analog and digital electronics feedback amplifiers.pdf

all about amplifiers and their
types.

1. Unit-2
FEEDBACK AMPLIFIERS

2. AMPLIFIER
•increasing the voltage, current, and power of an input signal
• various types depending on the demand of the electrical circuit
• two most important considerations are power output and its
efficiency

3. Feedback Amplifier
•A feedback amplifier is an amplifier whose feedback exists
between the output and input signal
•Feeding the output signal back to its input circuit is known as
feedback- feedback amplifier
•dependent between the output and input with effective control
• Feedback amplifiers are divided into two types: positive
feedback and negative feedback

4. •When feedback energy is applied so as to
increase the input signal
it is called the positive or direct or regenerative signal.
•When feedback energy is applied so as to
weaken the input signal
it is called negative or inverse or degenerative feedback.

5. Basic Feedback Circuit
•The amplifier has
–voltage gain A
–output voltage V
o

–factor β
–feedback voltage V
f
.
–instantaneous voltage V
i


It consists of two parts: An amplifier and a feedback
circuit.
And the voltage feedback is given by,
V
f
=βVo from the output of the amplifier

6. Block Diagram Of An Amplifier With Feedback

7. Concept of Feedback
•A feedback amplifier uses feedback from the output of the amplifier back to the input to
enhance its performance. This feedback is achieved through a feedback loop that can be
either positive or negative.
Each block of feedback amplifier:
•Signal Source: The signal source is generally a voltage source, represented by the symbol Vs
with source current Is The signal source can be connected either in series or in parallel with
the resistor in the electronic circuit.
•Feedback network: It is a linear two-port network that contains different components of the
electronic circuit, like resistors, inductors, capacitors, etc.
•Sampling Network: A sampling network extracts the output signal from a feedback amplifier
and “feeds” it back to the input signal.
Sampling networks are of two types: current sampling networks and voltage sampling
networks.
•Mixer: A mixer mixes the source and feedback signals to produce positive or negative
feedback. It is also known as a comparator and can be connected in series or parallel.

8. Transfer Ratio Or Gain
•A - gain of the ideal amplifier without feedback.
•A
f
- gain of the amplifier with feedback

9. POSITIVE FEEDBACK
Positive feedback :

Vi=Vs+Vf=Vs+βVo

10. NEGATIVE FEEDBACK
For negative feedback :

Vi=Vs−Vf=Vs−βVo

13. ADVANTAGES AND DISADVANTAGES
1.Positive Feedback Amplifiers
1.In this feedback amplifier, the input voltage or the current is in phase with the
input signal.
2.Both the input signal and feedback introduce a phase shift of 180° and make
a 360° resultant phase shift in phase with the input signal.
3.It increases the gain of the amplifier but also increases distortion and
instability.
2.Negative Feedback Amplifier
1.In this feedback, the input voltage or current is out of phase, opposing the
input signal.
2.In this type of circuit, a 180° phase shift is introduced, but the resultant
phase shift is zero. Hence the feedback voltage would be 180° out of phase
to the input signal.
3.It reduces the amplifier’s overall gain but also reduces distortion and overall
noise.

14. Feedback Amplifier Topologies

There are four types of feedback topology

Current series feedback amplifier
Voltage series feedback amplifier
Current shunt feedback amplifier
Voltage shunt feedback amplifier

15. Voltage series feedback amplifier


•The feedback circuit is connected in shunt with the output in such a way that
it decreases the output impedance and increases the input impedance.
•In this circuit, it is placed in a shunt with the output but in series to the input
signal.

16. Voltage shunt feedback amplifier


•Here the feedback circuit is placed in a shunt with respect to output and input as well.
•It decreases the input and output impedance.

17. Current series feedback amplifier

•In this feedback amplifier, both the input and output impedance are increased.
•The feedback circuit is placed in series with the input and output.
•Here a fraction of the output voltage is applied in series with the input voltage in the
feedback circuit.

18. Current shunt feedback amplifier

•It increases the output impedance and because of connecting the feedback circuit in
parallel with the input, the input impedance is decreased.
•Here, the feedback circuit is placed in series with the output and in parallel with the
input.

