第3讲：正弦电路B

1、 Lecturer:KangWanXinCollege of Electrial & Information Engineering XiHua University Electric Circuit Analysis电路分析电路分析 Lecturer:KangWanXinCollege of Electrial & Information Engineering XiHua University Electric Circuit Analysis电路分析电路分析 Lecturer:KangWanXinCollege of Electrial & Information

2、 Engineering XiHua University Electric Circuit Analysis电路分析电路分析+UIIUZ ZIUIUIUZiuiu Lecturer:KangWanXinCollege of Electrial & Information Engineering XiHua University Electric Circuit Analysis电路分析电路分析jXRZjZZ sincos2120 CCCLLLRXjXCjZXjXLjZRZ Lecturer:KangWanXinCollege of Electrial & Informatio

3、n Engineering XiHua University Electric Circuit Analysis电路分析电路分析RXiuarctan jeZZjZZjXRZ sincos)2(Im,Re)()(221121221121212121 ZjZZZXZRZZZZZZZZZZXXjRRZZZDCBA Lecturer:KangWanXinCollege of Electrial & Information Engineering XiHua University Electric Circuit Analysis电路分析电路分析. 1j. j. . . . . ICILIRUU

4、UUCLR IXXjRICLjRCL)()1( IjXR)( LCRuuLuCi+- -+- -+- -+- -uR ZjXRCjLjRIUZ1. Ij L. ULU. CU. Cj1R+- -+- -+- -+- -RU. Lecturer:KangWanXinCollege of Electrial & Information Engineering XiHua University Electric Circuit Analysis电路分析电路分析（1）Z=R+j( L- -1/ C)=R+jX=|Z| 为复数，为复数，故称故称复阻抗复阻抗（2 2） L 1/ C ，X0， 0，

5、电路为感性，电压领先电流；电路为感性，电压领先电流； L1/ C， X0， 1/ L ，B0， 0，电路为容性，电流超前电压电路为容性，电流超前电压 C1/ L ，B0， 0，电路为感性，电流落后电压电路为感性，电流落后电压 C=1/ L ，B=0， =0，电路为电阻性，电路为电阻性，电流电压同相电流电压同相（3）相量图：选电压为参考向量，设相量图：选电压为参考向量，设 C 1/ L，0 , u=0 2222)(CLGBGIIIIII UGI. LI. I CI. 分析分析 R、L、C 并联电路得出：并联电路得出：三角形三角形IR 、IB、I 称为电流三角形，称为电流三角形，它和导纳三角形相似

6、。即它和导纳三角形相似。即 Lecturer:KangWanXinCollege of Electrial & Information Engineering XiHua University Electric Circuit Analysis电路分析电路分析 |j |j YBGYZXRZ ZYXRXBXRRG , |1| , 2222BGXRXRXRZYjjj11 22 GRRG1,1 Lecturer:KangWanXinCollege of Electrial & Information Engineering XiHua University Electric Circ

7、uit Analysis电路分析电路分析XRBGBGBGYZZXRZYBGYjjj11 |j ,|j 22 ZYBGBXBGGR , |1| , 2222 Lecturer:KangWanXinCollege of Electrial & Information Engineering XiHua University Electric Circuit Analysis电路分析电路分析 02 .501 .786050jjXRZL 601006. 010 36LXL 0.06mH50 LRLjBGSjZY 0098. 00082. 0 2 .500128. 02 .501 .781100

8、 1220082. 011GRmHBLL102. 00098. 011 Lecturer:KangWanXinCollege of Electrial & Information Engineering XiHua University Electric Circuit Analysis电路分析电路分析ZIZZZIUUUUnn )(2121Z+- -UIUZZUii 分压公式分压公式 nknkkkkjXRZZ11)(Z1+Z2ZnUI Lecturer:KangWanXinCollege of Electrial & Information Engineering XiHua

9、University Electric Circuit Analysis电路分析电路分析 nknkkkkjBGYY11)(分流公式分流公式IYYIii Y1+Y2YnUIY+- -UIYUYYYUIIIInn )(21212121ZZZZZ Lecturer:KangWanXinCollege of Electrial & Information Engineering XiHua University Electric Circuit Analysis电路分析电路分析9 .31j2028. 6 j10)9 .31j20)(28. 6 j10(2121 ZZZZZ例例1 已知已知 Z1

