Title of Presentation - KUET · 2021. 3. 7. · Department of Electronics and Communication...

Feedback Amplifiers

Dr. Monir Hossen ECE, KUET

Department of Electronics and Communication Engineering, KUET

Department of Electronics and Communication Engineering, KUET 2

Feedback Concepts

The input signal Vs and a feedback signal Vf is applied to the mixer.

For negative feedback the difference between Vs and Vf equal to Vi is applied to the amplifier.

Vo is the output and a portion of output β connected to the feedback network.

The process of injecting a fraction of output energy of

some device back to the input is known as feedback.


Positive Feedback

When the feedback signal is in phase with the input signal and

thus aids it, it is called positive feedback.

Both amplifier and feedback network introduce a phase shift

of 180°.

The result is a 360° phase shift around the loop, causing the

feedback voltage Vf to be in phase with the input signal Vin.

The positive feedback increases the gain of the amplifier.

However, it increased distortion and instability.


Negative Feedback

o When the feedback signal is out of phase with the input signal

and thus opposes it, it is called negative feedback.

o The amplifier introduces a phase shift of 180° into the circuit

while the feedback network is so designed that it introduces 0°

phase shift.

o The result is that the feedback voltage Vf is 180° out of phase

with the input signal Vin.

o Negative feedback reduces the gain of the amplifier.

o However, it provides low distortion, stability in gain, increased

bandwidth and improved input and output impedances.


Advantages of Negative Feedback

Higher input impedance.

Better stabilized voltage gain.

Improved frequency response.

Lower output impedance.

Reduced noise.

More linear operation.

Reduce non-linear distortion.


(i) When negative voltage feedback is applied, the

gain of the amplifier is reduced.

(ii) When negative voltage feedback is employed,

the voltage actually applied to the amplifier is

extremely small.

(iii) In a negative voltage feedback circuit, the

feedback fraction mv is always between 0 and

1.

(iv) The gain with feedback is sometimes called

closed-loop gain while the gain without

feedback is called open-loop gain.

Worth Noting Points


Feedback Connection Types

Feedback can be connected in four basic ways.

Both voltage and current can be feed back to the

input either in series or parallel.

1) Voltage – series feedback.

2) Voltage – shunt feedback.

3) Current – series feedback.

4) Current – shunt feedback.

oSeries feedback connections increase the input resistance.

oShunt feedback connections decrease the input resistance.

oVoltage feedback decrease the output impedance.

oCurrent feedback increase the output impedance.


Voltage Series Feedback Here, a portion of output voltage

feedback in series to the input.

Negative feedback results overall

gain reduction.

If there is no feedback (vf = 0).

The voltage gain of the amplifier

is:

i

o

s

o

v

v

v

vA

If vf is connected in series with the input, then => vi = vs – vf

Since vo = Avi = A(vs – vf) = Avs – Avf

= Avs – A(βvo)

=> vo(1+ βA) = Avs

A

A

v

v

s

o

1 A

A

v

vA

s

of

1

So overall voltage

gain with feedback is


Example Ex. 01) When negative voltage feedback is applied to an amplifier of

gain 100, the overall gain falls to 50. (i) Calculate the fraction of the

output voltage fedback. (ii) If this fraction is maintained, calculate the

value of the amplifier gain required if the overall stage gain is to be 75.


Example


Ex. 2) The gain of an amplifier without feedback is 50 whereas

with negative voltage feedback, it falls to 25. If due to ageing, the

amplifier gain falls to 40, find the percentage reduction in stage

gain (i) without feedback and (ii) with negative feedback.

Example


Ex. 03) An amplifier is required with a voltage gain of 100 which does

not vary by more than 1%. If it is to use negative feedback with a basic

amplifier the voltage gain of which can vary by 20%, determine the

minimum voltage gain required and the feedback factor.

Example


The gain with feedback

Voltage Shunt Feedback

fi

i

s

of

II

AI

I

vA

Here,

Vo = AIi

Is = Ii+ If

oi

if

vI

AIA

ii

if

AII

AIA

A

AAf

1

Ii

Is i

o

I

vA

o

f

v

I

of vI

vo RL


Input Impedance with Feedback (1/3) Voltage Series Feedback:

The input impedance of the network can be determined as:

i

is

i

os

i

fs

i

ii

z

Avv

z

vv

z

vv

z

vI


Input Impedance with Feedback (2/3)

isii AvvZI

iiis AvZIv

iiiis ZAIZIv

i

iiii

i

sif

I

ZAIZI

I

vZ

We know,

)1(So, AZZ iif


Input Impedance with Feedback (3/3) Voltage Shunt Feedback:

Ii

Is

If = βvo

Ri Ro

AIi vo RL

o

f

v

I

oi

i

fi

i

s

iif

vI

v

II

v

I

vZ

Here,

Zi = vi /Ii

A=vo / Ii

ioii

iiif

IvII

IvZ

//

/

A

ZZ i

if

1


Voltage Series Feedback:

o The output impedance is determined by applying a voltage v

resulting in a current I with vs shorted out ( vs = 0)

o The voltage v is then –

v = IZ0 + Avi

Output Impedance with Feedback (1/3)

for vs = 0, vi = - vf



fo AvIZv , thatSo

)( vAIZv o

Rewriting the equation as:

oIZAvv

A

Z

I

vZ o

of

1


Current Series Feedback:

IAZ

vAv

Z

vAv

Z

vI

o

f

o

i

o


By applying a signal

voltage v to the output

with vs shorted out

resulting a current I, the

ratio of v to I being the

output impedance.

