EE100Su08 Lecture 5 July 2nd 2008 Outline Questions Lab notes Labs 2 and 3 have been shortened Monday lab go to your SECOND lab section next week Node Voltage Analysis wrap up Mesh analysis read it OPTIONAL Superposition Thevenin s Theorem EE100 Summer 2008 Slide 1 Bharathwaj Muthuswamy Nodal Analysis Example 2 R1 Va R3 V 1 R2 I1 R4 R5 V2 Challenges Determine number of nodes needed Deal with different types of sources EE100 Summer 2008 Slide 2 Bharathwaj Muthuswamy Nodal Analysis w Floating Voltage Source A floating voltage source is one for which neither side is connected to the reference node e g VLL in the circuit below VLL Va Vb I1 R2 R4 I2 Problem We cannot write KCL at nodes a or b because there is no way to express the current through the voltage source in terms of VaVb Solution Define a supernode that chunk of the circuit containing nodes a and b Express KCL for this supernode Incorporate voltage source constraint into KCL equation EE100 Summer 2008 Slide 3 Bharathwaj Muthuswamy Nodal Analysis Example 3 supernode VLL Va I1 R2 Vb R4 I2 Eq n 1 KCL at supernode Substitute property of voltage source EE100 Summer 2008 Slide 4 Bharathwaj Muthuswamy Superposition A linear circuit is one constructed only of linear elements linear resistors and linear capacitors and inductors linear dependent sources and independent sources Linear means I V charcteristic of elements sources are straight lines when plotted Principle of Superposition In any linear circuit containing multiple independent sources the current or voltage at any point in the network may be calculated as the algebraic sum of the individual contributions of each source acting alone EE100 Summer 2008 Slide 5 Bharathwaj Muthuswamy Superposition Procedure 1 Determine contribution due to one independent source Set all other sources to 0 Replace independent voltage source by short circuit independent current source by open circuit 2 Repeat for each independent source 3 Sum individual contributions to obtain desired voltage or current EE100 Summer 2008 Slide 6 Bharathwaj Muthuswamy Open Circuit and Short Circuit Open circuit i 0 Cut off the branch Short circuit v 0 replace the element by wire Turn off an independent voltage source means V 0 Replace by wire Short circuit Turn off an independent current source means i 0 Cut off the branch open circuit EE100 Summer 2008 Slide 7 Bharathwaj Muthuswamy Superposition Example 2 Find Vo 24 V 4V 4 Vo 4A EE100 Summer 2008 Slide 8 Bharathwaj Muthuswamy EE100 Summer 2008 Slide 9 Bharathwaj Muthuswamy EE100 Summer 2008 Slide 10 Bharathwaj Muthuswamy Equivalent Circuit Concept A network of voltage sources current sources and resistors can be replaced by an equivalent circuit which has identical terminal properties I V characteristics without affecting the operation of the rest of the circuit iA network A of sources and resistors iB vA network B of sources and resistors vB iA vA iB vB EE100 Summer 2008 Slide 11 Bharathwaj Muthuswamy Th venin Equivalent Circuit Any linear 2 terminal 1 port network of indep voltage sources indep current sources and linear resistors can be replaced by an equivalent circuit consisting of an independent voltage source in series with a resistor without affecting the operation of the rest of the circuit Th venin equivalent circuit RTh a iL vL RL VTh network of sources and resistors a b iL vL RL b load resistor EE100 Summer 2008 Slide 12 Bharathwaj Muthuswamy I V Characteristic of Th venin Equivalent The I V characteristic for the series combination of elements is obtained by adding their voltage drops For a given current i the voltage drop vab is equal to the sum of the voltages dropped across the source VTh and across the resistor iRTh RTh a vab vab VTh iR v i VTh i I V characteristic of resistor v iR b I V characteristic of voltage source v VTh EE100 Summer 2008 Slide 13 Bharathwaj Muthuswamy EE100 Summer 2008 Slide 14 Bharathwaj Muthuswamy EE100 Summer 2008 Slide 15 Bharathwaj Muthuswamy EE100 Summer 2008 Slide 16 Bharathwaj Muthuswamy EE100 Summer 2008 Slide 17 Bharathwaj Muthuswamy Th venin Equivalent Example Find the Thevenin equivalent with respect to the terminals a b EE100 Summer 2008 Slide 18 Bharathwaj Muthuswamy Th venin Equivalent Example contd EE100 Summer 2008 Slide 19 Bharathwaj Muthuswamy Aside Prelab 1 question 3 EE100 Summer 2008 Slide 20 Bharathwaj Muthuswamy Th venin Equivalent Example contd EE100 Summer 2008 Slide 21 Bharathwaj Muthuswamy Th venin Equivalent Example contd EE100 Summer 2008 Slide 22 Bharathwaj Muthuswamy Th venin Equivalent Example contd EE100 Summer 2008 Slide 23 Bharathwaj Muthuswamy RTh Calculation Example 1 Set all independent sources to 0 EE100 Summer 2008 Slide 24 Bharathwaj Muthuswamy
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