Unit 2.1 Node Voltage Analysis

# Unit 2.1 Node Voltage Analysis - Node Voltage Analysis In...

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1 1 Unit 2: Node and Mesh Circuit Analysis Unit 2.1 – Node Voltage Analysis 2 Node Voltage Analysis f In these lectures, you will learn: ± The difficulty in using only KVL, KCL, and Ohm’s Law in the analysis of large DC circuits. ± How node voltage analysis simplifies the solution of large DC circuits. ± How to apply Node-Voltage Analysis. 3 Example Circuit f To get the power I need the voltage and current for every element. f What if I was going to use KVL, KCL and Ohm’s Law to solve for this? f How many unknowns? ± 1 current for the voltage source. ± 2 voltages for the current sources. ± 5 voltages or 5 currents for the resistors. f I need 13 equations! Calculate the power associated with each element in the circuit below. R3 1 A 2 A R1 R2 R4 R5 2 V + - 4 How Many Equations? f I have 13 unknowns so I need 13 equations: ± I can write an Ohm’s Law equation for each resistor. • 5 Equations. ± I can write 3 independent KCL equations. ± I can write 5 independent KVL equations. f Now I am all done except for the algebra. Calculate the power associated with each element in the circuit below. R3 1 A 2 A R1 R2 R4 R5 2 V + - There has got to be an easier way! 5 The Easier Way f Systematic methods allow us to solve circuits using the minimum number of equations. f Systematic methods allow us solve every circuit in the same manner. ± We don’t have to be clever. ± We don’t have to see “the trick”. f We will learn two systematic methods. The first is nodal analysis . R3 1 A 2 A R1 R2 R4 R5 2 V + - With Nodal Analysis, we need: 2 Equations and 2 unknowns 6 Concept of Nodal Analysis f If I know the voltage across each element in a circuit, then I know everything. ± Resistors • Current can be found via Ohm’s Law • Power can be calculated by V 2 /R ± Current Sources • Power can be calculated once the voltage across it are known ± Voltage Sources • Finding the current through the voltage sources is a bit harder – may have to use KCL. f Nodal analysis is a systematic method for finding all of the voltages in any circuit.

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2 7 Review of Definitions f What is a node? ± A node is a point in the circuit where two or more elements are connected f What is an essential node? ± An essential node is a node where three or more elements are connected. (This concept is not used in your text, but it greatly simplifies the analysis.) 4! How many nodes are there in this circuit? How many essential nodes are there in this circuit? 4! R3 1 A 2 A R1 R2 R4 R5 2 V + - 8 Node Voltage f What does a Node Voltage mean? ± We can define the value of a voltage at a node if we have a point of reference. Where are the nodes? What if we say the voltage at node A is 0 V… What is the value at node B? + - 0 V 20 V 10 k Ω 10 k Ω A B C 20 V 10 V What is the value at node C?
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Unit 2.1 Node Voltage Analysis - Node Voltage Analysis In...

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