电路原理第十二章

1、12.1 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12.2 周期函数分解为傅里叶级数周期函数分解为傅里叶级数 )sin()cos()sin()cos()2sin()2cos()sin()cos()(111011121211110tkbtkaatkbtkatbtatbtaatfkkkkk )cos()cos()2cos()cos()(110121121110kkmkkkmmmtkAAtkAtAtAAtf 00aA 22kkkmbaA kkmkAb sin )arctan(kkkab kkmkAa cos A A0 0 )cos()cos()2cos()cos()(1101

2、21121110kkmkkkmmmtkAAtkAtAtAAtf A A1m1mcos(cos(1 1t +t +1 1 ) ) 2200)(1)(1TTTdttfTdttfTa)()cos()(1)()cos()(1)cos()(2)cos()(211201122101 tdtktftdtktfdttktfTdttktfTaTTTk)()sin()(1)()sin()(1)sin()(2)sin()(211201122101 tdtktftdtktfdttktfTdttktfTbTTTk )sin()cos()sin()cos()2sin()2cos()sin()cos()(111011121

3、211110tkbtkaatkbtkatbtatbtaatfkkkkk 例0Akmk115141312161f(t)Em-Em021ttT/2TmmEtfEtf )()(TtTTt 2200)(100 TdttfTa 0)()cos(2)()cos()()cos(1)()cos()(10112110112011 tdtkEtdtkEtdtkEtdtktfammmk )cos(12)cos(12)()sin(2)()sin()()sin(1)()sin()(1010112110112011 kkEtkkEtdtkEtdtkEtdtkEtdtktfbmmmmmk )5sin(51)3sin(31)

4、sin(4)(111tttEtfm 0k115131AkmmE434mE54mEtf f( (t t) )tf f( (t t) )tf f( (t t) )12.3 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 200201IdtITT 122023222120kkIIIIIII21202)(cos1kkTkmIdttkIT 0)cos(21100 dttkIITkkmT )0)cos()cos(21110qkdttqtkIITqkqmTkm ，（ dtiTITav 01IItTIdt

5、tTIdttITImTmTmTmav898. 0637. 0)sin(4)cos(4)cos(140400 )cos()cos(100100ikkkmukkkmtkIItkUUuip TpdtTP01 kkkIUIUIUIUP coscoscos22211100，2122 kIIUUikukkkmkkmk 12.4 12.4 非正弦电流电路的计算非正弦电流电路的计算 CkXLkXCkLk111 ， 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CkjR

6、UIksk1)()(1 RC+-us0,0,10,0000 PIVUk直直流流分分量量WRIPAAjIVUks02.30539.7208.1045.9301000100,12)1()1()1()1( WRIPAAjIVUks93.1754.4666.715.33033.33033.33,32)3()3()3()3( ,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.

7、 4)21.325cos(258. 5)4 .463cos(266. 7)39.72cos(208.1011111 WPPPPP80.6699310 同理求得：同理求得：Lus+-CRusUm021t Vttus )4cos(151)2cos(3121157411 ，用用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 )(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 usCRL例：图示电路中，激

8、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Vttuts)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 HLCjLjCjLjLj31021221222112 ARUI1200 ARUI16