19. 1.Voltage-series feedback (Fig.2a). 2. Voltage-shunt feedback (Fig.2b). 3. Current-series feedback (Fig.2c). 4.
Current-shunt feedback (Fig.2d)
In the list , voltage refers to
connecting the output voltage
as input to the feedback
network; current refers to
tapping off some output
current through the feedback
network. Series refers to
connecting the feedback signal
in series with the input signal
voltage; shunt refers to
connecting the feedback signal
in shunt (parallel) with an input
current source

21. Criteria Based on (1-Aβ)
•(1-Aβ) < 1
–A
f
exceeds A
–This condition corresponds to positive feedback.
•(1-Aβ) = 0
–A
f
becomes infinite
–This is possible only when input is 0
–Under this situation, the circuit operates as an oscillator
•(1-Aβ) > 1
–A
f
is smaller than A
–This corresponds to negative feedback in an amplifier

22. •Most oscillators consist of three basic parts:
•An amplifier
•A wave shaping network
•A POSITIVE feedback path
•A fraction of the amplifier's output signal is fed back to be in phase with the input
•By adding together the feedback and input signals, the amplitude of the input signal is increased.
•If the amount of positive feedback is large enough however, the result is oscillation, where the
amplifier circuit produces its own signal.

Principle of Feedback in Oscillator

23. Barkhausen criterion
oProvides a set of conditions for sustained oscillations.
oOutput regenerates even though input is removed.
oTo make it happen, Barkhausen criterion has to be satisfied.
oThe Barkhausen criterion states that:
oThe loop gain is equal to unity in absolute magnitude
othat is, | β A | = 1 and
oThe phase shift around the loop is zero or an integer multiple of 2π
o∠ β A = 2 π n, n ∈ 0, 1, 2,….
oThe product β A is called as the “loop gain”.

24. OSCILLATORS

25. Principle of Feedback in Oscillator

28. Classification of Oscillators
•Electronic oscillators are classified mainly into the following two
categories −
•Sinusoidal Oscillators −
•The oscillators that produce an output having a sine waveform are
called sinusoidal or harmonic oscillators.
•Such oscillators can provide output at frequencies ranging from 20
Hz to 1 GHz.
•Non-sinusoidal Oscillators
•The oscillators that produce an output having a square,
rectangular or saw-tooth waveform are
called non-sinusoidal or relaxation oscillators.
•Such oscillators can provide output at frequencies ranging from 0
Hz to 20 MHz.

29. Classification of Sinusoidal Oscillators
•Sinusoidal oscillators can be classified in the following categories :
•Crystal Oscillators: Use quartz crystals
Used to generate highly stabilized output signal with
frequencies up to 10 MHz.
Example: Piezo Oscillator

•Negative-resistance Oscillator: Use negative-resistance
characteristic of the devices such as tunnel devices.
Example: Tuned diode oscillator

30. Continued….
•Tuned Circuit/Radio-frequency Oscillators
Use a tuned circuit consisting of inductors (L) and capacitors (C)
Used to generate high-frequency signals.
Such oscillators are Hartley, Colpitts, Clapp oscillators, etc.

•RC Oscillators/ Audio-frequency oscillators
Use resistors and capacitors
Used to generate low or audio-frequency signals.
Such oscillators are Phase –shift and Wein-bridge oscillators.

31. Nature of Sinusoidal Oscillations
•Damped Oscillations
The electrical oscillations whose amplitude goes on decreasing
with time
The frequency of the damped oscillations may remain constant
depending upon the circuit parameters.




Damped oscillations are generally produced by the
oscillatory circuits that produce power losses and doesn’t
compensate if required.

32. Continued….
•Undamped Oscillations
The electrical oscillations whose amplitude remains
constant with time are called as Undamped Oscillations.
The frequency of the Undamped oscillations remains
constant.



Undamped oscillations are generally produced by the
oscillatory circuits that produce no power losses and
follow compensation techniques if any power losses occur.

33. Oscillatory Circuit
•An oscillatory circuit produces electrical oscillations of a desired
frequency. They are also known as tank circuits.
•A simple tank circuit comprises of an inductor L and a capacitor C
both of which together determine the oscillatory frequency of the
circuit.
•To understand the concept of oscillatory circuit, let us consider the
following circuit.

