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TRANSCRIPT
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UNIT - IV FEEDBACK AMPLIFIERS & OSCILATTORS
OBJECTIVES
i)The basics of feedback.
ii)The properties of negative feedback.
iii)The basic feedback topologies.
iv)An example of the “ideal” feedback case.
v)Some realistic circuit examples and how to analyze them.
INTRODUCTION TO FEEDBACK
• There are two types of feedback: regenerative (positive feedback) and
degenerative
(negative feedback).
• Unless you want your circuit to oscillate, we usually use NEGATIVE
FEEDBACK...
• This idea came about in the late 1920’s when they were able to build
amplifiers with reasonable gains, but with gains that were difficult to
control from amplifier to amplifier...
• One day, while riding the Staten Island Ferry, Harold Black invented
negative feedback....
DEFINITION
By building an amplifier whose gain is made deliberately, say 40
decibels higher than necessary (10,000-fold excess on an energy basis)
and then feeding the output back to the input in such a way as to throw
away the excess gain, it has been found possible to effect extraordinary
improvement in constancy of amplification and freedom from non-
linearity. Harold Black, inventor of negative feedback, 1934
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PROPERTIES OF NEGATIVE FEEDBACK
• The gain of the circuit is made less sensitive to the values of individual
components.
• Nonlinear distortion can be reduced.
• The effects of noise can be reduced (but not the noise itself).
• The input and output impedances of the amplifier can be modified.
• The bandwidth of an amplifier can be extended.
• All you have to do to “get some feedback” (of the negative kind) is to
supply a scaled replica of the amplifier’s output to the inverting (negative)
input (more on this below) and presto!
• Of course, if you use negative feedback, overall gain of the amplifier is
always less than the maximum achievable by the amplifier without
feedback.
THE BASIC FEEDBACK CIRCUIT
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• With an input signal xs, an output signal xo, a feedback signal xf, and an
amplifier input
signal xi, let’s look at the basic feedback circuit illustrated above.
• The amplifier has a gain of A and the feedback network has a gain of
• The input to the amplifier is,
xi = xs - xf
• The output of the amplifier is,
xo = Axi
• So we can obtain an expression for the output signal in terms of the input
signal and the feedback gain...
xo = A xs - xf = A xs - β xo
• Rearranging,
xo = Axs - A β xo β o 1 + A β s
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FROM BASIC BLOCK DIAGRAM TO ACTUALDIFFERENT
TYPES OF FEEDBACK CIRCUITS
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The comparison of parameters of different types of amplifiers is given in
the form of tabular column which is shown below.
COMPARISON TABLE
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BASIC STRUCTURE OF THE CIRCUIT
• Here we have assumed that there was an input “comparator” or “mixer”
and an output
“sampler” that provided us with a copy of the output signal for use as a
feedback signal.
• The form these devices take depends upon whether the amplifier’s input
and output
are current or voltage based...
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SERIES-SHUNT FEEDBACK - VOLTAGE AMPLIFIER
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SHUUNT-SERIES FEEDBACK - CURRENT AMPLIFIER
SERIES-SERIES FEEDBACK -TRANSCONDUCTANCE
AMPLIFIER
VOLTAGE -IN, CURRENT -OUT (SHUNT [VOLTAGE]
MIXING, CURRENT -SAMPLING)
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SHUNT-SHUNT FEEDBACK -TRANSRESISTANCE
AMPLIFIER
CURRENT-IN, VOLTAGE-OUT (SHUNT [CURRENT]
MIXING, VOLTAGE-SAMPLING)
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83
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SUMMARY OF STEPS YOU WILL
USE
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LINEAR OSCILLATORS
• A linear oscillator ideally produces a pure sinusoidal output at a single
frequency
(hopefully).
• To achieve linear oscillation, a linear amplifier must oscillate without
external stimuli
(other than a start-up transient to get it going, perhaps).
• In order to understand this type of oscillator, a minor excursion into
theory will be
required (it’s worth it, since a little bit of intuitive understanding goes a
long way!).
• What is required to make a linear oscillator (that works, that is!) is the
arrangement
shown below (this is just POSITIVE feedback)...
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• Actually, it is a necessary condition for this type of oscillator (linear) to
work.
• Intuitively, however the fact that the overall gain is infinity means that
the output of the
circuit is some signal (to be determined!), even with NO input at all!
