chapter 3 feedback circuits by: pn norizan binti mohamed nawawi ekt 214 – analog electronic...
DESCRIPTION
1.1Voltage amplifier if then and if then hence with represent the open circuit voltage gain.TRANSCRIPT
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)
Voltage-Shunt FeedbackVoltage-Shunt Feedback
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
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 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
6.4 Modification of input and output 6.4 Modification of input and output impedanceimpedance
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
6.4 Modification of input and output 6.4 Modification of input and output impedanceimpedance
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
6.4 Modification of input and output 6.4 Modification of input and output impedanceimpedance
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)
Voltage-Shunt FeedbackVoltage-Shunt Feedback
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)