EE202 Circui Theory II 2018 2019, Spring Dr. Yılmaz KALKAN & Dr. Ailla DÖNÜK
1. Basic Conceps (Chaper 1 of Nilsson - 3 Hrs.) Inroducion, Curren and Volage, Power and Energy 2. Basic Laws (Chaper 2&3 of Nilsson - 6 Hrs.) Volage and Curren Sources, Ohm s Law, Kirchhoff s Laws, Resisors in parallel and in series, Volage and Curren Division 3. Techniques of Circui Analysis (Chaper 4 of Nilsson - 12 Hrs.) Node Analysis, Node-Volage Mehod and Dependen Sources, Mesh Analysis, Mesh-Curren Mehod and Dependen Sources, Source Transformaions, Thevenin and Noron Equivalens, Maximum Power Transfer, Superposiion Theorem 4. Operaional Amplifier (Chaper 5 of Nilsson - 6 Hrs.) Op-Amp Terminals & Ideal Op-Amp, Basic Op-Amp Circuis, Buffer circui, Invering and Non-invering Amplifiers, Summing Inverer, Difference Amplifier, Cascade OpAmp Circuis 5. Capaciors and Inducors (Chaper 6 of Nilsson - 3 Hrs.) Inducors, Capaciors, Series and Parallel Combinaions of hem 6. Firs Order Circuis (Chaper 7 of Nilsson - 6 Hrs.) The Naural Response of an RL & RC Circuis, The Sep Response of RL and RC Circuis, A General Soluion for Sep and Naural Responses, Inegraing Amplifier Circui 7. Second Order Circuis (Chaper 8 of Nilsson - 6 Hrs.) The Naural Response of a Parallel RLC Circui, The Forms of Naural Response of a Parallel RLC Circui, The Sep Response of a Parallel RLC Circui, Naural and Sep Responses of a Series RLC Circui
Sources Volage/Curren AC/DC Dependen/Independen Ohm s Law Resisors Nodes, Branches, Loops Kirchhoff s Laws Kirchhoff s Curren Law (KCL) Kirchhoff s Voage Law (KVL) v i. R Series & Parallel Connecions of Resisors Dela-o-Wye Transform Curren & Volage Division N n1 i 0 0 n M m1 v m
Having undersood he fundamenal laws of circui heory, Ohm s law Kirchhoff s laws (KVL & KCL) Apply hese laws o develop wo powerful echniques for circui analysis. Nodal analysis, which is based on a sysemaic applicaion of Kirchhoff s curren law (KCL) Mesh analysis, which is based on a sysemaic applicaion of Kirchhoff s volage law (KVL).
Source Transformaions Maximum Power Transfer
Nodal Analysis (Node-Volage Mehod) Example: Calculae he node volages in he circui given? Answer : 20V, 40/3 V Seps: 1. Choose a reference node, assign volages o oher nodes w.r.. reference one. 2. Apply KCL o each node. (Arbirary bu Consisen). Apply Ohm s law o find node volages. 3. Solve all obained equaions ogeher. 1. Subsiuion mehod 2. Eliminaion mehod 3. Cramer s rule 4. Marix inversion 5...
Mesh Analysis (Mesh-Curren Mehod) Pracice Problem : Use mesh-curren mehod o find he power dissipiaed in he 1Ω resisor in he circui shown (Assesmen problem 4.12 from exbok) P 36W
IDEAL OP-AMPS (Oupu curren sill exis!) (Virual shor condiion.) These are only valid for LINEAR REGION.!!!! Unless oherwise is saed, OP-AMP s are IDEAL in his course.
Analyzing he OP-AMP Circuis Example : Find i0 and v0? (Op-amp is ideal) if Vs V i 0.65mA, v 9V 1 0 0
Capaciors (C) i C dv d We can also express he volage of an inducor wih respec o he curren hrough on i by using he equaion above. or id Cdv dv 1 C id v 1 C i( ) d v 1 C 0 i( ) d v( 0 )
Inducors (L) v L di d We can also express he curren of an inducor wih respec o he volage drop on i by using he equaion above. or vd Ldi di 1 L vd i 1 L v( ) d i 1 L 0 v( ) d i( 0 )
The General Soluion for Sep and Naural Responses 0 ; 1 ) ( 0 e I e R V i s L 0 ; 1 ) ( 0 V e e R I v s C 0 ; ) ( 0 e I i L 0 ; ) ( 0 V e v C Naural Responses for RL & RC Circuis Sep Responses for RL & RC Circuis WE CAN FIND A GENERAL SOLUTION FOR THEM
The General Soluion for Sep and Naural Responses The iniial value of ha unknown variable. Time of swiching. x( ) X f ( 0 X ( ) X e ; 0 0 f ) Time consan. The unknown variable as a funcion of ime. v C ( ), i ( ) L The final value of ha unknown variable. L, R RC
A second-order circui is characerized by a second-order differenial equaion. I consiss of resisors and he equivalen of wo energy sorage elemens.
For series RLC For parallel RLC Overdamped Case ( 0) 2 roos are real and negaive ( s, s 1 2 ) Criically Damped Case ( = 0) s 1 s 2 Underdamped Case ( < 0) 2 2 s1,2 jd, d 0
The Complee Responses of a Series and Parallel RLC Circuis Thus, he complee soluions for he overdamped, underdamped, and criically damped cases are: For Series RLC Circui For Parallel RLC Circui
Example: Find v() and i() for >0. Consider hese cases R=5, R=4 and R=1.
Example:
END OF Review Par Dr. Y. KALKAN & Dr. A. DÖNÜK