電路課件一七

§13.1拉普拉斯變換的定義第13章拉普拉斯變換一.拉氏變換的定義時(shí)域f(t)稱為原函數(shù)復(fù)頻域F(s)稱為象函數(shù)1.雙邊拉氏變換復(fù)頻率f(t)與F(s)一一對(duì)應(yīng)積分下限從0開(kāi)始，稱為0拉氏變換。積分下限從0+開(kāi)始，稱為0+拉氏變換。f(t)=(t)時(shí)此項(xiàng)02.單邊拉氏變換f(t)t[0,)F(s)稱為f(t)的象函數(shù)，用大寫字母表示，如I(s)、U(s)。f(t)為原函數(shù)用小寫字母表示，如i(t),u(t)。3.拉氏變換存在條件電工中常見(jiàn)信號(hào)為指數(shù)階函數(shù)，指二.扔常用雕函數(shù)婦的拉型氏變購(gòu)換=狹11f1(t)e-tt01f2(t)e-tt0三個(gè)奇函數(shù)毫的拉徹氏變美換式勾相同1f3(t)e-tt0§1禁3確.墳2拉普乘拉斯啞變換蘋的基徹本性慮質(zhì)一.籮線性掛性質(zhì)二.爆時(shí)雁域?qū)藬?shù)性哭質(zhì)三.惱時(shí)域?yàn)E的積殃分性撲質(zhì)四.敢時(shí)域輸平移夏(延肌遲定劍理)f(t)(t)ttf(t-t0)(t-t0)t0f(t)(t-t0)tt0例1：1Ttf(t)TTf(t)例稠2序：例3愉：倦周羊期慘函嶺數(shù)題的泄拉朵氏歐變躲換...tf(t)1T/2T設(shè)f1(t)為第莖一個(gè)然周期顛的函筐數(shù)波形物的特邀殊性...tf(t)1T/2T五量.蹈復(fù)閑頻約域格平群移輝性扇質(zhì)六.復(fù)究頻渾域步導(dǎo)袍數(shù)墊性跪質(zhì)七.所初值投定理鉛和終壇值定洲理初貓值備定斯理若L逼[f(t)掉]悔=F(s)，且f(t)在t=川0處無(wú)舊沖激俊則終猜值鹿定澡理客：f(t)，f(t)的四導(dǎo)籠數(shù)東可裳進(jìn)榜行撿拉唇氏期變謠換例1例2例3e(t)RC+u-+-用初達(dá)值定工理和彩終值俊定理派驗(yàn)證§13祝.3油拉技普拉等斯反幫變換一.衡由象榨函數(shù)鋤求原燙函數(shù)(1除)懇利找用軍公騾式(2)攪經(jīng)數(shù)聯(lián)學(xué)處暢理后廢查拉楊普拉歷斯變挺換表象顧函拋數(shù)征的蒼一惰般裝形偷式姨：二鄉(xiāng)豐.阿將F(s)進(jìn)勿行具部債分滅分搬式儲(chǔ)展叛開(kāi)f(t)=熊L-袖1[F(s)父]ki也可既用分戀解冠定將理求例言1例2用分芹解定別理求世原函定數(shù)例3k1,k2也露是講一傻對(duì)厚共壞軛貿(mào)復(fù)跌根注意支：S1虛部序+例法二扛：用建配方槐法例1例柳2一般幕多重摘根情沙況相裹量耍形拴式KC挎L、燒KV精L元件探復(fù)屯阻勾抗持、側(cè)復(fù)怎導(dǎo)雪納相量形式電路模型§13輩.4復(fù)頻踩域中萬(wàn)的電投路定奴律、罵電路艘元件您與模察型類甘似娛地元許件拌運(yùn)議算堡阻眾抗定、盞運(yùn)拋算晚導(dǎo)帽納運(yùn)論算召形宇式KC孩L、母KV甚L運(yùn)算形式電路模型一.雀電路喚元件里的運(yùn)宿算形將式R：u=R礦i+u-iR+U(s)

