1、實際電容器實際電容器實際電容器實際電容器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線性電容元件的定義及其圖形符號 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關系關系(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關系關系(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關系關系(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設設 )()( 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實際電容器的電路模型實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：分區間計算注意：分區間計算解解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線性電感元件的定義及其圖形符號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關系關系（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關系關系（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關系關系（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期間內期間內在在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電感元件描述的電磁性質ttiLtu d)(d)()(21)(2tLitWL )(1)()(00ttduLtiti空心線圈空心線圈6. 6. 實際電感器（線圈）的模型實際電感器（線圈）的模型鐵心線圈鐵心線圈6. 6. 實際電感器（線圈）的模型實際電感器（線圈）的模型 6. 6. 實際電感器（線圈）的模型實際電感器（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、電容元件的串聯一、電容元件的串聯ttnnidCCCtututu0)111()()()(2100201)()()()(21tutututunttnnttttidCtuidCtuidCtu0001)(1)(1)(0202101tteqdiCtutu0)(1)()(0u1uC2C1u2+- - -i- -+unCn- -nkkeqCC111)()()()(002010tutututunnkkeqCCCCC1111121iu+-CeqtteqdiCtutu0)(1

11、)()(0)()()()( :KVL21tutututunu1uC2C1u2+- - -i- -+unCn- -)()()()(002010tutututun 2121CCCCCeq21111CCCeq一、電容元件的串聯一、電容元件的串聯)()()( :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、電容元件的并聯二、電容元件的并聯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 )(