Unit 1 Feedback Amplifiers

Feedback: Is the process where by a portion of the output is returned to the input to form a part of the system excitation.

Introduction to feedback amplifier

Open-Loop Amplifier Closed loop Amplifier

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Why feedback?

• Positive Feedback (oscillators)

2

• Negative Feedback (Amplifiers)

•The feedback improve the frequency response and make the amplifier more stable

•The feedback improve the sensitivity of the amplifier•The feedback decrease the nonlinear distortion.•The feedback decrease the noise effect on the amplifier

Types



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Block diagram of amplifier with feedback

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General Feedback Structure

Open loop gain & closed loop gain are )(- + fsi XXX

fisf XX

XXXA

00

iXXA 0

sf X

XA 0



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Dividing the numerator and denominator by

5

ifi

if XXX

XXA/)(

/0

iff XX

AA/1

i

o

o

ff

XX

XX

AA

1

AAA f

1

iX



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Gain De-sensitivity • Feedback can be used to desensitize the closed-loop gain to variations in the

basic amplifiler. • Assume is constant. Take differentials of the closed loop gain equation

gives,

• Divided by Av, the close loop gain sensitivity is equal to,

• This result shows the effects of variations in A on ACL is mitigated by the feedback amount.

• (1+A) is also called the desensitivity amount.

22 )1(or

)1(1

1 AdAdA

AdAdA

AAA CL

CLCL

Differential respected with A

AdA

AAA

AdA

AdA

CL

CL

1

1)1()1( 2



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Bandwidth improvement

8

AAAf

1

fhigh

fhighfhigh

flow

flowflow

mid

midfmid

AA

A

AA

A

AAA

1

1

1

We can write

-----1

---2

---3



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Lower cutoff frequency

ffjA

ALmid

low

1

1

ffj

AAL

midlow

1

Substituting the value of in equation 2 lowA

ffj

A

ffj

A

A

L

mid

L

mid

flow

1(1

1



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ffjA

AAL

mid

midflow

)1(

fAfj

AA

A

mid

L

mid

mid

flow

)1(1

1

fAfj

AA

mid

L

fmidflow

)1(1



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ff

j

AA

Lf

fmidflow

1

Lower cutoff frequency is given by

)1( mid

LLf A

ff

Upper cutoff frequency

H

mid

high

ffj

AA

1

1

H

midhigh

ffj

AA1



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Substituting the value of in equation 3 highA

H

mid

H

mid

fhigh

ffj

A

ffj

A

A

1(1

1

Dividing numerator and denominator by

Hmid

mid

mid

fhigh

fAfj

AA

A

)1(1

1



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Hmid

fmidfhigh

fAfj

AA

)1(1

Hf

fmidfhigh

ffj

AA

1

where upper cutoff frequency with feedback is given as

HmidHf fAf )1(

)1()1(

mid

LHmidf A

ffABW

Bandwidth = Upper cutoff frequency – lower cutoff frequency



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Effect of negative feedback on gain and bandwidth

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Basic Feedback Topologies

Depending on the input signal (voltage or current) to be amplified and form of the output (voltage or current), amplifiers can be classified into four categories. Depending on the amplifier category, one of four types of feedback structures should be used.

(Type of Feedback) (Type of Sensing)• Series (Voltage) Shunt (Voltage)• Series (Voltage) Series (Current)• Shunt (Current) Shunt (Voltage)• Shunt (Current) Series (Current)



16

Figure 8.4 The four basic feedback topologies: (a) voltage-mixing voltage-sampling (series–shunt) topology; (b) current-mixing current-sampling (shunt–series) topology; (c) voltage-mixing current-sampling (series–series) topology; (d) current-mixing voltage-sampling (shunt–shunt) topology.www.Vidyarthiplus.com


17

The series–shunt feedback amplifier: (a) ideal structure and (b) equivalent circuit.

Series–shunt feedback amplifier



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• Voltage amplifier voltage-controlled voltage source

• Requires high input impedance, low output impedance

• Voltage-voltage feedback

io VAV

of VV

oo

fis VA

VVVV

)1(1

get weAnd,

AVVA

AVV

is

so

Voltage Gain Calculation:

i

o

VVA

A

AVVA

s

of 1

Gain) Voltage Loop (Close



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Input Resistance (Series-Shunt)

Input Resistance:

i

i

s

i

s

RVV

IVR if

i

iii

i

si V

AVVRIVRR

if

)1(if ARR i

)1( AVV s

i

)()(1)()( ssAsZsZ iif

In general input impedance can be written as



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Output Resistance (Series-Shunt)

Measuring the output resistance of the feedback amplifier

IVR t

of

0RAVVI it

tofi VVVV

0RAVVI tt

ARRof

1

0

)()(1)()( 0

0 ssAsZsZ f

To find output resistance Rof , put Vs = 0 and apply test voltage at output

Since Vs =0,



Derivation of the A circuit and b circuit for the series–shunt feedback amplifier. (a) Block diagram of a practical series–shunt feedback amplifier. (b) The circuit in (a) with the feedback network represented by its h parameters.

Practical series–shunt feedback amplifier.



22

(Continued) (c) The circuit in (b) with h21 neglected.



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iVVA 0

021

2110 //)(

//)(rRRR

RRRVVL

L

)//( 211 RRRR

VRVids

iid

series–shunt feedback amplifier.



