Lecture #8. Thévenin Equivalent Circuit
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1 ecture #8 ANNOUNCEMENTS HW#2 solutons, HW#3 re posted onlne Chnge n Frhn s O.H. : 5-6 nsted of Mo 3-4 wll e wy next Mondy & Wednesdy Guest lecturer: Prof. Neureuther s offce hour on Wed. 9/17 cncelled OUTINE évenn nd Norton equvlent crcuts Mxmum power trnsfer Superposton edng Chpter ecture 8, Slde 1 évenn Equvlent Crcut Any network of voltge sources, current sources, nd resstors cn e replced y n equvlent crcut consstng of n ndependent voltge source n seres wth resstor wthout ffectng the operton of the rest of the crcut. évenn equvlent crcut network of sources nd resstors v V v lod resstor ecture 8, Slde 2
2 I-V Chrcterstc of évenn Equvlent e I-V chrcterstc for the seres comnton of elements s otned y ddng ther voltge drops: For gven current, the voltge drop v s equl to the sum of the voltges dropped cross the source (V ) nd the cross the resstor ( ) v V v V v I-V chrcterstc of resstor: v I-V chrcterstc of voltge source: v V ecture 8, Slde 3 Fndng V nd Only two ponts re needed to defne lne. Choose two convenent ponts: 1. Open crcut cross termnls, 0, v v oc V 2. Short crcut cross termnls, v 0, - sc -V / v oc V v oc sc - sc v V v V ecture 8, Slde 4
3 Clcultng évenn Equvlent 1. Clculte the open-crcut voltge, v oc 2. Clculte the short-crcut current, sc Note tht sc s n the drecton of the open-crcut voltge drop cross the termnls,! network of sources nd resstors network of sources nd resstors ecture 8, Slde 5 v oc sc V v v oc oc sc évenn Equvlent Exmple Fnd the evenn equvlent wth respect to the termnls,: ecture 8, Slde 6
4 Alterntve Method of Clcultng For network contnng only ndependent sources nd resstors: 1. Set ll ndependent sources to zero voltge source short crcut current source open crcut 2. Fnd equvlent resstnce eq etween the termnls eq For network contnng dependent sources: 1. Set ll ndependent sources to zero 2. Apply test voltge source V TEST 3. Clculte I TEST VTEST I TEST network of ndependent sources nd resstors, wth ech source set to zero network of ndependent sources nd resstors, wth ech source set to zero V TEST eq I TEST ecture 8, Slde 7 Clculton Exmple #1 Set ll ndependent sources to 0: ecture 8, Slde 8
5 Comments on Dependent Sources A dependent source estlshes voltge or current whose vlue depends on the vlue of voltge or current t specfed locton n the crcut. (mgnry devce, used to model ehvor of trnsstors & mplfers) To specfy dependent source, we must dentfy: 1. the controllng voltge or current (must e clculted, n generl) 2. the reltonshp etween the controllng voltge or current nd the suppled voltge or current 3. the reference drecton for the suppled voltge or current e reltonshp etween the dependent source nd ts reference cnnot e roken! Dependent sources cnnot e turned off for vrous purposes (e.g. to fnd the évenn resstnce). ecture 8, Slde 9 Clculton Exmple #2 Fnd the evenn equvlent wth respect to the termnls,: ecture 8, Slde 10
6 Networks Contnng Tme-Vryng Sources Cre must e tken n summng tme-vryng sources! Exmple: 10 sn (100t) 1 kω 20 cos (100t) 1 kω V 1kΩ 1kΩ 1kΩ [ 20 cos(100t) ] 10sn(100t) 10 o 2 sn(100t 90 ) 1kΩ 1kΩ 500Ω ecture 8, Slde 11 Norton Equvlent Crcut Any network of voltge sources, current sources, nd resstors cn e replced y n equvlent crcut consstng of n ndependent current source n prllel wth resstor wthout ffectng the operton of the rest of the crcut. Norton equvlent crcut network of sources nd resstors v N N v ecture 8, Slde 12
7 Fndng I N nd N We cn derve the Norton equvlent crcut from évenn equvlent crcut smply y mkng source trnsformton: v v N N v v N v v N N oc ; N sc sc N ecture 8, Slde 13 V Mxmum Power Trnsfer eorem évenn equvlent crcut dp d V v p 2 2 ( ) 2( ) 4 ( ) 2 ( ) 2( ) 0 Power sored y lod resstor: 2 A resstve lod receves mxmum power from crcut f the lod resstnce equls the évenn resstnce of the crcut. V dp To fnd the vlue of for whch p s mxmum, set to 0: d 0 2 ecture 8, Slde 14
8 Superposton A lner crcut s constructed only of lner elements cn e descred y lner dfferentl equton Prncple of Superposton: In ny lner crcut contnng multple ndependent sources, the current or voltge t ny pont n the network my e clculted s the lgerc sum of the ndvdul contrutons of ech source ctng lone. Note: Superposton cnnot e used to fnd power! s prncple s useful for nlyss of op-mp crcuts. Procedure: 1. Determne contruton due to n ndependent source Set ll other sources to 0 2. epet for ech ndependent source 3. Sum ndvdul contrutons to otn desred voltge or current ecture 8, Slde 15 Superposton Exmple Fnd V o 2 Ω 4 V 24 V 4 A 4 Ω V o ecture 8, Slde 16
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