• If one can arrange it so that the Barkhausen Criterion is met at only a
single frequency,
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it is possible to obtain a very pure sinewave output (if it is met at multiple
frequencies,
you might get an interesting mix of frequencies).
TYPES OF OSCILLATORS
1. Non-sinusoidal Oscillator
These Oscillators produce other than sine wave. (eg.) Triangular
wave, square wave,sawtooth wave…They are generated by using
relaxation oscillator circuits. In this type of circuit, the V or I change
abruptly one or more times during each cycle and thus result in a non-
sinusoidal oscillation.
Application
Used as a timing circuit
A few non-sinusoidal oscillators are,
(i) Multivibrator
(ii) Saw-tooth wave generator
(iii) Rectangular wave generator
(iv) Triangular wave generator
2. Sinusoidal Oscillator
In a Sinusoidal Oscillator the voltage varies continuously with respect to
time. They are generated using any one of the following property.
(i) Negative resistance
(ii) Feedback
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(iii) Heterodyne
(iv) Crystal
(v) Magnetostriction
(vi) Ultra high frequency
(vii)
Nature of sinusoidal oscillation
1. damped Oscillation
The electrical oscillation whose amplitude goes on decreasing with
time is known as damped Oscillation
2. Undamped Oscillation
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The electrical oscillation whose amplitude remains constant with time
is known as undamped Oscillation
BARKHAUSEN CRITERION
The overall gain of a positive feedback amplifier is given by the relation
Af=A/(1-βA)
Where, Af is the voltage gain with feedback
βA is the loop gain
If βA is made equal to unity then Af is infinity. (i.e) the circuit had
stopped amplifying and started oscillating. To provide positive feddedback
the feedback network should produce a phase shift of 180º in addition to
180º phase shift produced by the amplifier.
Therefore the total phase shift should be 360º.
Hence the condition for oscillations is
(i) βA must be equal to one
(ii) The total phase shift should be 360º.
FREQUENCY STABILITY
The ability of the oscillator to maintain constant frequency is
called Frequency stability
Factors affecting Frequency stability
1. operating point
2. Parameters of active device
3. Power source
4. Temperature variation
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5. Mechanical vibration
A. RC OSCILLATOR
1. WEIN BRIDGE OSCILLATOR
It consists of two transistors connected in cascade and a bridge
network used to provide positive feedback.
Transistor Q1 provides amplifications and phase shift of 180º.
Transistor Q2 provides further amplifications and a phase shift of 180º.
Signals at base Q1are amplified and they appear with a phase shift of 360º
at the collector of Q1. Though the signal at the output of Q2 is in phase
with the input of Q1 it cannot be directly fed as a feedback signal; since it
would affect the frequency stability.
Circuit operation
The bridge circuit consists of two arms, the resistive arm and
reactive arm. The resistive arm consists of swamping resistor which
introduces a negative feedback to Q1. Thus it improves bias stability since
the arm consists of only resistive components alone. The amount of
feedback is determined only by voltage divider R3 and R4.
The reactive arm consists of two RC networks, out of which one is
in shunt and another is in series . since capacitors are connected in this
arm they are frequency sensitive. Hence the feedback signal from this
arms changes w.r.to frequency and magnitude depends upon the voltage
divider formed by R3-R4. The bridge is said to be balanced if the voltage
at point A equals to voltage at point D and this occurs only at one
frequency.
The circuit consists if two RC coupled amplifier, which provides
phase shift of 360º.So the feedback network has no need to provide any
additional phase shift. When the circuit is energized by switching on the
supply a small random oscillations are produced at base1. They are further
amplified at Collector of Q2 .Since the oscillations at collector of Q2 have
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been inverted twice, the input signal is in phase with the output signal,
apart of output form the collector of Q2 is feedback to Wein Bridge which
is further amplified. The process continues still a sustained oscillation is
produced.
Frequency calculation
Impendence of series arm 1C
1S s
1R)S(Z
1
11
sC
1CsR
Impendence of parallel arm 2
2p SC
1R)S(Z
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22
22
SC1R
SC1xR
1CsR
R)S(Z
22
2P
Feedback Voltage
)S(Z)S(Z
)S(Z)S(V)S(V
Sp
p0p
1
11
22
2
222
0f
sC
1CsR
1CsR
R1CsR
R
)S(V)S(V
WKT,
)S(V
)S(V
0
f feedback fraction ratio.
