Theory of Electric Circuits IILecture #1: Resonant Circuits

Fall 2008

Department of Electronics and Communications Engineering, Cairo University

© Mahmoud H. Ismail, 2008

Introduction Series Resonance

Outline

IntroductionIntroductionCourse contents, references and course planCourse contents, references and course plan

11

Resonance Circuits: types and applicationsResonance Circuits: types and applications

S i RS i RSeries ResonanceSeries ResonanceDefinitionDefinitionPhasor diagram for the series resonant circuitPhasor diagram for the series resonant circuit

22

Phasor diagram for the series resonant circuitPhasor diagram for the series resonant circuitThe quality factor of a resonant circuitThe quality factor of a resonant circuitThe detuning factor and narrowThe detuning factor and narrow band (nearband (near resonance)resonance)The detuning factor and narrowThe detuning factor and narrow--band (nearband (near--resonance) resonance)

operation operation

Introduction Series Resonance

Course ContentsSeries and Parallel Resonance CircuitsSeries and Parallel Resonance CircuitsApplications on Passive Electric FiltersApplications on Passive Electric Filtersoo LP, HP, BP, BS filtersLP, HP, BP, BS filters

D blD bl t d filtt d filtoo DoubleDouble--tuned filterstuned filtersResonance in MutuallyResonance in Mutually--Coupled CircuitsCoupled Circuitsoo SingleSingle tuned transformerstuned transformersoo SingleSingle--tuned transformerstuned transformersoo DoubleDouble--tuned transformerstuned transformersoo Frequency response using Bode plotsFrequency response using Bode plotsoo Frequency response using Bode plotsFrequency response using Bode plotsTwoTwo––port Networksport Networksoo Admittance, impedance, hybrid and transmission parametersAdmittance, impedance, hybrid and transmission parametersoo Equivalent circuitsEquivalent circuitsoo Parameters conversionsParameters conversionsoo InterInter--connection of twoconnection of two--ports (series, parallel and cascade)ports (series, parallel and cascade)oo TwoTwo--port networks embedded within a networkport networks embedded within a network

Introduction Series Resonance

ReferencesReferences:References:11 S dS d AA NN “El t i Ci it ”“El t i Ci it ” S h ’S h ’ S l d P blS l d P bl1.1. SyedSyed A. A. NasarNasar, “Electric Circuits,” , “Electric Circuits,” Schaum’sSchaum’s Solved Problems Solved Problems

Series, Series, McgrawMcgraw--Hill, New York, Hill, New York, 19881988..2.2. Richard C. Richard C. DorfDorf, “Introduction to Electric Circuits,” John Wiley & , “Introduction to Electric Circuits,” John Wiley & , , y, , y

Sons Inc., New York, Sons Inc., New York, 19931993..3.3. Cunningham Stuller, “Circuit Analysis,” John Wiley & Sons Inc., Cunningham Stuller, “Circuit Analysis,” John Wiley & Sons Inc.,

New YorkNew York 19951995New York, New York, 19951995..4.4. James W. Nilsson and Susan A. Riedel, “Electric Circuits,” James W. Nilsson and Susan A. Riedel, “Electric Circuits,”

AddisonAddison--WisleyWisley Publishing Company, New York, Publishing Company, New York, 19961996..Important topics to be revised:Important topics to be revised:1.1. Analyzing circuits with D.C. and A.C. input signals.Analyzing circuits with D.C. and A.C. input signals.22 Using loop and node analysisUsing loop and node analysis2.2. Using loop and node analysis.Using loop and node analysis.3.3. Calculating input impedances and admittances of networks.Calculating input impedances and admittances of networks.4.4. Calculations of maximum power transfer to a load.Calculations of maximum power transfer to a load.4.4. Calculations of maximum power transfer to a load.Calculations of maximum power transfer to a load.5.5. Dealing with independent and dependent sources in ideal & Dealing with independent and dependent sources in ideal &

actual cases.actual cases.