34. Concept of oscillatory circuit
Condition 1
•The capacitor in this circuit is already
charged using a dc source.
• In this situation, the upper plate of the
capacitor has excess of electrons whereas
the lower plate has deficit of electrons.
The capacitor holds some electrostatic
energy and there is a voltage across the
capacitor.
Condition 2
•When the switch S is closed, the capacitor
discharges and the current flows through
the inductor. Due to the inductive effect,
the current builds up slowly towards a
maximum value. Once the capacitor
discharges completely, the magnetic field
around the coil is maximum

35. Continued…
Condition 3
•Once the capacitor is discharged
completely, the magnetic field begins to
collapse and produces a counter EMF
according to Lenz’s law. The capacitor is
now charged with positive charge on the
upper plate and negative charge on the
lower plate.




Condition 4
•Once the capacitor is fully charged, it
starts to discharge to build up a
magnetic field around the coil, as
shown in the following circuit
diagram.

36. Continued…
•This continuation of charging and discharging results in alternating
motion of electrons or an oscillatory current. The interchange of
energy between L and C produce continuous oscillations.
•In an ideal circuit, where there are no losses, the oscillations would
continue indefinitely. In a practical tank circuit, there occur losses
such as resistive and radiation losses in the coil and dielectric
losses in the capacitor. These losses result in damped oscillations

37. Continued…
•Frequency of Oscillations
The frequency of the oscillations produced by the tank circuit are
determined by the components of the tank circuit, the L and the C.
The actual frequency of oscillations is the resonant frequency (or
natural frequency) of the tank circuit which is given by

38. Capacitance of the capacitor
•The frequency of oscillation f
o
is
inversely proportional to the
square root of the capacitance
of a capacitor. So, if the value of
the capacitor used is large, the
charge and discharge time
periods will be large. Hence the
frequency will be lower.

------ Eqn (1)


Self-Inductance of the coil
•The frequency of the oscillation f
o
is
proportional to the square root of the
self-inductance of the coil.
•If the value of the inductance is large,
the opposition to change of current
flow is greater and hence the time
required to complete each cycle will
be longer, which means time period
will be longer and frequency will be
lower.
• ------- Eqn (2)

39. Continued…
•Combining eqn )1) & (2), we get,




•The above equation, though indicates the output frequency, matches
the natural frequency or resonance frequency of the tank circuit.

40. Basic Elements of Oscillator
•An Oscillator circuit is a complete set of all the parts of circuit which
helps to produce the oscillations. Practical Oscillator Circuit
•A Practical Oscillator circuit consists of a tank circuit, a transistor
amplifier, and a feedback circuit. The following circuit diagram shows
the arrangement of a practical oscillator.

41. Parts of the practical oscillator circuit
•Tank Circuit − The tank circuit consists of an inductance L connected in
parallel with capacitor C. The values of these two components
determine the frequency of the oscillator circuit and hence this is
called as Frequency determining circuit.
•Transistor Amplifier − The output of the tank circuit is connected to
the amplifier circuit so that the oscillations produced by the tank
circuit are amplified here. Hence the output of these oscillations are
increased by the amplifier.
•Feedback Circuit − The function of feedback circuit is to transfer a part
of the output energy to LC circuit in proper phase. This feedback is
positive in oscillators while negative in amplifiers.

42. Types of Tuned Circuit Oscillators
•Most of the oscillators used in radio transmitters and receivers are of
LC oscillators type.
•Depending upon the way the feedback is used in the circuit, the LC
oscillators are divided as the following types.
•Tuned-collector or Armstrong Oscillator − It uses inductive feedback
from the collector of a transistor to the base. The LC circuit is in the
collector circuit of the transistor.
•Tuned base Oscillator − It uses inductive feedback. But the LC circuit
is in the base circuit.
•Hartley Oscillator − It uses inductive feedback.
•Colpitts Oscillator − It uses capacitive feedback.