At, vs = 0, vi = - vf

IAZvIZ oo

vIAZo )1( )1( AZI

vZ oof


Effect of Negative Feedback on Gain and Bandwidth (1/2)

We know overall gain with negative feedback is:

For a practical amplifier the open-loop gain drops off at high frequencies due to the active device and circuit capacitance.

Gain also drop off at low frequencies for capacitively coupled amplifier stages.

When open-loop gain A drops enough low then the βA is no longer larger than 1, so Af = 1/ β is not true.

A

A

A

AAf

1

1So, fA

1for A


The figure shows that the amplifier with negative feedback has more bandwidth Bf than the amplifier without feedback B.

The feedback amplifier also has a higher upper 3-dB frequency

and smaller lower 3-dB frequency.

However, the product of gain and frequency for both cases are

same value.

Ao*f1 = Afo*f1f and Ao*f2 = Afo*f2f

Effect of Negative Feedback on Gain and Bandwidth (2/2)


Gain Stability with Feedback In addition to the β factor setting a precise gain value, we are

also interested in how stable the feedback amplifier is

compared to an amplifier without feedback.

This shows that the magnitude of the relative change in gain

is reduced by the factor compared to that without

feedback

f

f

A

dAA

A

dA


Example

The improvement is 100 times. Thus, while the amplifier gain changes by 20%, the gain with feedback changes by only 0.2%.

Ex. 04) If an amplifier with gain of 1000 and feedback of 0.1 has a

gain change of 20% due to temperature, calculate the change in

gain of the feedback amplifier.

Soln:

We know


Practical Feedback Circuits (1/2) Here, R1 and R2

resistors are used as a

feedback network.

A part of output

signal is obtained

from R2 to ground.

vf is connected in

series with the source

signal vs.

Without feedback the

amplifier gain is:

A = vo/vi = -gmRL

where RL is the

parallel combination

of RD, Ro and (R1+R2).

Voltage series feedback:


The feedback factor:

21

2

RR

R

v

v

o

f

Practical Feedback Circuits (2/2)

We know the gain with negative feedback is:

mL

Lmf

gRRR

R

Rg

A

AA

21

211

If βA>>1 we have:

2

211

R

RRAf


Example Exam: 05) Calculate the gain without and with feedback for the

FET amplifier circuit of figure bellow and the following values: R1

= 80 kΩ, R2 = 20 kΩ, Ro = 10 kΩ, RD = 10 kΩ, and gm = 4000 µS,


Example Soln:


Example 06) Calculate the amplifier gain of the circuit of Fig.

bellow for op-amp gain A 100,000 and resistances R1 1.8 k and R2

200 .

Example


Barkhausen Criterion (1/3)

Typically, the feedback network is composed of

passive lumped components that determine the

frequency of oscillation.

So, the feedback is complex-transfer function,

hence denoted as β.

We can derive the requirements for oscillation as

follows:

o Initially, sinusoidal source is xin .

o The condition of oscillation is even xin is zero

the output xout can be non-zero.


β

A

xin +

-

xin + βxout

βxout

xout


The output of the amplifier block can be written as

][ outinfout xxAx

infoutfout xAxAx

inffout xAAx )1(

f

inf

outA

xAx

1



If xin is zero, the only way the output can be

nonzero is to have βAf = 1.

This condition is known as Barkhausen

criterion.


Example/ Problem Ex/Pb 07): An amplifier has an open-loop gain A = 100,000. A

negative feedback of 10 dB is applied. Find (i) voltage gain with

feedback, (ii) value of feedback fraction β.

Soln: (i) Open-loop gain without feedback in dB

= 20log10 100,000

= 20log10105

= 100 dB

voltage gain with feedback = 100-10 = 90 dB

Now, 20log10(Af) = 90

=> log10 (Af) = 90/20 =4.5

so, Af = antilog 4.5 = 31622

(ii)

A

AAf

1 *000,1001

000,10031622

510*17.2


Nonlinear Distortion in Feedback Amplifier (1/3)

Nonlinear

distortion

Fundamental

& Harmonics

In nonlinear distortion, elongate +ve half cycle and

compress –ve half cycle.


Nonlinear Distortion in Feedback

Amplifier(2/3) Nonlinear distortion produces harmonics of the input

signal.

If a input signal has a 1KHz frequency then the

output signals frequencies are 1, 2, 3 … KHz.

Here, 1KHz is fundamental frequency, and all others

are harmonics.

Sometime nonlinear distortion is called harmonic

distortion.

Total Harmonic Distortion (THD) without feedback

is:

%100VoltagelFundamenta

VoltageHarmonicTotalTHD

Total Harmonic Distortion (THD) with feedback is:

So THDf <THD


Nonlinear Distortion in Feedback

Amplifier (3/3)

A

THDTHD f

1 Here, A is gain

without feedback. β is the feedback

fraction

Thanks for Your Kind

Attention


Date post:	21-Jun-2021
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Title of Presentation - KUET · 2021. 3. 7. · Department of Electronics and Communication...

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