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ECE 3336 Introduction to Circuits Electronics

2. The Node-Voltage Method. 3. Overview of this Part. In this part, we will cover the following topics:Some basic definitionsThe steps for writing the Node-Voltage EquationsTips on picking the best reference nodeHow to handle dependent sources. 4. Textbook Coverage. Approximately this same mate

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ECE 3336 Introduction to Circuits Electronics

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    1. 1 ECE 3336 Introduction to Circuits & Electronics

    2. 2 The Node-Voltage Method

    3. 3 Overview of this Part In this part, we will cover the following topics: Some basic definitions The steps for writing the Node-Voltage Equations Tips on picking the best reference node How to handle dependent sources You can click on the blue text to jump to the subject that you want to learn about now.You can click on the blue text to jump to the subject that you want to learn about now.

    4. 4 Textbook Coverage Approximately this same material is covered in your textbook in the following sections: Principles and Applications of Electrical Engineering by Rizzoni, Revised 4th Edition: Sections 3.1 and 3.2 You should also read these sections in your text. This material is intended to complement your textbook coverage, not replace it.You should also read these sections in your text. This material is intended to complement your textbook coverage, not replace it.

    5. 5 Some Basic Definitions Node – a place where two or more components meet Essential Node – a place where three or more components meet Reference Node – a special essential node that we choose as a reference point for voltages

    6. 6 Some Review (notes #2)– Nodes

    7. 7 How Many Nodes – Correct Answer The nodes are the darker blue shapes. The shape is unimportant to us; we can draw the circuit in many ways. The key here, for example, is that a voltage source, a current source, and a resistor called RF are connected to the bottom node.The nodes are the darker blue shapes. The shape is unimportant to us; we can draw the circuit in many ways. The key here, for example, is that a voltage source, a current source, and a resistor called RF are connected to the bottom node.

    8. 8 How Many Nodes – Wrong Answer In the example circuit schematic given here, the two red nodes are really the same node. There are not four nodes. Remember, two nodes connected by a wire are really only one node in the first place. Remember, two nodes connected by a wire were not really two nodes at all. It is all one node.Remember, two nodes connected by a wire were not really two nodes at all. It is all one node.

    9. 9 The Node-Voltage Method (NVM) The Node-Voltage Method (NVM) is a systematic way to write all the equations needed to solve a circuit, and to write just the number of equations needed. The idea is that any other current or voltage can be found from these node voltages. This method is not that important in very simple circuits, but in complicated circuits it gives us an approach that will get us all the equations that we need, and no extras. It is also good practice for the writing of KCL and KVL equations. Many students believe that they know how to do this, but make errors in more complicated situations. Our work on the NVM will help correct some of those errors.

    10. 10 The Node-Voltage Method (NVM) The Node-Voltage Method steps are: Find the essential nodes. Define one essential node as the reference node. Define the node voltages, the essential nodes with respect to the reference node. Label them. Apply KCL for each non-reference essential node. Write an equation for each current or voltage upon which dependent sources depend, as needed.

    11. 11 Kirchhoff’s Current Law (KCL) – a Review The algebraic (or signed i.e with directions ) summation of currents through a closed surface (such as a node) must equal zero.

    12. 12 Kirchhoff’s Current Law (KCL) – a Review Example For this set of material, we will always assign a positive sign to a term that refers to a current that leaves a node, and a negative sign to a term that refers to a current that enters a node. In this example, we have already assigned reference polarities for all of the currents for the nodes indicated by the arrows. For this circuit, and using my rule, we have the following equation: The node that we are using here is highlighted in darker blue.The node that we are using here is highlighted in darker blue.

    13. 13 NVM – 1st Example The Node-Voltage Method steps are: Find the essential nodes. Define one essential node as the reference node. Define the node voltages, the essential nodes with respect to the reference node. Label them. Apply KCL for each non-reference essential node. Write an equation for each current or voltage upon which dependent sources depend, as needed.

    14. 14 NVM – 1st Example – Step 1 Answer this question before going to the next slide.Answer this question before going to the next slide.

    15. 15 NVM – 1st Example – Step 1(Done) The Node-Voltage Method steps are: Find the essential nodes. Define one essential node as the reference node. Define the node voltages, the essential nodes with respect to the reference node. Label them. Apply KCL for each non-reference essential node. Write an equation for each current or voltage upon which dependent sources depend, as needed.

    16. 16 NVM – 1st Example – Step 2 The Node-Voltage Method steps are: Find the essential nodes. Define one essential node as the reference node. Define the node voltages, the essential nodes with respect to the reference node. Label them. Apply KCL for each non-reference essential node. Write an equation for each current or voltage upon which dependent sources depend, as needed.