43. Continued…
•Tuned circuit oscillators are the circuits that produce oscillations with
the help of tuning circuits.
• The tuning circuits consists of an inductance L and a capacitor C. These
are also known as LC oscillators, resonant circuit oscillators or tank
circuit oscillators.
•The tuned circuit oscillators are used to produce an output with
frequencies ranging from 1 MHz to 500 MHz.
•Hence these are also known as R.F. Oscillators. A BJT or a FET is used as
an amplifier with tuned circuit oscillators.
•With an amplifier and an LC tank circuit, we can feedback a signal with
right amplitude and phase to maintain oscillations

44. Hartley Oscillator
•Hartley oscillator was invented in 1915 by the american engineer
Ralph Hartley while he was working for the Western Electric
company. A very popular local oscillator circuit that is mostly used
in radio receivers is the Hartley Oscillator circuit.
•LC Oscillator which uses two inductive reactances and one capacitive
reactance Iin its feedback network.

45. Continued…
•In a Hartley oscillator the oscillation frequency is determined by a
tank circuit comprising of two inductors and one capacitor.
• The inductors are connected in series and the capacitor is connected
across them in parallel. Hartley oscillators are commonly used in radio
frequency (RF) oscillator applications and the recommended
frequency range is from 20KHz to 30MHz.
•Hartley oscillators can be operated at frequencies lower than 20KHz,
but for lower frequencies the inductor value need to be high and it
has a practical limit.

46. Circuit Diagram: Transistorised Hartley
Oscillator
•In a Hartley oscillator the oscillation frequency is determined by a
tank circuit comprising of two inductors and one capacitor.
•In the circuit diagram resistors R1 and R2 give a potential divider bias
for the transistor Q1.

47. Construction
•The resistances R1 and r2 - Biasing resistances
•RFC – radio frequency choke
•Reactance value is very high for high frequencies, hence it can be
treated as open circuit.
•While for d.c conditions, the reactance is zero hence causes no
problem for d.c capacitors.
•Hence due to RFC, the isolation between a.c. and d.c. operation is
achieved.RE –biasing circuit resistance S& Ce – Emitter bypass
capacitor.Cc1 and Cc2 – coupling capacitor
•Common emitter amplifier provides a phase shift of 180 degree.

48. Continued…
•As emitter is grounded, the base and the collector voltages are out of
phase by 180.
•As the centre of L1 and L2 is grounded, when upper end becomes
positive, the lower becomes negative and vice versa. So, the LC
feedback network gives an additional phase of 180 degree,necessary
to satisfy oscillation conditions

49. Operation:
•When the power supply is switched ON the transistor starts
conducting and the collector current increases. As, a result the
capacitor C1 starts charging and when the capacitor C1 is fully
charged it starts discharging through coil L1.
•This charging and discharging creates a series of damped oscillations
in the tank circuit .
•The oscillations produced in the tank circuit is coupled (fed back) to
the base of Q1 and it appears in the amplified form across the
collector and emitter of the transistor.

50. Continued…
•The output voltage of the transistor (voltage across collector and
emitter) will be in phase with the voltage across inductor L1.
•Since the junction of two inductors is grounded, the voltage across L2
will be 180° out of phase to that of the voltage across L1.
•The voltage across L2 is actually fed back to the base of Q1. From this
we can see that, the feed back voltage is 180° out of phase with the
transistor and also the transistor itself will create another 180° phase
difference.
•So the total phase difference between input and output is 360° and it
is very important condition for creating sustained oscillations.

51. Continued…
•The oscillations produced in the tank circuit is coupled (fed back) to the
base of Q1 and it appears in the amplified form across the collector and
emitter of the transistor.
•The output voltage of the transistor (voltage across collector and emitter)
will be in phase with the voltage across inductor L1. Since the junction of
two inductors is grounded, the voltage across L2 will be 180° out of phase to
that of the voltage across L1.
•The voltage across L2 is actually fed back to the base of Q1.

52. Continued…
•From this ,it has been seen that, the feed back voltage is 180° out of phase
with the transistor and also the transistor itself will create another 180°
phase difference.
• So, the total phase difference between input and output is 360° and it is
very important condition for creating sustained oscillations.

