1、實(shí)際電容器實(shí)際電容器實(shí)際電容器實(shí)際電容器6-1 6-1 電容元件電容元件+ q- -q Us6-1 6-1 電容元件電容元件Ri0+ q- -q Us1. 1. 線性電容元件的定義及其圖形符號(hào)線性電容元件的定義及其圖形符號(hào) 0, 00, 0ququ Cuq uqC Cuq uqo0),(quf uqC Cuq Riu Cuq tuCtCutqiddd)d(dd3. 線性電容元件的線性電容元件的u-i關(guān)系關(guān)系(VCR)（約束方程）（約束方程）ttuCtid)(d)( Cuq )()( tGutiRRGttuCtid)(d)(i dtdu tuOt0dttiCtdu)(1)()()(0tutudu

2、ttdttiC0)(1 diCtututt 1)()(00ttuCtid)(d)( diCutut01)0()( , 00t令3. 線性電容元件的線性電容元件的u-i關(guān)系關(guān)系(VCR)（約束方程）（約束方程） )()( tCutqtuCidd diCtututt0 1)()(0 diCtututt 1)()(00ttuCtid)(d)()()(tRituui+R)()(tGutiCui diCtututt 1)()(003. 線性電容元件的線性電容元件的u-i關(guān)系關(guān)系(VCR)（約束方程）（約束方程）4.4.電容元件的功率和能量電容元件的功率和能量tuCuuipddttCpdtW0dtdtdu

3、uC tutuuduC0 tutuCu0221 )(21)(21)( 022tCutCutWCttuCtid)(d)(0)(21)(2CtCutW)(21)(21)(022tCutCutWC 1212222121tWtWtCutCuWCCC 01222CWtutu, 01222CWtutu,0)()(0 utu設(shè)設(shè) )()( tCutq 4.4.電容元件的功率和能量電容元件的功率和能量0)(21)(2CtCutW 1212222121tWtWtCutCuWCCCttuCtid)(d)()(21)(2CtCutWCui )(21)(21)( 022tCutCutWC diCtututt 1)()

4、(00i0CuR6 6實(shí)際電容器的電路模型實(shí)際電容器的電路模型Cui+ q- -q UsCRL例題)(tusi電源電壓電源電壓的波形的波形s2 0s21 42s10 20 0)(Stttttttusttttttuti2 0s21A 1s 10A 10 0d)(d5 . 0)(SttuCtid)(d)(21t /s1i/A- -1O21t /s2Ous /Vs2 0s21)W 42(s 10 W 20 0)()()(tttttttitutps21t /s2Op/W- -2注意：分區(qū)間計(jì)算注意：分區(qū)間計(jì)算解解s2 0s21 42s10 20 0)(StttttttusttttttuCti2 0s2

5、1 1s 10 10 0d)(d)(S電容功率電容功率的波形的波形)(tusis2 0s21 )2(s 10 0 0)(25 . 0)(222CtttttttutWs)(21)(2CtCutWs2 0s21 V)42(s10 V 20 0)(Stttttttu0.5F)(tusCi21t /s2Op/W- -221t /s1oWC/Js2 0s21 1s 10 10 0)(ttttti 已知電容的電流已知電容的電流波形，求電容的電壓波形，求電容的電壓u。V 220d15 .01)0()(s 100 tttutu t ：42)22(2d) 1(5 . 01) 1 ()(1ttutut：s21 t

6、：ts2 tutu20d05 .01)2()(：0t0 05 . 01)()(dutut diCtututt0 1)()(021t /s1i/A- -1OCuiF5 . 0s2 0s21 V)42(s 10 V 20 0)(tttttttu6-2 6-2 電感元件電感元件1線性電感元件的定義及其圖形符號(hào)線性電感元件的定義及其圖形符號(hào)iuL )()( tLitLiuL 2 2. .線性電感元件的特性線性電感元件的特性韋安特性韋安特性iLLLioL0),(ifLiLo )()(tLitL 2 2. .線性電感元件的特性線性電感元件的特性韋安特性韋安特性iuLttiLttuL d)(d dd)(3線

7、性電感元件的線性電感元件的u-i關(guān)系關(guān)系（VCR）(約束方程約束方程) )()(tLitLttiLtu d)(d)( iu+ +- -LttuCtid)(d)(CuittiLtu d)(d)(6-2 6-2 電感元件電感元件u dtdi ,tiOiu+ +- -Lt06-2 6-2 電感元件電感元件ttiLtu d)(d)( )()(tLitL 0,0t令令 3線性電感元件的線性電感元件的u-i關(guān)系關(guān)系（VCR）(約束方程約束方程)iu+ +- -L )(1)()(00ttduLtiti )(1)0()(0tduLitittiLtud)(d)(ttiLtu d)(d)(iu+ +- -Liu+

