits (2015) E1.1 Circuit Analysis. Problem Sheet 2  Solutions
Ver 8 E. Analysis of Circuits (0) E. Circuit Analysis Problem Sheet  Solutions Note: In many of the solutions below I have written the voltage at node X as the variable X instead of V X in order to save
More informationHomework 1 solutions
Electric Circuits 1 Homework 1 solutions (Due date: 2014/3/3) This assignment covers Ch1 and Ch2 of the textbook. The full credit is 100 points. For each question, detailed derivation processes and accurate
More informationFundamental of Electrical circuits
Fundamental of Electrical circuits 1 Course Description: Electrical units and definitions: Voltage, current, power, energy, circuit elements: resistors, capacitors, inductors, independent and dependent
More informationEIE/ENE 104 Electric Circuit Theory
EIE/ENE 104 Electric Circuit Theory Lecture 01a: Circuit Analysis and Electrical Engineering Week #1 : Dejwoot KHAWPARISUTH office: CB40906 Tel: 024709065 Email: dejwoot.kha@kmutt.ac.th http://webstaff.kmutt.ac.th/~dejwoot.kha/
More information1. Review of Circuit Theory Concepts
1. Review of Circuit Theory Concepts Lecture notes: Section 1 ECE 65, Winter 2013, F. Najmabadi Circuit Theory is an pproximation to Maxwell s Electromagnetic Equations circuit is made of a bunch of elements
More informationNotes on Electric Circuits (Dr. Ramakant Srivastava)
Notes on Electric ircuits (Dr. Ramakant Srivastava) Passive Sign onvention (PS) Passive sign convention deals with the designation of the polarity of the voltage and the direction of the current arrow
More informationKirchhoff Laws against NodeVoltage nalysis and Millman's Theorem Marcela Niculae and C. M. Niculae 2 on arbu theoretical high school, ucharest 2 University of ucharest, Faculty of physics, tomistilor
More informationECE2262 Electric Circuit
ECE2262 Electric Circuit Chapter 7: FIRST AND SECONDORDER RL AND RC CIRCUITS Response to FirstOrder RL and RC Circuits Response to SecondOrder RL and RC Circuits 1 2 7.1. Introduction 3 4 In dc steady
More informationSinusoids and Phasors
CHAPTER 9 Sinusoids and Phasors We now begins the analysis of circuits in which the voltage or current sources are timevarying. In this chapter, we are particularly interested in sinusoidally timevarying
More informationTactics Box 23.1 Using Kirchhoff's Loop Law
PH203 Chapter 23 solutions Tactics Box 231 Using Kirchhoff's Loop Law Description: Knight/Jones/Field Tactics Box 231 Using Kirchhoff s loop law is illustrated Learning Goal: To practice Tactics Box 231
More informationHomework 3 Solution. Due Friday (5pm), Feb. 14, 2013
University of California, Berkeley Spring 2013 EE 42/100 Prof. K. Pister Homework 3 Solution Due Friday (5pm), Feb. 14, 2013 Please turn the homework in to the drop box located next to 125 Cory Hall (labeled
More informationTutorial #4: Bias Point Analysis in Multisim
SCHOOL OF ENGINEERING AND APPLIED SCIENCE DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING ECE 2115: ENGINEERING ELECTRONICS LABORATORY Tutorial #4: Bias Point Analysis in Multisim INTRODUCTION When BJTs
More information