Chapter 3 Feedback Circuits BY: PN NORIZAN BINTI MOHAMED NAWAWI EKT 214 – Analog Electronic...

Chapter 3Chapter 3Feedback CircuitsFeedback Circuits

BY: PN NORIZAN BINTI MOHAMED NAWAWIBY: PN NORIZAN BINTI MOHAMED NAWAWI

EKT 214 – Analog EKT 214 – Analog Electronic CIRCUIT IIElectronic CIRCUIT II

1.0 Classification of 1.0 Classification of AmplifiersAmplifiers

Before proceeding with the concept of feedback it is useful to classify amplifiers into 4 basic categories based on their input & output signal relationships. Voltage amplifierVoltage amplifier Current amplifierCurrent amplifier Transconductance amplifierTransconductance amplifier Transresistance amplifier Transresistance amplifier

1.11.1 Voltage amplifierVoltage amplifierif

si RR

then si VV

and if Lo RR

then

svivo VAVAV

hence i

ov VV

A

with LR

represent the open circuit voltage gain.

iV oV

1.21.2 Current amplifierCurrent amplifierif

si RR

then si II

and if Lo RR

then

siiio IAIAI

hence i

oi IIA

with 0LR

represent the short circuit current gain.

iI oI

1.31.3 Transconductance amplifierTransconductance amplifierif

si RR

then si VV

and if Lo RR

then

smimo VGVGI

hence i

om V

IG

with 0LR represent the short circuit mutual or transfer conductance

iV oI

1.41.4 Transresistance amplifierTransresistance amplifierif

si RR

then si II

and if Lo RR

then

smimo iRIRV

hence i

om IVR

with LR represent the open circuit mutual or transfer resistance.

iI oV

FeedbackFeedback is a technique where a proportion of the output of is a technique where a proportion of the output of a system (amplifier) is a system (amplifier) is fed backfed back and and recombinedrecombined with input. with input.

There are two types of feedback amplifier.There are two types of feedback amplifier. Positive feedbackPositive feedback Negative feedbackNegative feedback

input outputA

2.0 Feedback2.0 Feedback

Positive feedback is the process when the output is Positive feedback is the process when the output is addedadded to the input, amplified again, and this process continues. to the input, amplified again, and this process continues.

ExampleExample. In a PA system, you get feedback when you put . In a PA system, you get feedback when you put the microphone in front of a speaker and the sound gets the microphone in front of a speaker and the sound gets uncontrollably loud (you have probably heard this uncontrollably loud (you have probably heard this unpleasant effect. unpleasant effect.

2.1 Positive Feedback2.1 Positive Feedback

input outputA

Negative feedback is when the output is Negative feedback is when the output is subtracted subtracted from the input. from the input.

ExampleExample. Speed control. If the car starts to speed up above . Speed control. If the car starts to speed up above the desired set-point speed, negative feedback causes the the desired set-point speed, negative feedback causes the throttle to close, thereby reducing speed; similarly, if the car throttle to close, thereby reducing speed; similarly, if the car slows, negative feedback acts to open the throttle. slows, negative feedback acts to open the throttle.

The use of negative feedback reduces the gain. Part of the The use of negative feedback reduces the gain. Part of the output signal is taken back to the input with a negative sign. output signal is taken back to the input with a negative sign.

2.2 Negative Feedback2.2 Negative Feedback

input outputA

3.0 Feedback Concept3.0 Feedback Concept

Basic structure of a single - loop feedback amplifier

3.1 Feedback Network3.1 Feedback Network

• This block is usually a passive two-port network.• contain resistors, capacitors, and inductors.• Usually it is simply a resistive network.

3.2 Sampling Network3.2 Sampling Network

• The output voltage is sampled by connecting the feedback network in shunt across the output.

• Type of connection is referred to as voltage or shunt or node sampling.

3.2 Sampling Network3.2 Sampling Network

• The output current is sampled by connecting the feedback network in series with the output

• Type of connection is referred to as current or series or loop sampling.