    17. 17 NVM – 1st Example – Step 2 Note The Node-Voltage Method steps are: Find the essential nodes. Define one essential node as the reference node. Define the node voltages, the essential nodes with respect to the reference node. Label them. Apply KCL for each non-reference essential node. Write an equation for each current or voltage upon which dependent sources depend, as needed.

    18. 18 NVM – 1st Example – Step 3 The Node-Voltage Method steps are: Find the essential nodes. Define one essential node as the reference node. Define the node voltages, the essential nodes with respect to the reference node. Label them. Apply KCL for each non-reference essential node. Write an equation for each current or voltage upon which dependent sources depend, as needed.

    19. 19 NVM – 1st Example – Step 4, Part 2 The Node-Voltage Method steps are: Find the essential nodes. Define one essential node as the reference node. Define the node voltages, the essential nodes with respect to the reference node. Label them. Apply KCL for each non-reference essential node. Write an equation for each current or voltage upon which dependent sources depend, as needed.

    20. 20 NVM – Currents Explained 1 The Node-Voltage Method steps are: Find the essential nodes. Define one essential node as the reference node. Define the node voltages, the essential nodes with respect to the reference node. Label them. Apply KCL for each non-reference essential node. Write an equation for each current or voltage upon which dependent sources depend, as needed.

    21. 21 NVM – Currents Explained 2 The Node-Voltage Method steps are: Find the essential nodes. Define one essential node as the reference node. Define the node voltages, the essential nodes with respect to the reference node. Label them. Apply KCL for each non-reference essential node. Write an equation for each current or voltage upon which dependent sources depend, as needed.

    22. 22 NVM – Currents Explained 3 The Node-Voltage Method steps are: Find the essential nodes. Define one essential node as the reference node. Define the node voltages, the essential nodes with respect to the reference node. Label them. Apply KCL for each non-reference essential node. Write an equation for each current or voltage upon which dependent sources depend, as needed.

    23. 23 NVM – 1st Example – Step 4, Part 3 The Node-Voltage Method steps are: Find the essential nodes. Define one essential node as the reference node. Define the node voltages, the essential nodes with respect to the reference node. Label them. Apply KCL for each non-reference essential node. Write an equation for each current or voltage upon which dependent sources depend, as needed.

    24. 24 NVM – 1st Example – Step 4 – Notes The Node-Voltage Method steps are: Find the essential nodes. Define one essential node as the reference node. Define the node voltages, the essential nodes with respect to the reference node. Label them. Apply KCL for each non-reference essential node. Write an equation for each current or voltage upon which dependent sources depend, as needed.

    25. 25 NVM – 1st Example – Step 5 The Node-Voltage Method steps are: Find the essential nodes. Define one essential node as the reference node. Define the node voltages, the essential nodes with respect to the reference node. Label them. Apply KCL for each non-reference essential node. Write an equation for each current or voltage upon which dependent sources depend, as needed.

    26. 26 NVM – 2nd Example

    27. 27 NVM – 2nd Example – Step 1

    28. 28 NVM – 2nd Example – Step 2

    29. 29 NVM – 2nd Example – Step 3

    30. 30 NVM – 2nd Example – Step 4

    31. 31 NVM – 2nd Example – Step 5

    32. 32 NVM – 2nd Example – Solution

    33. 33 How many node-voltage equations do I need to write? This is a very important question. It is a good idea to figure this out before beginning a problem. Then, you will know how many equations to write before you are done. The fundamental rule is this: If there are ne essential nodes, you need to write ne-1 equations. Remember that one essential node is the reference node, and we do not write a KCL equation for the reference node. If there are dependent sources present, then the number of equations has to increase. In general, each dependent source introduces a variable which is unknown. If v is the number of variables that dependent sources depend on, then you need to write ne -1+v equations.

    34. 34 What do we do when we have voltage sources? This is another important question. In general, a voltage source requires some special attention, since the current through it depends entirely on what it is connected to. We will develop a set of plans for dealing with this situation. We will lay out these plans in the next set of lecture notes.

    35. 35 Node-Voltage Method with Voltage Sources

    36. 36 Overview of this Part In this part, we will cover the following topics: Voltage sources in the Node-Voltage Method Voltage sources in series with an element Voltage sources between reference node and another essential node Voltage sources between two non-reference essential nodes You can click on the blue text to jump to the subject that you want to learn about now.You can click on the blue text to jump to the subject that you want to learn about now.

    37. 37

    38. 38 The Node-Voltage Method (NVM) The Node-Voltage Method steps are: Find the essential nodes. Define one essential node as the reference node. Define the node voltages, the essential nodes with respect to the reference node. Label them. Apply KCL for each non-reference essential node. Write an equation for each current or voltage upon which dependent sources depend, as needed.