-I(s)RL:iL+

uL

-L+

-sLUL(s)IL(s)sL+-UL(s)IL(s)C:

1/sCCuC(0-)IC(s)UC(s)IC(s)1/sCuC(0-)/sUC(s)+uC-iCM:ML1L2i1i2+u1-+u2-L1i1(0-)Mi2(0-)Mi1(0-)L2i2(0-)+U2(s)-+U1(s)-I1(s)I2(s)sL1sL2+-sM+_++__受控柜源：(s)+-U+1(s)-

RI1(s)U2U1(s)+u1-+u2-Ri1u1二酒.納電酒路旦定榆律吉的品運(yùn)運(yùn)算頓形興式+u-iRLC運(yùn)算氣阻抗運(yùn)算恐形式歐菜姆民定您律+U(s)-I(s)RsL1/sC三.基運(yùn)算袋電路內(nèi)模型運(yùn)頸算外電搏路時(shí)孝域爹電棗路1.冠電遮壓、飄電流返用象暑函數(shù)缺形式2珠.什元償件載用翼運(yùn)雕算馳阻繁抗府或勺運(yùn)毯算歌導(dǎo)戴納3廉.束電梅容帽電膠壓褲和等電槍感禮電成流肌初獵始頃值限用吉附伙加袍電浮源煎表圣示RRLLCi1i2E(t)+-RRLsL1/sCI

1(s)E/sI

2(s)+-時(shí)飯域幣電巖路例5Ω2F20Ω10Ω10Ω0.5H50V+-uc+

-iLt=0時(shí)打開(kāi)開(kāi)關(guān)uC(頭0-)美=努2港5餃ViL(0-)=磨5At>0運(yùn)算電路200.5s-++-1/2s25/s2.55IL(s)UC(s)§1秒3織.玻5拉脹普態(tài)拉挑斯飼變踐換蓮法睜分詠析硬電板路步驟做：1給.庸由結(jié)換雄路竭前止電悲路愧計(jì)繼算uC(0-)槽,iL(0-)醬。2頸.畫(huà)運(yùn)寨算電石路模翁型3督.據(jù)應(yīng)淋用晉電滾路銀分填析謠方召法糞求允象陵函姨數(shù)盾。4誰(shuí).控反天變付換蒼求哀原吸函坦數(shù)致。t=殿0時(shí)陸閉博合k茅,求iL，uL。例1：200V30Ω0.1H10Ω-uc+1000μFiL+-uL(2臺(tái))快畫(huà)騎運(yùn)施算同電無(wú)路200/s300.1s0.5101000/s100/sI1(s)I2(s)例1：200V30Ω0.1H10Ω-uc+1000μFiL+-uL200/s300.1s0.5101000/s100/sIL(s)I2(s)(4)自反變塌換求倦原函雖數(shù)求UL(s唇)UL(S)200/s300.1s0.5101000/s100/sI1(s)I2(s)例2求沖得激響叫應(yīng)RC+ucisicR1/sC+Uc(s)Is(s)Ic(s)tuc(V)0tic例3

+-UskR1L1L2R2i1i20.3H0.1H10V2Ω3Ωt=羊0時(shí)打芝開(kāi)開(kāi)怖關(guān)k碰,求電艇流i1,浮i2。10/s20.3s1.530.1sI1(s)ti523.750顯竭然犧：UL1(s)10/s20.3s1.530.1sI1(s)uL1-6.56t-0.375(t)0.375(t)uL2t-2.19ti1523.750小奪結(jié)愉：1謊、掀運(yùn)進(jìn)算盟法確直垃接蔥求診得償全主響托應(yīng)3、同運(yùn)算寇法分怕析動(dòng)狹態(tài)電禍路的過(guò)步驟2鍛、貞用塔0-初緩始券條厘件殘，采跳星變樹(shù)情池況臉自行動(dòng)杰