电工技能培训专题-电路-正弦稳态电路分析

JiangSuUniversityOfScienceandTechnology.ZhangjiagangCampus.CircuitCourseLecturedByXuebinJiang/InformationSchoolThursday,April08,20211第九章正弦稳态电路的分析9.1阻抗和导纳9.2电路的相量图9.3正弦稳态电路的分析9.4正弦稳态电路的功率9.5复功率9.6最大功率传输JiangSuUniversityOfScienceandTechnology.ZhangjiagangCampus.CircuitCourseLecturedByXuebinJiang/InformationSchoolThursday,April08,20212基本要求熟练掌握阻抗和导纳的物理意义并了解它们之间等效变换的概念；熟练地运用相量法分析正弦电流电路；掌握正弦电流电路中的平均功率，无功功率、视在功率及功率因数的概念；掌握最大功率传输条件。直流电路的分析+相量法基础→正弦稳态电路的分析方法，在第10、11、12章节中都要用到。本章与其它章节的联系JiangSuUniversityOfScienceandTechnology.ZhangjiagangCampus.CircuitCourseLecturedByXuebinJiang/InformationSchoolThursday,April08,202131.阻抗Z(1)定义jz就是该阻抗两端的电压与通过该阻抗电流的相位差j！.I含线性无源元件的一端口N0+-.U设：.U=Ufu.I=Ifi则：Zdef.U.I=UIfu-fi=|Z|jz|Z|=UI为阻抗的模，也可以简称为阻抗。jz=fu-fi为阻抗角。阻抗的单位与电阻相同。9.1阻抗和导纳JiangSuUniversityOfScienceandTechnology.ZhangjiagangCampus.CircuitCourseLecturedByXuebinJiang/InformationSchoolThursday,April08,20214R2+X2(2)阻抗参数间的关系指数式：Z=|Z|ejjz代数式：Z=|Z|cosjz+j|Z|sinjzZ=|Z|jzZ=R+jX实部R称为电阻，虚部X称为电抗。Z+-.U.IN0R=|Z|cosjzX=|Z|sinjzjzRX|Z|、R、X构成的直角三角形称为阻抗三角形。极坐标式：|Z|=jz=arctgRX9.1阻抗和导纳JiangSuUniversityOfScienceandTechnology.ZhangjiagangCampus.CircuitCourseLecturedByXuebinJiang/InformationSchoolThursday,April08,20215(3)单个元件的阻抗R+-.U.IN0LN0+-.U.ICN0+-.U.I说明Z可以是纯实数，也可以是纯虚数。Z=.U.I=RZ=.U.I=jwL=jXL纯电阻纯电感XL=ωL称感性电抗，XL∝f！纯电容Z=.U.I=jwC1=wC1-j=jXCXC=-wC1称容性电抗，XC∝(1/f)！9.1阻抗和导纳JiangSuUniversityOfScienceandTechnology.ZhangjiagangCampus.CircuitCourseLecturedByXuebinJiang/InformationSchoolThursday,April08,20216(4)RLC串联电路根据KVL和VCR的相量形式可得：.U=wL-wC1+-+-RjwL+-.UR.UL.UCjwC1+-.U.IN0=R.I+jwL.I-jwC1.I=R+jwL-wC1.Ij=[R+j(XL+XC)].I.I=(R+jX)=Z.IZ=.I.U=R+jX=|Z|jzX=XL+XCjz=arctgRX9.1阻抗和导纳JiangSuUniversityOfScienceandTechnology.ZhangjiagangCampus.CircuitCourseLecturedByXuebinJiang/InformationSchoolThursday,April08,20217①当wL＞结论：表现为电压超前电流，Z呈感性，称电路为感性电路。wC1时，有X＞0，jz＞0以电流为参考相量相量图.I.UR.UC.UL.Ujz9.1阻抗和导纳JiangSuUniversityOfScienceandTechnology.ZhangjiagangCampus.CircuitCourseLecturedByXuebinJiang/InformationSchoolThursday,April08,20218②当wL＜表现为电压滞后电流，Z呈容性，称电路为容性电路。wC1时，有X＜0，jz＜0。.I.UR.UC.ULjz结论：以电流为参考相量相量图9.1阻抗和导纳JiangSuUniversityOfScienceandTechnology.ZhangjiagangCampus.CircuitCourseLecturedByXuebinJiang/InformationSchoolThursday,April08,20219③当wL=表现为电压与电流同相位，电路发生了串联谐振，Z呈纯电阻性。wC1时，有X=0，jz=0。.I.UR.UC.UL.U=从相量图可以看出，正弦交流RLC串联电路中，会出现分电压大于总电压的现象。以电流为参考相量相量图结论：9.1阻抗和导纳JiangSuUniversityOfScienceandTechnology.ZhangjiagangCampus.CircuitCourseLecturedByXuebinJiang/InformationSchoolThursday,April08,202110④当R=0，X0时，Z为纯电感性；RLC串联电路的电压UR、UX、U构成电压三角形。