    39. 39 Voltage Sources and the NVM The NVM steps are: Find the essential nodes. Define one essential node as the reference node. Define the node voltages, the essential nodes with respect to the reference node. Label them. Apply KCL for each non-reference essential node. Write an equation for each current or voltage upon which dependent sources depend, as needed.

    40. 40 Voltage Sources and the NVM Solution The NVM steps are: Find the essential nodes. Define one essential node as the reference node. Define the node voltages, the essential nodes with respect to the reference node. Label them. Apply KCL for each non-reference essential node. Write an equation for each current or voltage upon which dependent sources depend, as needed.

    41. 41 NVM – Voltage Source in Series with Another Element

    42. 42 NVM – Voltage Source in Series Step 1

    43. 43 NVM – Voltage Source in Series Step 2

    44. 44 NVM – Voltage Source in Series Step 3

    45. 45 NVM – Voltage Source in Series Step 4 – Part 1

    46. 46 NVM – Voltage Source in Series Step 4 – Part 2

    47. 47 NVM – Voltage Source in Series Step 4 – Part 3

    48. 48 NVM – Voltage Source in Series Step 4 – Part 4

    49. 49 NVM – Voltage Source in Series Step 4 – Notes

    50. 50 NVM – Voltage Source in Series Step 5

    51. 51 NVM – Voltage Source Between the Reference Node and Another Essential Node

    52. 52 NVM – Voltage Source Between the Reference Node and Another Essential Node – Step 1

    53. 53 NVM – Voltage Source Between the Reference Node and Another Essential Node – Step 2

    54. 54 NVM – Voltage Source Between the Reference Node and Another Essential Node – Step 3

    55. 55 NVM – Voltage Source Between the Reference Node and Another Essential Node – Step 4 – Part 1

    56. 56 NVM – Voltage Source Between the Reference Node and Another Essential Node – Step 4 – Part 2

    57. 57 NVM – Voltage Source Between the Reference Node and Another Essential Node – Step 4 – Part 3

    58. 58 NVM – Voltage Source Between the Reference Node and Another Essential Node – Step 5

    59. 59 NVM – Voltage Source Between Two Non-Reference Essential Nodes

    60. 60 NVM – Voltage Source Between Two Non-Reference Essential Nodes – Steps 1, 2, and 3

    61. 61 NVM – Voltage Source Between Two Non-Reference Essential Nodes – Step 4 – Part 1

    62. 62 NVM – Voltage Source Between Two Non-Reference Essential Nodes – Step 4 – Part 2

    63. 63 NVM – Voltage Source Between Two Non-Reference Essential Nodes – Step 4 – Part 3

    64. 64 NVM – Voltage Source Between Two Non-Reference Essential Nodes – Step 4 – Part 4

    65. 65 NVM – Voltage Source Between Two Non-Reference Essential Nodes – Step 4 – Part 5

    66. 66 NVM – Voltage Source Between Two Non-Reference Essential Nodes – Step 4 – Part 6

    67. 67 NVM – Voltage Source Between Two Non-Reference Essential Nodes – Step 4 – Part 7

    68. 68 NVM – Voltage Source Between Two Non-Reference Essential Nodes – Step 4 – Part 8

    69. 69 NVM – Voltage Source Between Two Non-Reference Essential Nodes – Step 4 – Part 9

    70. 70 NVM – Voltage Source Between Two Non-Reference Essential Nodes – Step 4 – Part 10

    71. 71 NVM – Voltage Source Between Two Non-Reference Essential Nodes – Step 4 – Part 11

    72. 72 NVM – Voltage Source Between Two Non-Reference Essential Nodes – Step 4 – Part 12

    73. 73 NVM – Voltage Source Between Two Non-Reference Essential Nodes – Step 5

    74. 74 How many node-voltage equations do we need to write? This has not changed. The presence or absence of voltage sources does not change the rules about the number or equations. In addition, it does not matter whether the voltage sources are dependent or independent. The fundamental rule is this: If there are ne essential nodes, you need to write ne-1 equations. Remember that one essential node is the reference node, and we do not write a KCL equation for the reference node. If there are dependent sources present, then the number of equations has to increase. In general, each dependent source introduces a variable which is unknown. If v is the number of variables that dependent sources depend on, then you need to write ne -1+v equations.

    75. 75 What do we do when we have voltage sources? Our steps when we have voltage sources depend on how the voltage sources appear. If the voltage source is in series with another element, we use that series element to come up with an expression for the current. If the voltage source is between the reference node and another essential node, we set that node-voltage equal to the voltage source, being careful about the polarity. If the voltage source is between two non-reference essential nodes, we write a supernode equation using a closed surface around the source (supernode equation), and write a KVL using the voltage source and the two node-voltages (constraint equation).

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