EE1 Circui Theory I 17 Fall
1. Basic Conceps Chaper 1 of Nilsson - 3 Hrs. Inroducion, Curren and Volage, Power and Energy. Basic Laws Chaper &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 - 9 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. Firs Order Circuis Chapers 6&7 of Nilsson - 9 Hrs. Inducors, Capaciors, Series and Parallel Combinaions of hem, Differeniaor & Inegraor Circuis wih Op-amp, he Naural Response of an RL & RC Circuis, The Sep Response of RL and RC Circuis, A General Soluion for Sep and Naural Responses. 6. Second Order Circuis Chaper 8 of Nilsson - 9 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 Review 3 Hrs EE1 - Circui Theory I 14.1.17
Now ha we have considered he hree passive elemens resisors, capaciors, and inducors and one acive elemen he op amp individually. We are prepared o consider circuis ha conain various combinaions of wo or hree of he passive elemens. In his chaper, we shall examine wo ypes of simple circuis: a circui comprising a resisor and capacior and a circui comprising a resisor and an inducor. These are called RC and RL circuis, respecively. EE1 - Circui Theory I
We carry ou he analysis of RC and RL circuis by applying Kirchhoff s laws, as we did for resisive circuis. The only difference is ha applying Kirchhoff s laws o purely resisive circuis resuls in algebraic equaions, while applying he laws o RC and RL circuis produces differenial equaions, which are more difficul o solve han algebraic equaions. The differenial equaions resuling from analyzing RC and RL circuis are of he firs order. Hence, he circuis are collecively known as firs-order circuis. EE1 - Circui Theory I
A firs-order circui is characerized by a firs-order differenial equaion. In addiion o here being wo ypes of firs-order circuis RC and RL, here are wo ways o excie he circuis. The firs way is by iniial condiions of he sorage elemens in he circuis. In hese so called source-free circuis, we assume ha energy is iniially sored in he capaciive or inducive elemen. The energy causes curren o flow in he circui and is gradually dissipaed in he resisors. Alhough source free circuis are by definiion free of independen sources, hey may have dependen sources. EE1 - Circui Theory I
A firs-order circui is characerized by a firs-order differenial equaion. The second way of exciing firs-order circuis is by independen sources. In his chaper, he independen sources we will consider are dc sources. In EE, we shall consider sinusoidal and exponenial sources. The wo ypes of firs-order circuis and he wo ways of exciing hem add up o he four possible siuaions we will sudy in his chaper. EE1 - Circui Theory I
RL and RC circuis are also known as firs-order circuis, because heir volages and currens are described by firs-order differenial equaions. No maer how complex a circui may appear, if i can be reduced o a Thevenin or Noron equivalen conneced o he erminals of an equivalen inducor or capacior, i is a firsorder circui. Noe ha if muliple inducors or capaciors exis in he original circui, hey mus be inerconneced so ha hey can be replaced by a single equivalen elemen. EE1 - Circui Theory I
The Naural Response of An RL Circui Source-Free RL Circui A source-free RL circui occurs when is dc source is suddenly disconneced. The energy already sored in he inducor/capacior is released o he resisors. EE1 - Circui Theory I
The Naural Response of An RL Circui Source-Free RL Circui Assume ha he independen curren source generaes a consan curren of I s A, and ha he swich has been in a closed posiion for a long ime. Long ime means ha all currens and volages have reached a consan value. Thus only consan, or dc, currens can exis in he circui jus prior o he swich's being opened, and herefore he inducor appears as a shor circui Ldi/d = prior o he release of he sored energy. EE1 - Circui Theory I
The Naural Response of An RL Circui Source-Free RL Circui Assume ha he independen curren source generaes a consan curren of I s A, and ha he swich has been in a closed posiion for a long ime. v L di d v L ir ir i L I s EE1 - Circui Theory I
The Naural Response of An RL Circui Source-Free RL Circui If a =, he swich is opened Now he problem becomes of finding v and i for EE1 - Circui Theory I
The Naural Response of An RL Circui Source-Free RL Circui by using KVL L di d Ri This equaion is known as a firs order ordinary differenial equaion. The highes order derivaive appearing in he equaion is 1; hence he erm firs-order. di d R L i di R L id di i R L d i i e R L EE1 - Circui Theory I
The Naural Response of An RL Circui Source-Free RL Circui We know ha an insananeous change of curren canno occur in an inducor. i i i R L I i Ie, The curren sars from an iniial value I and decreases exponenially oward zero as increases The coefficien of namely, R/L deermines he rae a which he curren or volage approaches zero. The reciprocal of his raio is he ime consan of he circui denoed by. EE1 - Circui Theory I
The Naural Response of An RL Circui Source-Free RL Circui L R i Ie, EE1 - Circui Theory I
EE1 - Circui Theory I The Naural Response of An RL Circui Source-Free RL Circui, e I i R L, Re I v R i v??, v R I v v There will be a jump in volage a =, so v is NOT DEFINED!!
