EE201 Lecture 14 P 1 Maximum Power Transfer What is the value of RL that maximizes power transferred to load vOC vL RTH pL t RL iL t 2 where iL t pL t vOC t RTH RL vOC2 t RL RTH RL 2 iL RL EE201 Lecture 14 P 2 To find RL for max load power satisfy d pL t 0 d RL d pL t d RL 2 vOC2 t RL vOC2 t RTH RL 2 RTH RL 3 RTH RL 2 RL RTH RL To find the maximum power transfer put RTH RL into power equation pL t max vOC2 t 4 RTH 0 EE201 Lecture 14 P 3 For circuit on P 1 what is the effect of varying RTH RTH 0 for fixed RL RL 0 Take derivative d pL t 2 RL vOC2 t 0 RTH RL 3 d RTH Maximum power transfer occurs when RTH 0 Example Find RL for maximum power transfer and power absorbed by load 12 10 1A 18 78 I1 RL EE201 Lecture 14 P 4 Step 1 Find Thevenin equivalent circuit RTH 10 90 18 25 vOC 18 I1 I1 1 30 1 30 1 78 1 A vOC 13 V 25 13 V Thevenin equivalent circuit EE201 Lecture 14 P 5 Step 2 Equate RL RTH and solve for power 25 13 V iL vL 25 vL 25 50 13 6 5 V pL vL2 RL vL2 RTH 1 69 W Using equation on P 2 for maximum power transfer pL t max vOC2 t 4 RTH pL t max 1 69 W 169 100 EE201 Lecture 14 P 6 Example Find RL and the maximum power transfer to the load 10 ix ix A 32 V 5 k 18 mA 2 k Step 1 Determine ix KCL A ix 0 018 10 ix ix 0 002 A Step 2 Calculate vOC and iSC vOC 5 k 10 ix 100 V iSC 10 ix 0 02 A RL EE201 Lecture 14 P 7 Step 3 Calculate RTH and maximum power transfer MPT RTH vOC iSC 100 0 02 5 k For MPT pmax RL RTH vOC2 t 4 RTH pmax 0 5 W 100 2 4 5000 EE201 Lecture 14 P 8 Example Find the maximum power that can be absorbed by placing a load resistor across terminals a b vab V 45 a 30 Linear 15 circuit b 0 1 Draw Thevenin equivalent circuit vOC RTH 0 1 i A 0 2 a i vL b RL EE201 Lecture 14 P 9 From KVL vab RTH i vOC Compare with plot vab 150 i 15 RTH 150 vOC 15 V Maximum power pmax vOC2 4 RTH pmax 0 38 W 15 2 4 150
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