EE302Lecture12 - Node Voltage Analysis 2 Node Voltage...

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Unformatted text preview: Node Voltage Analysis 2 Node Voltage Analysis In these lectures, you will learn: The difficulty in using only KVL, KCL, and Ohms 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. Node Voltage Analysis is the most important technique we will cover in EE302. It is essential that you master this method! 3 Definitions What is a node? A node is a point in the circuit where two or more elements are connected 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.) How many essential nodes are there in this circuit? 4! R3 1 A 2 A R1 R2 R4 R5 2 V +-4 Example Circuit To get the power we need the voltage and current for every element. What if we use KVL, KCL and Ohms Law to solve this? How many unknowns? 1 current for the voltage source. 2 voltages for the current sources. 5 voltages or 5 currents for the resistors. We 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 +-5 How Many Equations? We have 13 unknowns so we need 13 equations: We can write an Ohms Law equation for each resistor. 5 Equations. We can write 3 independent KCL equations. We can write 5 independent KVL equations. Now we are 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! 6 The Easier Way Systematic methods allow us to solve circuits using the minimum number of equations. Systematic methods allow us solve every circuit in the same manner. We dont have to be clever. We dont have to see the trick. 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 only: 2 Equations with 2 unknowns 7 Concept of Nodal Analysis If I know all of the voltages in a circuit, then I know everything! Resistors Current can be found via Ohms Law Power can be calculated by V 2 /R Current Sources Power can be calculated once the voltage is known. Voltage Sources Finding the current through the voltage sources is harder often have to use KCL. Nodal analysis is a systematic method for finding all of the voltages in any circuit. 8 Finding Current from Voltages Circuit A Circuit B + V a-+ V b-How can we use Ohms Law to find the resistor current? What is the voltage across the resistor (V R )? + V R-V R = V a- V b I R = V R /R R What is the current through the resistor (I R )?...
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EE302Lecture12 - Node Voltage Analysis 2 Node Voltage...

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