Theory of Electric Circuits II Lecture #1: Resonant Circuits

Transcription

1 Thery f Electric Circuits II Lecture #1: Resnant Circuits Fall 2009 Department f Electrnics and Cmmunicatins Engineering, Cair University Mahmud H. Ismail, 2009

2 Intrductin Outline 1 Intrductin Curse cntents, references and curse plan Resnance Circuits: types and applicatins 2 Definitin Phasr diagram fr the series resnant circuit The quality factr f a resnant circuit The detuning factr and narrw-band (near-resnance) resnance) peratin

3 Intrductin Curse Cntents Series and Parallel Resnance Circuits Applicatins n Passive Electric Filters LP, HP, BP, BS filters Duble-tuned filters Resnance in Mutually-Cupled Circuits Single-tuned transfrmers Duble-tuned transfrmers Frequency respnse using Bde plts Tw prt Netwrks Admittance, impedance, hybrid and transmissin parameters Equivalent circuits Parameters cnversins Inter-cnnectin f tw-prts (series, parallel and cascade) Tw-prt netwrks embedded within a netwrk

4 Intrductin References References: 1. Syed A. Nasar, Electric Circuits, it Schaum s Slved Prblems Series, Mcgraw-Hill, New Yrk, Richard C. Drf, Intrductin t Electric Circuits, Jhn Wiley & Sns Inc., New Yrk, Cunningham Stuller, Circuit Analysis, Jhn Wiley & Sns Inc., New Yrk, James W. Nilssn and Susan A. Riedel, Electric Circuits, Addisn-Wisley Publishing Cmpany, New Yrk, Imprtant tpics t be revised: 1. Analyzing circuits with D.C. and A.C. input signals. 2. Using lp and nde analysis. 3. Calculating input impedances and admittances f netwrks. 4. Calculatins f maximum pwer transfer t a lad. 5. Dealing with independent and dependent surces in ideal & actual cases.

5 Intrductin Tentative Curse Plan Instructrs: TA:?? Prf. Dr. Afaf Abdel-Fattah, Dr. Mahmud H. Ismail Grading: 20% %Midt Midterm, 10% %Q Quizzes, 70% %Fi Final le Exam. Meeting times: Sunday, Lecture Hall Office Hurs:First 4-5 weeks, Saturday. 9:30-11:30 AM, later: Sunday 1 10:30-12:30 PM Sme Classrm Regulatins Late arrivals Attendance in first lecture

6 Intrductin Resnance Circuits What is Electric Resnance? A resnance circuit is a cmbinatin f R, L and C elements having a frequency respnse as shwn. Radi and TV receivers have respnse curves similar t the ne shwn. Resnance ccurs when the inductive and capacitive reactances f the circuit are equal. In ther wrds, it ccurs when the input impedance t a circuit is pure real (resistive). At resnance, the energy absrbed at any instant by ne reactive element is exactly equal t that released by the ther element. At resnance, energy pulsates frm ne reactive element t the ther. Once at resnance, the system requires n reactive pwer and the ttal apparent pwer is equal t the average pwer dissipated in the resistive elements.

7 Intrductin Resnance Circuits Types f Resnance Circuits R L R + I V C - I L C V Parallel resnance

8 Intrductin Rs Rl L + Es Cil C -

9 Intrductin Analysis At resnance: Current and vltages at resnance: Vltage acrss cil Vltage acrss capacitr Vltage acrss resistr

10 Intrductin Phasr Diagrams Imag Imag Real Phasr diagram fr the series resnant circuit it at resnance Real Pwer triangle fr the series resnant circuit it at resnance

11 Intrductin The Quality Factr (Q s ) at Resnance The quality factr Qf aseries resnant circuit is defined as the rati f the reactive pwer f either the cil r the capacitr t the average pwer f the resistance at resnance.

12 Intrductin Analysis II Vltages at resnance in terms f quality factr: Nte that usually Impedance in terms f quality factr: : Detuning factr

13 Intrductin Analysis II (cntd.) Current in terms f quality factr: Let Fractinal detuning factr, represents deviatin frm resnance freq. Fr narrwband (near resnance) peratin, i.e.,