NCKU/EE S.F.Lei 1 MicroElectronics Ⅲ Exercise 8.1 (a) Assume infinite R in and zero R out. Find...

1MicroElectronics Ⅲ NCKU/EE S.F.Lei

Exercise 8.1

(a) Assume infinite Rin and zero Rout. Find feedback factor .

(b) If the open-loop gain A= , find R1/R2 to obtain a closed-loop voltage gain of 10.

(c) What is the amount of feedback in decibels?(d) If =1 V, find , and .(e) If A decreases by 20%, what is the correspo

nding decrease in ?

410

fA

sV oV fV iV

fA


Exercise 8.1


Exercise 8.1

0.02%about by decreases Thus

9975.9)0999.0)(108.0(1

108.0 )(

001.0999.010

999.0100999.0

10 1 )(

60)1log(20

)1( )(

0999.010101

10

1 )(

)/( )(

4

4

4

4

211

f

f

fSi

Of

SfOS

f

A

Ae

VVVV

VVV

VVAVVd

dBA

AfeedbackofAmountc

A

AAb

RRRa


Exercise 8.2

Consider the noninverting op-amp circuit of EXERCISE 8.1. Let the open-loop gain A have a low-frequency value of and a uniform -6 dB/octave rolloff at high frequencies with a 3-dB frequency of 100 Hz. Find the low-frequency gain and upper 3-dB frequency of a closed-loop amplifier with and .

410

kR 11 kR 92


Exercise 8.2

kHzAff

A

AA

RRR

oHHf

o

of

1.100)10/101(100)1(

999.9)1.0(101

10

1

1.0)91/(1)/(

4

4

4

211


Example 8.1

Fig.(a) shows an noninverting op amp, given μ= , =100kΩ , =1kΩ, =2kΩ, =1kΩ, = 1MΩ, =10kΩ. Find expressions

for A,β,closed-loop gain , input resistance ,and the output resistance .

410 idR

Or LR 1R 2R SRSO VV inR

outR


Example 8.1


Example 8.1

kRRRRR

ARR

VVA

A

V

VA

VVRR

R

V

V

VVRRRR

R

rRRR

RRR

V

VA

idsi

iif

s

of

o

f

sid

id

oL

L

i

o

111)//(

)1(

/8577

6000

1

/10

/6000)//()]//([

)]//([

21

3

21

1

2121

21


Example 8.1

100

//

3.957

667

667)//(//

1

12

out

Loutof

of

Loo

oof

sifin

R

RRR

R

RRRrR

A

RR

RRR


Example 8.2 In fig(a), Given , , , , Find the open-loop gain A, the feedback factor β, the closed loop

gain ,the voltage gain ,the input resistance and the output resistance . Now, if of is 25kΩ, estimate an

approximate value of .

SOf VIA SO VVifin RR

ofR

mAIC 6.01 mAIC 12 mAIC 43 100feh Or

Or 3QoutR


Example 8.2


Example 8.2

VmAA

A

V

IA

RRRR

R

I

V

VAV

IA

VmARRRrV

I

V

I

VVRRRrhRgV

V

VVRRRr

rR

V

V

s

of

EEFE

E

o

f

i

o

EFEeb

e

c

o

EFEeefcmc

c

EFEe

c

i

c

/7.831

9.11

/7.20106.102.13192.14

/6.10)740//100(25.6

1

)]//([

1

/2.131))]}//(()[1//({

/92.14)]//([

)//(

112

2

3

1233

3

2

123221

2

211

2111


Example 8.2

MrRrgrR

kARR

h

RrRRRR

MR

kRRRrhR

ARR

VVRAV

RI

V

RI

V

V

ofomoout

oof

ef

CeEFEo

if

EFEefei

iif

Cfs

Co

s

Cc

s

o

5.2)//)(1(

6.35)1(

9.1431

)]//([

34.3

65.13))]//(()[1(

)1(

/2.50

33

2312

211

333


Example 8.3 Analyze the circuit of Fig(a), use β=100, determine the small-signal voltage gain , the input resistance , and th

e output resistance . SO VV inRofout RR


Example 8.3


Example 8.3

kRV

I

kRRR

krRRR

krRRRRgI

VA

RRVgV

rRRIV

IV

IIV

fo

f

Cfo

fsi

fsCfmi

o

Cfmo

fsi

BC

BBC

47

11

27.4)//(

4.1)////(

7.358)////)(//(

)//(

)////(

07.0)1(7.4

12

and 4799.347)07.0(7.0


Example 8.3

4951

2.1621

/16.4

6.411

A

RR

A

RR

VVRI

V

V

V

RIV

kA

A

I

VA

oof

iif

ss

o

s

o

sss

s

of


Example 8.4 Fig(a) shows a feedback circuit. Find , , and Assume the transistors to have β=100 and .

