enee204Lectures_14_15_Gomez

enee204Lectures_14_15_Gomez - Another Practice Example:...

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1 10/19/2005 1 Welcome to ENEE 204 Basic Circuit Theory Lecture 14 Chapter 5: Non linear Reactive Circuits 10/19/2005 2 Another Practice Example: Find the Thevenin and Norton equivalents 10 10 10 10 A B 60V 4A 40V 10 10 10 + + What is the maximum voltage, current and power that can be transmitted to a load between points A and B ? 10/19/2005 3 The answer: + Z s V S ˆ Thevenin equivalent 65 V 27.5 I s Y s Norton equivalent 2.36 A 36(m Ω) −1 Maximum Voltage Maximum Current Maximum Power for R L = 27.5 R L P AVE = Watt I V S S 4 . 38 2 2 = 10/19/2005 4 Another example: The bridge circuit problem: Using Thevenin to calculate all currents 2R R R R R V s I ^ Let’s first find the current through 2R by replacing the rest of the circuit by itsThevenin equivalent I 1 I 2 I 3 I 5 I 4
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2 10/19/2005 5 Step 1: Identifying the LOAD, Removing it from the circuit R R R R V s A B B A V T R eq 10/19/2005 6 Step 2: Calculating open circuit voltage between A and B R R R R V s B A V + C D Resistance between points C and D is R CD R CD =2R||R = 2/3 R V CD = V s 2/3 R R + 2/3 R = 2/5 V S V BD = 1/2 V CD = 1/5 V S V AB = V S V BD = 4/5 V S 10/19/2005 7 Step 3: Calculating the input resistance between A and B; voltage source is shorted R R R R B A V + C D R R R R B A V + C D ``` R AB = R||3/2 R = 3/5 R Remember: || connections always split at node 10/19/2005 8 The Thevenin equivalent circuit R R R R V s A B B A 4/5 V 4/5 V S 3/5 R 3/5 R
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3 10/19/2005 9 Calculating the voltage and current across the load resistor ^ 2R R R R R V s I I 1 I 2 I 3 I 5 I 4 A 4/5 V 4/5 V S 3/5 R 3/5 R 2R I 1 B V AB = 2R 2R + 3/5 R 4/5 V S = 8/13 V = 8/13 V S I 1 = 4/5 V 4/5 V S 2R + 3/5 R 3/5 R = 13R 4 V S 10/19/2005 10 Calculating the other voltages and currents ^ 2R R R R R V s I I 1 I 2 I 3 I 5 I 4 I = 13R 11V S s AB s V V R V I 13 8 ; 13 4 1 = = R V I V V V V s s AB s 13 5 ; 13 5 4 4 = = = 13 ; 13 13 5 13 4 3 3 4 1 3 s s s s V R I V R V R V R V I I I = = = = = s s s s V R I V V V V V V 13 6 ; 13 6 13 13 5 5 3 4 5 = = = = s s V V R V I I I 13 7 ; 13 7 2 3 5 2 = = = 10/19/2005 11 Why is it important to UNDERSTAND GRAPHICAL SOLUTION? Much easier to model NON-LINEAR ELEMENTS Examples of Non-Linear Elements: 1. DIODES 2. TRANSISTORS 3. Any element in which the V vs. I curves is not a straight line. 10/19/2005 12 Graphical illustration of a solution to a circuit problem Z S + - V ˆ - + Z L V S I ˆ I Z V ˆ ˆ L = Terminal relation for the load: S S Z I - V V = Equation for Thevenin equivalent of active circuit: V I Solution V S I SC
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4 10/19/2005 13 If only one element in a circuit is non-linear, we can replace the rest of the circuit with a Thevenin Equivalent. Z nL 1 2 V ˆ I ˆ 2 1 Z nL Non-linear Element 10/19/2005 14 Graphical approach allows us to visualize solutions to circuits with non-linear circuit elements. I Z - V V S S = Linear active circuits V I Non-linear elements V = f ( I ).
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enee204Lectures_14_15_Gomez - Another Practice Example:...

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