122
221122112
12
222
sC1CsR
1CsRCsRCRCRsCsR
1CsRR
1CsRCsRCRCRsCsR
CsR
221122112
12
12
Let CCC&RRR 2121
1.....1sRC3CRs
sRC222
GAIN of op. amp 2....R
R1
)S(V
)S(VA
i
f
f
0
WKT, for oscillation to start,
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3....1A
Sub 1 & 2 in 3
11sRC3CRs
sRC
R
R1
222i
f
replace s = js
where f2
f is the frequency of oscillation
j is the complex variable
11RCj3CRj
RCj
R
R1
2222i
f
Real part,
01CR 222
1CR 222
222
CR
1
RC
1
f2
RC2
1f
Imaginary part,
RC3jRCjR
R1
i
f
if R2R
Frequency Range
20Hz to 1MHz
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Advantages
1. Good Frequency stability
2. Good amplitude stability
3.
Application
Audio signal generator.
2. RC PHASE SHIFT OSCILLATOR
A fraction of output of a single stage amplifier is passed thro, a
phase shift network, before feeding back to the input. The phase shift
network provides a phase shift of 180º and another 180º phase shift is
produced by the amplifier.
Hence the total phase shift is 360º.
Circuit Diagram.
The feedback network consists of three identical RC section. Each
section produces a phase shift of 60º. Therefore the total phase shift of the
feedback network is180º and another 180º phase shift is produced by the
amplifier.
Therefore the total phase shift should be 360º.
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Circuit operation
When the circuit is energized by switching on the supply a small
random oscillations are produced .The oscillation may start due to minor
variation in d.c supply. The output form the collector is feedback to phase
shift network and finally applied to the base. The oscillation will be
maintained if loop gain is made equal to unity.
frequency calculation
Node 1
)S(I)S(I)S(I 321
C
211
C
10
s1
)S(V)S(V
R
)S(V
s1
)S(V)S(V
1....1sRC2
sRC)S(V)S(V)S(V 02
1
Node 2
)s(I)S(I)S(I 543
C
f22
C
21
s1
)S(V)S(V
R
)S(V
s1
)S(V)S(V
96
2....sRC
1sRC2
)S(V)S(V)S(V 02
2
Node 3
Since 0)S(IRR 7i
)S(I)6(I 65
3....)S(VsRC
1sRC)S(V f2
Sub 3 in 1
sRC
1sRC2
)S(V)S(VsRC
1sRC
)S(V0f
1
sRC1sRC2sRC
)S(sRcV)S(V1sRC)S(V 0f
1
4....1sRC2
)S(sRcV)S(V1sRC)S(V 0f
1
Now Sub 3 in 2
Equating 4 & 5
3330
222s333f CRs)S(VsRC5CR6CRs)S(V
WKT, ,)S(V
)S(V
0
f feedback fraction ratio
1sRC5CRs6CRs
CRs222333
333
Put js
6....1RCj5CR6CjR
CjR322333
333
Gain of op- amp, 7....R
RA
i
f
WKT, condition for oscillation is 8....1A
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Sub 6, 7 in 8
11RCj5CR6CjR
CjR
R
R222333
333
i
f
Equating real and imaginary part to zero,
Real part,
01CR6 222
1CR6 222
222
CR6
1
RC6
1
f2
6RC2
1f
Imaginary part,
RCj533C3jR33C3jRiRfR
522C2R22C2RiRfR
5CR1R
R 222
i
f
29R
R
i
f
Frequency Range
20Hz to 1MHz
Advantages
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4. Good Frequency stability
5. Good amplitude stability
Application
Audio signal generator.
B. LC Oscillators
They are also known as tuned Oscillators or tank circuit oscillator.
They are used to produce frequency in the range of 1MHz to 500MHz.
Hence they are also known as R.F oscillators.
TYPES OF LC OSCILLATORS
1.TUNED COLLECTOR OR ARMSTRONG OSCILLATOR
It uses inductive feedback
The LC circuit is in collector of transistor
Hartley Oscillator
It uses inductive feedback
Colpitt’s Oscillator
It uses capacitive feedback
Clapp Oscillator
It uses capacitive feedback
2. TUNED BASE OSCILLATOR
It uses inductive feedback
The LC circuit is in base of transistor
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1.TUNED COLLECTOR OSCILLATOR
It uses inductive feedback. The LC circuit is in collector of transistor.
The feedback signal is taken from the secondary winding L1and fed back
to the base terminal. There is phase shift of 180ºin the transformer and
another 180º phase shift is produced by transistor amplifier. Hence the
total phase shift is 360º.