3.3 Comparator or Mixer Network3.3 Comparator or Mixer Network

• voltage - applied feedback • identified as voltage or series or loop mixing.

3.3 Comparator or Mixer Network3.3 Comparator or Mixer Network

• current - applied feedback• identified as current or shunt or node mixing.

4.0 Feedback Amplifier Topologies4.0 Feedback Amplifier Topologies

Series - shunt

shunt - series

series - series shunt -

shunt

5.0 Feedback Connection Types5.0 Feedback Connection Types

• Voltage-series feedback• Voltage-shunt feedback• Current-series feedback• Current-shunt feedback

There are four basic ways of connecting the feedback signal:

Fig. 3-2: Feedback amplifier types: (a) voltage-series feedback; (b) voltage-shunt feedback; (c) current-series feedback; (d) current-shunt feedback.

SeriesSeries refers to refers to connecting the connecting the feedback signal in feedback signal in series with the series with the input signal input signal voltage.voltage. ShuntShunt refers to refers to connecting the connecting the feedback signal in feedback signal in shunt (parallel) shunt (parallel) with an input with an input current source. current source.

Series feedback connections tend to Series feedback connections tend to increaseincrease the the input resistance, whereas shunt feedback input resistance, whereas shunt feedback connections tend to connections tend to decreasedecrease the input resistance. the input resistance.

Voltage feedback tends to Voltage feedback tends to decreasedecrease the output the output impedance, whereas current feedback tends to impedance, whereas current feedback tends to increaseincrease the output impedance. the output impedance.

Gain with FeedbackGain with Feedback

Voltage-Voltage-SeriesSeries

Voltage-Voltage-ShuntShunt

Current-Current-SeriesSeries

Current-Current-ShuntShunt

Gain without Gain without feedbackfeedback

AA

FeedbackFeedback ββ

Gain with Gain with feedbackfeedback

AAff

i

o

VV

o

f

VV

s

o

VV

i

o

IV

o

f

VI

s

o

IV

i

o

VI

o

f

IV

s

o

VI

i

o

II

o

f

II

s

o

II

TABLE 3-1: Summary of Gain, Feedback, and Gain with Feedback from Figure 3-2

Voltage-Series FeedbackVoltage-Series FeedbackFigure 3-2 (a) below shows the voltage-series feedback connection with a part of the output voltage fed back in series with the input signal.

If there is no feedback (Vf = 0), the voltage gain of the amplifier is

i

o

s

o

VV

VVA

If a feedback signal Vf is connected with the input in series, the overall voltage gain is

AA

VVAs

of

1

(3-1)

Voltage-Shunt FeedbackVoltage-Shunt Feedback

The gain with feedback for the network of Fig. 3-2 (b) is

AAAf

1

(3-2)

Input Impedance with FeedbackInput Impedance with FeedbackVoltage-Series FeedbackVoltage-Series Feedback

Fig. 3-3: A more detailed voltage-series feedback connection

The input impedance can be determined as follows:

)1( AZIVZ ii

sif

(3-3)


Fig. 3-4: A more detailed voltage-shunt feedback connection

The input impedance can be determined to be:

AZZ i

if 1

(3-4)

Output Impedance with FeedbackOutput Impedance with Feedback

Voltage-Series FeedbackVoltage-Series Feedback

The output impedance for the connections of Fig. 3-2 is dependent on whether voltage or current feedback is used.

For voltage feedback, the output impedance is decreased, whereas current feedback increases the output impedance.