)//(//)(//)(

21021

21

RRRRVR

rRRRRRRA

ids

iid

L

L

21

1

0 RRR

VV f

AA

VVA

sf

1

0

)1( ARR iif

series–shunt feedback amplifier.



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21 // RRRRR idsi

sifin RRR

ARRof

1

0

)//(// 2100 RRRrR L

Loutof RRR //



The series–series feedback amplifier: (a) ideal structure and (b) equivalent circuit.

series–series feedback amplifier



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of IV

i

o

VIA

A

AVIA

s

of 1


Transconductance gain

)1(if ARR i

tof I

VR

Measuring the output resistance of the feedback amplifierTo find output resistance Rof , put Vs = 0 and apply test voltage at output



Measuring the output resistance Rof of the series–series feedback amplifier.

tofi IIVV

00 )()( RIAIRAVIV ttit

)1(0 ARRof

Since Vs =0,



29

Series series Circuits



30

)]//([)//(

211

211

FEEe

c

i

c

RRRrrR

VV

))]}//(()[1//({ 123221

2FEEefecm

c

c RRRrhRgVV




31

)]//([1

1233

3

2 FEEeb

e

c

o

RRRrVI

VI

i

o

VIA

112

2E

FEE

E

o

f RRRR

RIV

A

AVIA

s

of 1





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3303

cfs

c

s

cc

s

o RAV

RIV

RIVV

)1(if ARR i

))]//(()[1( 211i EFEefe RRRrhR

1)]//([ 2

312

fet

ceEFEo h

RrRRRR

)1(0 ARRof

)//)(1( 3030 rRrgrR ofmout

Voltage gain is

Measuring the output resistance of the feedback amplifier To find output resistance Rof , put Vs = 0 and apply test voltage at output



Ideal structure for the shunt–shunt feedback amplifier.

s

of I

VA

A

AA f 1


)1(if ARR i

)1(0

ARRof



34

Block diagram for a practical shunt–shunt feedback amplifier.

sRR

R11

1

if

in

Lof RR

R11

1out



35

Finding the A circuit and b for the current-mixing voltage-sampling (shunt–shunt) feedback amplifier



36

)////( rRRIV fsi

)//(0 cfm RRVgV

)////)(//(0rRRRRg

VVA fscfm

i

)////( rRRR fsi

)//( cfo RRR

shunt–shunt) feedback amplifier



37

fo

f

RVI 1

A

AIVA

s

of 1

Gain) Voltage Loop (Close )1(if ARR i

)1(0

ARRof

shunt–shunt) feedback amplifier



38

Ideal structure for the shunt–series feedback amplifier.

s

of I

IA

A

AIIA

s

of 1


)1(if ARR i

)1(0 ARRof



39

Block diagram for a practical shunt–series feedback amplifier.

sRR

R11

1

if

in

Lof RRR out



40

Finding the A circuit and b for the current-mixing current-sampling (shunt–series) feedback amplifier .



41

121 ////)//( rRRRRIV BfEsi

)]//)(1(//[// 2211112 fEcomb RRrRrVgV

)//( 22

2

fEe

bo RRr

VI

shunt–series) feedback amplifier .



42

Voltage gain is

i

o

IIA

12 ////)//( rRRRRR BfEsi

1//)//( 11

22

oc

efEirRrRRR

fE

E

o

f

RRR

II

2

2

)1(if ARR i

sRR

R11

1

if

in




43




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AA

IIA

s

of

1

s

o

Lc

c

s

c

Lc

c

s

out

in

out

II

RRR

II

RRR

II

II

2

2

2

2

)1(0 ARRof

)]//(1[ 222out ofmo RrgrR




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46

The Stability Problem

• Closed-loop transfer function is similar to the one of the middle band gain.

• The condition for negative feedback to oscillate

• Any right-half-plane poles results in instability. Amplifier with a single-pole is unconditionally stable. Amplifier with two-pole is also unconditionally stable. Amplifier with more than two poles has the possibility to be

unstable.• Stability study using bode plot

1)()()( jjAjL



47

The Definitions of the Gain and Phase margins

Gain margin represents the amount by which the loop gain can be increased while stability is maintained.

Unstable and oscillatory

Stable and non-oscillatory

Only when the phase margin exceed 45º or gain margin exceed 6dB, can the amplifier be stable.



48

Stability analysis using Bode plot of |A|.



49

Stability Analysis Using Bode Plot of |A|

• Gain margin and phase margin• The horizontal line of inverse of feedback factor in dB.• A rule of thumb:

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

• The general rule states:At the intersection of 20log[1/ | β (jω)| ] and 20log |A(jω)| the difference of slopes should not exceed 20dB/decade.



50

Frequency Compensation

• The purpose is to modifying the open-loop transfer function of an amplifier having three or more poles so that the closed-loop amplifier is stable for any desired value of closed-loop gain.

• Theory of frequency compensation is the enlarge the –20dB/decade line.

• ImplementationCapacitance Cc addedMiller compensation and pole splitting



51


Two cascaded gain stages of a multistage amplifier.

Equivalent circuit for the interface between the two stages in (a).

Same circuit as in (b) but with a compensating capacitor CC added. www.Vidyarthiplus.com


52

Frequency compensation for = 102. The response labeled A is obtained by introducing an additional pole at fD. The A response is obtained by moving the original low-frequency pole to f D.



53


A gain stage in a multistage amplifier with a compensating capacitor connected in the feedback path

An equivalent circuit.



Documents

Unit 1 Feedback Amplifiers