Introduction Series Resonance

Tentative Course Plan

Instructors:Instructors: Prof. Dr. Prof. Dr. AfafAfaf AbdelAbdel--Fattah, Fattah, Dr. Dr. MahmoudMahmoud H. IsmailH. Ismail

TA: TA: ????G diG di 2020% Midt% Midt 1010% Q i% Q i 7070% Fi l E% Fi l EGrading:Grading: 2020% Midterm, % Midterm, 1010% Quizzes, % Quizzes, 7070% Final Exam.% Final Exam.Meeting times:Meeting times: Sunday, Lecture Hall Sunday, Lecture Hall 83108310..Office Hours:Office Hours: ThursdayThursday 99::3030 AMAM 1212::1515 PMPMOffice Hours:Office Hours: ThursdayThursday, , 99::30 30 AM AM –– 1212::15 15 PMPMSome Classroom RegulationsSome Classroom Regulations•• Late arrivalsLate arrivalsLate arrivalsLate arrivals•• Attendance in first lectureAttendance in first lecture

Introduction Series Resonance

Resonance CircuitsWhat is Electric Resonance?What is Electric Resonance?

A resonance circuit is a combination of R L and C elementsA resonance circuit is a combination of R L and C elementsoo A resonance circuit is a combination of R, L and C elements A resonance circuit is a combination of R, L and C elements having a frequency response as shown.having a frequency response as shown.

oo Radio and TV receivers have response curves similar to the Radio and TV receivers have response curves similar to the ppone shown.one shown.

oo Resonance occurs when the inductive and capacitive Resonance occurs when the inductive and capacitive reactancesreactances of the circuit are equalof the circuit are equalreactancesreactances of the circuit are equal.of the circuit are equal.

oo In other words, it occurs when the input impedance to a circuit In other words, it occurs when the input impedance to a circuit is is purepure real (resistive).real (resistive).pp ( )( )

oo At resonance, the energy absorbed at any instant by one At resonance, the energy absorbed at any instant by one reactive element is exactly equal to that released by the other reactive element is exactly equal to that released by the other

l tl telement.element.oo At resonance, energy pulsates from one reactive element to At resonance, energy pulsates from one reactive element to

the other. Once at resonance, the system requires no reactive the other. Once at resonance, the system requires no reactive , y q, y qpower and the total apparent power is equal to the average power and the total apparent power is equal to the average power dissipated in the resistive elements.power dissipated in the resistive elements.

Resonance Circuits

Introduction Series Resonance

Types of Resonance CircuitsR L

+V C

II

R

C

V- L

V

Series ResonanceSeries Resonance Parallel resonanceParallel resonance

Introduction Series Resonance

Series Resonance

LRlRs LRlRs

CoilCoilC+

-

EsCoilCoil

Introduction Series Resonance

Series Resonance

At resonance:At resonance:Analysis

Current and voltages at resonance:Current and voltages at resonance:Current and voltages at resonance:Current and voltages at resonance:

Voltage across coilVoltage across coil

Voltage across capacitorVoltage across capacitor

Voltage across resistorVoltage across resistor

Series Resonance

Introduction Series Resonance

Phasor Diagrams

ImagImag ImagImaggg gg

RealReal RealRealRealReal

Phasor diagram for the series Phasor diagram for the series t i it tt i it t

RealReal

Power triangle for the series Power triangle for the series t i it tt i it tresonant circuit at resonanceresonant circuit at resonance resonant circuit at resonanceresonant circuit at resonance

Series Resonance

Introduction Series Resonance

The Quality Factor (Qs) at Resonance

•• TheThe qualityquality factorfactor QQ ofof aa seriesseries resonantresonant circuitcircuit isis defineddefinedasas thethe ratioratio ofof thethe reactivereactive powerpower ofof eithereither thethe coilcoil oror thethecapacitorcapacitor toto thethe averageaverage powerpower ofof thethe resistanceresistance atatresonanceresonanceresonanceresonance..

Introduction Series Resonance

Series Resonance

Analysis II

Voltages at resonance in terms of quality factor:Voltages at resonance in terms of quality factor:g q yg q yNote that usually Note that usually

Impedance in terms of quality factor:Impedance in terms of quality factor:

:: DetuningDetuning factorfactor

Introduction Series Resonance

Series Resonance

Analysis II (contd.)

Current in terms of quality factor:Current in terms of quality factor:

•• LetLet

Fractional detuning factor, represents deviation Fractional detuning factor, represents deviation f ff f

•• ForFor narrowbandnarrowband (near(near resonance)resonance) operation,operation, ii..ee..,,

from resonance freq.from resonance freq.