Hence the feedback fraction β=M/L
M- Mutual inductance between primary and secondary winding.
L- self inductance between primary and secondary winding.
WKT,
βA=1
A=1/β
For the oscillation to start, voltage gain must be greater than 1/β
R1,R2 Re are used to produce d.c bias to the transistor. The capacitor C'
and Ce act as a bypass capacitor to the resistor R2 and Re respectively.
Operation
When the circuit is energized by switching on the supply small
random oscillations are produced, hence the collector current increase to
quiescent value. These current charges the capacitor C. when it is fully
charged it discharges thro, the primary winding of L producing a magnetic
field around it. When the capacitor I s fully discharged, magnetic field
collapses and charges the capacitor in reverse direction. The process
continues still a sustained oscillation is produced.
HARTLEY OSCILLATOR
It uses inductive feedback. The tank circuit consists of two coils L1
and L2. The L1 is inductively coupled to L2 and the combination works as
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auto transformer. The feedback between output and input is accomplished
thro; this autotransformer action which also introduces a phase shift of
180º and the transistor Q1 provides amplifications and a phase shift of
180º. Hence the total phase shift is 360º.
Hence the feedback fraction β=L2/L1
WKT,
βA=1
A=1/β
For the oscillation to start, voltage gain must be greater than 1/β
A= L1/L2
R1,R2 Re are used to produce d.c bias to the transistor. The capacitor Cc
permits only a.c current to pass thro, tank circuit.Cb acts as blocking
capacitor, which blocks the d.c current reaching the base terminal. and Ce
act as a bypass capacitor.
Operation
When the circuit is energized by switching on the supply small
random oscillations are produced, hence the collector current increase to
quiescent value. The oscillations are produced because of positive
feedback from the tank circuit. The process continues still a sustained
oscillation is produced.
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COLPITTS OSCILLATOR
It uses capacitive feedback. The tank circuit consists of two capacitor
C1 and C2connected in series with each other which introduces a phase
shift of 180º and the transistor Q1 provides amplifications and a phase shift
of 180º. Hence the total phase shift is 360º.
Hence the feedback fraction β=C1/C2
WKT,
βA=1
A=1/β
For the oscillation to start, voltage gain must be greater than 1/β
A= C2/C1
R1,R2 Re are used to produce d.c bias to the transistor. The capacitor Cc
permits only a.c current to pass thro, tank circuit.Cb acts as blocking
capacitor, which blocks the d.c current reaching the base terminal. and Ce
act as a bypass capacitor.
Operation
When the circuit is energized by switching on the supply a small random
oscillation are produced, hence the collector current increase to quiescent
value. The oscillations are produced because of positive feedback from the
tank circuit. The process continues still a sustained oscillation is produced.
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CLAPP OSCILLATOR
It uses capacitive feedback. The circuit differs from the colpitt only in
one respect, that it contained one additional capacitor C3 connected in
series with inductor. This additional capacitor eliminates the effect of
frequency stability and improves the frequency stability. The tank circuit
consists of two capacitor C1 and C2 connected in series with each other
which introduces a phase shift of 180º and the transistor Q1 provides
amplifications and a phase shift of 180º. Hence the total phase shift is
360º.
Hence the feedback fraction β=C1/C2
WKT,
βA=1
A=1/β
For the oscillation to start, voltage gain must be greater than 1/β
A= C2/C1
R1,R2 Re are used to produce d.c bias to the transistor. The capacitor Cc
permits only a.c current to pass thro, tank circuit.Cb acts as blocking
capacitor, which blocks the d.c current reaching the base terminal. and Ce
act as a bypass capacitor.
Operation
When the circuit is energized by switching on the supply small random
oscillations are produced, hence the collector current increase to quiescent
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value. The oscillations are produced because of positive feedback from the
tank circuit. The process continues still a sustained oscillation is produced.
2.TUNED BASE OSCILLATOR
It uses inductive feedback. The LC circuit is in base of transistor. The
feedback signal is taken from the secondary winding L1and fed back to
the base terminal. Thers is phase shift of 180ºin the transformer and
another 180º phase shift is produced by transistor amplifier. Hence the
total phase shift is 360º.
Hence the feedback fraction β=M/L
M- Mutual inductance between primary and secondary winding.
L- self inductance between primary and secondary winding.
