EE201 Lecture 12 P 1 Thevenin s and Norton s Theorems Thevenin s Theorems for Passive Networks For any linear resistive network i Linear resistive network v There exists a Thevenin equivalent network i RTH vOC v EE201 Lecture 12 P 2 Where vOC is the open circuit voltage appearing across the terminals of the network and RTH is the Thevenin equivalent resistance when all independent sources are deactivated There also exists a Norton equivalent network i iSC RTH v Which is equivalent to the Thevenin network if iSC vOC RTH iSC is the short circuit current through a short wire between the terminals of the network EE201 Lecture 12 P 3 Concept of modifying configuration at external terminals to obtain parameter of interest For any linear resistive network with an attached load resistor i Linear resistive network v RL To find voc remove the load resistor Now there is an open circuit condition at the external terminals Linear resistive network voc EE201 Lecture 12 P 4 To find isc replace the load resistor with a wire Now there is a short circuit condition at the external terminals Note that v 0 V because the wire brings the terminals to the same potential Linear resistive network v 0V isc For circuits with dependent current or voltage sources the portion of the circuit to be replaced by a Thevenin or Norton equivalent must include the controlling circuit element for the dependent source EE201 Lecture 12 P 5 Example Find the Thevenin and Norton equivalent seen by the 1 k load resistor 2k 3k 2mA 4V vL 1k Solution Use source transformations to find Thevenin equivalent Note this is not the only way to solve the problem 3k 2k 2 mA vL 2mA 1k 4V source 2k resistor transformed to 2mA source in parallel with 2k resistor EE201 Lecture 12 P 6 Combine current sources defined between same nodes 3k 2k 4 mA vL 1k Use source transformations to replace current source with voltage source 3k 8V 2 k vL 1k EE201 Lecture 12 P 7 Add series resistances 5 k vL 8V 1k Now either short or open the external terminals see pages 3 and 4 to obtain isc or voc respectively RTH 5 k RTH 5 k vOC 8V vL vL Thevenin Equivalent iSC 1 6 mA Norton Equivalent EE201 Lecture 12 P 8 Example Find the Thevenin and Norton equiv cir 31 V 1A 7 5 i1 6 i2 2 vOC RTH Solution Step 1 Find RTH by deactivating all independent voltage sources short and all independent current sources open 6 12 2 RTH 4 2 6 EE201 Lecture 12 P 9 Step 2 Find vOC using mesh analysis M1 31 7i1 6i1 5 i1 i2 0 M2 i2 1 A from M1 i1 2 A vOC 6i1 2i2 14 V Step 3 Combine vOC and RTH to define Thevenin equivalent RTH 6 vOC 14V vL EE201 Lecture 12 P 10 Step 4 Obtain Norton equivalent using source transformations RTH 6 iSC vOC RTH iSC 14 6 2 33 A vL iSC 2 33A EE201 Lecture 12 P 11 Example Find the Thevenin and Norton equivalent for circuits with dependent sources v1 16 1 5 vOC 6 1 5 v1 RTH General principle Since there are no independent sources vOC 0 iSC 0 How to evaluate RTH Attach a variable current or voltage source v1 16 1 5 1A 6 1 5 v1 EE201 Lecture 12 P 12 Use mesh analysis to find voltage across terminals 1 5 v1 16 i1 i2 v 6 1 5 v1 M1 1A 1 5 v1 1 5i1 6 i1 i2 0 M2 i2 1 A v1 16 V and from M1 i1 4 A Computing the voltage drop across terminals v 16 1 6 i1 1 0 v 2 V and the Thevenin equivalent resistance is RTH v i2 2 EE201 Lecture 12 P 13 The Thevenin and Norton equivalent circuits are shown below RTH 2
View Full Document
Unlocking...