EE201 Lecture 13 P 1 Thevenin s and Norton s Theorems cont More on circuits with dependent sources In Lecture 12 we saw that combinations of resistors and dependent source have Thevenin and Norton equivalent networks that consist of a resistor RTH only To determine RTH we added a variable current or voltage source to the circuit Consider the circuit below Let s short the external terminals equivalent to adding a deactivated voltage source ix 100 20 ix 0 2 iy 50 iy iSC EE201 Lecture 13 P 2 Find the Thevenin and Norton equivalent circuits To find iSC short circuit external terminals Then iy 0 From this ix can be calculated 100 ix 20 ix 0 ix 0 A and iSC 0 A This is a quantitative verification of the statement made on P 1 Since iSC 0 A vOC 0 V Therefore the Thevenin and Norton equivalent circuits will be RTH EE201 Lecture 13 P 3 Conclusion combination of dependent sources and resistors behave similar to a resistor To find RTH apply a variable source to the circuit We will solve for RTH using a voltage source and a current source Voltage source added i iy ix 1V 20 ix 50 0 2 iy 100 By adding a voltage source we only need to solve for the current i to calculate RTH EE201 Lecture 13 P 4 From KVL 1 20 ix 100 ix 0 ix 1 120 A Now solve for iy using nodal voltage VB 1 iy 1 50 A To find i use KCL at supernode below A ix 100 0 2 iy i B 20 ix iy 50 i 1 250 1 50 1 120 i 0 024 A 1V EE201 Lecture 13 P 5 Calculate RTH RTH 1 0 024 41 1 Current source added A ix 100 20 ix 0 2 iy i B iy 50 v KCL A 1 iy 0 2iy 1 0 8iy ix KVL 20ix 50iy 100ix 0 Solving for ix and iy ix 0 342 A iy 0 822 A 1A EE201 Lecture 13 v equals drop over 50 resistor v 50 0 822 41 1 V and the Thevenin resistance RTH 41 1 1 41 1 P 6 EE201 Lecture 13 P 7 Circuits with independent and dependent sources 2 A 3 vOC vOC 4 4V Example Find the Thevenin and Norton equivalent circuits Step 1 Find vOC Apply KCL at node A 4 VA 2 vOC 0 4 vOC 8 V Note VA voc because no current flows through 3 resistor EE201 Lecture 13 P 8 Step 2 Find iSC 2 A 3 vOC 4 4V iSC vOC 0 V current from dependent current source is zero iSC 4V 2 3 iSC 0 8 A EE201 Lecture 13 P 9 Step 3 Calculate RTH RTH vOC iSC 8V 0 8 A 10 RTH 10 vOC 8V vOC Thevenin Equivalent iSC 0 8 A Norton Equivalent EE201 Lecture 13 P 10 Example For a complex circuit two sets of measurement data are shown below Find the Thevenin and Norton equivalent circuits v 10 V iL 0 A v 10 V iL 2 A Equation of line representing iL v relation iL 1 10 v 1 Step 1 Find vOC If iL 0 open circuit then vOC v vOC 10 V Step 2 Find RTH by comparing with theorem Thevenin s theorem v RTH i vOC Norton s theorem i 1 RTH v iSC EE201 Lecture 13 P 11 iL i iL 1 RTH v iSC Compare this with iL v equation on P 9 RTH 10 iSC 1 A 10 10 V Thevenin Equivalent 1A 10 Norton Equivalent EE201 Lecture 13 P 12 Example Find the Thevenin and Norton equivalent circuits for the circuit below 0 25 iA 4A iA v 1 3 0 5 A B Step 1 Define supernode and connect to variable current source 4A 0 25 iA 0 5 iA 1 3 i EE201 Lecture 13 P 13 Step 2 Apply KCL at supernode 4 2 v 0 25 i 3 v i i 10 v 8 Step 3 Compare with theory i vOC RTH v vOC RTH i v i 1 RTH v iSC RTH 0 1 iSC 8 A vOC 0 8 V 0 1 0 8 V 8A 0 1 EE201 Lecture 13 P 14 Strategies for solving for Thevenin and Norton Equivalent Circuits 1 Are two of three parameters vOC iSC RTH known If so find unknown parameter using vOC RTH iSC 2 Are two datapoints of i v relationship known If so then compare line defined by data to theory v RTH i vOC i 1 RTH v iSC iL 1 RTH v iSC EE201 Lecture 13 P 15 3 Are dependent sources absent from circuit If so is deactivated circuit series parallel arrangement of resistors If both true RTH is found by evaluating equivalent resistance RTH Req and vOC is found by KCL KVL source transformation or any other general method discussed in the course 4 If dependent sources are present or if deactivated circuit is not series parallel then solve for Thevenin Norton equivalents by applying external sources or by general methods
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