WKT,
βA=1
A=1/β
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For the oscillation to start, voltage gain must be greater than 1/β
R1,R2 Re are used to produce d.c bias to the transistor. The capacitor C'
and Ce act as a bypass capacitor to the resistor R2 and Re respectively.
Operation
When the circuit is energized by switching on the supply small
random oscillations are produced, hence the collector current increase to
quiescent value. These current charges the capacitor C. when it is fully
charged it discharges thro, the primary winding of L producing a magnetic
field around it. When the capacitor I s fully discharged, magnetic field
collapses and charges the capacitor in reverse direction. The process
continues still a sustained oscillation is produced.
C. CRYSTAL OSCILLATOR
It is basically a tuned oscillator. It uses a piezoelectric crystal in the
tank circuit. The crystal is usually made up of quartz crystal and provides
a high frequency of stability and accuracy. Therefore the crystal oscillators
are used in applications where frequency stability is very essential. They
are widely used in digital watches and clocks.
Quartz crystal
It has a very peculiar property known as piezoelectric effect. When an
a.c voltage is applied to the crystal, it stars vibrating at a frequency of
applied voltage. Conversely if a force is applied to the crystal, it generates
the a.c voltage.
Electric equivalent of a crystal
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It consists of series R-L-C1 circuit in parallel with a capacitance
C2.When the crystal is not vibrating, it is equivalent to capacitance C2.
When the crystal is vibrating , it is equivalent to series R-L-C1 circuit.
The series resonant frequency (fs) occurs when reactance of inductance
equals to the reactance of capacitance C2.
12
1
LCsf
The parallel resonant frequency occurs when reactance of inductance
equals to the reactance of series R-L-C1 circuit.
LCfp
2
1
where C=C1*C2/(C1+ C2)
Q=Factor of the crystal is given by
Q=(2*∏* sf *L)/R
Crystal Oscillator circuit
The crystal is connected as a series element in the feedback path from
collector to base.R1,R2 Re are used to produce d.c bias to the transistor.
The capacitor Cc permits only a.c current to pass thro, tank circuit.Cb acts
as blocking capacitor, which blocks the d.c current reaching the base
terminal and Ce act as a bypass capacitor. he coupling capacitor C has a
negligible impedance at the circuit operating frequency.
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The circuit operating frequency of oscillation is set by series resonant frequency
of crystal and its value is given by relation,
OSCILLATORS USING OP-AMP
RC –PHASE SHIFT OSCILLATOR
An example of a sinewave generator is shown in Figure 21. This is a
phase-shift oscillator, and amongst other things demonstrates that negative
feedback becomes positive feedback if there is enough phase-shift around
the feedback loop. Here, the opamp is connected as an inverting amplifier,
but the connection between output and input of three RC sections in
cascade introduces 180 phase shift at some particular frequency. If the
gain of the amplifier section is sufficient to make up for the attenuation of
the phase-shift network at that frequency, then the system will oscillate. If
the gain is too high, the oscillations build up until the amplifier output
reaches its maximum values and the system “saturates” (that is it becomes
non-linear). If the gain is too low, the system may show resonance, but it
will not oscillate. In fact, the diode network provides controlled non-
linearity to keep the overall loop gain at unity, and so provide stable
oscillation. Note that at least three RC sections are required, since each
section can produce only just under 90 phase-shift at most, so that two
cannot provide the necessary 180 shift. This circuit is quite tricky to
analyse, just because each RC section loads the preceding section. A
sinewave oscillator based on the Wien bridge, somewhat easier to analyse
and also rather better in performance, appears in the tutorial exercises. The
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circuit in Figure 21 was in fact “designed” by adjusting values in a PSpice
model.
C
_
+ R
R2
Sinewave R
C C R1
V(Sinewave)
-3
-2
-1
0
1
2
3
0.06 0.07 0.08 0.09 0.1
Time (s)
Ou
tpu
t (V
)
108
Phase-shift oscillator voltages
-3
-2
-1
0
1
2
3
0.1 0.101 0.102 0.103 0.104 0.105
Time (s)
Wav
efo
rms
(V)
V(Sinewave) V(C2:1) V(C3:1)
Figure 21. Phase-shift oscillator. Waveforms are calculated for R = 10 k,
R1 = R2 = 200 k, C = 10 nF. Note the initial exponential rise of
oscillation amplitude, followed by levelling off as the diode limiter
operates. Note also the phase-shifted waveforms at each stage of the
phase-shift network.