feedback. 8.4 the series-shunt feedback amplifier 8.4.1 the ideal situation

Feedback

8.4 The Series-Shunt Feedback Amplifier

AA

V

VA

s

of

1

?

?

of

if

R

R

8.4.1 The Ideal Situation

8.4 The Series-Shunt Feedback Amplifier

)1(/

AR

V

VAVR

V

VVR

V

VR

RV

V

I

V

I

VR i

i

iii

i

fii

i

si

ii

s

i

s

s

sif

))()(1)(()( ssAsZsZ iif

8.4.1 The Ideal Situation (cont.)

Series mixing

8.4 The Series-Shunt Feedback Amplifier

A

RR

R

AV

R

VAV

R

VAV

R

AVVI

I

V

I

VR

oof

o

t

o

tt

o

ft

o

it

t

t

tof

1

)1()()(

)()(1

)()(

ssA

sZsZ i

of

8.4.1 The Ideal Situation (cont.)

Shunt sampling

8.5 The Series-Series Feedback Amplifier

8.5.1 The Ideal Situation

i

iii

i

ioi

ii

if

i

sif

V

VAVR

V

VIR

RV

VV

I

VR

/

)1( ARR iif

Series mixing

8.5 The Series-Series Feedback Amplifier

8.5.1 The Ideal Situation (cont.)

t

tto

t

fto

t

oit

tof

I

IAIR

I

AVIR

I

RAVI

I

VR

)()(

)(

)1( ARR oof

Series sampling

8.6 The Shunt-Shunt and Shunt-Series Feedback Amplifier

8.6.1 The Shunt-Shunt Configuration

A

R

VAV

VR

AIV

VR

RAIV

V

I

VR

A

R

IAI

IR

VI

IR

II

RI

I

VR

o

oo

oo

fo

oo

oio

ooof

i

ii

ii

oi

ii

fi

ii

s

iif

1/)(

1

8.6 The Shunt-Shunt and Shunt-Series Feedback Amplifier

8.6.3 The Shunt-Series Configuration

)1()(

1

ARI

IAIR

I

AIIR

I

RAII

I

VR

A

R

IAI

IR

II

IR

II

RI

I

VR

oo

ooo

o

foo

o

oio

o

oof

i

ii

ii

oi

ii

fi

ii

s

iif

8.6 The Shunt-Shunt and Shunt-Series Feedback Amplifier

8.6.3 Summary

Ri Rif: Mixing

Voltage (series) mixing always increases the input resistance.

Current (shunt) mixing always reduces it.

Ro Rof: Sampling

Voltage (shunt) sampling always reduces the output resistance

Current (series) sampling increases it

8.8 The Stability Problem

8.8.1 Transfer Function of the Feedback Amplifier

Open-loop gain: A, A(s)

Loop gain: A, A(s)(s)

Close-loop gain: )()(1

)()(

1 ssA

sAsA

A

AA ff

)()(1

)()(

jjA

jAjAf

)()()( jjAjL 180For

)()()()()()( jejjAjjAjL

unstable Else

stable)()( then ,1)()( If

jAjAjjA f

Oscillator: =-1, zero input, infinite output

8.8 The Stability Problem

8.8.2 The Nyquist Plot

unstable Else

stable)()( then ,1)()( If

jAjAjjA f

8.9 Effect of Feedback on the Amplifier Poles

8.9.1 Stability and Pole Location

Figure 8.29 Relationship between pole location and transient response.

)cos(2)( 00 teeeetv nttjtjt nn

8.9 Effect of Feedback on the Amplifier Poles

8.9.2 Poles of the feedback amplifier

)()(1

)()(

ssA

sAsAf

ps

AsA

/1)( 0

Simplified case

)1(/1

)1/()(

0

00

As

AAsA

pf

)1( 0 Apf

)()( 0 sAs

AsA p

f

8.10 Stability Study Using Bode Plots

8.10.1 Gain and Phase Margin

8.10 Stability Study Using Bode Plots

8.10.2 Effect of Phase Margin on Closed-loop Response

1

1

1

f

A

f AA

AA

margin phase180

where

1)(

thenunity, isgain loopwhen

1

jejA

jfj

j

f ejA

e

e

jA

jAjA

1

)/1()(

1

)/1(

)(1

)()( 1

1

11

peaksgain ,margin Phase

1

3.1)(135 1 jAf

Zero margin?

8.10 Stability Study Using Bode Plots

8.10.3 An Alternative Approach for Investigating Stability

|AB|<1 20log|A| < 20log(1/)

The closed-loop amplifier will be stable if the 20log(1/) line intersects the 20log|A| curve at a point on the -20-dB/decade segment.

)10/j1)(10/j1)(10/j1(

10765

5

fffA

)10/j1)(10/j1)(10/j1(

10765

5

fffA

8.11 Frequency Compensation

8.11.1 Theory

Df

20

40

60

80

100

104 105 106 107 10810 103 103

'Df 1Pf 2Pf 3Pf

f(Hz)

dB

-20dB/decade

-40dB/decade

-60dB/decade

dB40)1

log(2010 2

A

A’

dB40)1

log(20 Y

Y’

'1:PoleShift

poles Three

Dp ff

• Four poles• Simplest• Reduced the bandwidth

Homework: 8.37, 8.43, 8.47, Ex-8.14, 8.70, 8.76, 8.77, 8.79