EE202 Circuit Theory II
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1 EE202 Circui Theory II , Spring Dr. Yılmaz KALKAN
2 I. Inroducion & eview of Fir Order Circui (Chaper 7 of Nilon - 3 Hr. Inroducion, C and L Circui, Naural and Sep epone of Serie and Parallel L/C Circui II. Second Order Circui (Chaper 8 of Nilon - 9 Hr. The Naural epone of a Parallel LC Circui, The Form of Naural epone of a Parallel LC Circui, The Sep epone of a Parallel LC Circui, Naural and Sep epone of a Serie LC Circui III. Sinuoidal Seady-Sae Analyi (Chaper 9 of Nilon - 9 Hr. The Sinuoidal Source, he Sinuoidal epone, he Phaor. The Paive Circui Elemen in he Freq. Domain, Kirchhoff Law in he Freq. Domain. Serie, Parallel, and Dela-o-Wye Simplificaion, Source Tranformaion Thevenin and Noron Equivalen Circui, he Node- Volage Mehod, he Meh-Curren Mehod. The Tranformer, Muual Coupling IV. Sinuoidal Seady-Sae Power Calculaion (Chaper 10 of Nilon - 6 Hr. Inananeou Power, Average and eacive Power, The rm Value and Power Calculaion, Maximum Power Tranfer V. Balanced Three-Phae Circui (Chaper 11 of Nilon - 6 Hr. Balanced Three-Phae Volage, Three-Phae Volage Source, Analyi of he Wye-Wye and Wye- Dela Circui, Power Calculaion in Balanced Three-Phae Circui, Meauring Average Power in Three-Phae Circui VI. The Laplace Tranformaion in Circui Analyi (Chaper of Nilon - 6 Hr. Circui Elemen in he Domain, Circui Analyi in he Domain, The Tranfer Funcion, The Tranfer Funcion in Parial Fracion Expanion, The Tranfer Funcion and he Convoluion Inegral, The Tranfer Funcion and he Seady-Sae Sinuoidal epone, The Impule Funcion in Circui Analyi EE202 - Circui Theory II
3 The Sep epone of L and C Circui We are now ready o dicu he problem of finding he curren and volage generaed in fir-order L or C circui when eiher dc volage or curren ource are uddenly applied. The repone of a circui o he udden applicaion of a conan volage or curren ource i referred o a he ep repone of he circui. Uni ep funcion EE202 - Circui Theory II
4 The Sep epone of an L Circui Energy ored in he inducor a he ime he wich i cloed i given in erm of a non-zero iniial curren i(0. The ak i o find he expreion for he curren in he circui and for he volage acro he inducor afer he wich ha been cloed. We ue circui analyi o derive he differenial equaion ha decribe he circui in erm of he variable of inere, and hen we ue elemenary calculu o olve he equaion. EE202 - Circui Theory II
5 The Sep epone of an L Circui Uing exbook Afer he wich ha been cloed, KVL require ha; V i. L di d EE202 - Circui Theory II
6 The Sep epone of an L Circui Afer hee calculaion, he ep repone of an L circui can be obained a; L e V I V i ; ( ( 0 When he iniial energy in he inducor i zero, (1 ( ( e V i e V V i EE202 - Circui Theory II
7 The Sep epone of an L Circui i( 5 V EE202 - Circui Theory II
8 The Sep epone of an L Circui L e V I V i ; ( ( 0 The volage acro an inducor i L di/d, hence, for >0, 0 ; ( ( 0 e I V v If he iniial curren i zero, 0 ; ( V e v EE202 - Circui Theory II
9 Example : (7.5 from exbook The wich in he circui ha been in poiion a for a long ime. A = 0, he wich move from poiion a o poiion b. The wich i a makebefore-break ype; ha i, he connecion a poiion b i eablihed before he connecion a poiion a i broken, o here i no inerrupion of curren hrough he inducor. EE202 - Circui Theory II
10 Example : (7.5 from exbook - Soluion EE202 - Circui Theory II
11 Example : Find i( in he circui for > 0. Aume ha he wich ha been cloed for a long ime. Anwer: i( 2 3e 15 A; 0 EE202 - Circui Theory II