55. Advantages
•Instead of using a large transformer, a single coil can be used as an
auto-transformer.
•Frequency can be varied by employing either a variable capacitor or a
variable inductor.
•Less number of components are sufficient.
•The amplitude of the output remains constant over a fixed frequency
range.

58. Colpitts Oscillator
•Colpitts oscillator was invented by American scientist Edwin Colpitts in 1918.
•It is another type of sinusoidal LC oscillator and is basically a harmonic
oscillator, which has a lot of applications.
•The Colpitts oscillator can be realized using valves, transistors, FETs or
op-amp.
•It is much similar to the Hartley oscillator except the addition of tank circuit.
•In Colpitts oscillator the tank circuit consists of two capacitors in series and
an inductor connected in parallel to the serial combination.
•The frequency of the oscillations are determined by the value of the
capacitors and inductor in the tank circuit.

59. •Thus, the main difference between a Colpitts Oscillator and a Hartley
Oscillator is that the former uses tapped capacitance, while the latter
uses tapped inductance.
•Colpitts oscillator is generally used in RF applications and the typical
operating range is 20KHz to 300MHz.
•In Colpitts oscillator, the capacitive voltage divider setup in the tank
circuit works as the feed back source and this arrangement gives
better frequency stability when compared to the Hartley oscillator
which uses an inductive voltage divider setup for feedback.


Colpitts Oscillator

60. Circuit Diagram
•The circuit diagram of a typical Colpitts oscillator using transistor is
shown in the figure below.

61. Construction
•In the circuit diagram, resistors R1 and R2 gives a voltage divider biasing to the transistor
•Resistor R4(RFC) limits the collector current of the transistor. Cin is the input DC
decoupling capacitor while Cout is the output decoupling capacitor. Re is the emitter
resistor and its meant for thermal stability. Ce is the emitter by-pass capacitor
•The function of emitter by-pass capacitor is to by-pass the amplified AC signals from
dropping across Re.
•The the emitter by-pass capacitor is not there, the amplified AC signal will drop across Re
and it will alter the DC biasing conditions of the transistor and the result will be reduced
gain.
•Capacitors C1, C2 and inductor L1 forms the tank circuit. Feedback to the base of
transistor is taken from the junction of Capacitor C2 and inductor L1 in the tank circuit.

62. Operation
•When power supply is switched ON, capacitors C1 and C2 starts
charging. When they are fully charged they starts discharging through the
inductor L1.
•When the capacitors are fully discharged, the electrostatic energy stored
in the capacitors gets transferred to the inductor as magnetic flux.
•The the inductor starts discharging and capacitors gets charged again.
•This transfer of energy back and forth between capacitors and inductor is
the basis of oscillation. Voltage across C2 is phase opposite to that of the
voltage across the C1 and it is the voltage across C2 that is fed back to the
transistor.

63. •The feedback signal at the base of transistor appears in the amplified
form across the collector and emitter of the transistor.
•The energy lost in the tank circuit is compensated by the transistor
and the oscillations are sustained. The tank circuit produces 180°
phase shift and the transistor itself produces another 180° phase
shift.
•That means the input and output are in phase and it is a necessary
condition of positive feedback for maintaining sustained oscillations.

Colpitts Oscillator

65. Advantages
•Colpitts oscillator can generate sinusoidal signals of very high frequencies.
•It can withstand high and low temperatures.
•The frequency stability is high.
•Frequency can be varied by using both the variable capacitors.
•Less number of components are sufficient.
•The amplitude of the output remains constant over a fixed frequency range.

66. Disadvantages
•Due to the use of inductor, L circuit becomes bulky and cost of circuit is
more.
•Poor frequency stability.
•Difficult to adjust feedback as capacitor values has to be changed.
•Poor Isolation .
•Hard to design.

67. Applications
•Colpitts oscillator can be used as High frequency sinewave generator.
•It can be used as a temperature sensor with some associated
circuitry.
•Mostly used as a local oscillator in radio receivers.
•It is also used as R.F. Oscillator & Mobile applications.

