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LECTURE 2

LECTURE 2. Circuit Analysis Techniques. Voltage Division Principle Current Division Principle Nodal Analysis with KCL Mesh Analysis with KVL Superposition Thévenin Equivalence Norton’s Equivalence. Circuit Analysis Techniques.

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LECTURE 2

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  1. LECTURE 2

  2. Circuit Analysis Techniques

  3. Voltage Division Principle Current Division Principle Nodal Analysis with KCL Mesh Analysis with KVL Superposition Thévenin Equivalence Norton’s Equivalence Circuit Analysis Techniques

  4. Begin by locating a combination of resistances that are in series or parallel. Often the place to start is farthest from the source. Redraw the circuit with the equivalent resistance for the combination found in step 1. Repeat steps 1 and 2 until the circuit is reduced as far as possible. Often (but not always) we end up with a single source and a single resistance. Solve for the currents and voltages in the final equivalent circuit. Circuit Analysis using Series/Parallel Equivalents

  5. Working Backward

  6. Voltage Division

  7. Application of the Voltage-Division Principle

  8. Current Division

  9. Application of the Current-Division Principle

  10. Voltage division and • current division • Voltage division

  11. Current division

  12. Although they are veryimportant concepts,series/parallel equivalents andthe current/voltage divisionprinciples are not sufficient to solve all circuits.

  13. Node Voltage (Nodal) Analysis

  14. Definitions of node and Supernode

  15. Obtain values for the unknown voltages across the elements in the circuit below. At node 1 At node 2

  16. Writing KCL Equations in Terms of the Node Voltages forFigure 2.16 node 1 node 2 node 3

  17. node 1 node 2 node 3

  18. No. of unknown: v1, v2, v3 No. of linear equation : 3 Setting up nodal equation with KCL at Node 1, Node 2, Node 3

  19. No. of unknown: v1, v2, v3 No. of linear equation : 3 Setting up nodal equation with KCL at Node 1, Node 2, Node 3

  20. Problem with node 3, it is rather hard to set the nodal equation at node 3, but still solvable. Why? As there is no way to determinethe current through the voltage source, but v3=Vs v3 Problem with node 3, it is rather hard to set the nodal equation at node 3 but still solvable. Same as before.

  21. May Not Be That Simple

  22. Circuits with Voltage Sources • We obtain dependent equations if we use all of the nodes in a network to write KCL equations. • Any branch with a voltage source: • define SUPERNODE, sum all current either in or out at the supernode with KCL • use KVL to set up dependent equation involving the voltage source.

  23. (a) The circuit of Example 4.2 with a 22-V source in place of the 7-W resistor. (b) Expanded view of the region defined as a supernode; KCL requires that all currents flowing into the region must sum to zero, or we would pile up or run out of electrons. At node 1: At the “supernode:”

  24. EXCLUDE THE SOURCE For supernode A, A B Summing all the current out from the supernode A Why? As the current via the 10V source is equal to the current via R4 plus the current via R3

  25. EXCLUDE THE SOURCE For supernode B, B Summing all the current into the supernode B

  26. -v1 -10 + v2 = 0

  27. Any branch with a voltage source: • define supernode, sum all current either in or out at the • supernode with KCL • use KVL to set up dependent equation involving the • voltage source.

  28. Node-Voltage Analysis with a Dependent Source • First, we write KCL equations at each node, including the current of the controlled source just as if it were an ordinary current source. • Next, we find an expression for the controlling variable ixin terms of the node voltages.

  29. Substitution yields

  30. Node-Voltage Analysis 1. Select a reference node and assign variables for the unknown node voltages. If the reference node is chosen at one end of an independent voltage source, one node voltage is known at the start, and fewer need to be computed. 2. Write network equations. First, use KCL to write current equations for nodes and supernodes. Write as many current equations as you can without using all of the nodes. Then if you do not have enough equations because of voltage sources connected between nodes, use KVL to write additional equations. 3. If the circuit contains dependent sources, find expressions for the controlling variables in terms of the node voltages. Substitute into the network equations, and obtain equations having only the node voltages as unknowns. 4. Put the equations into standard form and solve for the node voltages. 5. Use the values found for the node voltages to calculate any other currents or voltages of interest.

  31. Step 1.Reference node Step 1. v1 Step 2. Step 1 v2

  32. Step1 Step 1 v2 v1 Step 2 v3 node 1 supernode Step1 ref supernode Step 3

  33. Mesh Current Analysis

  34. Definition of a loop Definition of a mesh

  35. Choosing the Mesh Currents When several mesh currents flow through one element, we consider the current in that element to be the algebraic sum of the mesh currents.

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