EE_10_F07_Lecture 6

EE_10_F07_Lecture 6 - UCLA ELECTRICAL ENGINEERING...

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UCLA E LECTRICAL E NGINEERING D EPARTMENT : EE 10: C IRCUIT A NALYSIS 1 L ECTURE 6 LECTURE NOTES: OCT 24, 2007 OUTLINE REVIEW 1. Dependent Sources 2. Node Voltage Methods for Circuits with Dependent Sources SIMPLIFIED NODE VOLTAGE SOLUTIONS FOR SPECIAL CIRCUIT STRUCTURES Certain arrangement of dependent and independent voltage and current sources reduces the complexity of the circuit solution. If a source is connected between two Essential Nodes, then one less equation is required to specify the circuit, than would otherwise be required. We will develop a new rule: o When a voltage source is connected between two Essential Nodes , then this node can be replaced with a “ supernode ” for the purposes of computing currents for the KCL sum. o The currents that arrive at each node of the voltage source are treated as if the voltage source is one node. 4.8A 2.5 Ω 12V 10 Ω 1 Ω i x -+ v = i x 7.5 Ω 2.5 Ω + v 1 - + - Figure 1. Example Problem First, lets write down the Node Voltage Equations in the normal way. 1) List the information that is requested by the problem. 1
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UCLA E LECTRICAL E NGINEERING D EPARTMENT : EE 10: C IRCUIT A NALYSIS 1 L ECTURE 6 lution 2) Examine the circuit to determine the approach for a so 3) Determine if a circuit simplification may be accomplished using an equivalent circuit, for example, a parallel, series, delta, or Y, circuit structure. 4) List known values of circuit variables 5) Identify and label the N E Essential Nodes 6) Choose one Essential Node and label it with a Reference Potential Symbol. The choice of this node will determine the level of simplicity of the calculation. However, any choice of an Essential Node will yield the same problem results. You should select in the circuit, that Essential Node that is connected to the most branches. 7) Identify and label the non-reference node voltages. 8) Each non-reference node voltage is labeled as positive. 9) Use KCL to write down an equation for each non-reference node, writing the equations in terms of the resistances, and node voltages. 10) Write down N E – 1 equations. 11) Solve the set of equations. 1) Information requested: Find v 2 de voltage method es ssential Nodes. These are b, and c, e, 6) e and label it with a Reference Potential Symbol. The choice of No . This is clearly the proper ) Identify and label the non-reference node voltages. a is not an independent node. 8) E 9) ve three steps and they are shown in Figure 6. 2) Determine approach: Simple no 3) No circuit simplification is attempted 4) List known values: 4.8A and 12V sourc 5) For this step, we must label the circuit E and d, shown in Figure 3. Choose one Essential Nod this node will determine the level of simplicity of the calculation. However, any choice of an Essential Node will yield the same problem results. You should select in the circuit, that Essential Node that is connected to the most branches.
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This note was uploaded on 03/06/2008 for the course EE 10 taught by Professor Chang during the Fall '07 term at UCLA.

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EE_10_F07_Lecture 6 - UCLA ELECTRICAL ENGINEERING...

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