第十一講元件復(fù)阻抗課件

3.1正弦量及其三要素（最大值）（頻率、周期）(Um)(f、T)1、有效值2、角頻率3、初相位UI(Im)

u

、i一一對應(yīng)正弦量三要素3.1正弦量及其三要素（最大值）（頻率、周期）(14、相位差同頻率正弦量的相位之差

=(t+

u)-(t+

i)=

u－

i等于兩個(gè)正弦量的初相位之差常數(shù)i=ImSin(t+

i)?u=UmSin(t+

u)

=

u-i＞0＜0=0同相位電壓超前電流電壓滯后電流

=±π/2

=±π正交反相4、相位差同頻率正弦量的相位之差=(t+u)-23.2相量法----正弦量用復(fù)數(shù)表示和運(yùn)算的方法相量只是用復(fù)數(shù)表示正弦量的一種表示方法,它是用正弦量的有效值與初相位來表示。u=2ISin(t+

u)√=IejiI?I

i=i=2ISin(t+

i)√一一對應(yīng)U

?U

u=相量圖)

uU·3.2相量法----正弦量用復(fù)數(shù)表示和運(yùn)算的方法33.3單一元件的正弦交流電路i+u–u=Ri

i=2ISin(t+

i)√

=2RISin(t+

i)√

=2USin(t+

u)√U=RI

u

=

i

I?I

i=U

?U

u==RI

i=RI?RRI?+–U

?相量模型相量關(guān)系U

?一、電阻元件的交流電路3.3單一元件的正弦交流電路i+u4+1+j0相量圖I?U

?+1+j0相量圖I?U?5i+u–

L

i=2ISin(t+

i)√u=Ldidt

Cos(t+

i

)√I2=L×=

LISin(t+

i+90°

)√2

=2USin(t+

u)√U=

LI

u

=

i

+90°二、電感元件的交流電路i+u–Li=6

j

LI

i=I?U

u==

LI

i+90°=

L90°I

i

×=j

LI?I?+–U

?相量模型相量關(guān)系U

?+1+j0相量圖

i=2ISin(t+

i)√=

LISin(t+

i+90°)√2uU

?I?U

?電壓超前電流90°jLIi=I?Uu==LIi+90°7感抗，對照U=RI可見：XL單位為Ω變電所，變壓器與輸電線之間加幾匝線圈？----防高頻閃電U=

LI=XLIXL=

Lf高，XL大，UL一定時(shí)，iL小----阻交流f=0，XL=0(相當(dāng)于短路)-------通直流=j

LI?U

?與f及L成正比感抗，對照U=RI可見：XL單位為Ω變電所，變壓器與輸電8

u=2USin(t+

u)√i=Cdudt

Cos(t+

u

)√U2=C×=

CUSin(t+

u+90°

)√2I=

CU

i

=

u

+90°=2ISin(t+

i)√U=I

C1Ci+-u三、電容元件的交流電路u=2USin(t+u)√i=CdudtCo9I

i=I?U

?U

u==

CU

u+90°=

C90°U

u×=j

C+–U

?相量模型相量關(guān)系U

?j

C

u=2USin(t+

u)√I?I?–j

C1+–U

?=

CUSin(t+

u+90°)√2iI?–j

C1U

?I?=+1+j0相量圖I?U

?Ii=I?U?Uu==CUu+90°=C9010容抗，對照U=RI可見：XC單位為Ωf高，XC小，UC一定時(shí)，Ic大----通交流f=0，XC→∞(相當(dāng)于開路)-----隔直流

C1XC=U=I

C1U

?=j

CI?–j

C1U

?I?=I=

CU=XCI與f及C成反比容抗，對照U=RI可見：XC單位為Ωf高，XC小，UC一11i+u–Ru=RiRI?+–U

?=RI?U

?時(shí)域復(fù)數(shù)域U=RI

u

=

i

+1+j0I?U

?i+u–Ru=RiRI?+12時(shí)域復(fù)數(shù)域i+u–

Lu=Ldidt

j

LI?+–U

?=j

LI?U

?=

j

XLI?U=

LI

u

=

i

+90°+1+j0I?U

?時(shí)域復(fù)數(shù)域i+u–Lu13時(shí)域復(fù)數(shù)域i+u–Ci=CdudtI?–j

C1+–U

?–j

C1U

?I?==

－jXCI?

i

=

u

+90°U=I

C1+1+j0I?U

?時(shí)域復(fù)數(shù)域i+u–Ci=CdudtI?–j14下列各式是否正確？iu=XLIU=XL??IU=jLiu=jCIU=–XC??=jCIU??××××××下列各式是否正確？iu=XLIU=XL??IU=jLi15RI?+–U

?=RI?U

?