10、=10+j6.28 , Z2=20- -j31.9 , Z3=15+j15.7 6 .359 .3156.18j89.25 86. 2 j89.107 .15j153ab ZZZ 5 .4045.3961.5765.3713.3281.11 86.2j89.10 Lecturer:KangWanXinCollege of Electrial & Information Engineering XiHua University Electric Circuit Analysis电路分析电路分析例例2 2A1A2A0Z1Z2U已知电流表读数：已知电流表读数：A18AA26ACjXZRZ 2

11、1 , 1 ）（若若A0?为何参数为何参数）（21 , 2 ZRZ A0I0max=?为何参数为何参数）（21 , 3 ZjXZL A0I0min=?为何参数为何参数）（21 , 4 ZjXZL 解：解：AI1068 1 220 ）（1)(IU2I0IAIZ1468 2 max02 为电阻，为电阻，）（AIjXZC268 , 3 min02 ）（AIAIIjXZC16 ,8 , 4 2102 ）（A0A1A2? Lecturer:KangWanXinCollege of Electrial & Information Engineering XiHua University Elect

12、ric Circuit Analysis电路分析电路分析例例3 3)(:),5sin(2120 tit u(t)求求已知已知 +_15 u4H0.02Fi解：解：00120 U 2054jjjXL 1002. 051jjjXC相量模型相量模型Uj20 - -j15 1I2I+_15 3IICLCLRjXUjXURUIIII Ajjjjj09 .3610681268101201151120 At i(t)9 .365sin(210 0 Lecturer:KangWanXinCollege of Electrial & Information Engineering XiHua Unive

13、rsity Electric Circuit Analysis电路分析电路分析例例4 4)(:),1510sin(25 06tuti(t)S求求已知已知 +_5 uS0.2 Fi解：解：AI 155 5102 . 010166jjjXCVttuVjUUUSCRS)3010sin(50)(302254525155551556相量模型相量模型+_5 SUI-j5 RUI)(CUSUCU Lecturer:KangWanXinCollege of Electrial & Information Engineering XiHua University Electric Circuit Ana

14、lysis电路分析电路分析例例5 5I1=I2=5A，U50V，U与与I同相位，求同相位，求I、R、XC、XL。00 CCUU设设解：解：5 ,05201jII 0452555 jI)1(2505)55(45500jRjXjUL 252505 LLXX 2102502552505CXRR也可以画相量图计算也可以画相量图计算令等式两边令等式两边实部等于实部实部等于实部，虚部等于虚部虚部等于虚部U- -jXC1I2I+_RI- -jXLUC+- - Lecturer:KangWanXinCollege of Electrial & Information Engineering XiHua

15、 University Electric Circuit Analysis电路分析电路分析例例6 6图示为图示为RC选频网络，试求选频网络，试求u1和和u0同相位的条件及同相位的条件及?01 UU-jXCRRuou1-jXC解：解：设：设：Z1=RjXC, Z2=R/(-jXC)2121ZZZUUo 2122111ZZZZZUUo 实数实数 CCCCCCCCCCRXXRjjRXRXjXRjRXjXRjXRjRXjXRZZ222222122)()(CXR 3211 oUU Lecturer:KangWanXinCollege of Electrial & Information Engi

16、neering XiHua University Electric Circuit Analysis电路分析电路分析 GuiRiuui : 0 :KVL 0 :KCL :或或元件约束关系元件约束关系电阻电路电阻电路 : 0 :KVL 0 :KCL : UYIIZUUI或或元件约束关系元件约束关系正弦电路相量分析正弦电路相量分析 Lecturer:KangWanXinCollege of Electrial & Information Engineering XiHua University Electric Circuit Analysis电路分析电路分析 Lecturer:KangW

17、anXinCollege of Electrial & Information Engineering XiHua University Electric Circuit Analysis电路分析电路分析例例1:R2+_Li1i2i3R1CuZ1Z2UR2+_R11I2I3ICj 1Lj 画出电路的相量模型画出电路的相量模型 13.28911.923 .7245.303 7 .175 .1049901047.31847.3181000)47.318(10001)1(3111jjjCjRCjRZ ,/314,100,10,500,10,100021sradVUFCmHLRR 求求: :各

