第5章正弦交流电路的稳态分析5.1RLC串联电路和RLC并联电路5.2复阻抗的串联和并联5.3正弦稳态电路的分析与计算5.4正弦稳态电路的功率5.5正弦稳态电路的串联谐振5.6正弦稳态电路的并联谐振重点:复阻抗用相量法分析简单正弦交流电路正弦交流电路中的功率分析{end}第5章正弦交流电路的稳态分析tωIisin2设:)90(sin)1(2)90(sin)(2sin2tωCωItωLωItωIRu则1、瞬时值表达式根据KVL可得:CLRuuuutiCtiLiRd1dd为同频率正弦量RLC串联电路RLCRu+_Lu+_Cu+_u+_i5.1RLC串联电路和RLC并联电路(1)2、相量法CLCLXXRIXIXIRIUj)j()(jCLRUUUU0II设(参考相量))j(CCXIU)(jLLXIU则RIUR总电压与总电流的相量关系式RjXL-jXCRU+_LU+_CU+_U+_I(1)相量式5.1RLC串联电路和RLC并联电路(2)CLXXRIUjCLXXRZj令则ZIUZ是一个复数,不是相量,上面不能加点。复阻抗复数形式的欧姆定律注意根据5.1RLC串联电路和RLC并联电路(3)iuiuIUZIUIUZ当电源频率一定时,电路参数决定了电压U和I的比值,决定了电压u与i电流之间的相位差角。22)(CLXXRZIURXXarctgCLiuZXXRZCLj5.1RLC串联电路和RLC并联电路(4)则RXXarctgCLiu电路参数与电路性质的关系:当XLXC时,0,u超前i呈感性当XLXC时,0,u滞后i呈容性当XL=XC时,=0,u.i同相呈电阻性5.1RLC串联电路和RLC并联电路(5)22)(CLXXRIUZ阻抗模:CLXXRZZjRXXψψCLiuarctan阻抗角:5.1RLC串联电路和RLC并联电路(6)ZRCLXXX阻抗三角形(2)相量图LUICLUUURU(0感性)XLXC参考相量URUCLUUXU电压三角形CUIRU(0容性)XLXCCULUCLUUURjXL-jXCRU+_LU+_CU+_U+_I5.1RLC串联电路和RLC并联电路(7)22()RLCUUUU例1某RLC串联电路,其电阻R=10KΩ,电感L=5mH,电容C=0.001uF,正弦电压源。求电流i和各元件上电压,并画出相量图。tus610sin102iLR+-suC解:KLXL51051036KCXC110001.0101166画出相量模型.Ij5kΩ10kΩ+-+-+-VUs0010.LU.CU.kj1+-RU)(CLXXjRUImAj008.2193.04100105.1RLC串联电路和RLC并联电路(8)mAI08.2193.0VRIUR08.213.9VjXIULL02.6865.4VjXIUCC08.11193.0)(相量图:+1IRULUCUXUsURU.Ij5kΩ10kΩ+-+-+-VUs0010.LU.CU.kj1+-RU5.1RLC串联电路和RLC并联电路(9)例2:已知图示电路中,电压表V1、V2、V3的读数分别为15V,80V,100V,求电压US。LR+-suCV1V2V3I1U3U2USUVUUUU25)(23221解:以电流为参考相量画相量图22)(CLRUUUU在RLC串联电路中5.1RLC串联电路和RLC并联电路(10)例2如图所示为一个相位后移电路。如果C=0.01uF,电源电压,要使输出电压相位向后移动,问应配多大电阻?此时输出电压等于多少?))(1200sin(2Vtui060oUiuouiRC解:画出相量模型KCXC5.261方法一:iCCoUjXRjXU)](90[022RXarctgXRUXCCiC0060)(90RXarctgCiUoUIRCjXRU由题意得5.1RLC串联电路和RLC并联电路(11)0060)(90RXarctgC030RXarctgCKctgXRC9.4535.26300iCCoUXRXU22V5.015.269.455.2622iUoUIRCjXRU5.1RLC串联电路和RLC并联电路(12)方法二:以电流为参考相量定性画出相量图iUoUIRCjXRUIRUoU由相量图可知:030tgRXC060iUKctgXRC5.49300VUUio5.060cos05.1RLC串联电路和RLC并联电路(13)RLC并联电路由KCL:CLRIIII....iLCRuiLiC+-iL.j.j.UCULUG1.jjUCLG)1(.j(UBBGCL)[.jUBG)(.IjL.ULI.CI.Cωj1RI.R+-YjBGLjCjGUIY15.1RLC串联电路和RLC并联电路(14)Y—复导纳;G—电导(导纳的实部);B—电纳(导纳的虚部);|Y|—复导纳的模;'—导纳角。