第12章-非正弦周期电流电路和信号的频谱课件.ppt

1、BACKNEXTBACKNEXTBACKNEXT12.1 非正弦周期信号非正弦周期信号例ut方波电压ut锯齿波it脉冲波形BACKNEXTBACKNEXT12.2 周期函数分解为傅里叶级数周期函数分解为傅里叶级数 BACKNEXT )sin()cos()sin()cos()2sin()2cos()sin()cos()(111011121211110tkbtkaatkbtkatbtatbtaatfkkkkk )cos()cos()2cos()cos()(110121121110kkmkkkmmmtkAAtkAtAtAAtf 00aA 22kkkmbaA kkmkAb sin )arctan(kk

2、kab kkmkAa cos BACKNEXT A A0 0)cos()cos()2cos()cos()(110121121110kkmkkkmmmtkAAtkAtAtAAtf A A1m1mcos(cos(1 1t+t+1 1 )BACKNEXT 2200)(1)(1TTTdttfTdttfTa)()cos()(1)()cos()(1)cos()(2)cos()(211201122101 tdtktftdtktfdttktfTdttktfTaTTTk)()sin()(1)()sin()(1)sin()(2)sin()(211201122101 tdtktftdtktfdttktfTdttkt

3、fTbTTTk )sin()cos()sin()cos()2sin()2cos()sin()cos()(111011121211110tkbtkaatkbtkatbtatbtaatfkkkkk BACKNEXT例0Akmk115141312161BACKNEXTf(t)Em-Em021ttT/2TmmEtfEtf )()(TtTTt 220BACKNEXT0)(100 TdttfTa 0)()cos(2)()cos()()cos(1)()cos()(10112110112011 tdtkEtdtkEtdtkEtdtktfammmk )cos(12)cos(12)()sin(2)()sin()(

4、)sin(1)()sin()(1010112110112011 kkEtkkEtdtkEtdtkEtdtkEtdtktfbmmmmmk BACKNEXT )5sin(51)3sin(31)sin(4)(111tttEtfm 0k115131AkmmE434mE54mEBACKNEXTtf f(t t)tf f(t t)tf f(t t)BACKNEXT12.3 有效值、平均值和平均功率有效值、平均值和平均功率 TdtiTI021)cos(110kkkmtkIIi TkkkmdttkIITI01210)cos(1 BACKNEXT200201IdtITT 122023222120kkIIIIII

5、I21202)(cos1kkTkmIdttkIT 0)cos(21100 dttkIITkkmT )0)cos()cos(21110qkdttqtkIITqkqmTkm ，（BACKNEXTdtiTITav 01IItTIdttTIdttITImTmTmTmav898.0637.0)sin(4)cos(4)cos(140400 BACKNEXTBACKNEXT)cos()cos(100100ikkkmukkkmtkIItkUUuip TpdtTP01 kkkIUIUIUIUP coscoscos22211100，2122 kIIUUikukkkmkkmk BACKNEXT12.4 12.4 非

6、正弦电流电路的计算非正弦电流电路的计算 BACKNEXTCkXLkXCkLk111 ，BACKNEXT VtttttuCRs )9cos(71.15)7cos(20.20)5cos(28.28)3cos(13.47)cos(40.14110:,45.91,3111111 输输入入电电源源为为CkjRUIksk1)()(1 RC+-usBACKNEXT0,0,10,0000 PIVUk直直流流分分量量WRIPAAjIVUks02.30539.7208.1045.9301000100,12)1()1()1()1(WRIPAAjIVUks93.1754.4666.715.33033.33033.33

7、,32)3()3()3()3(BACKNEXT,29.1949.3,23.2434.4,21.3258.5)9()7()5(AIAIAI (5)(7)(9)95.5256.5536.60PWPWPW最后按时域形式迭加为：最后按时域形式迭加为：Attttti )29.199cos(249.3)23.247cos(234.4)21.325cos(258.5)4.463cos(266.7)39.72cos(208.1011111 WPPPPP80.6699310 同理求得：同理求得：BACKNEXTLus+-CRusUm021t Vttus )4cos(151)2cos(3121157411 ，用用

8、结结点点电电压压法法有有：次次谐谐波波为为设设负负载载两两端端的的第第)(kUk BACKNEXT)(1)(11111kskUULjkCjkRLjk 1111)()(LjkCjkRkskUU 令令k=0,2,4,并代入数据并代入数据,可分别求得可分别求得:VUVUVU12.05.2100)4()2(0 usCRLBACKNEXTBACKNEXT例：图示电路中，激励例：图示电路中，激励 u1(t)=u11(1)+u12(2)，包含包含 1、2 两个频率分量，且两个频率分量，且 1 2，要求响应要求响应 u2(t)只含只含有有 1 频率电压，如何实现？频率电压，如何实现？+_u1(t)u2(t)可

9、由下列滤波电路实现：可由下列滤波电路实现：CRC2C3L1+_u1(t)+_u2(t)2121CL )(13211CCL 并联谐振，开路并联谐振，开路串联谐振，短路串联谐振，短路BACKNEXTVttuts)2cos(216)cos(21512)(+-us(t)L1L2CRuR(t)+-VUs25161512222 中中不不含含基基波波，即即则则，对对并并联联谐谐振振与与（)1)(tRuCL 11LC HCL1101000116221 BACKNEXTHLCjLjCjLjLj31021221222112 ARUI1200 ARUI1622 WIUIUP400cos22200 BACKNEXT其它形式的滤波电路：其它形式的滤波电路：L2L1C2L3C1C3L2L1C2C1L3C3带通滤波器带通滤波器(band-pass filter)带阻滤波器带阻滤波器(band elimination filter)