Superposton, Thevenn nd Norton OUTINE Superposton Thevenn Equvlent Crcut Norton Equvlent Crcut Mxmum Power Theorem ecture 6, 9/1/05 Redng Chpter.6-.8 ecture 6, Slde 1 Superposton A lner crcut s one constructed only lner elements (lner resstors, nd lner cpctors nd nductors, lner dependent ) nd ndependent. ner mens I-V chrcterstc elements/ re strght lnes when plotted Prncple Superposton: In ny lner crcut contnng multple ndependent, the current or voltge t ny pont n the network my e clculted s the lgerc sum the ndvdul contrutons ech source ctng lone. ecture 6, Slde 1
Superposton Procedure: 1. Determne contruton due to one ndependent source Set ll other to 0: Replce ndependent voltge source y short crcut, ndependent current source y open crcut. Repet for ech ndependent source 3. Sum ndvdul contrutons to otn desred voltge or current ecture 6, Slde 3 Superposton Exmple Fnd V o Ω 4 V 4 V 4 A 4 Ω V o ecture 6, Slde 4
Equvlent Crcut Concept A network voltge, current, nd resstors cn e replced y n equvlent crcut whch hs dentcl termnl propertes (I-V chrcterstcs) wthout ffectng the operton the rest the crcut. A B network A nd resstors v A _ network B nd resstors v B _ A (v A ) = B (v B ) ecture 6, Slde 5 Thévenn Equvlent Crcut Any* lner -termnl (1-port) network ndep. voltge, ndep. current, nd lner resstors cn e replced y n equvlent crcut consstng n ndependent voltge source n seres wth resstor wthout ffectng the operton the rest the crcut. Thévenn equvlent crcut network nd resstors V Th lod resstor ecture 6, Slde 6 3
I-V Chrcterstc Thévenn Equvlent The I-V chrcterstc for the seres comnton elements s otned y ddng ther voltge drops: For gven current, the voltge drop v s equl to the sum the voltges dropped cross the source (V Th ) nd cross the resstor ( ) V Th v v = V Th R v I-V chrcterstc resstor: v = R I-V chrcterstc voltge source: v = V Th ecture 6, Slde 7 Clculton Exmple #1 Hnt: Set ll ndependent to 0: ecture 6, Slde 8 4
Clculton Exmple # Fnd the Thevenn equvlent wth respect to the termnls,: ecture 6, Slde 9 Norton Equvlent Crcut Any* lner -termnl (1-port) network ndep. voltge, ndep. current, nd lner resstors cn e replced y n equvlent crcut consstng n ndependent current source n prllel wth resstor wthout ffectng the operton the rest the crcut. Norton equvlent crcut network nd resstors N R N ecture 6, Slde 10 5
I-V Chrcterstc Norton Equvlent The I-V chrcterstc for the prllel comnton elements s otned y ddng ther currents: For gven voltge v, the current s equl to the sum the currents n ech the two rnches: N R N v = -I N Gv v I-V chrcterstc resstor: =Gv I-V chrcterstc current source: = -I N ecture 6, Slde 11 Fndng I N nd R N = Anlogous to clculton Thevenn Eq. Ckt: 1) Fnd o.c voltge nd s.c. current I N sc = V Th / ) Or, fnd s.c. current nd Norton (Thev) resstnce ecture 6, Slde 1 6
Fndng I N nd R N We cn derve the Norton equvlent crcut from Thévenn equvlent crcut smply y mkng source trnsformton: v Th N R N v v R N = RTh = = oc Th ; N = sc sc RTh ecture 6, Slde 13 V Th Mxmum Power Trnsfer Theorem Thévenn equvlent crcut dp dr = V R p = ( RTh R ) R ( RTh R ) Th 4 ( RTh R ) ( R R ) R ( R R ) = 0 Th Th = R Power sored y lod resstor: Th A resstve lod receves mxmum power from crcut f the lod resstnce equls the Thévenn resstnce the crcut. R VTh = RTh R dp To fnd the vlue for whch p s mxmum, set to 0: d = 0 R ecture 6, Slde 14 7