关系:arctg'||22GBφBGY或G=|Y|cos'B=|Y|sin'导纳三角形|Y|GBuiUIY5.1RLC串联电路和RLC并联电路(15)(1)Y=G+j(C-1/L)=|Y|∠为复数,故称复导纳;(2)C1/L,B0,‘0,电路为容性,电流超前电压C1/L,B0,‘0,电路为感性,电流落后电压;C=1/L,B=0,=0,电路为电阻性,电流与电压同相(3)相量图:选电压为参考相量,设C1/L,02222)(CLGBGIIIIIIUGI.LI.I'CI.0u分析R、L、C并联电路得出:三角形IR、IB、I称为电流三角形,它和导纳三角形相似。即5.1RLC串联电路和RLC并联电路(16)例3)(:),5sin(2120titu(t)求已知+_15u4H0.02Fi解1:00120U2054jjjXL1002.051jjjXC相量模型Uj20-j15RILI+_15CIICLCLRjXUjXURUIIIIAjjjjj09.3610681268101201151120Ati(t))9.365sin(21005.1RLC串联电路和RLC并联电路(17))(:),5sin(2120titu(t)求已知2054jjjXL1002.051jjjXC00120UUj20-j15RILI+_15CIIURILICIIiAIR815120AIL620120AIC1210120AIIIICLR10)(22019.36RLCiIIItgAti(t))9.365sin(2100解2:以电压为参考相量画相量图5.1RLC串联电路和RLC并联电路(18){end}CXC1复阻抗的定义IZU+-无源线性IU+-IUZ阻抗纯电阻RZRLLjXLZj纯电感CCjXCjZ1纯电容LXL感抗容抗ICUj1IRUILjU注意:单一参数元件的阻抗5.2复阻抗的串联和并联(1)21ZZZ阻抗的串联ººZ1Z2abZab分压公式1U2UUUZZZU2111等效阻抗UZZZU2122阻抗的并联Z2Z1abZab212121//ZZZZZZZ等效阻抗分流公式1I2IIIZZZI2121IZZZI21125.2复阻抗的串联和并联(2)86.289.105.4045.3961.5765.3713.3281.11ooojZZZZZZZZ321213ab9.312028.610)9.3120)(28.610(jjjjZo36.359.3156.1889.2586.289.107.1515jjjZZZab例1已知Z1=10+j6.28Z2=20-j31.9Z3=15+j15.7求ZabººZ1Z2Z3ab解:5.2复阻抗的串联和并联(3)例2求如图所示电路的等效阻抗(输入阻抗)及由两个元件串联的等效电路。srad/105已知30Ω1mH100Ω0.1uF解:1001011035LXL100101.0101165CXC相量模型30Ωj100Ω100Ω-j100ΩZ100130100100100)100100(10030jjjjjZ130Ω1mH5.2复阻抗的串联和并联(4){end}IU、若正弦量用相量表示,电路参数用复数阻抗()表示,则直流电路中介绍的基本定律、定理及各种分析方法在正弦交流电路中都能使用。CωCLωLRR1jj、、相量形式的基尔霍夫定律0KCLI0KVLU相量(复数)形式的欧姆定律电阻电路RIU)(jLXIU纯电感电路)j(CXIU纯电容电路一般电路UIZ5.3正弦稳态电路的分析与计算(1)解:.45,3030j,A904321oSIZZZZI求:已知:ΩΩΩ例1.Z2SIZ1ZZ3IsIZZZZZZI2312111109043045130130130451jjjA09.8113.15.3正弦稳态电路的分析与计算(2)例2:已知:,s/rad314,100,F10,mH500,10,100021VUCLRR求:各支路电流。Z1Z2R2+_Li1i2i3R1CuUR2+_R11I2I3ICj1Lj解:画出电路的相量模型3.28920.9232.726.30367.17104990105.3185.3181000)5.318(10001)1(3111jjjCjRCjRZΩ1571022jLjRZAZUI3.52598.031.522.16701001AjICjRCjI0.20182.03.52598.067.1710495.31811112AICjRRI0.70570.03.52598.067.171049100011113Ati)3.52314sin(2598.01Ati)20314sin(2182.02Ati)70314sin(257.03瞬时值表达式Z=Z1+Z2=92.20-j289.3+10+j157=102.20-j132.3=167.252.31oΩ5.3正弦稳态电路的分析与计算(4)解:已知:U=115V,U1=55.4V,U2=80V,R1=32Ω,f=50Hz。求线圈的电阻R2和电感L2。例3R1R2L2+_1UU2U+_+_I32/4.55/11RUIILRRU2221)()(ILRU2222)(324.55)314()32(115222LR324.55)314(80222LR6.192RH133.02L5.3正弦稳态电路的分析与计算