Referring to Fig. 3-3, the output impedance can be determined by applying a voltage V, resulting in a current I. Then the output resistance with feedback is

AZ

IVZ o

of 1 (3-5)

Current-Series FeedbackCurrent-Series Feedback

Fig. 3-5: A more detailed current-series feedback connection

The output impedance is determined as

IVZof

(3-6)

)1( AZZ oof

A summary of the effect of feedback on input and output impedance is provided in Table 3-2:

Voltage-Voltage-SeriesSeries

Current-Current-SeriesSeries

Voltage-Voltage-ShuntShunt

Current-Current-ShuntShunt

ZZifif

(increased(increased))

(increased)(increased)(decreased(decreased

))(decreased(decreased

))ZZofof

(decreased(decreased))

(increased)(increased)(decreased(decreased

))

(increased(increased))

TABLE 3-2:

)1( AZi )1( AZi A

Z i1 A

Z i1

AZo1

)1( AZo A

Zo1

)1( AZo

6.0 Negative Feedback Gain6.0 Negative Feedback Gain

The gain with feedback (or closed-loop gain) Af as follows:

io XAX .

of XX .fsi XXX

AA

XXAs

of

1

The quantity A is called the loop gain, and the quantity (1+A)is called the amount of feedback.

oXiX

fX

sX A

6.0 Advantages of Negative Feedback6.0 Advantages of Negative Feedback

1. Stabilization of gain make the gain less sensitive to changes in circuit

components e.g. due to changes in temperature.

2. Reduce non-linear distortion make the output proportional to the input, keeping

the gain constant, independent of signal level.

3. Reduce the effect of noise minimize the contribution to the output of

unwanted signals generated in circuit components or extraneous interference.

6.0 Advantages of Negative Feedback6.0 Advantages of Negative Feedback

4. Extend the bandwidth of the amplifier Reduce the gain and increase the bandwidth

5. Modification the input and output impedances raise or lower the input and output impedances by

selection of the appropriate feedback topology.

6.1 Stabilization of Gain6.1 Stabilization of Gain Stabilization of the gain of an amplifier against changes in

the components (e.g., with temperature, frequency) If you represent the gain without feedback (the open loop

gain) by Ao, then the system gain with negative feedback is

where is the fraction of the output which feeds back as a negative voltage at the input. The extent of this stabilizing influence can be illustrated as follows:

1

1

o

o

in

outf A

AVV

A

6.1 Stabilization of Gain6.1 Stabilization of Gain

6.2 Decreasing Distortion/noise with 6.2 Decreasing Distortion/noise with FeedbackFeedback

The use of negative feedback can discriminate against sources of noise or distortion within an amplifier.

6.2 Decreasing Distortion/noise with 6.2 Decreasing Distortion/noise with FeedbackFeedback

• showing that distortion within the feedback loop is discriminated against, with more reduction of distortion which arises near the output.

6.3 Increasing the Bandwidth6.3 Increasing the Bandwidth

oo

f AAA

1

6.4 Modification of input and output 6.4 Modification of input and output impedanceimpedance

i)i) Input Resistance Input Resistance The input resistance with negative feedback will be The input resistance with negative feedback will be raised raised

for series or voltage mixingfor series or voltage mixing. .

i

ii IV

Z

fsi VVV

AZIV

Z ii

sif 1


i)i) Input Resistance Input Resistance The input resistance with negative feedback will be The input resistance with negative feedback will be lowered lowered

for shunt or current mixing. for shunt or current mixing.

i

ii IV

Z

fsi III

AZ

IV

Z i

s

iif

1


ii)ii) Output Resistance Output Resistance The output resistance with negative feedback will be The output resistance with negative feedback will be

lowered for shunt or voltage samplinglowered for shunt or voltage sampling..

tfi VXX

o

t

o

tt

o

itt R

AvRAvv

RAXv

i

1

AR

iv

Z o

t

tof

1

Let 0sX

replaced load with test voltage


ii)ii) Output Resistance Output Resistance The output resistance with negative feedback will be The output resistance with negative feedback will be

raised for series or current samplingraised for series or current sampling. .