j

LI?+–U

?=j

LI?U

?=jXLI?I?–j

C1+–U

?–j

C1U

?I?==－jXCI?RI?+–U?=RI?U?16一、RLC串聯(lián)電路3.4復(fù)阻抗和復(fù)導(dǎo)納

LRCU=

?UR

?+–UC

?+–UL

?+–j

L

R–j

C1+–uR+–uC+–uLu=uR+uL+uCUR

?UC

?UL

?++=RI?I?++j

LI?–j

C1I?()=I?–j

C1(R+j

L)–j

C1(R+j

L)令：Z=復(fù)阻抗U

?+–+–ui一、RLC串聯(lián)電路3.4復(fù)阻抗和復(fù)導(dǎo)納17–j

C1(R+j

L)Z==R+jXL–jXC=R+j(XL–XC)=R+jX電阻電抗=Z

Z=√R2+X2

=arctgRX模阻抗角＞0＜0=

0感性電阻性容性–jC1(R+jL)Z==R+18=jXL=–jXC=RI?U

?=j

LI?U

?=jXLI?–j

C1U

?I?==–jXCI?=RI?U

?=ZZI?U

?+–=ZI?U

?復(fù)數(shù)形式的歐姆定律復(fù)阻抗=jXL=–jXC=RI?U?=jLI?U?=jXL19無源網(wǎng)絡(luò)i+–u無源網(wǎng)絡(luò)I?U

?+–

i=2ISin(t+

i)√u

=2USin(t+

u)√I?I

i=U

?U

u=I?U

?=Z無源網(wǎng)絡(luò)i+u無源網(wǎng)絡(luò)I?U?+i=20I?U

?=ZI

iU

uIU–

i

u=R==R+jX=Z

=√R2+X2arctgRX=ZCos=ZSinXZI?U

?+–Z=

u–

iIU

=I?U?=ZIiUuIU–iu=R==R+j21ZI?U

?+–=ZI?U

?

u=0

i=？=Z

Z已知若令：問：

i=0

u=？若令：問：例：2

60°Z=

i=0

i=

u=60°

u=0–60°2

60°Z1=

i=–

u=

ZI?U?+–=ZI?U?u=0i22U=

?UR

?UC

?UL

?++UR

?+–UC

?+–UL

?+–j

L

R–j

C1I?U

?+–I?U

?UR

?UC

?UL

?U2=UR2+(UL–UC)2電壓三角形U=?UR?UC?UL?++UR?+–U23V2V1V0RC10V10VV0V1V2R40V100V

L例：求V0的讀數(shù)I?UC

?UL

?UR

?U

?I?UR

?U

?V2V1V0RC10V10VV0V1V2R40V100V24二、RLC并聯(lián)電路iRiCiLi+–uiLiCiRi=+++–U?I?IC?IL?IR?）））RLC）））RjXL–jXC?IC?IL?IR?I=++=++–jXC1U?jXL1U?R1U?=()U?++–jXC1jXL1R1二、RLC并聯(lián)電路iRiCiLi+uiLiCiRi=+++U25–jXC1jXL1R1=G=j

L1=–j

L1?I==jBC=–jBL=–j

C11=j

CU

?[G+(–jBL)+jBC]=()++–jXC1jXL1R1?IU

?U

?=[G+j(BC–BL)]BLBC感納容納–jXC1jXL1R1=G=jL1=–jL1?I==j26G+j(BC–BL)Y==G+jB令：復(fù)導(dǎo)納=Y

模導(dǎo)納角Y=√G2+B2

=arctgGB＞0＜0=0感性電阻性容性電導(dǎo)電納G+j(BC–BL)Y==G+jB令：復(fù)導(dǎo)納=Y27U?I

?=YYI?U

?+–=YI?U

?復(fù)數(shù)形式的歐姆定律復(fù)導(dǎo)納U

?–jXC1I?=jXL1I?=U

?R1I?=U

?=–jBL=jBC–jXC1jXL1R1U?I?=YYI?U?+–=YI?U?28無源網(wǎng)絡(luò)i+–u無源網(wǎng)絡(luò)I?U

?+–

i=2ISin(t+

i)√u

=2USin(t+

u)√I?I

i=U

?U

u=I?U

?=Y無源網(wǎng)絡(luò)i+u無源網(wǎng)絡(luò)I?U?+i=29+–U?I?IC?IL?IR?）））RjXL–jXC?IC?IL?IR?I=++U

??IC?IL?IR?II2=IR2+(IL–IC)2電流三角形+U?I?IC?IL?IR?）））RjXL–jXC?IC?I30例：求A0的讀數(shù)I?IR

?U

?I?

LRA0A2A110A6ARCA1A0A24A3AIC

?U

?IR

?IL

?例：求A0的讀數(shù)I?IR?U?I?LRA0A31三、復(fù)阻抗串聯(lián)U1?+–+–U?+–Un?+–U2?I?Z1ZnZ2ZeqU?+–I?Un?U2?U1?U=?+++……=Z1+Z2+……+ZnI?I?I?=(Z1+Z2+……+Zn)I?=(Z1+Z2+……+Zn)ZeqUK?U?=ZeqZK三、復(fù)阻抗串聯(lián)U1?+–+32UR

?+–UC

?+–UL

?+–j

L

R–j

C1I?U

?+––j

C1Z=R+j

L=ZR+ZL+ZCUR?+–UC?+UL?+–jL33四、復(fù)阻抗并聯(lián)Z1Z2

ZnY1Y2YnIn?I?I2?I1?I1?I?In?I2?=++……+=++……+YnU?Y2U?Y1U?+

–U?U?=(++……+)Y1Y2Yn=(++……+)Y1Y2YnYeqI?+

–U?YeqZeqIK?I?=YeqYK四、復(fù)阻抗并聯(lián)Z1Z2ZnY1Y2YnIn?I?I2?I134+–U?I?IC?IL?IR?）））RjXL–jXCY=G–j

L1+j

C=YR+YC+YL+U?I?IC?IL?IR?）））RjXL–jXCY=G–35RI?