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Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2019-2019AsposePtyLtd.第14章线性动态电路的复频域分析14.1拉普拉斯变换的定义14.2拉普拉斯变换的基本性质14.3拉普拉斯反变换的部分分式展开14.4运算电路14.5用拉普拉斯变换法分析线性电路首页本章重点QQ:906168402iworldi.taobaoEvaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2019-2019AsposePtyLtd.重点(1)拉普拉斯变换的基本原理和性质(2)掌握用拉普拉斯变换分析线性电路的方法和步骤(3)网络函数的概念(4)网络函数的极点和零点返回Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2019-2019AsposePtyLtd.拉氏变换法是一种数学积分变换,其核心是把时间函数f(t)与复变函数F(s)联系起来,把时域问题通过数学变换为复频域问题,把时域的高阶微分方程变换为频域的代数方程以便求解。应用拉氏变换进行电路分析称为电路的复频域分析法,又称运算法。14.1拉普拉斯变换的定义1.拉氏变换法下页上页返回Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2019-2019AsposePtyLtd.例一些常用的变换①对数变换ABBAABBAlglglg乘法运算变换为加法运算②相量法IIIiii2121相量正弦量时域的正弦运算变换为复数运算拉氏变换F(s)(频域象函数)对应f(t)(时域原函数)下页上页返回Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2019-2019AsposePtyLtd.)s(L)()(L)s(FtftfF-1,简写js2.拉氏变换的定义定义[0,∞)区间函数f(t)的拉普拉斯变换式:d)(πj21)(d)()(0sesFtftetfsFstjcjcst正变换反变换s复频率下页上页返回Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2019-2019AsposePtyLtd.000积分下限从0开始,称为0拉氏变换。积分下限从0+开始,称为0+拉氏变换。①积分域注意今后讨论的均为0拉氏变换。tetftetftetfsFstststd)(d)(d)()(0000[0,0+]区间f(t)=(t)时此项0②象函数F(s)存在的条件:tetfstd)(0下页上页返回Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2019-2019AsposePtyLtd.如果存在有限常数M和c使函数f(t)满足:),0[)(tMetfcttMetetftctdd)(0)s(s0csM则f(t)的拉氏变换式F(s)总存在,因为总可以找到一个合适的s值使上式积分为有限值。下页上页③象函数F(s)用大写字母表示,如I(s),U(s)原函数f(t)用小写字母表示,如i(t),u(t)返回Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2019-2019AsposePtyLtd.3.典型函数的拉氏变换(1)单位阶跃函数的象函数d)()(0tetfsFst)()(ttftettsFstd)()]([L)(001stess10dtest下页上页返回Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2019-2019AsposePtyLtd.(3)指数函数的象函数01)(taseasas1(2)单位冲激函数的象函数00d)(tetst)()(ttftettsFstd)()]([L)(010seatetf)(teeesFstatatdL)(0下页上页返回Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2019-2019AsposePtyLtd.14.2拉普拉斯变换的基本性质1.线性性质tetfAtfAstd)()(02211tetfAtetfAststd)(d)(022011)()(2211sFAsFA)()(2211sFAsFA)(])(L[,)(])(L[2211sFtfsFtf若)(L)(L)()(L22112211tfAtfAtfAtfA则)()(L2211tfAtfA下页上页证返回Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2019-2019AsposePtyLtd.的象函数求)1()(:ateKtfj1j1j21ss22s例1解asKsK-atKeKsFL]L[)(-例2的象函数求)sin()(:ttf解)(sinL)(ωtsF)(j21Ltjtjee根据拉氏变换的线性性质,求函数与常数相乘及几个函数相加减的象函数时,可以先求各函数的象函数再进行相乘及加减计算。下页上页结论)(assKa返回Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2019-2019AsposePtyLtd.2.微分性质0)d)((0)(tsetftfestst)()0(ssFf)0()(sd)(dLfsFttf则:)()(LsFtf若:00)(ddd)(dtfetettfststttfd)(dL下页上页证uvuvvudd利用若足够大0返回Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2019-2019AsposePtyLtd.0122ss22ss的象函数)(cos)(1)(ttf例解)(sin(dd1L][cosLttt)(cosd)dsin(ttt下页上页利用导数性质求下列函数的象函数tttd)d(sin1)(cos返回Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2019-2019AsposePtyLtd.推广:)0()0()('2fsfsFs的象函数)()(2)(tδtf解tttd)(d)(s1)]([Lt]d)(d[Lnnttf)0()0()(11nnnffssFs]d)(d[L22ttf)0()]0()(['ffssFs101ss]d)(d[L)(Lttt下页上页返回Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2019-2019AsposePtyLtd.下页上页3.积分性质)s()]([LFtf若:)s(s1]d)([L0Fft则:证)s(]d)([L0tttf令tttfttf0d)(ddL)]([L应用微分性质00d)()(s)(ttttfssFs)s()s(F0返回Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2019-2019AsposePtyLtd.的象函数和求)()t()()(:2ttftttf下页上页]d2[L0ttt例)(Ltt2111sss]d)([L0tt)]([L2tt32s解返回Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2019-2019AsposePtyLtd.4.延迟性质tettfsttd)(00)(0sFest)()]([LsFtf若:)()]()([L000sFettttfst则:tettttfttttfstd)()()()(L00000d)(0)(0tsef0tt令延迟因子0ste下页上页证d)(00sstefe返回Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2019-2019AsposePtyLtd.例1)()()(TtttfTeFss1s1)s()]()([)(Tttttf)()()()()(TtTTtTttttfTTeTeFss22ss1s1)s(例2求矩形脉冲的象函数解根据延迟性质求三角波的象函数解下页上页TTf(t)o1Ttf(t)o返回Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2019-2019AsposePtyLtd.求周期函数的拉氏变换设f1(t)为一个周期的函数)2()2()()()()(111TtTtfTtTtftftf])[(321sTsTsTeeesF)(111sFesT例3解)()]([L11sFtf)()()()]([L1211sFesFesFtfsTsT下页上页...tf(t)1T/2To返回Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2019-2019AsposePtyLtd.)s1s1()s(2/s1TeF)2()()(1Ttttf)11(12/sTes)(11)]([L1sFetfsT)11(112/sTsTesse)]([Ltf下页上页对于本题脉冲序列5.拉普拉斯的卷积定理)()]([L)()]([L2211sFtfsFtf
本文标题:邱关源第五版全部课件14-PPT课件
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