inout II inR outRVVA 75


Example 8.4


Example 8.4

V

mA

V

V

mA

V

V

8.884.012V

4.04.3/2.1I

3.17.02V

211012V

187.0/87.0I

87.07.057.1V

57.115100

1512V

C2

E2

E2

C1

E1

E1

B1


Example 8.4

1.521

254.0

69.21

//)//(

535.1////)//(

/45.201

)//(

)]}//)(1(//[//{

]////)//([

2

2

1122

12

22

2

2211112

121

A

RR

R

I

I

krR

rRRR

krRRRRR

AAI

IA

RRr

VI

RRrRrVgV

rRRRRIV

fE

E

o

f

oCefEo

BfEsi

i

o

fEe

bo

fEComb

BfEsi


Example 8.4

MRrgrR

kARR

AAI

I

RR

R

I

I

RR

R

I

I

I

I

AAA

A

I

IA

RRR

A

RR

ofmoout

oof

s

o

CL

C

s

c

CL

C

s

out

in

out

s

of

sifin

iif

1.18)]//(1[

1.140)1(

/44.3

/87.31

5.29/1/1

1

5.291

222

2

2

2

2


Exercise 8.10 Consider a feedback amplifier for which the o

pen-loop transfer function A(s) is given by

Let be a constant independent of frequency. Find . Then, show that amplifier will be stable if and unstable if and find the value of .

34)

10/1

10()(s

sA

cr

crcr

180


Exercise 8.10

008.0))3(1/(1000

1

|)(|

1 : ||When

at 1|| if stableAmplifier

/1033)10/(

60)10/(tan180 , At

)10/(tan3 Thus

)10/1

10()(

2/33

180

180

4180

4180

4180

1

180

41

34

cr

cr

oo

jAA

A

srad

jjA

o

o


Exercise 8.11 An op amp having a signal-pole rolloff

ar 100Hz and a low-frequency gain of is operated in a feedback loop with

. What is the factor by which feedback shifts the pole? To what frequency? If is changed to a value that results in a closed-loop gain of +1, to what frequency does the pole shift?

510

01.0


Exercise 8.11

Hz 10)1001(10)1(

1 , 1gain loop closedFor

kHz 1.1001001100)1(

100101.0101)1(

factor by shift is Pole

75'''

5

oppf

oppf

o

Aff

Aff

A


Exercise 8.12

An amplifier with low-frequency gain of100 and poles at is incorporated in a negative-feedback loop with feedback factor . For what value of do the poles of the closed-loop amplifier coincide? Corresponding Q? For value of is a maximally flat response achieve? What is the low-frequency closed-loop gain in this case?

sradsrad /10 and /10 64


Exercise 8.12

VVA

AA

Q

sradA

A

o

o

ppo

ppopp

/96.15.01001

100

1

5.01010

10)1001(

2

1 and

707.0 responseflat maximally For

5.0

245.04/100)01.1(1001

010)1(4)1010(

/10 , 10 , 100 Using

0)1(4)(

whencoincide willpoles 8.63 eq From

64

10

2

100

264

62

41

212

21

Corresponding

Corresponding gain is


Exercise 8.13

34)

10/1

10()(s

sA

Find the closed-loop poles as function of , and show that the root locus is that of Fig. E8.13. Also find the value of at which the amplifier becomes unstable.

Consider a feedback amplifier for which the open-loop transfer function A(s) is given by


Exercise 8.13


Exercise 8.13

008.0260cos

110

when is axis on lie poles

complex when unstable becomesAmplifier

3551 , )101( Roots

10for 0)1001(33

0)1001(10

3

10

3

10

0)10/1(

101

0)(1

using found are poles loop Closed

3/1

cr

3/13/13/1

43

4

1

8

2

12

3

34

3

crocr

nnnn

j

j

sSSSS

sss

s

sA


Exercise 8.14

Consider an op amp having a signal-poleopen-loop response with Let the op amp be ideal otherwise. If thisamplifier is connected in the noninvertingconfiguration with a normal low-frequency closed-loop gain of 100, find the frequency at which . Also, find the phase margin.

Hz 10 and 1050 pfA

1|| A


Exercise 8.14

o

o

p

o

p

o

fAt

ffThus

fA

jfff

j

A

j

AA

9090180margin phase making

90)10/10(tan

Hz 10

Hz 1010100/1

1100/1

01.010||

01.0

/1

10

11

41

4

462

2

5

5


Exercise 8.17

A multipole amplifier having a first pole at

1 MHz and an open-loop gain of 100 dB is

to be compensated for closed-loop gains

as low as 20 dB by the introduction of a new dominant pole. At what frequency must the new pole be placed?


Exercise 8.17

Hz 10010

10

at poledominant new placeMust

4

6

D

pD

fA

ff


Exercise 8.18

If the frequency of the second pole is 10 MHz and if it remains unchanged while Additional capacitance is introduced as mentioned, find the frequency to which the first pole must be lowered so that

the resulting amplifier is stable for closed-loop gains as low as 20 dB. By what factor must the capacitance at the controlling node be increased?


Exercise 8.18

Hz 10

20dB)-(100dB

10

1010

pole 2nd ofFrequency When

to a move bemust pole The

3

4

6

1

D

Dp

f

ff

1000 oldnew CC

The capacitance at the controlling node must be increased by same factor as f is lowered

Ans. 1000 Hz; 1000

NCKU/EE S.F.Lei 1 MicroElectronics Ⅲ Exercise 8.1 (a) Assume infinite R in and zero R out. Find...

Documents

Transcript of NCKU/EE S.F.Lei 1 MicroElectronics Ⅲ Exercise 8.1 (a) Assume infinite R in and zero R out. Find...