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9 电路的频率特性. 9-1 电路的频率特性与网络函数 9-2 RC 电路的频率特性 9-3 RLC 串联谐振电路 9-4 GCL 并联谐振电路 9-5 电源电阻及负载对谐振电路的 影响. 本章讨论正弦激励频率变化时,动态电路的特性 —— 频率特性。 首先介绍在正弦稳态条件下的网络函数。然后利用网络函数研究几种典型 RC 电路的频率特性。最后介绍谐振电路及其频率特性。动态电路的频率特性在电子和通信工程中得到了广泛应用,常用来实现滤波、选频、移相等功能。. 9-1 电路的频率特性与网络函数.

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9 电路的频率特性

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9

9-1

9-2 RC

9-3 RLC

9-4 GCL

9-5


RC


9-1

9-1-1

1

2 H(j)


()()

3

H(j)

|H(j)| ()


|H(j)|

()


N0

9-1-2

1.

2.


N0

N0

3.

4.


N0

N0

5.

6.


9-1-3


l(a)

(b)



R

92 RC

9-2-1 RC

RC


=0

=C


1

0.707

0 C

0 C

0 -90


=C=C|H(jC)|=0.707|H(j0)|(|H(j0)|)

(3)

()0.707 (3dB)0C ,

> C


1

1

0 C

0 C


R1

R2

2R1=R2=1K,C=0.1uF,: 1.2.3. 4.=104rad/s,10V,U2=?


1

R0= R1//R2 =0.5K

C=1/(R0C)=2104


2

=0

=C


1/2

0.35

0 C

3

C

02104 rad/s


4

=104rad/s,U1=10 V


R

9-2-2 RC

RC


=0

=C


1

0.707

0 C

0 C

=C

>C

0<<C


R

R

9-2-3 RC

:


13

0 0

0 0

C1=0.30 C2 =3.30

C1<<C2

0


R

R

C

C

R2

2C

T


1

0 0

0 0

0


R

C

C

R

1

0

:

0


93 RLC

LC


9-3-1 RLC

(a)RLC(b)


L

X

R

0 0

-1 C

X<0 X=0 X>0


1

Z=0, |Z(j)|=R,u(t)i(t)RLC

0

LC


RLC

LC


1. = 0

()

2. LC () ()


2

RLC



LC

Q


Q>>1,UL=UC>>US=UR

,


3

uS(t)=USmcos0t


uX0(t)=uL0(t)+uC0(t)=0 ()pL0(t)+pC0(t)=0

pS(t)=pR(t)



wL0wC0w=wL0+wC0

LI02

uC0

0

Tt

i0


Q()

()


LC


3,

:(l)

(2), UL0UC0

(l)

(2):


9-3-2 RLC


()


=0=|H(j)|=0

|H(j)|=1


:


QQQ()


410MHzRLCf=100kHz,C=100pF


5RLC,

f=1MHzCI0=100uA,UC0=100mV:RLCQBW

US=0.707mV

:


9-3-3 RLC



= 0 Q()

0

Q



= 0 Q()

0

Q


1.Q>>1 ;

2.

3.LC

4.

Q=1.25


9-4 GCL

9-4-1 GCL

GCL


C

B

G

0 0

-1 L

B<0 B=0 B>0


1

, u(t)i(t)GCL

0

Y(j0)=G=1/R


2


GCL

Q

LC


3

iS(t)=ISmcos0t


iL0(t)+iC0(t)=0 ()pL0(t)+pC0(t)=0

pS(t)=pR0(t)



GCL



6GCLR=10k,L=1H,C=1F3dB


9-4-2


rLC

1.

2.


C



RLC

GCL

:

QQL0


7R=1,L=0.1mH,C=0.01F

(b)

:


0L>>R ,



=0

ab

ab


X)

(B)


::


L

a

C2

C1

b

R

8C1 C2 L=20mH,

u1(t)3Ra,b


L

a

C2

C1

b

R

u1(t)Ra-b


500uF

a

b

i1

i3

15

i2

10

30

1H

0.1H

100uF

0.4H

9i1i3I3=1AuS(t)

i1


-j20

a

b

15

10

30

j100

j10

-j100

j40

c

:


-j20

a

b

15

10

30

j100

j10

-j100

j40

c


-j20

a

b

15

10

30

j100

j10

-j100

j40

c


L

C

ZL

10US=200V , f=50Hz 1ZLILD10ALC2ZL=11.7-j30.9 uL(t)

1ZLILD


L

C


ZL

2ZL=11.7-j30.9


R1

L1

C

R2

L2

11uS(t)=5+10cos(10t)+15cos(30t) R1=R2=5L1 =0.4HL2 =0.05HC=0.025F u(t)


R1

L1

C

R2

L2

5V u1(t)=0

uS2(t)=10cos(10t)

L1 ,CuS2(t)

u2(t)= 0.5uS2(t)=5cos(10t)V


R1

L1

C

R2

L2

uS3(t)=15cos(30t)

uS3(t) u3(t)= 0

u(t)=u1 (t)+u2(t)+u3(t)=5cos(10t)V


RS

R0

RL

C

L

9-5

9-5-1



+

-

5

4

3

13V2Q


1

H(j)ui(t)=Umcos(t+i)


2|H(j)|()

3RCRL


RC


4 RLC

Q


5RLC

Q


6RLC RLC

QQ


17p299

9-1 (b)(c)

9-2(b)

9 -3


18p300

9-6

9-7

9-9

9 -10

9 -14


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