68. Drawbacks of LC circuits
•Frequency instability
•Waveform is poor
•Cannot be used for low frequencies
•Inductors are bulky and expensive
•Another type of oscillator circuit which are made by replacing the inductors with
resistors. By doing so, the frequency stability is improved, and a good-quality
waveform is obtained. These oscillators can also produce lower frequencies. As
well, the circuit becomes neither bulky nor expensive.
•All the drawbacks of LC oscillator circuits are thus eliminated in RC oscillator
circuits. Hence the need for RC oscillator circuits arise. These are also called
as Phase–shift Oscillators

69. RC phase-shift oscillators use a resistor-capacitor (RC)
network (Figure 1) to provide the phase-shift required by the feedback
signal. They have excellent frequency stability and can yield a pure
sine wave for various loads.
Ideally, a simple RC network is expected to have an output that leads
the input by 90
o
.
However, in reality, the phase difference will be less than this as the
capacitor used in the circuit cannot be ideal. Mathematically the phase
angle of the RC network is expressed as

71. Where , X
C
= 1/(2πfC) is the reactance of the capacitor C and R is the
resistor. In oscillators, this kind of RC phase-shift network, each offering
a definite phase-shift can be cascaded to satisfy the phase-shift condition
led by the Barkhausen Criterion.
One such example is the case in which RC phase-shift
oscillator is formed by cascading three RC phase-shift
networks, each offering a phase-shift of 60
o

72. Here the collector resistor RC limits the collector current of the transistor, resistors
R
1
and R (nearest to the transistor) form the voltage divider network while the
emitter resistor R
E
improves the stability. Next, the capacitors C
E
and C
o
are the
emitter by-pass capacitor and the output DC decoupling capacitor, respectively.
Further, the circuit also shows three RC networks employed in the feedback path.
This arrangement causes the output waveform to shift by 180
o
during its course of
travel from output terminal to the base of the transistor. Next, this signal will be
shifted again by 180
o
by the transistor in the circuit due to the fact that the
phase-difference between the input and the output will be 180
o
in the case of
common emitter configuration. This makes the net phase-difference to be 360
o
,
satisfying the phase-difference condition.
One more way of satisfying the phase-difference condition is to use four RC
networks, each offering a phase-shift of 45
o
. Hence it can be concluded that the RC
phase-shift oscillators can be designed in many ways as the number of RC
networks in them is not fixed. However it is to be noted that, although an increase
in the number of stages increases the frequency stability of the circuit, it also
adversely affects the output frequency of the oscillator due to the loading effect.

73. The generalized expression for the frequency of
oscillations produced by a RC phase-shift oscillator is
given by
Where, N is the number of RC stages formed by the
resistors R and the capacitors C.
Frequency of the oscillator: (the frequency where the phase shift is 180º) Feedback gain β = 1/[1 –
5α
2
– j (6α – α
3
) ] where α = 1 / (2πfRC) Feedback gain at the frequency of the oscillator β = 1 / 29
The amplifier must supply enough gain to compensate for losses. The overall gain must be unity.
Thus the gain of the amplifier stage must be greater than 1/β, i.e. A > 29 The RC networks provide
the necessary phase shift for a positive feedback. They also determine the frequency of oscillation.

74. Advantages of RC Phase Shift Oscillator
The advantages of this phase shift oscillator include the
following.
•The oscillator circuit designing is easy with basic
components like resistors as well as capacitors.
•This circuit is not expensive and gives excellent frequency
stability.
•These are mainly suitable for low-frequencies
•This circuit is simpler compared with a Wein bridge oscillator
because it doesn’t require the stabilization planning & negative
feedback.
•The circuit output is sinusoidal that is somewhat distortion free.
•The frequency range of this circuit will range from a few Hz to
hundreds of kHz

75. Disadvantages of RC-Phase Shift Oscillator
The disadvantages of this phase shift oscillator include the
following.
•The output of this circuit is small because of the smaller
feedback
•It requires 12 volts battery for developing a suitably huge
feedback voltage.
•It is hard for this circuit to create oscillations because of the
small feedback
•The frequency stability of this circuit is not good to compare
with Wien bridge oscillator.

