电路原理Chapter10Resonance.ppt

Rj L+_2.series resonance in the series RLC circuit1)resonant condition：resonant angular frequency10.1 series resonance1.resonance definitionChapter 10 Resonance2)the resonant condition in an series RLC circuita.L and C keep constant，changesb.keeps constant，L or C changes(usually C changes)resonant angular frequencyresonant frequency resonant period3)characteristics of the series RLC resonanceb.The input impedance Z is purely resistive，Z=R.The impedance magnitude of the circuit|Z|reaches its minimum.|Z|0 0O ORc.Current I reaches its maximum.I0=U/R (U keeps constant)。Rj L+_+_d.The sum of voltages across L and C is equal to zero.Phasor diagram at resonanceIf 0L=1/(0C)R，UL=UC U 。e.powerP=RI02=U2/R，the resistor absorbs the maximum power.3.characteristic impedance and quality factor1).characteristic impedance unit：2).quality factor QdimensionlessReactance of the inductor or the capacitor at resonance:a.Voltage relation：Quality factor：or UL0=UC0=QUb.Power relationThe source supplies：reactive poweraverage power+_PQLCRc.Energy relationletthenenergy stored in electrical fieldenergy stored in magnetic field4.resonance curve and selectivity of the series RLC circuit1).Frequency characteristic of impedance ZThe frequency response of the impedance magnitudeThe frequency response of the impedance phaseX()|Z()|XL()XC()R 0 Z()OFrequency response of the impedance magnitude ()0 O/2/2Frequency response of the impedance phase 0 O|Y()|I()I()U/R2).Current amplitude versus frequency for the resonant circuitresonant curve：implies voltage(current)-frequency relationamplitude：The I-relation is similar with that of|Y|-.3).Selectivity and general resonant curvea.selectivity 0 OI()b.General resonant curveThe higher the value of Q，the narrower the resonant curve,the better the circuit selectivity.Q=10Q=1Q=0.51 2 10.7070 general resonant curve：Q=10Q=1Q=0.51 2 10.7070 Is called Band Width(BW).It can be proved：I/I0=0.707 expressed in dB：20log10I/I0=20lg0.707=3 dB.So 1，2 are called 3db frequencies(half-power frequency).Q=1 0 2 10.707I00 4.Frequency responses of UL()and UC()UUC(Cm)QU Cm Lm 0UL()UC()U()1According to the mathematical analysis，when =Cm，UC()reaches its maximum；when =Lm，UL()reaches its maximum;and UC(Cm)=UL(Lm)。The higher the value of Q，the closer Lm and Cm are to 0.Lm Cm =0。1、the parallel GCL circuitduality：RLC in seriesGCL in parallel10.2 parallel resonance+_GCLRLC in seriesGCL in parallel|Z|0 0O OR 0 OI()U/R 0 OU()IS/G|Y|0 0O OGRLC in seriesGCL in parallelvoltage resonancecurrent resonanceUL(0)=UC(0)=QUIL(0)=IC(0)=QIS Deducing procedure：for definition2.the inductor coil and the capacitor in parallelAt resonance B=0，CLRAt resonance，the circuit is purely resistive：CLREquivalent circuit：C is constant.At resonance：GeCLeApproximately equivalent circuit：CLRIf Q is high,orthe above expression can be written as：GeCLApproximately equivalent circuit：L and C keep constant，circuits consisting of pure inductors and capacitors：(a)(b)10.3 series and parallel resonanceL1L3C2L1C2C3Quantitative analysis：(a)When Z()=0，numerator is zero：L1L3C2The following results can be derived：When Y()=0，denominator is zero:1 2L1L3C2(b)Let numerator and denominator be zero respectively:series resonanceparallel resonanceL1C2C3Frequency response of impedance：1 X()O 2Z()=jX()1 X()O 2(a)(b)Ex：The source u1(t)includes two parts of different frequencies 1、2(1 2)：Find the way to make u2(t)only include the 1 part.u1(t)=u11(1)+u12(2)Application of LC series and parallel circuit：1.various types of passive filters+_u1(t)u2(t)Various types of filter circuits：L2L1C2L3C1C3L2L1C2C1L3C3band-pass filterband-stop filter