18、支路电流。各支路电流。已知：已知：解解 Lecturer:KangWanXinCollege of Electrial & Information Engineering XiHua University Electric Circuit Analysis电路分析电路分析 1571022jLjRZ 3 .5299.166 13.13211.102 1571013.28911.92 21jjjZZZAZUI3 .526 . 03 .5299.16601001 AjICjRCjI20181. 03 .526 . 07 .175 .104947.31811112 AICjRRI7057. 0

19、3 .526 . 07 .175 .1049100011113 Z1Z2UR2+_R11I2I3ICj 1Lj Lecturer:KangWanXinCollege of Electrial & Information Engineering XiHua University Electric Circuit Analysis电路分析电路分析例例2. +_susiLR1R2R3R4CSI+_R1R2R3R4Lj cj 1SU1I2I4I3ISUIRILjRILjRR3221121)()( 0)()(33112431IRILjRILjRRR 01)1(42312332ICjIRIRICj

20、RRSII 4 Lecturer:KangWanXinCollege of Electrial & Information Engineering XiHua University Electric Circuit Analysis电路分析电路分析1nU2nU3nUSnUU1011)111(33122321nnnURURURRLjR SnnnIUCjURUCjRR1233431)11( SI+_R1R2R3R4Lj cj 1SU Lecturer:KangWanXinCollege of Electrial & Information Engineering XiHua Uni

21、versity Electric Circuit Analysis电路分析电路分析. 45 , 30 30j , A904 321oSIZZZZI求求：已已知知： 方法一：电源等效变换方法一：电源等效变换 15153030)30(30/31jjjZZ解：解：例例3.Z2SIZ1ZZ3IS31)/(IZZZ2Z1 Z3ZI+- -ZZZZZZII23131/)/(S 45301515)1515(4jjjjoo36.9-5455.657 A o9 .8113. 1 Lecturer:KangWanXinCollege of Electrial & Information Engineeri

22、ng XiHua University Electric Circuit Analysis电路分析电路分析方法二：戴维南等效变换方法二：戴维南等效变换V4586.84 )/(o310 ZZIUSZeqZ0 U I+- -Z2SIZ1Z30U45j15 /231 ZZZZeqA9 .8113. 1 4545154586.84o00 jZZUIZ2Z1Z3Zeq Lecturer:KangWanXinCollege of Electrial & Information Engineering XiHua University Electric Circuit Analysis电路分析电路分

23、析例例4 求图示电路的戴维南等效电路。求图示电路的戴维南等效电路。6030030060300601002000111 jUIIIUoj300 +_0060 0U+_1 4 I1 I50 50 j300 +_0060 0U+_1200I1 I100 _解解045230160 jUo求短路电流：求短路电流：006 . 010060 SCI000452506 . 045230SCeqIUZSCI Lecturer:KangWanXinCollege of Electrial & Information Engineering XiHua University Electric Circuit

24、 Analysis电路分析电路分析例例5 用叠加定理计算电流用叠加定理计算电流2 IZ2SIZ1Z32IS U+- -. 3050 ,3050 A,04 V,45100 :o3o31oS oS ZZZIU已知已知解解:)( )1(SS 短短路路单单独独作作用用 UI323S2 ZZZII oooo30503050305004 A3031. 235030200 oo 32S 2 ZZUI oo222135155. 13031. 2 :)3( IIIKCLA135155. 135045100 oo A9 .1523. 1 o :)( )2(SS 开开路路单单独独作作用用 IU2I2I Lectur

25、er:KangWanXinCollege of Electrial & Information Engineering XiHua University Electric Circuit Analysis电路分析电路分析已知：已知：Z=10+j50 , Z1=400+j1000 。?90o1相相位位差差和和等等于于多多少少时时，问问：SUI11111S)1(IZIZIZIZU 例例6解解: I1 I1 IZZ1+_S U.90 , o11相位差为相位差为实部为零实部为零，关系：关系：和和分析：找出分析：找出eqeqSSZIZUUI )10005050( j10410)1( 11S ZZIU41 010410 ，令令.90 1000j o1S故故电电流流领领先先电电压压 IU Lecturer:KangWanXinCollege of Electrial & Information Engineering XiHua University Electric Circuit Analysis电路分析电路分析I 已知：已知：U=115V , U1=55.4V , U2=80V , R1=32 , f=50Hz 求：求： 线圈的电阻线圈的电阻R2和电感和电感L2 。例例7：