满足：U=UR+UX22.I.UR.Ujz.UX|Z|XR⑤当R=0，X0时，Z为纯电容性。结论：9.1阻抗和导纳JiangSuUniversityOfScienceandTechnology.ZhangjiagangCampus.CircuitCourseLecturedByXuebinJiang/InformationSchoolThursday,April08,2021112.导纳Y(1)阻抗Z的倒数定义为导纳Y，即：Y=1Z.I=|Y|jY[单位是S]Y=fi-fu.U=IU也可以简称为导纳。jY=fi-fu称为导纳角。|Y|=导纳的代数形式为：Y=G+jB实部G称为电导，虚部B称为电纳。称为导纳模，IU9.1阻抗和导纳JiangSuUniversityOfScienceandTechnology.ZhangjiagangCampus.CircuitCourseLecturedByXuebinJiang/InformationSchoolThursday,April08,2021129.1阻抗和导纳G、B、|Y|、jY之间的关系为G=|Y|cosjYB=|Y|sinjY|Y|=G2+B2jY=arctgGBjYGB导纳三角形(2)单个R、L、C元件的导纳当无源网络内为单个元件时，等效导纳分别为：Y+-.U.IN0JiangSuUniversityOfScienceandTechnology.ZhangjiagangCampus.CircuitCourseLecturedByXuebinJiang/InformationSchoolThursday,April08,202113称为感性电纳；Y=.U.I纯电阻=R1=G纯电感Y=.U.I=jwL1=jBLBL=—wL1纯电容Y=.U.I=jwC=jBCBC=wC称为容性电纳；Y可以是纯实数，也可以是纯虚数。称为电导；9.1阻抗和导纳Y+-.U.IN0JiangSuUniversityOfScienceandTechnology.ZhangjiagangCampus.CircuitCourseLecturedByXuebinJiang/InformationSchoolThursday,April08,202114(3)RLC并联电路.I3jwLjwC1.I2.I1R.U+-.I根据VCR和KCL的相量形式可得：.I=G.U.UjwL1++jwC.U.U.U=Y.U=wL1+jwC.U=[G+j(BL+BC)]=(G+jB)G-j9.1阻抗和导纳=-wL1B=BL+BC+wCjY=arctgGBJiangSuUniversityOfScienceandTechnology.ZhangjiagangCampus.CircuitCourseLecturedByXuebinJiang/InformationSchoolThursday,April08,202115结论：对于RLC并联电路①B＜0或jY＜0，称Y为感性；②B＞0或jY＞0，称Y为容性；③B=0或jY=0，Y为纯电阻性；④G=0，B＜0，Y为纯电感性；⑤G=0，B＞0，Y为纯电容性。以电压为参考相量相量图.U.I1.I2.I3.IjY.I3+.I2电流三角形9.1阻抗和导纳JiangSuUniversityOfScienceandTechnology.ZhangjiagangCampus.CircuitCourseLecturedByXuebinJiang/InformationSchoolThursday,April08,202116.U.I1.I2.I3.I=从相量图可以看出，正弦交流RLC并联电路中，会出现分电流大于总电流的现象。③B=0、jY=0，时的相量图9.1阻抗和导纳JiangSuUniversityOfScienceandTechnology.ZhangjiagangCampus.CircuitCourseLecturedByXuebinJiang/InformationSchoolThursday,April08,2021173.阻抗与导纳的相互等效一端口的阻抗和导纳可以互换，等效互换的条件为：.I含线性无源元件的一端口N0+-.UN0的等效阻抗(导纳)、输入阻抗(导纳)或驱动点阻抗(导纳)，它们的实部和虚部都是外施正弦激励的角频率ω的函数：Z(jw)=R(w)+jX(w)Y(jw)=G(w)+jB(w)Z(jw)Y(jw)=1分开写|Z||Y|=1jZ+jY=09.1阻抗和导纳JiangSuUniversityOfScienceandTechnology.ZhangjiagangCampus.CircuitCourseLecturedByXuebinJiang/InformationSchoolThursday,April08,202118若已知Z=R+jX，求等效的Y=G+jB。若已知Y=G+jB则：.IR+-.UjXjB.I+-.UGY=Z1=R+jX1=(R+jX)(R-jX)(R-jX)=R2+X2R+jR2+X2-X=G+jBG=|Z|2RB=-|Z|2X则：R=|Y|2GX=-|Y|2B等效成Z=R+jX9.1阻抗和导纳JiangSuUniversityOfScienceandTechnology.ZhangjiagangCampus.CircuitCourseLecturedByXuebinJiang/InformationSchoolThursday,April08,202119例：电路如图，求各支路电流和解：设串联支路阻抗为Z1.U10。Z1并联支路导纳为Y10Y10=+jwC=10-3+j3.14×10-3=3.2954×10-372.33oS+-R1.I.U10jwC1+-.UsR2jwL01.I2.I110W0.5H10m1k100Vw=314rad/s则Z1=10+j157ΩR21Z10=Y101