EE302-3-Analysis Methods

EE302-3-Analysis Methods - NodeVoltageAnalysis...

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Node Voltage Analysis 
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2 Node Voltage Analysis  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. Node Voltage Analysis is the most important technique we will cover  in EE302.   It is essential that you master this method!
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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 + -
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4 Example Circuit To get the power we need the voltage  and current for every element. What if we use KVL, KCL and  Ohm’s 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 + -
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5  How Many Equations? We have 13 unknowns so we need 13  equations: We can write an Ohm’s 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!
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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 don’t have to be clever. We don’t 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
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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 Ohm’s 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.
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