EE1 - Circui Theory I The Naural Response of An RL Circui Source-Free RL Circui, Re. I P R v R i v i P Power & Energy The energy delivered o he resisor during any inerval of ime afer he swich has been opened is;, Re dx e R I dx I pdx w x x, 1 1 e LI w
The Naural Response of An RL Circui Source-Free RL Circui Example: 7.1from exbook The swich in he circui has been closed for a long ime before i is opened a =. Find i L, i and v for Also find he percenage of he oal energy sored in he H inducor ha is dissipaed in he 1 Ω resisor. EE1 - Circui Theory I
The Naural Response of An RL Circui Source-Free RL Circui Example: 7.1soluion EE1 - Circui Theory I
The Naural Response of An RL Circui Source-Free RL Circui Example: 7.1soluion EE1 - Circui Theory I
The Naural Response of An RL Circui Source-Free RL Circui Example: 7.1soluion EE1 - Circui Theory I
The Naural Response of An RL Circui Source-Free RL Circui Example: The swich in he circui has been closed for a long ime. A =, he swich is opened. Calculae i for >. i 6e 4 A ; EE1 - Circui Theory I
EE1 - Circui Theory I The Naural Response of An RL Circui Source-Free RL Circui Example: Assuming ha i = 1 A, calculae i and ix in he circui. ; 3 5 ; 1 3 3 A e i A e i x
The Naural Response of An RC Circui Source-Free RC Circui The naural response of an RC circui is analogous o ha of an RL circui. Assume ha he swich has been in posiion a for a long ime, and he capacior C o reach a seady-sae condiion. We know ha a capacior behaves as an open circui in he presence of a consan volage. Cdv/d = The imporan poin is ha when he swich is moved from posiion a o posiion b a =, he volage on he capacior is Vg. EE1 - Circui Theory I
The Naural Response of An RC Circui Source-Free RC Circui Therefore he problem reduces o solving he circui shown in following figure EE1 - Circui Theory I
The Naural Response of An RC Circui Source-Free RC Circui i c By using KCL dv v i C d R dv d 1 dv 1 RC v d v v e RC v RC ; EE1 - Circui Theory I
The Naural Response of An RC Circui Source-Free RC Circui We know ha an insananeous change of volagecanno occur in a capacior. v v v V V g and RC The volage sars from an iniial value v and decreases exponenially oward zero as increases angen a = The coefficien of namely, RC deermines he rae a which he olage or curren approaches zero. The reciprocal of his raio is he ime consan of he circui denoed by. EE1 - Circui Theory I
EE1 - Circui Theory I The Naural Response of An RC Circui Source-Free RC Circui,. e R V P R v R i v i P, 1 1 e CV w ; ; e R V i V e v
The Naural Response of An RC Circui Source-Free RL Circui Example: 7.3from exbook The swich in he circui has been in posiion x for a long ime. A =, he swich moves insananeously o posiion b. Find, v C for, v and i for Also find he oal energy dissipaed in he 6 kω resisor. EE1 - Circui Theory I
The Naural Response of An RC Circui Source-Free RL Circui Example: 7.3soluion EE1 - Circui Theory I
The Naural Response of An RC Circui Source-Free RL Circui Example: 7.3soluion EE1 - Circui Theory I
EE1 - Circui Theory I The Naural Response of An RC Circui Source-Free RL Circui Example: Le vc = 15 V. Find vc, vx, and ix for > J w A e i V e v V e v c x x c 1.15 ;.75 ; 9 ; 15 5 5 5
The Naural Response of An RC Circui Source-Free RL Circui Example: If he swich opens a =, find v for and wc. v w c 8e V 5.33J EE1 - Circui Theory I
END OF CHAPTER 5 Par References: Elecric Circuis, J. W. Nilsson and S. A. Riedel, Pearson Prenice Hall. Fundamenals of Elecric Circuis, C. K. Alexander and M. N. O. Sadiku, McGraw- Hill Book Company EE1 - Circui Theory I