8、 +- -L6-2 6-2 電感元件電感元件 3線性電感元件的線性電感元件的u-i關(guān)系關(guān)系（VCR）(約束方程約束方程) )(1)()(00ttduLtiti )(1)()(00ttduLtiti4. 電感元件的功率和能量電感元件的功率和能量itiLuipddttiLtu d)(d)()(21)(21)(022tLitLitWLttttttLLittiLitptW000) (21dddd)(2iu+ +- -L0)(21)(2tLitWL)()()(21)(21121222tWtWtLitLiWLLL 0,1222LWtiti 0,1222LWtiti)(21)(21)(022tLitLitW

9、L期間內(nèi)期間內(nèi)在在tt 04. 4. 電感元件的功率和能量電感元件的功率和能量iu+ +- -L 5. 5. 電感元件描述的電磁性質(zhì)電感元件描述的電磁性質(zhì)ttiLtu d)(d)()(21)(2tLitWL )(1)()(00ttduLtiti空心線圈空心線圈6. 6. 實(shí)際電感器（線圈）的模型實(shí)際電感器（線圈）的模型鐵心線圈鐵心線圈6. 6. 實(shí)際電感器（線圈）的模型實(shí)際電感器（線圈）的模型 6. 6. 實(shí)際電感器（線圈）的模型實(shí)際電感器（線圈）的模型LRLRCiu- -L)(21)(2CtCutW)(21)(2tLitWLttiLtu d)(d)( diCtututt01)()(0ttuC

10、tid)(d)( )()(tCutq )()(tLitL )(1)()(00ttduLtiti diCtututtkkk 001)()(一、電容元件的串聯(lián)一、電容元件的串聯(lián)ttnnidCCCtututu0)111()()()(2100201)()()()(21tutututunttnnttttidCtuidCtuidCtu0001)(1)(1)(0202101tteqdiCtutu0)(1)()(0u1uC2C1u2+- - -i- -+unCn- -nkkeqCC111)()()()(002010tutututunnkkeqCCCCC1111121iu+-CeqtteqdiCtutu0)(1

11、)()(0)()()()( :KVL21tutututunu1uC2C1u2+- - -i- -+unCn- -)()()()(002010tutututun 2121CCCCCeq21111CCCeq一、電容元件的串聯(lián)一、電容元件的串聯(lián))()()( :02010tututu等效電容的初始電壓等效電容的初始電壓u1uC2C1u2+- - -i- -iu+-CeqtiCtud)(1)(11tiCtud)(1)(22uCCCuCCueq21211uCCCuCCueq21122 2121CCCCCeq diCtututtkkk0 1)()(0 diCututkkk 1)()(teqituCd)()(

12、 diCtutkk 1)(tteqidCtutu01)()(0u1uC2C1u2+- - -i- -teqdiCtu)(1)(niiii21ttuCtikkd)(d)(i2i1u+ +- -C1C2iinCndtduCdtduCdtduCn21dtduCdtduCCCeqn)(21 21neqCCCC)()()()(002010tutututundttduCtieq)()(iu+-Ceqi2i1u+ +- -C1C2i)()(2111tiCCCti)()(2122tiCCCti21 CCCeq二、電容元件的并聯(lián)二、電容元件的并聯(lián)21)()(d)(dCCtiCtittueqdttduCtieq)

13、()(ttuCtid)(d)(22ttuCtid)(d)(11neqLLLL21 iu+ +- -LeqdtdiLdtdiLdtdiLn21 )()()()( 002010titititinttiLtukk d)(d)(u1uL2L1u2+ + + +- - -Lnun+ +- - -nuuuu21dtdiLdtdiLLLeq)(n21dttdiLtueq)()( ttiLtud)(d)(11ttiLtud)(d)(2221 LLLequLLLu2111uLLLu2122dttdiLtueq)()( dttdiLtueq)()( u1uL2L1u2+ + + +- - -i- -ttnnttttudLtiudLtiudLti0001)(1)(1)(0202101)()()()(21titititinduLtitittkkk0)(1)()(0ttnnudLLLtititi0)111()()()(2100201duLtititteq0)(1)()(0u+ +L1L2i2i1LninikkeqLL11)()()()(002010titititinttequdLti01)(0neqLLLL111121)()()()(002010titititiniu+ +- -LeqduLtititteq0)(1)()(0 )(