76. RC Phase Shift Oscillator Applications
The applications of this type of phase shift oscillator include the following
•This phase shift oscillator is used to generate the signals over an extensive
range of frequency. They used in musical instruments, GPS units, & voice
synthesis.
•The applications of this phase shift oscillator include voice synthesis,
musical instruments, and GPS units.

77. Multivibrators

81. Operation
Suppose that at switch on, TR1 is conducting heavily and TR2 is
turned off. The collector of TR1 will be almost at zero volts as will the
left hand plate of C1. Beause TR2 is turned off at this time, its collector
will be at supply voltage and its base will be at almost zero potential,
the same as TR1 collector, because C1 is still un-charged and its two
plates are at the same potential.
C1 now begins to charge via R2 and its right hand plate becomes
increasingly positive until it reaches a voltage of about +0.6V. As this
plate of the capacitor is also connected to the base of TR2, this
transistor will begin to conduct heavily. The rapidly increasing collector
current through TR2 now causes a voltage drop across R4, and TR2
collector voltage falls, causing the right hand plate of C2 to fall rapidly
in potential.

82. It is the nature of a capacitor that when the voltage on one plate
changes rapidly, the other plate also undergoes a similar rapid
change, therefore as the right hand plate of C2 falls rapidly from
supply voltage to almost zero, the left hand plate must fall in
voltage by a similar amount.
With TR1 conducting, its base would have been about 0.6V, so as
TR2 conducts TR1 base falls to 0.6 −9V = −8.4V, a negative
voltage almost equal and opposite to that of the +9V supply
voltage.

83. This rapidly turns off TR1 causing a rapid rise in its collector
voltage. Because a sudden voltage change on one plate of a
capacitor causes the other plate to change by a similar amount,
this sudden rise at TR1 collector is transmitted via C1 to TR2
base causing TR2 to rapidly turn on as TR1 turns off. A change
of state has occurred at both outputs.
This new state does not last however. C2 now begins to charge
via R3, and once the voltage on the left hand plate (TR1 base)
reaches about +0.6V another rapid change of state takes place

84. Frequency Calculations
The circuit keeps on changing state in this manner producing a
square wave at each collector. The frequency of oscillation can
be calculated, as the time for the relevant capacitor to charge
sufficiently for a change of state to take place, will be
approximately 0.7CR and, as two changes of state occur in each
cycle the periodic time T will be:

If C1 = C2 and R2 = R3 the mark to space ratio will be 1:1and in
this case the frequency of oscillation will be:

85. What is the frequency of an astable multivibrator of mark/space
ratio 1:1 using timing components of C=100nF and R=33K?

90. The tuned collector oscillator circuit used in the local
oscillator of a radio receiver makes use of an LC tuned
circuit with L
1 
= 58.6 µH and C
1
 = 300 pF. Calculate the
frequency of oscillations

91. Determine the (i) operating frequency and (ii)
feedback fraction for Colpitt’s oscillator shown in
Fig.

93. Calculate the (i) operating frequency and (ii) feedback fraction for
Hartley oscillator shown in Fig. 2. The mutual inductance between the
coils, M = 20 μH.

94. A phase shift oscillator uses 5 pF capacitors. Find the value of R to produce a frequency of 800
kHz.

95. Negative feedback amplifiers
•The voltage gain of an amplifier without feedback is 3000. Calculate the
voltage gain of the amplifier if negative voltage feedback is introduced in
the circuit. Given that feedback fraction m
v
 = 0.01.

96. The overall gain of a multistage amplifier is 140. When negative voltage feedback is
applied, the gain is reduced to 17.5. Find the fraction of the output that is feedback
to the input.

97. 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 feedback.
(ii) If this fraction is maintained, calculate the value of the amplifier gain required if
the overall stage gain is to be 75.

98. With a negative voltage feedback, an amplifier gives an output of 10 V
with an input of 0.5 V. When feedback is removed, it requires 0.25 V
input for the same output. Calculate (i) gain without feedback (ii)
feedback fraction mv .

99. 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.

100. An amplifier has a voltage gain of 500 without feedback. If a negative
feedback is applied, the gain is reduced to 100. Calculate the fraction of
the output fed back. If, due to ageing of components, the gain without
feedback falls by 20%, calculate the percentage fall in gain with
feedback.