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第九章 正弦稳态电路的分析 PowerPoint PPT Presentation


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第九章 正弦稳态电路的分析. 内容:.  阻抗和导纳及其串、并联.  电路的相量图.  正弦稳态电路的分析.  正弦稳态电路的功率(包括复功率).  串联和并联谐振电路. +. 无源 线性. +. Z. -. -. |Z|. X. j. R. 阻抗三角形. 9. 1 阻抗和导纳. 1. 阻抗和导纳. 正弦激励下,稳定状态时,端口电压和电流同频率. 电阻. 电抗. 阻抗模. 单位: . 阻抗角. |Y|. 感纳 B L =. B. j . G. 导纳三角形. 容抗 X C =. 导纳模. 导纳角.

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第九章 正弦稳态电路的分析

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3891696


3891696

+

+

Z

-

-

|Z|

X

j

R

9. 1

1.


3891696

|Y|

BL=

B

j

G

XC=

Y

S

:

2. RLC

1R

2L

3C

BC

XL


3891696

j L

R

+

-

+

+

-

-

9. 2

1.

KVL


3891696

RLC

Z=R+j(wL-1/wC)=|Z|j

1wL=1/w C X=0 j =0

2wL > 1/w CX>0 j >0

3wL<1/w C X<0 j <0


3891696

+

R

j L

-

2.

KCL


3891696

RLC

Y=G+j(wC-1/wL)=|Y|j

1wC=1/w L B=0 j =0

2wC > 1/w LB>0 j >0

3wC<1/w L B<0 j <0


3891696

a

Z3

Z2

Z1

b

Z1=10+j6.28, Z2=20-j31.9 , Z3=15+j15.7

Zab


3891696

9. 3


3891696

i

R

L

j L

R

+

uL

-

+

+

-

+

+

+

u

uC

C

-

-

-

-

.

R=15, L=0.3mH, C=0.2F,

i, uR , uL , uC .


3891696

-3.4

UL=8.42>U=5


3891696

+

R

j L

-

'

(wC < 1/w L<0 )

RLC


3891696

9. 4


3891696

1: :

:

i2

R1

R1

i1

i3

C

R2

+

R2

+

u

_

Z2

L

Z1

_


3891696

R1

R2

+

Z2

Z1

_


3891696


3891696

_

_

+

+

R2

R2

R1

C

R1

L

R3

R3

R4

R4

2.

:


3891696

_

+

R2

R1

R3

R4

:


3891696

Z2

Z1

Z

Z3

Z2

Z1Z3

+

Z

-

3.


3891696

Z2

Z0

Z1

Z3

+

Z

-


3891696

Z1

Z2

Z3

Z1

Z2

+

Z3

-

4.


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Z1

Z2

+

Z3

-


3891696

Z1

Z2

|Z1||Z3|= |Z2||Zx|

* |Z1|1|Z3|3= |Z2|2|Zx|x

Zx

Z3

1+3= 2+x

5.

Z1=R1 , Z2=R2 , Z3=R3+jw L3

Zx=Rx+jwLx

Z1 Z3=Z2 Zx

R1(R3+jw L3)=R2(Rx+j wLx)

Rx=R1R3 /R2 , Lx=L3 R1/R2


3891696

Z

+

Z1

_

6.

Z=10+j50W , Z1=400+j1000W


3891696

R1

_

+

+

+

R2

_

L2

_

q

q2

U=115V , U1=55.4V , U2=80V ,

R1=32W , f=50Hz

R2L2

7.


3891696

R20

+

R2

R1

+

a

b

-

+

_

+

R1

-

-

8.

R2=0q =-180R2q =0


3891696

i

+

u

_

9. 5

( u, i )

1. (instantaneous power)


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p

UIcos

u

i

t

O

-UIcos(2 t )

UIcos (1-cos2 t)

t

O

-UIsin sin2 t

p,

p>0, p<0

UIcos (1-cos2 t)

UIsin sin2 t


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2. (average power)P

P W

=u-i

cos


3891696

1,

cosj

0

, 0cosj1

X>0, j >0 ,

X<0, j <0 ,

cosj =0.5 () j =60o (60o)

cosj ,


3891696

3. (reactive power) Q

var ()

Q>0

Q<0

Q LC

4. ()S


3891696

i

+

R

u

-

i

+

u

L

-

5. RLC

PR =UIcos =UIcos0 =UI=I2R=U2/R

QR =UIsin =UIsin0 =0

u, i Q=0()

PL=UIcos =UIcos90 =0

QL =UIsin =UIsin90 =UI=LI2=U2/(L)

ui 90, PL=0QL>0


3891696

i

+

i

R

L

u

C

-

+

uL

-

+

+

u

uC

C

-

-

PC=UIcos =Uicos(-90)=0

QC =UIsin =UIsin (-90)= -UI

=-I2/(C)=-CU2

iu 90, PC=0QC<0

6. RLC


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*

A

W

*

+

R

V

Z

L

_

.

f=50HzU=50VI=1AP=30WR, L


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+

_

9. 6

1.


3891696

+

: VA

_

: P=UIcosj W

: P=UIsinj var

: S=UIVA


3891696

_

+

+

+

_

_


3891696

+

5W

10W

100o A

_

j25W

-j15W

1.


3891696

+

5W

10W

100o A

_

j25W

-j15W


3891696

+

+

P=20kW

cosj1=0.6

R

j1

j2

C

C

_

L

_

f=50Hz, U=380V, P=20kW, cosj1=0.6()0.9 , C

2.


3891696

QC

QL

Q

j2

j1

P

cosj ?

cosj


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+

R

j1

j2

C

L

_

(1)

(2) I=P/(Ucosj)

()

:


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Zi

+

ZL

-

9. 7

Pmax

Zi= Ri + jXi ZL= RL + jXL

ZL= RL + jXL


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RL= Ri

ZL= Zi*

XL =-Xi

PXLRL

RL= Ri

YL= Yi*

9-12209


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R,L,C

9. 8

(resonance)

LC


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R

+

j L

_

RLC

1

(resonant angular frequency)

(resonant frequency)

(resonant period)


3891696

2RLC

1. L C w

w0 R L C w0 ,

2. L C ( C)

C


3891696

|Z|

R

w0

w

O

R

+

_

+

+

j L

_

+

_

_

3RLC

(2). ZZ=R|Z|

(3). II0=U/R (U)

(4). LC


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w0L=1/(w0C )>>R UL= UC >>U

(5).

P=RI02=U2/R=1

LC


3891696

1. (characteristic impedance)

2. (quality factor)Q


3891696

(a)

UL0 = UC0=QU

UL0(UC0)


3891696

UL0UC0Q w0L=1/(w0C )>>R Q L C ,

C=150pFL=250mHR=20

10mV , 650mV


3891696

C

L

Q

+

R

_

P

(b)


3891696

(c)

WLm=WCm

Q


3891696

Q


3891696

R

+

j L

_

U=10VR=10L=20mH

C=200pFI=1AuULUCQ


3891696

+

L

C

G

_

9. 9

GCL

G C L

R L C


3891696

|Y|

+

L

C

G

G

_

w0

w

O

GCL

(2). YY=G|Y|

(3). UU=RIS(IS)

(4). LC


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(5).

P=RIS2=1

LC


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R L C

IL(w 0)=IC(w 0)=QIS

UL(w 0)=UC (w 0)=QU


3891696

R

C

L

B=0


3891696


3891696

GLC


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