12 The Sep epone of an C Circui Energy ored in he capacior a he ime he wich i cloed i given in erm of a non-zero iniial volage v(0. The ak i o find he expreion for he curren in he circui and for he volage acro he capacior afer he wich ha been cloed. We ue circui analyi o derive he differenial equaion ha decribe he circui in erm of he variable of inere, and hen we ue elemenary calculu o olve he equaion. EE202 - Circui Theory II
13 The Sep epone of an C Circui For 0, KCL a node A d dv C V I i i I C C C Afer he imilar calculaion wih L circui, he ep repone of an C circui can be obained a; C e I V I v C 0 ; ( ( 0 EE202 - Circui Theory II
14 The Sep epone of an C Circui 0 ; ( ( 0 e I V I v C d dv C i C C 0 ; ( 0 e V I i C EE202 - Circui Theory II
15 The Sep epone of an C Circui 0 ; 1 ( I e v C 0 ; ( e I i C If he iniial energy ored i zero, hen EE202 - Circui Theory II
16 Example : (7.6 from exbook EE202 - Circui Theory II
17 Example : (7.6 from exbook - Soluion EE202 - Circui Theory II
18 Example : In Figure, he wich ha been cloed for a long ime and i opened a = 0. Find i and v for all ime. EE202 - Circui Theory II
19 The General Soluion for Sep and Naural epone The general approach o finding eiher he naural repone or he ep repone of he fir-order L and C circui hown in Figure below are baed on heir differenial equaion having he ame form. EE202 - Circui Theory II
20 The General Soluion for Sep and Naural epone 0 ; 1 ( 0 e I e V i L 0 ; 1 ( 0 V e e I v C 0 ; ( 0 e I i L 0 ; ( 0 V e v C Naural epone for L & C Circui Sep epone for L & C Circui WE CAN FIND A GENEAL SOLUTION FO THEM EE202 - Circui Theory II
21 The General Soluion for Sep and Naural epone The iniial value of ha unknown variable. Time of wiching. x( X f ( 0 X ( X e ; 0 0 f Time conan. The unknown variable a a funcion of ime. v C (, i ( L The final value of ha unknown variable. L, C EE202 - Circui Theory II
22 Example : (7.7 from exbook EE202 - Circui Theory II
23 Example : (7.7 from exbook - Soluion EE202 - Circui Theory II
24 Example : (7.7 from exbook - Soluion EE202 - Circui Theory II
25 Example : (7.9 from exbook EE202 - Circui Theory II
26 Example : (7.9 from exbook - Soluion EE202 - Circui Theory II
27 Sequenial Swiching Whenever wiching occur more han once in a circui, we have equenial wiching. Wih equenial wiching problem, a premium i placed on obaining he iniial value x(0. ecall ha anyhing bu inducive curren and capaciive volage can change inananeouly a he ime of wiching. EE202 - Circui Theory II
28 Example : A = 0, wich 1 (S1 in figure above i cloed, and wich 2 (S2 i cloed 4 laer. Find i( for > 0. Calculae i for = 2 and = 5. EE202 - Circui Theory II
29 Example : Soluion EE202 - Circui Theory II
30 Example : Soluion EE202 - Circui Theory II
31 Example : Soluion EE202 - Circui Theory II
32 Example : Soluion EE202 - Circui Theory II
33 Unbounded epone A circui repone may grow, raher han decay, exponenially wih ime. Thi ype of repone, called an unbounded repone, i poible if he circui conain dependen ource. In ha cae, he Thevenin equivalen reiance wih repec o he erminal of eiher an inducor or a capacior may be negaive. Thi negaive reiance generae a negaive ime conan, and he reuling curren and volage increae wihou limi. In an acual circui, he repone evenually reache a limiing value when a componen break down or goe ino a auraion ae, prohibiing furher increae in volage or curren. EE202 - Circui Theory II
34 Example : (7.13 from exbook EE202 - Circui Theory II
35 Example : (7.13 from exbook -Soluion EE202 - Circui Theory II
36 Example : (7.13 from exbook -Soluion EE202 - Circui Theory II
37 END OF eview Dr. Yılmaz KALKAN EE202 - Circui Theory II
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