电路课件一七

§13.1拉普拉斯变换的定义第13章拉普拉斯变换一.拉氏变换的定义时域f(t)称为原函数复频域F(s)称为象函数1.双边拉氏变换复频率f(t)与F(s)一一对应积巴分睁下撒限帝从披0

开定始贸，剥称平为该0

拉它氏屿变鸡换棵。积鄙分汇下福限侄从葱0+开筹始难，循称枯为馒0+拉鸭氏么变键换投。f(t)招=

(t)时垄此滋项理

安02广.核单铺边秤拉骗氏飞变掀换f(t)t

泊[晋0忍,守

敲)F(稿s稠)称药为f(t)的拴象觉函原数纤，叙用茫大论写支字绣母劲表幻玉示区，甜如I(缸s棵)度、U(迟s迟)锦。f(t)为葱原瞎函题数莫用议小倍写损字肢母举表扣示崖，糖如i(t)鬼,u(t)童。3扑.咳拉糖氏贱变话换忧存突在颗条丝式件电预工只中箱常聋见梦信赵号躲为界指拜数诱阶桥函藏数栋，慰指二巧.定常浮用梨函漠数觉的线拉肚氏勿变扇换=昏11f1(t)e-tt01f2(t)e-tt0三曾个定函任数给的晴拉姻氏祸变廊换抓式尝相年同1f3(t)e-tt0§1林3嫁.铸2拉饼普具拉贼斯固变破换泥的旋基公本找性炎质一车.芬线屈性国性烛质二辨.训时毙域首导雾数著性垫质三达.离时蹦域甲的箩积利分怒性河质四吸.较时闷域谜平垂移深(附延松迟模定歪理简)f(t)(t)ttf(t-t0)(t-t0)t0f(t)(t-t0)tt0例1卵：1Ttf(t)TTf(t)例基2边：例3叛：那周详期庸函载数狠的驴拉烂氏种变轧换...tf(t)1T/2T设f1(t)为祸第反一触个私周勒期戴的比函歉数波钓形揭的野特活殊剃性...tf(t)1T/2T五广.若复田频算域植平援移认性门质六煌.复灿频遍域嗽导绩数昨性路质七米.抱初矮值桌定文理捧和邻终徐值爹定案理初遵值他定穷理若L世[f(t)虽]旷=F(s)诸，且f(t)在t=触0处潜无呈冲份激嚷则终勉值艘定枝理悔：f(t)磨，f

(t)的治导劳数狭可营进邻行荣拉扔氏剃变忧换例餐1例快2例3e(t)RC+u-+-用纤初沈值搁定垒理拴和钳终伸值锣定跑理胸验榜证§1熔3灾.宇3湿拉纸普院拉茧斯堆反例变兵换一煮.志由挎象蚀函伍数纺求乓原娃函傲数(1胁)油利晓用水公窑式(2辛)榆经找数挺学补处驼理符后淡查忽拉菜普婚拉怎斯锡变票换同表象端函辆数赢的剥一戚般桶形拥式绒：二副.扭将F(s)进巷行饰部佳分晋分格式工展趴开f(t)舱=罚L-让1[F(s)说]ki也催可即用分权解冒定眠理求例袜1例即2用矮分忌解幕定批理凯求絮原充函援数例台3k1,k2也肃是诞一赌对字共爬轭锋复轧根注戒意返：S欠1虚希部竹+例法括二目：刚用桑配加方趣法例偷1例糠2一星般育多惜重接根航情拆况相珍量僵形米式K缘瑞C间L确、股K子V伤L元匪件

置复存阻芦抗板、正复赏导文纳相量形式电路模型§1绝3悼.4复拍频崇域弦中狂的铸电腿路屈定原律坏、判电律路腔元捕件棉与俩模氧型类额似宣地元谊件

惰运鲁算浩阻跳抗搭、烧运叼算夕导捎纳运筒算馆形旱式K产C浊L锅、辞K竿V或L运算形式电路模型一歼.蓝电岔路冷元范件导的婆运非算倡形锡式R：u鸭=R禾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+_++__受吸控菌源拳：(s)+-U+1(s)-

RI1(s)U2U1(s)+u1-+u2-Ri1

u1二室.斯电杏路碧定考律天的轿运各算勒形圣式+u-iRLC运蒸算咳阻嫂抗运揭算姑形斜式欧签姆滑定抹律+U(s)-I(s)RsL1/sC三闭.改运廉算部电腊路蓄模狮型运权算菜电棉路时税域骑电欣路1兴.壮电翠压裂、塔电蔬流什用卸象败函脚数程形篇式2游.粗元弹件肝用克运车算折阻搂抗饭或之运缠算敬导勇纳3陪.早电歇容剑电份压标和发电面感衰电钓流赖初春始气值炮用命附扫加克电唤源颜表度示RRLLCi1i2E(t)+-RRLsL1/sCI

1(s)E/sI

2(s)+-时基域筑电闭路例5Ω2F20Ω10Ω10Ω0.5H50V+-uc+

-iLt=0时打开开关uC(可0-)直=阻2础5脖ViL(劳0-)刮=月5办At>0运算电路200.5s-++-1/2s25/s2.55IL(s)UC(s)§1隐3尿.蜂5拉仍普傍拉丙斯膊变南换矛法竭分盼析垦电诱路步拆骤弱：1樱.污由晋换罚路充前抚电新路础计探算uC(直0-)结,iL(锅0-)朝。2地.画恋运娃算矩电薄路者模拨型3篮.或应莫用壮电肥路贞分然析战方话法猾求惹象锡函健数竞。4遇.豪反兴变哑换竭求甲原属函专数忘。t=洪0时刻闭莫合k卖,求iL，uL。例1：200V30Ω0.1H10Ω-uc+1000μFiL+-uL(2途)鞠画读运捏算研电亦路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辩)版反辟变搅换物求撕原雪函话数求UL(舞s祸)UL(S)200/s300.1s0.5101000/s100/sI1(s)I2(s)例2求纪冲捆激喷响悉应RC+uc

isicR1/sC+Uc(s)

Is(s)Ic(s)tuc(V)0tic例3

+-UskR1L1L2R2i1i20.3H0.1H10V2Ω3Ωt=回0时棉打虽开课开出关k把,求共电谎流i1,劣i2。10/s20.3s1.530.1sI1(s)ti523.750显凝然馅：UL1(s)10/s20.3s1.530.1sI1(s)uL1-6.56t-0.375(t)0.375(t)uL2t-2.19ti1523.750小太结富：1零、肥运酿算妙法筋直愉接加求湾得伙全歪响步应3烧、识运椒算恐法将分巧析素动抱态想电才路齐的槐步命骤2绵、谨用俭0-初露始薄条斯件存，益跳炮变工情翻况需自逮动农包蜘