The output resistance with feedback for current or series sampling to be:

ARZ oof 1


SummarySummary For a For a series series connection at input or output, the connection at input or output, the

resistance is resistance is increasedincreased by (1+ by (1+A) andA) and For a For a shuntshunt connection at input or output, the connection at input or output, the

resistance is resistance is loweredlowered by (1+ by (1+A).A).

7.0 Practical Feedback Circuits7.0 Practical Feedback Circuits

Voltage-Series FeedbackVoltage-Series Feedback

Fig. 3-7: FET amplifier with voltage-series feedback.

The feedback voltage Vf is connected in series with the source signal Vs, their difference being the input signal Vi.

Without feedback the amplifier gain is

Lmi

o RgVVA

where,gm = transconductance factor

(3-7)

Whereas RL is combination of resistors:

Do

DooDL RR

RRRRRRR

)( 21

The feedback network provides a feedback factor of

21

2

RRR

VV

o

f

Using the values of A and β, we find the gain with negative feedback to be

21

211RRgRRRg

AAA

mL

Lmf

If βA >>1, we have

2

211RRRAf

(3-7)

Current-Series FeedbackCurrent-Series Feedback

Fig. 3-8: (a) a single transistor amplifier circuit and (b) ac equivalent circuit without feedback

The feedback voltage VE is resulted in by the current through resistor RE.

Without FeedbackWithout Feedback

Referring to the Fig. 3-8 and summarized in Table 3-1, we have

Eie

fe

Ebieb

feb

i

o

Rhh

RIhIhI

VIA

Eo

Eo

o

f RIRI

IV

The input and output impedances are, respectively,

EieEieBi RhRhRZ )//(

Co RZ

(3-8)

(3-9)

(3-10)

(3-11)

With FeedbackWith Feedback

Efeie

fe

Eie

feE

iefe

s

of Rhh

h

Rhh

R

hhA

AVIA

)(1

/1

The input and output impedances are calculated as specified in Table 3-2,

Efeieie

Efeieiif Rhh

hRh

hAZZ

1)1(

ie

EfeCoof h

RhRAZZ 1)1(

(3-12)

(3-13)

(3-14)

The voltage gain A with feedback is

Efeie

CfeCfC

s

o

s

Co

s

ovf Rhh

RhRAR

VI

VRI

VVA

(3-15)


Fig. 3-9: Voltage-shunt negative feedback amplifier: (a) constant-gain circuit; (b) equivalent circuit.

Referring to Fig. 3-9 and Table 3-1 and the op-amp ideal characteristics Ii = 0, Vi = 0, and voltage gain of infinity, for a constant-gain we have:

i

o

IVA

oo

f

RVI 1

(3-16)

(3-17)

The gain with feedback is then

oi

o

s

of R

AA

IV

IVA

1

1

The more usual gain is the voltage gain with feedback,

111

1)(RR

RR

VI

IVA o

os

s

ovf

(3-18)

(3-19)

Fig. 3-10: Voltage-shunt feedback amplifier using an FET: (a) Fig. 3-10: Voltage-shunt feedback amplifier using an FET: (a) circuit; (b) equivalent circuit.circuit; (b) equivalent circuit.

With no feedback, Vf = 0,

SDmi

o RRgIVA

The feedback is,

Fo

f

RVI 1

With feedback, the gain of the circuit is,

))(/1(11 SDmF

SDm

s

of RRgR

RRgA

AIVA

(3-20)

(3-21)

(3-22)

SDmF

FSDmf RRgR

RRRgA

Or,

SSDmF

FSDm

s

s

s

ovf RRRgR

RRRgVI

IVA 1

SDmF

FDmvf RRgR

RRgA

The voltage gain of the circuit with feedback is then

(3-23)

(3-24)

Chapter 3 Feedback Circuits BY: PN NORIZAN BINTI MOHAMED NAWAWI EKT 214 – Analog Electronic...

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Transcript of Chapter 3 Feedback Circuits BY: PN NORIZAN BINTI MOHAMED NAWAWI EKT 214 – Analog Electronic...